Home

DYNAMIC CHARACTERIZATION OF RIGID POLYURETHANE

1. It was found that for PU foam with relative densities of 0 065 0 128 and 0 249 at high enough rates between 950 s and 5300 s the viscous nature of the foam became saturated and the mechanisms creating rate dependence were ineffectual causing rate insensitivity for stress strain curves below the densification region Foam samples of higher relative density 0 37 over a similar strain rate range were observed to be strain rate dependent The relative density of the foam used in this study is 0 33 Goga investigated the impact response of PU foam as a function of density A free falling 13 45 lb weight was dropped onto foam specimens 3 15 x 3 15 x 2 inches from a height of 30 inches It was found that although the plateau region of the stress strain curve was initiated at similar strain magnitudes 08 the corresponding plastic collapse strength was proportional to foam density Density was also shown to have a substantial effect on deceleration during impact as well as impact duration Goga 2010 It is clear that composition effects foam behavior during impact Later discussion will highlight methods to minimize variation of foam composition 13 Polymeric foam behavior is evident in the response mechanisms of a softball impact Figure 2 5 shows a typical softball load displacement curve with displacement being that of the ball COM During compression the plastic deformation of the foam due to cell collapse absorbs some of the i
2. Mac Valve Electronics Box EA y i Accumulator 5 Tank Signal Conditioner Figure 3 2 Instrumentation used to impact foam samples ZS The foam samples were mounted with a thin coating of synthetic lubricating grease to a load cell which measured the force of impact The load cell PCB model 208C03 was designed for dynamic loading applications and had a compressive rating of 500 lbs Load measurements were taken at a sample rate of 1 0 MHz The load cell was connected to a signal conditioner PCB model 482A21 by a 10 32 Coaxial to BNC cable To securely attach the load cell to the device frame a threaded steel cylinder was machined and securely thread onto the load cell using a thread locking adhesive The steel insert was fit inside of a pillow block and aligned with set screws Once aligned additional pillow blocks were wedged behind the steel cylinder to prevent set screw slippage Three fiber optic sensors Banner D10 were used to measure incident striker bar speed Each sensor was set to a response time of 50 us and had a detection range of 6 inches Cables leading from each sensor were mounted to an aluminum plate which had three holes spaced 1 5 inches apart Fig 3 3 The cables were designed to both transmit and receive light As the striker bar passed in front of a cable the emitted light would reflect back into the cable and be measured by the sensor Adaptive light thresholds for each sensor were set so as to trigger an
3. eeeeeeees 64 Figure 4 11 Load displacement curves for cylindrical impacts at 60 95 and 120 mph 64 Figure 4 12 Load displacement curves for flat surface impacts at 60 95 and 120 mph 65 Figure 4 13 The ratio of impulse measurements as a function of ball speed 65 Figure 4 14 CCOR as a function of repeated impacts oooooonnnnnnncncnnnnnonnnnnnnnncnnnnnnnnnnnnnnnnos 67 Figure 4 15 DS as a function of repeated impacts ccccccononiocccnnnnnnnnnnnnnnonnnnnnnnnnnnnannnannnnnnnos 67 Figure 5 1 FEA setup of an aluminum striker bar colliding into a foam sample 71 Figure 5 2 Hourglassing caused by high deformations cc cee eeee eee e cece cece eens J2 Figure 5 3 Contact penetration between the striker bar and foam sample for Mat 57 73 Figure 5 4 Foam sample load displacement curves for Mat 57 scsseeeeeeeeeeeeees 76 Figure 5 5 Localization of deformation due to dynamic compression oocccccccncnnnnnccnnnnnnnoss 76 Figure 5 6 Experimental and numerical COR rate dependence for Mat 57 71 Eisute gt COR rate dependence OF Bela sanis e S 78 Figure 5 8 COR rate dependence for hysteretic unloading factor HU ooooccccnccc 79 Figure 5 9 COR rate dependence for Shape factor coooooononcnonnnoncnononocnnnnnnnnnnnnnannnnnnnnnnnos 79 Figure 5 10 COR rate dependence for Damp factor oooooonnnnnnncccccnnnnnnnnnnonnnnnnnannnnnnnnnnccnnos 80 xi
4. k x t 2 3 where f t and x t are force and displacement respectively This assumption is justified as the loading stiffness of a typical softball shown in Fig 2 5 is linear Setting the incident kinetic energy of the ball equal to the potential energy of a linear spring at maximum deflection results in 1 21 2 7 MY 5 KxX 2 4 where mp and v are respectively ball mass and initial velocity Using Newton s second law 2 t a 2 5 fO m 2 5 displacement x t of the ball center of mass COM is found by dividing the load signal by ball mass and integrating twice x t f w a dt 2 6 0 0 Mp Combining Eq 2 3 2 6 and evaluating at maximum force results in the equation for dynamic stiffness y Fs 27 C of M Displacement mm 0 9 1 1 6000 0 5 20 5000 Q y 4000 Load cells Force Ibs Q3 8 O NJ 39104 2000 1000 0 0 2 0 4 0 6 0 8 C of M Displacement inch Figure 2 5 Typical load displacement curves of a softball impact from Cross Cross 2000 2 2 5 Impulse The momentum of a translating object is a function of both mass and velocity Impulse or the change in momentum due to a collision 1s calculated by integrating the load signal over the duration of impact from to to t FOdt 2 8 0 The impulse calculated in Eq 2 8 can also be used to verify the measured initial and rebounding ball speeds by performing a momentum balance vimp I V My 2 9 solving fo
5. linear increase in COR as shown in Fig 5 12 Figure 5 13 Surface penetration for a 41 4 mph impact using Mat 83 While COR did not completely agree with experiment the load displacement curves agreed well as shown in Fig 5 14 An improvement over Mat 57 was shown in the viscous softening near peak displacement Rate effects were also properly characterized by an increased stiffness at higher rates through the plateau region of loading Oscillations in the FEA results at small strain magnitudes indicate the presence of elastic waves propagating through the sample 83 o Mat 83 e Experiment Load Ibs 0 00 0 05 0 10 0 15 0 20 Displacement inches Figure 5 14 Comparison of Experimental load displacement curves with Mat 83 at speeds of I 20 4 mph II 29 7 mph and III 41 4 mph 5 5 Summary Two foam material models were developed to simulate the PU foam sample impacts from Chapter 3 Large deformations in the foam sample caused issues with hour glassing and surface contact penetration which were minimized by using fully integrated elements and adjusting mesh densities and contact conditions Mat 57 showed good agreement with experimental load displacement curves However its inability to account for rate effects was manifest in a lack of viscous softening near peak displacement COR was shown to have minimal rate dependence which after a parametric study could not be attributed to a specific material
6. 2004 Duris performed a durability test on softballs to determine the effects of repeated impacts on ball performance Three softballs were impacted 100 times at 90 mph continuously within 120 minutes Surface temperature of the ball increased 10 F over 100 impacts and the data suggested that COR significantly changed A second test in which the balls were intermittently hit 100 times allowed the ball temperature to stabilize after 10 consecutive hits The COR remained relatively independent to the impact number This suggests that ball temperature as 10 well as testing frequency affects ball performance This also shows that damage to the ball s foam core as a result of repetitive impacting is minimal up to 100 impacts 2 4 Polymeric Foam The compressive response of closed cell foam like the foam core of a softball is governed by its cellular microstructure and is characterized by three regions of behavior shown in Fig 2 6 At small strains the foam behaves elastically as the inherent stiffness of the material controls compression with minimal energy absorption At a critical strain the structure can no longer support loading and the cell walls begin to collapse In the stress strain curve a plateau region in which the cells collapse at a relatively constant stress continues until the cells are near full compression Irrecoverable damage to the foam structure may occur during compression as the result of a brittle matrix exces
7. and V are the incident speeds of objects 1 and 2 Barnes 1957 The chosen coordinate system is such that V is negative A perfectly elastic collision results in e 1 while a perfectly inelastic collision sets e O Cross 2000 The ASTM standard test method for measuring the COR of baseballs and softballs as shown in Fig 2 2 requires the ball to contact a massive rigid flat wall of either wood or metal ASTM F1887 2009 BALL THROWING MACHINE 2st SPEED MONITOR 1st SPEED MONITOR STRIKE PLATE I 8 FT OR LESS 17 Ea Ug Ke 2 gt E 12 FROM WALL TARGET WITH 12 IN DIAMETER OPENING Figure 2 2 Schematic for measuring softball COR from ASTM F1887 A stationary impact surface simplifies Eq 2 1 to the ratio of the incident v and rebounding v ball speeds as a 2 2 Softballs used in bat certification testing have COR values ranging between 0 45 and 0 47 ASTM F1890 2009 Because baseball and softball bats have cylindrical shapes the cylindrical coefficient of restitution or CCOR is a useful property in defining ball impact behavior CCOR is lower than COR due to a reduction in contact area which increases both ball deformation and dissipated energy Equation 2 2 is used throughout this paper to calculate COR and CCOR Experimental results published elsewhere show a linear correlation between incident softball velocity and COR at speeds typical of play Duris 2004 Biesen 2006 The
8. earlier 1000 s agreed well with the strain rate at 60 mph Collision velocities above 95 mph however can be exceeded at higher levels of play With bat swing speeds approaching 100 mph for high level male players Smith 2012 and fastpitch pitch speeds above 70 mph National Pro Fastpitch 2012 the peak strain rate typical of play should be closer to 3500 gt 6 4 Mat 83 Fu Chang Foam The Fu Chang material model was implemented on both cylindrical and flat impact surfaces The softball however was much too compliant when simulated with parameters from the PU foam sample model As was done with Mat 57 damp and shape were adjusted to optimize agreement with experiment and are listed in Table 6 2 1 point elements were used and the timestep scale factor was lowered below default 0 9 to achieve the ideal damp values 95 Table 6 2 Material parameters used for Mat 83 p E Model lb s in ksi HU Shape Damp Mat 83 PU foam sample 3 90E 05 20 0 01 7 5 0 5 Mat 83 Softball 3 90E 05 20 0 01 0 57 5 5 Load displacement curves for cylindrical and flat surfaces are shown in Fig 6 12 and 6 13 While initial stiffness closely matched experiment at higher speeds a softening behavior indicated by a decrease in stiffness was shown near peak deformation The softening caused lower peak forces 16 average and larger displacements 8 average than experiment Performance values for Mat 83 are listed in Tables A 1 and A 2 in the appe
9. of play Devices such as a UTM drop towers and SHPB devices each have shortcomings inherent in their design which limit testing capabilities New instrumentation is needed to achieve the necessary strain rates and magnitudes Previous work in softball modeling has produced promising results but there still remains room for improvement Characterizations matching experimental COR and DS have been shown at a single speed but rate dependence as well as correct response to variation in surface geometry have not been accurately simulated While implementation of viscoelastic material models has been typical no work has yet treated the softball as structural foam High Poisson ratios and misshaped load displacement curves suggest that softballs have a different mechanism of deformation than what has been characterized previously 20 2 8 References ASTM F1887 2009 Standard test method for measuring the coefficient of restitution of baseballs and softballs West Conshohocken PA s n 2009 ASTM F1888 2009 Standard test method for compression displacement of baseballs and softballs West Conchohocken PA s n 2009 ASTM F1890 2009 Standard test method for measuring softball bat performance factor West Conshohocken PA s n 2009 ASTM F2845 2010 Measuring the Dynamic Stiffness DS and Cylinderical Coefficient of Restitution CCOR of Baseballs and Softballs s l American Society of Testing and Materials 2010 Barnes G 195
10. 1s not justified 14 Previous studies investigating the impact response of PU foam have used Split Hopkinson pressure bar SHPB devices Bryson 2009 Chen 2001 The device uses strain gages to measure the difference in reflected and transmitted compression waves propagating through two axially aligned long metal bars with a foam sample suspended between the two A striker bar propelled by compressed air causes a compression wave by colliding with one of the bars By adjusting either the initial striker bar velocity or material sample thickness strain rate can be adjusted Bryson achieved a minimal strain rate of 2780 s in PU foam samples by using a 9 inch long 0 5 inch diameter aluminum rod with an average foam specimen thickness of 08 inches Chen measured strain rates from 950 s to 5300 s in PU foam samples by using a 12 inch long 0 75 inch diameter aluminum striker bar to impact samples of thicknesses between 067 and 19 inches Besides the ability to measure foam properties at rates typical of play significant problems exist in a traditional SHPB The first is that the magnitude of the transmitted wave is often small and difficult to distinguish from the baseline electrical noise PU foam being a relatively soft material has low elastic impedance which results in a slower transmitted compression wave While many of the challenges of the SHPB can be overcome the minimum strain rate cannot Bryson 2009 2 6 Ball Mo
11. Average engineering strain in the foam sample was calculated by dividing the user defined sample thickness by the calculated displacement e t 2 3 2 lo 29 Engineering stress was calculated by dividing the load signal by the cross sectional area A a t Y 3 3 Eq 2 8 was used to calculate impulse Substitution of the calculated rebound velocity from Eq 3 1 into Eq 2 10 would result in Eq 2 8 Thus the method of speed and force measurement verification by means of calculating impulse described in Chapter 2 cannot be done for this device 3 3 Foam Samples In an effort to maintain consistency in softball composition and size a single ball model was used for all experimental testing as shown in Fig 2 1 DeMarini A9044 The ball was ASA certified with a rated COR of 0 44 and a nominal compression of 375 lbs The diameter of the foam samples used for impact testing was selected based on the consideration of several factors If the specimen diameter were larger than the striker bar diameter an undesirable non uniform load distribution would result If the specimen diameter were to decrease higher stresses would be developed for a given striker bar speed Smaller specimens are disadvantaged in that small imperfections such as surface finish or inhomogeneous foam produce more significant changes in experimental results Inspection of the foam under a microscope showed the average cell size to be about two orders of magnitu
12. DS values were equal to the square of the percent difference in peak force Thus comparison of both DS and peak force was superfluous Mesh density was determined to be sufficient as doubling the number of elements altered impulse displacement and impact force by only 2 Interestingly the mesh alignment between the ball and impact surface was found to have a small effect on impact performance These effects were however minimal compared to those caused by material type and surface geometry Figure 6 1 Softball model with cylindrical and flat impact surfaces using quarter symmetry 87 6 3 Mat 57 Low Density Foam Applying the material parameters from the PU foam sample model to the softball model resulted in poor agreement with experiment On the cylindrical surface impulse loading stiffness and displacement differed from experiment by 13 18 and 15 respectively while CCOR was 36 lower than experiment The damp factor was increased and the shape factor was decreased to improve correlation with the loading stiffness and CCOR respectively As damp was increased to better match experiment the solver would abort due to elements with negative volumes According to LS DYNA negative volumes can be caused by using fully integrated elements which are less robust than a 1 point element when deformation is large This is because a negative Jacobian can occur at one of the integration points while the element as a wh
13. Force Ibs 2000 1000 0 0 0 0 5 1 0 Time ms Figure 4 7 Load curves from 100 different DeMarini A9044 softballs impacting a cylindrical surface at 95 mph along with the selected ball To quantify the average ball response ASTM standard procedures were used to measure the COR DS and CCOR of 200 new balls ASTM F2845 2010 ASTM F1887 2009 The results summarized in Table 4 1 show a good level of consistency in performance with a standard deviation of less than 1 for ball mass COR and CCOR DS had a higher standard deviation 9 which is likely due to the spread of peak force shown in Fig 4 7 61 Table 4 1 Comparison of ball properties for a 200 ball population and the selected ball Average SD 200 Ball Sample Selected ball Mass 07 6 97 0 05 0 445 0 003 0 442 0 002 60264514 6 99 COR 60 mph DS Ib in 6196 571 CCOR 95 mph 0 377 0 003 0 375 0 003 A single ball was selected to quantify experimental performance The ball was selected based on both its similarity to the average loading curve in Fig 4 6 and its performance values listed in Table 4 1 The ball was impacted six times at 60 95 and 120 mph on both flat and cylindrical surfaces The impact properties shown in Table 4 2 were calculated using the equations from Chapter 2 and agree with trends and values of previous works Duris 2004 Faber 2010 Table 4 2 Performance measures as a function of
14. Gt 1 eht 2 13 E t RtH t 2 14 A constant strain rate R was assumed where v was Poisson s ratio and the step function H t was defined as O for t lt 0 and 1 for t gt 0 The shear moduli were obtained from finite element models created by Faber Faber 2010 which had the same DS as the foam samples tested in the SHPB An over prediction of stiffness in the mathematical model was attributed to collecting 19 data at excessively high strain rates 2780 s Strain rates could not be lowered as an increased sample thickness caused high signal to noise ratios and bar velocity was already minimized 2 7 Summary Standardized procedures to test softball impact properties which incorporate environmental conditioning have been established to obtain accurate and consistent experimental data Measureable properties like COR and DS are obtained from high speed impacts and are used to quantify ball performance The behavior of a softball during impact is governed by its composed material The closed cell foam microstructure produces a unique three phase compressive loading response while the viscoelastic PU matrix causes rate dependence The behavior of foam is also affected by 1ts density and external factors like humidity and temperature Neglecting the cover does not significantly change performance if the cover weight is accounted for Current instrumentation setups are not well suited to impact foam samples at rates typical
15. PU foams of varying densities to compare the accuracy of foam material models in LS DYNA Sambamoorthy 2001 From the results Mat 57 as well as Mat 83 Fu Chang Foam showed the best correlation with physical testing 73 5 3 1 Material Parameters The master curve developed from impacting foam samples in Chapter 3 was assigned as the nominal stress strain curve used by Mat 57 to control compressive response Because only one curve was used rate effects in loading could not be accounted for Small adjustments were made to the curve particularly in the area where the elastic region transitions to the plateau region to see how the master curve shape effected agreement with experiment The master curve which produced the best agreement with experiment is shown in Fig 3 17 The primary deformation mode in the foam sample was compression Thus Young s modulus E which governed tension had little effect in the simulation LSTC 2010 While the actual material would experience transverse tension during compression due to the Poisson effect Mat 57 had no Poisson formulation and thus had no transverse expansion when compressed Young s modulus was set as the initial slope of the master loading curve Unloading was controlled by a hysteretic unloading factor HU and a shape factor HU ranged in value between zero and one Low values of HU shifted the unloading path downward The lowest value of HU maximum hysteresis or energy lo
16. Scott D Burbank M S Washington State University May 2012 Chair Lloyd V Smith Numerical simulation of sport ball impacts is challenging due to the varied contact conditions involved and the difficulty in characterizing nonlinear materials at high strain rates The following considers rigid polyurethane PU foam used in softballs Past works have shown that load displacement curves from viscoelastic material models do not completely agree with experiment suggesting incorrect mechanisms of compressive deformation Additionally dynamic testing using a pressure bar apparatus was unable to achieve strain rates low enough and dynamic mechanical analysis was unable to achieve strain magnitudes large enough to represent play conditions A method was developed to impact PU foam samples over a range of displacement rates and magnitudes representative of play conditions A single rate independent master curve describing the stress strain loading response was experimentally developed and implemented into LS DYNA s Mat 57 foam material model Five constant rate loading curves were also derived experimentally and incorporated into a second foam material with rate dependent formulation Mat 83 Comparison of experimental and numerical load displacement curves 1V produced agreeable results for both materials Lack of temporal formulation for Mat 57 resulted in low rebounding rate dependence while Mat 83 showed penetration between contacting su
17. adnan aeiaed ancaneta eda eeek 54 DEO A a a a a a 55 Bank OSU oarn a E T E E S 56 AE TIPE OCC UOM E E eect 56 e IA E E Lo 0 E PUT E E S E E E T A 56 Bcd Re US a eet a E EN 60 A Damase Elec E acta etasaseaients 66 AD SUNAN A a E otguvadaaenmcacn do mawedenateetoancant 68 GO ROEN O 85 shah eter cette TE 69 PU Foam Sample Modela ees 70 XE io AA A tata 70 A eRe Tn ree et esters Dee pete Tene ne meen re oOo ren ne eee Teo Te 70 D2 Simulation Cadena idilio a E I2 39 Mat OW Demy O Ana sei a eet 73 Doo A nates nee dasaecadinaudeadnncnediettas 74 DD IRC SUNS i eee A we eh bnh a Rene Meantime then 75 5 3 3 COR Rate Dependence Parametric Study ooooccccnccccccnonnnnncnnnnnnnnnonananncnnnnnnnos TI vil dd Matos PU CUNAS PO AM a 80 SAL Material Development 80 AZ ISS US dada 81 O O nn A 84 A NC 85 O bc NIN Cea lt 1 U8 smears rai ii 86 OL SIN OGUCHON yr is 86 O Me 00 RP O 86 0 3 Ma7 Low Density PO aii dia 88 pA COR Rate Dependencia dd is 90 6 3 2 Stran Maemtude and Rates 93 O 4 Mat 83 FU Chano POr 95 6 5 Linear Viscoelastic Model Comparison oooooonnnnnnnnnnnnnnnnonnnnnnnnnnnnnnononnncnnnnnnnnnnnos 98 E A A O NAO 103 A A A TO 104 E SUMI AA NR ated ohana oan a ab peadiaten 105 Tel BUT Work aotearoa 106 O O arntcristgac deo napgsncsetesghased E 108 JON 5 Zar peneaye eae E O IN Ver Te 110 Vill List of Tables Table 4 1 Ball properties for a 200 ball population and the selected ball 63 Table 4
18. analog signal when the striker bar passed by Figure 3 3 Visual layout of the impact containment chamber 26 Striker bar speed was measured by dividing the distance between sensors by the difference in time between triggers The arrangement of three fiber optic sensors produced three speed measurements one measurement from sensors one and two v72 from sensors two and three v23 and from sensors one and three v73 This enabled each speed measurement to be verified by the other two As v23 was the speed measurement taken closest to impact it was used as the initial striker bar speed for calculating impact properties The source of propulsion for the striker bar was compressed air The device was supplied with compressed air which was stored in a five gallon accumulator tank The tank pressure was controlled using a digital regulator SMC ITV3050 31N3CL4 shown in Fig 3 4 Connected to the tank was a pneumatic valve MAC 57D 32 110AA which released the air to propel the striker bar The barrel was attached to the valve using a 0 5 inch diameter high pressure hose Measuring 24 inches long with a 0 5 inch bore the steel barrel had vent holes drilled radially along the last 6 inches The vent holes allowed compressed air within the barrel to be released as the striker bar exited the barrel producing a more consistent bar speed Line To Accumulator Tank Line From External Compressor Figure 3 4 Pressure Regulator
19. as the decrease in performance occurred over time DS for balls 2 and 3 remained constant while ball 1 showed a 12 increase in DS as shown in Fig 4 14 Because the balls showed varying effects no conclusion could be drawn relating DS performance to repeated impacting 67 The change in performance was most likely caused by decay of the foam structure due to fatigue Residual strain was visibly noticeable in the ball as testing progressed which indicates that structural damage was occurring While performance change was evident over time a significant number of impacts were required The results support the findings of Duris that repeated impacting up to 25 impacts per ear does not significantly change impact performance 4 5 Summary A sample of 200 softballs of the same model showed good consistency in performance when tested using standardized procedures Further experimentation on a single ball revealed a strong dependency of ball performance to both impact speed 60 to 120 mph and surface geometry flat and cylindrical Increasing impact speed tended to increase the absorbed energy deformation and force of impact Changing the impact surface from flat to cylindrical increased the absorbed energy and deformation but decreased force of impact Alternate methods of calculating momentum suggested a slight decrease in measurement accuracy as speed increased A durability test was performed to better understand the effects of repeate
20. cylindrical surface 96 Figure 6 13 Softball load displacement curves for Mat 83 on flat surface 97 Figure 6 14 Comparison of experimental and numerical CCOR for Mat 83 97 Figure 6 15 Cylindrical surface load displacement comparison of previous models 99 Figure 6 16 Flat surface load displacement comparison of previous models 99 Figure 6 17 Comparison of COR with previous models ooooonnnnnnnccccccnnnnncnnnnnnnnnnnnnnnnnos 100 Figure 6 18 Comparison of COR rate dependence with previous models 101 Figure 6 19 Comparison of dynamic stiffness with previous modelS oooooooncnnnann o 102 xiii Figure 6 20 Comparison of dynamic stiffness rate dependence with previous models 102 Figure B 1 Impactor device and startup SWItC HES ooooooccccccccccccccccnonnnnno no sere 111 Furo B2 E OMICS DOK AA A A 112 Figure B 3 Front panel user interface for the impactor deviCe oooocccccccccccconnnnss 113 Figure B 4 Two operations for the Controls box importing a previous impact file left ANG Erie Ene Cannon TOL eeso OPE O OR II II E 113 Figure B 5 Load Indexing Box and force time CUIVE cece cece cece cece cette eens 116 X1V 1 Introduction 1 1 Introduction Finite element analysis FEA has been widely implemented in sport ball simulations including golf cricket baseball tennis and softball As technology and
21. dependence of COR on speed was observed as early as the 19 centrury Hodgkinson 1835 and also applies to baseballs Russel 2005 and other sports balls Cross 2000 Miller 2006 2 2 3 Static Compression Ball compression 1s a measure of the quasi static stiffness of a ball ASTM F1888 2009 The softball is compressed 0 25 inches between two flat surfaces as shown in Fig 2 3 and ball compression is the corresponding peak force Softballs used in bat certification testing have compression values between 350 and 375 lbs Figure 2 3 Static compression test setup Compression is an important property in determining general ball performance and establishing consistency in standardized bat testing However the rate of compression is about 10 000 times lower than what occurs in play Duris 2004 2 2 4 Dynamic Stiffness Dynamic stiffness DS quantifies ball stiffness for impacts at high speeds The setup for measuring DS Fig 2 4 is also used to measure CCOR ASTM F2845 2010 Load cells mounted to a cylindrical surface capture the force exerted by the ball on the impact surface while speed monitors determine the incident and rebounding ball velocities IMPACT RIGID WALL SURFACE LOAD CELL S 457 SPEED 2 SPEED a VETOR BALL THROWING MACHINE 12 IN J IN a Figure 2 4 Schematic of Dynamic stiffness and CCOR measurement from ASTM F2845 Smith compared quasi static softball compression to DS and found bat perfor
22. during impact cannot be measured directly Thus it is difficult to apply these results to softballs Numerical simulations of softball impacts discussed in Chapter 6 will highlight cross sectional strain distributions 3 8 Summary A new device was developed to impact samples of softball foam at rates similar to play It was found that inbound striker bar speed and foam sample displacement measurements were quite accurate when compared to linear helical spring impacts at low rates lt 2 and high speed cameras at both high and low rates lt 2 A custom hole saw was manufactured to successfully produce uniform foam samples with square smooth surfaces Impacts with a two inch striker bar resulted in peak strain rates ranging between 1000 and 2700 s which is the range typical of play conditions A single master curve was developed to describe the compressive response of the foam Impacts of foam samples with differing thickness fit well with the master curve Impacts with striker bars of four different lengths produced similar results when compared as a function of striker bar kinetic energy These results are promising for possible future studies into dynamic energy absorption and rate effects of various types of foam The device s ability to use striker bars of differing length or mass allowed strain rate and magnitude to be independently adjusted This proved useful in the development of constant rate stress strain curves As would be expec
23. impact speed and surface geometry Average SD Impact Speed mph 60 1 0 3 94 8 0 2 120 2 0 6 60 2 0 2 94 7 0 5 120 0 0 5 COR CCOR 0 442 0 002 0 390 0 003 0 357 0 002 0 418 0 003 0 375 0 003 0 350 0 002 Peak Load Ibs 2995 52 4805 60 6285 90 2394 22 4132 177 5297 242 Impulse Ib s 1 79 0 005 2 72 0 006 3 34 0 016 1 74 0 020 2 67 0 017 3 28 0 027 Peak Disp in 0 378 0 007 0 568 0 012 0 687 0 032 0 425 0 013 0 631 0 007 0 780 0 012 DS 1b in 7235 213 7319 185 7828 170 5487 88 6026 514 6192 527 Compared to the flat surface the cylindrical surface had an inherently smaller contact region This increased the total deformation of the ball by 11 Greater deformation resulted in more energy absorption by the ball s foam core This lowered the COR by 4 and also lowered peak force by 17 The difference between peak force and displacement were evident in the load displacement curves in Fig 4 8 DS changed significantly with cylindrical stiffness being 27 lower than that of the flat surface The time to reach peak force was longer with the cylindrical surface taking an extra 0 01 seconds as shown in Fig 4 9 The change in impact 62 surface affected impulse the least 2 average The increase in energy dissipation for the cylindrical surface properly resulted in a lower impulse as shown in Fig 4 10 5000 e C
24. less than the PU foam sample model in Chapter 5 Mat 57 showed the best agreement with experimental load displacement curves and DS across variations in both impact speed and surface geometry The material s COR rate dependence improved over the PU foam sample model but was still below experiment A parametric study revealed that COR rate dependence improved slightly as parameters were adjusted to lower energy loss Cross sectional strain distributions showed peak strain magnitudes occurring near the collision surface with strain magnitudes well into the densification region of compressive foam response for typical impact speeds Mat 83 best agreed with experimental COR and CCOR rate dependence compared to any existing model A softening behavior was shown as loading rate decreased This is likely a result of the material s time dependent formulation Comparison with viscoelastic material models from previous studies showed key improvements Both foam models correctly characterized the effect of surface geometry on COR whereas previous viscoelastic models did not The oval shaped load displacement curves of the viscoelastic models incorrectly characterized the softball s linear loading which was well defined for both foam material models 103 6 7 References Allen T Good will S R and Haake J 2008 Experimental validation of a tennis ball finite element model for different temperatures The engineering of sport 7 Springer 12
25. low speeds and 1 7 at high speeds Sample displacement was also very similar with an average difference of 2 at low speeds and 1 5 at high speeds Rebound velocity did not match as well with the fiber optic sensors measuring low by an average of 9 8 low speeds and 13 9 high speeds compared to the high speed videos 34 E Device 29 E Camera 10 Inbound Speed mph y 1 2 3 4 5 6 l 8 9 10 Sample Figure 3 11 Comparison of initial striker bar speed as measured by the impactor device and the high speed camera 0 25 mw Device 020 E Camera 0 15 0 10 0 05 Sample Displacement in 0 00 l 2 3 4 5 6 7 S 9 10 Sample Figure 3 12 Comparison of sample displacement as measured by the impactor device and the high speed camera 35 mn E Device E Camera Rebound Speed mph 1 2 3 4 3 6 l 8 9 10 Sample Figure 3 13 Comparison of rebound speed as measured by the impactor device and the high speed camera A second method used to verify instrumented measurements involved impacting a 1 inch helical metal spring The collision between the striker bar and metal spring was modeled as a simple mass spring system represented as the differential equation M X t kx t 0 3 5 where k was the linear spring stiffness measured by a UTM The solution to Eq 3 5 with initial conditions of x 0 0 and x 0 v 3 is shown in Eq 3 6 k J kmp V23 sin m e x t 3 6 Spring di
26. on the mass of the striker bar This was expected as these variables would be affected by the bar momentum These results are promising for other potential uses of the device to investigate or compare the effects of energy absorption on foams or other soft materials All of the data from impacts with differing bar lengths at various speeds was used to further investigate the effect of strain rate on PU foam Strain rate was calculated as the derivative of Eq 3 2 which could be evaluated throughout each collision as shown in Fig 3 25 From 100 different impacts coupled stress and strain values were collected at strain rates closest to 250 750 1250 and 2000 s but no more than 50 gs Stress strain values at similar rates were combined to produce the constant strain rate curves shown in Fig 3 26 The temporal dependence of the viscoelastic foam is evident as an increase in stiffness was observed in both the cell collapse and densification regions A trend of increasing deviation between strain rates was also observed as strain magnitude increased When the master curve from Fig 3 17 was plotted alongside curves from Fig 3 26 it closely followed the 2000 s strain rate data 46 2500 2000 Eh tA Strain Rate 1 s Time s Figure 3 25 Strain rates plotted throughout impacts from a 2 inch striker bar 3500 3000 2500 2000 1500 Stress psi 1000 500 0 0 0 2 0 4 0 6 0 8 Strain Figure
27. softball samples with varying masses at multiple speeds resulted in compressive stress strain curves which were used in two different numerical foam material models Numerical softball impacts were directly compared with experiment An air cannon was used to fire softballs at both cylindrical and flat impact surfaces across a range of speeds typical of play 60 to 120 mph Impact properties including COR DS impulse peak force and displacement were measured and later used to both optimize and assess numerical agreement Experimental COR linearly decreased with increasing impact speed while impulse force displacement and DS increased The cylindrical impact surface had higher displacement but lower COR force and DS than the flat impact surface In optimizing the foam material models numerical simulations of the impacted PU foam softball samples were compared to experiment Mat 57 which had no formulation to implement rate effects showed good load displacement agreement but lacked the temporal dependence of COR typical of experiment Mat 83 used multiple curves from different loading rates to successfully characterize an increase in loading stiffness with impact speed Surface penetration 105 was however more significant than with Mat 57 resulting in a nonlinear increase in COR with impact speed Incorporating the foam material models into softball simulations impacting flat and cylindrical surfaces significantly improved correlation
28. the resultant modulus transitions between the two moduli Sandmeyer s softball model was implemented into a simulated bat ball collision The numerical ball COR was systematically adjusted to match experimental COR values obtained from 58 mph impacts with a 2 5 in thick rigidly mounted wood plank Duris also investigated a power law model as well as a general viscoelastic model based on a six term Prony series The Prony series was based on a spring damper system and used a series of Voight elements as shown in Fig 2 8 16 ly My yr Figure 2 8 Schematic of a Prony series material model characterized by multiple Voight elements in series The time dependent shear modulus G is defined as the summation of multiple Voight elements G t X giet 2 12 each having an individual shear modulus g and decay constant B Duris defined six shear moduli and decay constants from dynamic mechanical analysis DMA of a polyurethane softball core sample The softball model was developed in LS DYNA and was modeled as an isotropic homogeneous sphere using eight noded solid elements Both power law and Prony series viscoelastic models were applied to a simulated impact on cylindrical and flat surfaces and were compared to experimental data Duris concluded that the Prony series model did not match well with experiment because material deformation during DMA testing was low compared to deformation created in the model Good characterization was fo
29. 0 0 0 0 2 0 4 0 6 0 8 Strain Figure 3 28 Comparison of low rate loading and unloading behavior of samples of differing thickness According to Gibson the effect of loading rate on foam compression is significant when scaled by decades Fig 2 8 Because a softball experiences low strain rates near maximum deflection the compressive response of softball foam was tested across decades of low strain rates Six foam samples were compressed at constant strain rates of 0 01 0 33 and 3 33 s The average response at each loading rate along with the lower and upper constant rate curves from Fig 3 26 are shown in Fig 3 29 Results from the load frame were similar to those of the impactor device showing an overall stiffer behavior at higher loading rates Besides the 250 s strain rate curve slightly overlapping the 3 s strain rate curve at densification strains the data from the load frame and the impactor device correlated well showing good transition across the strain rate spectrum 49 3000 Strain Rate 2500 2000 o 5 a 3 2000 Stress psi a oa 1000 500 0 0 2 0 4 0 6 0 8 Strain Figure 3 29 Constant strain rate curves from the load frame 0 01 0 33 3 3 s and impactor device 250 2000 s 3 7 Damage Effects The damage to a foam structure due to deformation is specific to the material and its structure Open celled foams are frequently designed for applications involving large
30. 0 20 30 40 Bar Kinetic Energy ft Ib Figure 3 22 Comparison of peak strain in foam samples impacted with striker bars of varying length 44 07 Inch Bar 3 Inch Bar 6 Inch Bar 9 Inch Bar Bar Kinetic Energy ft Ib Figure 3 23 Comparison of COR in foam samples impacted with striker bars of varying length 2 Inch Bar o 3 Inch Bar e 6 Inch Bar 0 9 Inch Bar DS bin 10 20 30 40 Bar Kinetic Energy ft 1b Figure 3 24 Comparison of DS in foam samples impacted with striker bars of varying length Figure 3 24 showed an interesting response It would be expected that stiffness would increase with the energy of collision however the opposite is shown for impacts below 10 ft lb of kinetic energy Referring to Fig 3 22 impacts below 10 ft lb had peak strain magnitudes in the cell collapse region of compressive foam response according to Fig 3 17 An increase in 45 striker bar velocity without a corresponding increase in force of impact due to cell collapse will reduce DS as defined by Eq 2 7 A strong correlation with inbound striker bar kinetic energy mv was observed for peak stress peak strain and DS across bars of differing lengths The aligning results of differing bar lengths suggest that dynamic results obtained from the device are independent of both the physical dimensions and mass of the striker bar COR Impact duration and impulse were similarly compared and were found to be dependent
31. 2 Softball performance as a function of impact speed and surface geometry 63 Table 5 1 Parameters for Mat 57 Low Density Foam material model 76 Table 5 2 Parameters for Mat 83 Fu Chang Foam material model 82 Table 6 1 Parameters for Mat 57 comparing PU foam sample and softball models 90 Table 6 2 Parameters for Mat 83 comparing PU foam sample and softball models 97 Table 6 3 Parameters from previous viscoelastic softball models 99 Table A 1 Cylindrical surface performance of each model oooococcccccccccos 109 Table A 2 Flat surface performance of each model ccc ccc ccc eee eee e eee e eens 110 1X List of Figures Fieure 2 0 Sompall Cross cOn ca 3 Figure 2 2 Schematic for measuring softball COR ooooooococonnnnncccccnonnnnnnnnnonnnonononcnncncnnncnnnos 5 Figure 2 5 StaliG COMPLESSION TES SEU aid 6 Figure 2 4 Schematic of Dynamic stiffness and CCOR measurement cccceeeeeeeeees 7 Figure 2 5 Typical load displacement curves of a softball impact o oooooooononcnnononnnnos 9 Figure 2 6 Typical Stress strain loading response of polymeric foam ccceeeeeeeees 11 Figure 2 7 Rate dependent compressive response of rigid Polystyrene foam 12 Figure 2 8 Schematic of a Prony series material model occccccnncccnnnnnnnnnnnnnnnnnonnnnnnnnnos 17 Figure 2 9 Force time compar
32. 3 26 Constant strain rate curves derived from impact testing Duris stated that the Poisson ratio of softball foam is approximately 0 1 Duris 2004 To quantify the Poisson ratio five high speed videos of impacted PU foam samples were taken at 60 000 frames per second The average Poisson ratio was 0 28 with a standard deviation of 0 02 47 3 6 Quasi Static Data In conjunction with the dynamic results obtained from the impactor device low rate uniaxial compressive foam tests were performed on a customized load frame Fig 3 27 The screw driven device made by ADC was capable of measuring displacement to an accuracy of 1x10 inches at a sample rate of 1 kHz The samples were placed between two flat surfaces and then compressed as both force and displacement were measured to produce stress strain curves using Eqs 3 2 and 3 3 Figure 3 27 Load Frame used to conduct low rate compressive testing Foam samples of two different thicknesses 0 2 and 0 3 inches were compressed at a constant rate 0 01 s to determine if sample thickness affected compressive response Samples of each thickness were compressed at uniformly incremented strain magnitudes ranging from 0 2 to 0 8 to compare unloading behavior The results in Fig 3 28 show excellent agreement in both loading and unloading behavior of the 0 2 and 0 3 inch samples 48 3000 2 Samples 2500 4 0 3 Samples _ 2000 a 1500 Fad 7 1000 50
33. 5 105 110 120 and 130 mph on a cylindrical surface Biesen 2006 Each ball was tested once and 6 balls were used for each speed CCOR and DS were both found to be linearly dependent on speed Damage to the balls tested at 130 mph was found to be negligible as the COR and DS of the original 80 mph test group and the 130 mph group tested again at 80 mph were similar Faber tested DeMarini A9044 softballs as part of his work in normalizing softball bat performance Faber 2010 The CCOR and DS at 95 mph were found to be 0 373 and 5716 Ib in respectively Load displacement curves showed a peak force of 4300 Ibs and a peak displacement of 0 6 inches 60 Duris performed softball tests investigating the effects of rate and surface geometry Duris 2004 A decreasing trend of COR and CCOR as well as increasing trends of peak force with respect to ball speed was observed A flat impact surface was found to have a greater peak force lower impact time and an increased COR compared to a cylindrical surface Even among softballs of an identical model DeMarini A9044 some variation in performance was shown Figure 4 7 shows a qualitative comparison of load curves from 100 different DeMarini A9044 softballs impacting a cylindrical surface at 95 mph The greatest spread occurred at the impact apex According to Eq 2 7 this would also cause spread in DS 5000 Sample Population 4000 m Selected Ball o gt SO
34. 5 133 Bryson A J 2009 Impact response of polyurethane Master s thesis Washington State University 2009 Duris J G 2004 Experimental and numerical characterization of softballs Master s Thesis Washington State University 2004 Faber W L 2010 Reducing the effect of ball variation in bat performance measurements Master s thesis Washington State University 2010 LS DYNA 2003 LS DYNA Support Online 2003 Cited February 9 2012 http www dynasupport com howtos material negative volume in soft materials National Pro Fastpitch 2012 Fastpitch Facts Online 2012 Cited January 24 2012 http www profastpitch com fanz facts Smith L V 2012 Field Measurements of Softball Player Swing Speed 9th Conference of the International Sports Engineering Association Unpublished 104 7 Summary The foregoing has been concerned with improving numerical predictions of solid sport ball impacts Desired improvements over previous ball models included a rate dependent response and characterization across impact surfaces of varying geometry A key distinction from previous models which involved viscoelastically characterized materials was approaching the softball as a structural foam A new test method was developed to characterize the ball material at strain rates and magnitudes representative of play conditions Results of this method showed a material response that is consistent with structural foam Impacting PU foam
35. 7 Study of Collisions Am J Phys 1957 Vol 26 p 9 Biesen E D 2006 Prediction of plastic deformation in aluminum softball bats using finite element analysis Master s Thesis Washington State University 2006 Brody H 1997 The physics of tennis II The ball racket interaction s l American Journal of Physics 1997 Vol 65 10 p 981 987 Bryson A J 2009 Impact response of polyurethane Master s thesis Washington State University 2009 Chauvin D J and Carlson L E 1997 A comparative test method for dynamic response of baseballs and softballs International symposioum on safety in baseball softball 1997 p 38 46 Chen W Lu F Winfree N 2001 High strain rate compressive behavior of a rigid polyurethane foam with various densities Experimental Mechanics 2001 p 65 73 Cross R 2000 The coefficient of restitution for collisions of happy balls unhappy balls and tennis balls Am J Phys 2000 Vol 68 p 1025 1031 21 Drane P J Sherwood J A 2004 Characterization of the effect of temperature on baseball COR performance Proceedings from the Eng of Sport 5 2004 p 59 65 Duris J and Smith L V 2004 Evaluating test methods used to characterize softballs Sth International Conference on the Engineering of Sport 2004 Vol 2 p 80 86 Duris J G 2004 Experimental and numerical characterization of softballs Master s Thesis Washington State University 2004 Faber W L 2010 Reducing the e
36. 7383075 17113217 03170 0418 ONS S 9 2011 113513 AM 22120MPHD 2298312 17702673 7307078 0 3180 LOANO 02598 0091 SONU NIMAM 2 1ZOMPHD 2344 6365 18811486 7526264 03200 lOM 02541 5 9 2011 11 38 48 AM 2 120MPH D 2443 5688 21251929 8018148 03280 0418 02231 Figure B 3 Front panel and showing the blue Controls box used before firing Graphs of load time top right stress strain bottom right and strain center are updated after firing the cannon Controls Data Fror File y en Mange _ 500 Ib v Fires 1001 Impact Bar DAQ Parameters rie name otteet 2370 i enath in 43 Weight oz Stran Mate 11138 Data Recording E CA Users Power User Desktop Impactor Files New Data New Summary txt E C Users Power User Desktop Impactor Files Old tests AA New Fatigue Test11138_337_2_ 300_420 fatigue 6psi 6 b4 Users Power User Decktop Iimpactor Files New Data 300 420 test Lit 0 Controls Lee i gt mue 2 Fires 1001 harmeter Data Recording CAUsers Power User Desktop Impactor Files New Data New Summary bd Isers Power User Desktop Impactor Files New Data t 1607 182 6 300 420 test Ltd Gh m MOETE test Figure B 4 Two different operations are available for the Controls box importing a previous impact file left and firing the cannon right 112 Option 1 Data from File 1 Switch the Data From toggle switch down The Fire button should be bor
37. DYNAMIC CHARACTERIZATION OF RIGID POLYURETHANE FOAM USED IN FEA SOFTBALL SIMULATIONS By SCOTT D BURBANK A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN MECHANICAL ENGINEERING WASHINGTON STATE UNIVERSITY Department of Mechanical and Materials Engineering MAY 2012 To the Faculty of Washington State University The members of the Committee appointed to examine the thesis of SCOTT D BURBANK find it satisfactory and recommend that it be accepted Lloyd V Smith Ph D Chair y a William Cofer Ph D Acknowledgement This paper 1s dedicated to each individual who shared their time and talents thus enabling me to find success and reach my potential To my wife Beth who at least pretended to be interested in daily updates about FEA material characterization and who faithfully stood by my side through thick and thin To Dr Smith for giving me this opportunity and for being the best advisor I could ask for Also to Dr Ding and Cofer for being on my research committee To my parents and all my school teachers for filling me with knowledge and teaching me the value of hard work and perseverance To Jeff Jason Brendan Jacob Lindsey Duy Bryant Nathan and all the other SSL people for making the lab a satisfying and interesting place to work 111 DYNAMIC CHARACTERIZATION OF RIGID POLYURETHANE FOAM USED IN FEA SOFTBALL SIMULATIONS Abstract by
38. The load cell pressure regulator and MAC valve were wired to a Dell T3500 desktop computer using a connection block SCB 68 made by National Instruments NI The connection 2 block was wired to a NI analog to digital PCI 6111 board capable of sampling at 5 mega samples per second The MAC valve was activated by a 24 V signal supplied through a solid state relay It was given its own power supply to minimize signal spikes observed when the valve opened and closed The two analog channels on the PCI 6111 board were connected to the load cell and pressure regulator so a NI CB 68LP I O connector block and NI PCI 6602 board were installed to attach the fiber optic sensors to analog channels 3 2 2 Device Operation All electronic functions calculations and data logging for the device were controlled using NI s LabVIEW software A screen image of the user interface 1s shown in Fig 3 5 and detailed operating instructions of the device are listed in Appendix B Before the striker bar was fired accumulator tank pressure and load cell sampling frequency could be adjusted Foam sample diameter d and length l were input by the user as well as the mass of the striker bar mp After a foam sample was mounted to the load cell and the striker bar was pushed to the breach of the barrel using a small rod the fire button was pushed The MAC valve then opened releasing the pressurized air within the accumulator tank to the barrel which forced the striker bar
39. all performance Damage to the ball s foam core due to repeated impacting was also studied to determine if such effects were significant All testing was performed in the environmental chamber described in Chapter 3 and all balls were acclimatized for two weeks prior to testing 4 2 Instrumentation Instrumented ball impacts were performed on a dynamic stiffness test apparatus shown in Fig 4 1 ASTM F2845 2010 The test consisted of firing a ball from an air cannon against either a fixed solid steel half cylinder 2 25 inches in diameter or a 0 5 inch thick steel plate Light gates and load cells measured ball speed and the force of impact which were used to calculate impact properties and develop load displacement curves 56 Figure 4 1 Setup of the dynamic stiffness test apparatus The softballs were fired from a four foot long 5 5 inch diameter air cannon using compressed air stored in an accumulator tank Fig 4 2 The desired pitch speed was obtained by adjusting the pressure in the accumulator tank with a pressure regulator When fired a MAC valve released air from the accumulator tank All device components and measurement sensors were wired to a connection board and controlled by a PC using labVIEW software National Instruments Austin TX Arrestor Cannon ver errr Y opts Pressure _ Regulator Figure 4 2 Air cannon used to fire softballs and baseballs 57 While inside the cannon barrel the ba
40. am material models 106 Mat 83 incorporated rate effects well but was unable to match experimental stiffness near the climax of collision Improvement in low rate characterization could possibly be achieved through more rigorous experimentation Both Mat 57 and Mat 83 outperformed the viscoelastic models with contrasting behaviors which lends both materials to specialized uses in future simulations Mat 57 closely emulated experimental stiffness and forces which are critical for simulating collisions with objects which sustain structural damage Impacts with safety equipment or testing of bodily injury would be well suited Mat 83 best characterized the ball s rebounding rate dependence and would be best applied where rebounding properties are critical Simulations of bat ball collisions or other equipment performance testing would be ideal 107 Appendix A Table A 1 Cylindrical surface performance of each model A T 108 Table A 2 Flat surface model performance comparison of percent difference from experiment AT S O COR 95 mph COR 4800 0 560 0 470 6935 5363 7291 4189 120 mph COR 0 370 0 374 0 394 3 36 3 43 6496 5074 0 674 0 693 0 536 0 440 0 658 7268 5976 8369 5106 109 Appendix B Operation Procedures for the Impactor Device Boot up 1 Power strip located on the back of the frame should be ON 2 Turn the computer on and allow it to boot up 3 Make sure the black switch locat
41. astic material was applied to the simulated softball impact and the results were compared to the foam models developed in this study Performance values for the viscoelastic models are listed in Tables A 1 and A 2 in the appendix Table 6 3 FEA material parameters from previous viscoelastic softball models density p bulk modulus K instantaneous shear modulus GO long term shear modulus Goo and decay constant B p K Go Go p Model lb s lin psi psi psi Hz Duris 3 90E 05 1E7 1E4 700 68000 Faber 3 90E 05 1E5 2E4 1000 68000 Bryson 3 90E 05 1E6 3500 400 40000 The load displacement cylindrical surface response of the foam and viscoelastic models is compared at 95 mph in Fig 6 15 The loading stiffness peak displacement and peak force of Mat 57 agreed best with experiment Mat 57 also most accurately matched the unloading shape All three viscoelastic models displayed a generally oval shaped curve indicating a different mechanism of deformation than occurs with foam Mat 83 showed a linear loading response similar to Mat 57 but had a more oval unloading shape similar to the viscoelastic models A similar comparison but of a flat surface impact is shown in Fig 6 16 Mat 57 again shows the best agreement with experiment A clear difference was again shown between the linear loading of the foam models and the oval shaped viscoelastic curves 98 Viscoelastic 1 Viscoelastic 2 4000 Viscoelastic 3 o Expe
42. automatically increment with each impact and be included in the note Set Count to zero to deactivate it Press the fire button 114 After Pressing the Fire button 1 The Controls box will turn grey and the Load Indexing box will turn blue Fig B 5 2 The program tries to automatically crop the force signal to isolate the impact A suggested Start Index and Length of the impact is displayed along with the corresponding force time graph Manually refine Start Index and Length as needed to show the desired force time and stress strain curves 3 To save impact data click the Write File button to say yes and then push Done If the Write file says no then no data is recorded The data saved includes the Summary file of impact performance and the Wave Out file of time load and sample displacement A text file of tabulated stress strain values is also saved to the following directory by default C Users Power User Desktop Impactor Files Old tests Start Index Lengtl go po 0 Suggested 992 9 e J AS Done Figure B 5 Load Indexing Box and force time curve 115
43. competition in the field of sports equipment increases numerical modeling and simulation becomes a more viable and economical option in research and development Numeric models that reliably simulate the performance of sports equipment before manufacturing would result in increased design optimization and reduced time and cost associated with testing and manufacturing prototypes An accurate ball impact model may be used for instance to simulate sport equipment performance protective equipment or personal injury Softballs are difficult to model due to the dynamic environment of operation and the material sensitivity to temperature humidity composition and rate of impact Previous methods used to model softballs have been primarily phenomenological These models incorporated a viscoelastic material model based on the rate dependent nature of the polyurethane PU ball core Results however showed that load displacement curves from viscoelastic material models do not completely agree with experiment suggesting incorrect mechanisms of compressive deformation As the core of a softball consists of rigid structural foam a foam material model rather than viscoelastic was used for this study Numerical foam material models require input of experimentally derived compressive loading curves to describe the nonlinear response typical of foam As a softball s PU foam matrix is rate dependent the nonlinear compressive response necessitates development a
44. d force would only be 0 01 lower than the actual force after the time interval of 37 interest 0 001 s There 1s some confidence however in the load cell accuracy as it was newly purchased for this study and came with a calibration certificate stating that calibration procedures were in compliance with ISO 10012 1 3 5 Results All experimental testing was performed at the Sports Science Laboratory at Washington State University To reduce the effect of environmental conditions the temperature and humidity of the tests were regulated by a Stability Environment Inc environmentally controlled walk in chamber number 1332401 The environmental chamber was 429 square feet and 8 10 feet high and space was sufficient to both acclimatize materials and conduct tests The chamber was set to conditioning parameters defined in ASTM F2845 72 4 F 50 10 RH The environmental consistency over the period of experimental testing is shown in Fig 3 15 and 3 16 Two weeks were allowed for the foam samples to acclimatize prior to testing 78 J oN J Ja J ho Temperature F 6 66 9 1 2010 12 10 2010 20 2011 28 2011 Date Figure 3 15 Logged temperature over the duration of experimental testing 38 ON Un oN N un Un Relative Humidity Ja un 40 lar rr rr rr rr rn ee nn Ke 35 9 1 2010 12 10 2010 20 2011 28 2011 Date Figure 3 16 Logge
45. d humidity over the duration of experimental testing After being environmentally acclimatized thirty foam samples were impacted by a 2 inch long striker bar at speeds ranging from 17 to 45 mph which resulted in peak strain rates between 1000 and 2700 s Each sample was tested once so that the results would not be influenced by potential damage from cell wall collapse The stress strain curves of each impact along with the master compressive loading curve are shown in Fig 3 17 The three phases of polymeric foam compression were evident Foam collapse occurred at approximately 0 1 e and continued until the densification region at approximately 0 4 e This is consistent with the dynamic compressive behavior of PU foam published elsewhere Chen 2001 39 2000 1500 mm Vaster Curve Stress psi 1000 Strain Figure 3 17 Dynamic compressive response of softball foam at various rates and the corresponding master curve The master curve was developed to represent compressive response as a single rate independent curve Many of the stress strain curves in Fig 3 17 depart from the master curve as peak strain is approached and the strain rate nears zero This is consistent with viscoelastic effects where creep tends to increase as strain rate decreases The master curve was used as a parameter to control compressive response in a numerical foam material model discussed in Chapter 5 Oscillations in the stress strain c
46. de smaller than the specimen dimensions 0 004 inches as shown in Fig 3 6 It was determined that a specimen diameter slightly smaller than the striker bar 0 42 inches would ensure uniform load distribution and provide sufficient stress levels while minimizing the effects of possible surface defects or foam inhomogeneity 30 at Ca SUF Sa 900 um Figure 3 6 SEM image of softball foam cross section Specimen length also had limitations based on several factors Longer foam samples are harder to accurately manufacture A shorter foam sample would allow less stopping distance for the striker bar at a given speed This would increase the bar s deceleration and impact force Using a thinner sample would reduce the striker bar speed which would exceed the capacity of the load cell 500 lbs The same effect would result from impacting samples made of stiffer materials like solid plastics or metals Specimen length also directly affected strain rate Maximum strain rate in the sample occurred just as the impact began and was calculated as v Emax m 3 4 Dividing the striker bar speed which caused a 500 lb impact force 45 mph by the desired maximum strain rate of 2500 s t resulted in a sample length of 0 3 inches The foam samples were all machined from new softballs which had been impacted once on a dynamic stiffness test apparatus at 60 mph Each softball was tested to ensure COR and ball 31 weight were typical for th
47. deling Numerical modeling of softballs has received limited attention compared to the baseball which has been the focus of previous work by Mustone amp Sherwood Shenoy and others Munstone 2000 Shenoy 2000 Softballs have been previously modeled as isotropic and homogeneous with mass and diameter equal to a standard softball The contribution of the cover is often neglected as justified by Duris Duris 2004 He tested softballs with and without covers 15 at various speeds and observed a 4 2 increase in COR and a 16 6 decrease in maximum impact force without the cover Normalizing the results with ball momentum increased the maximum force by 4 4 suggesting the large change in maximum force was due to loss of the cover mass Removing the cover was also found to have a minimal effect on rate dependence as the COR slope with respect to pitch speed with and without a cover was observed to remain approximately constant An early softball model by Sandmeyer used a three parameter power law viscoelastic material model with a time dependent shear modulus defined by G t Go Go Go e Pt 2 11 where G and Go were the long term and instantaneous shear moduli and B was the decay constant Sandmeyer 1994 In the power law model stiffness is governed by the long term modulus for loading conditions of extended duration while brief time intervals are governed by the short term modulus The decay constant controls how quickly
48. dered in black 2 Select the desired file from the Force In selection box in the Data Recording section The file must have the same name as when it was created File names are produced by the program as follows strain rate_striker bar speed_bar length_ sample length sample diameter _ note 3 The directory for a Summary file can be set in the Data Recording section The summary file saves impact results including date comment strain rate max strain COR impulse bar velocity and sample diameter and length The summary file content is displayed in the table below the Controls box The Wave Out indicator shows the directory and filename of the last saved file 4 Under DAQ Parameters the File Name Offset is used to properly offset the file name characters so bar speed sample length etc can be read from the file name Adjust its value so that the characters in Strain Rate matches the strain rate in the file name in the Force In selection box 5 Make a comment in the Note text box if desired The Count number is an automated increment for repeated impacts with the same Note If you want an incremented number to follow the note set Count to 1 and 1t will automatically increment and be included in the note Set Count to zero to deactivate it 6 Press the Fire button The cannon will not fire 113 Option 2 Fire the Cannon l Switch the Data From toggle switch up which will turn it yellow The Fire button will be bordered in yell
49. dly impacting a ball Three balls were impacted 50 times at 95 mph on a single ear of the ball While CCOR decreased for all three balls two balls showed no change in DS 68 4 6 References ASTM F2845 2010 Measuring the Dynamic Stiffness DS and Cylinderical Coefficient of Restitution CCOR of Baseballs and Softballs s l American Society of Testing and Materials 2010 ASTM F1887 09 2009 Standard test method for measuring the coefficient of restitution of baseballs and softballs West Conshohocken PA s n 2009 Biesen E D 2006 Prediction of plastic deformation in aluminum softball bats using finite element analysis Master s Thesis Washington State University 2006 Duris J G 2004 Experimental and numerical characterization of softballs Master s Thesis Washington State University 2004 Faber W L 2010 Reducing the effect of ball variation in bat performance measurements Master s thesis Washington State University 2010 Smith L V Ison A 2006 Rigid wall effects on softball coefficient of restitution measurements The Engineering of Sport 6 Vol 1 p 29 34 69 5 PU Foam Sample Modeling 5 1 Introduction Many sport ball models including baseball tennis and golf balls are developed phenomenologically This involves iteratively adjusting material properties until structural response is duplicated Models developed in this way have the potential of describing and comparing structural r
50. e following will present the new device setup and the methods used to obtain experimental foam impact data As PU foam is viscoelastic and thus has rate dependent behavior the effect of loading rate was also explored 3 2 Apparatus 3 2 1 Device Hardware The device used a small horizontally mounted air cannon to fire a striker bar that could achieve a larger range in speed than is possible with a standard drop tower 7 to 46 mph Foam samples were mounted to a stationary load cell and impacted by the striker bar as shown in Fig 3 1 Bar speed and impact force were measured to calculate impact properties and produce stress strain curves These measurements enabled a more direct calculation of stress and strain in the tested material compared to a pressure bar device 24 Rigid Pillow Block iii Load Cell Striker Bar Infrared Speed Monitors C J 6d8 Foam Sample Figure 3 1 Schematic of the new device used to impact softball foam samples The device as shown in Fig 3 2 consisted of 45x45 Bosch aluminum structural framing which was reinforced by ninety degree gussets The main horizontal member was a 3 foot piece of 45x90 Bosch framing on which was mounted the barrel fiber optic sensors and load cell The cannon and the load cell were each secured to the frame using pillow blocks Set screws in each pillow block enabled the cannon and load cell to be aligned Impact Containment Chamber Barrel
51. e model discussed in Chapter 4 and that the load curves looked similar Only one impact was performed to limit possible damage effects The evolution of the samples from a softball is shown in Fig 3 7 After removing the leather cover two wafers were cut from each ball using a 12 inch miter saw The wafers were then sanded to 0 3 inches to produce a smooth flat surface and to achieve the correct thickness Bryson in making softball foam samples used a hole punch to stamp out specimens from 0 08 inch thick wafers Bryson 2009 Using a hole punch to make samples from 0 3 inch wafers produced jagged edges It was also difficult to use the hole punch to make samples with perpendicular edges A new approach was needed to produce clean square samples Figure 3 7 Step by step machining of a softball to obtain samples I Removal of the cover II Cutting wafers out of the ball III Drilling the samples using a custom hole saw Standard hole saws were considered but were found to have several downsides The smallest hole saw sold in a standard hardware set had a 0 5 inch diameter which was too large The teeth of standard hole saws were too course and would rip the soft PU foam as the holes were made The blade material was also too thick This caused the saw to not stay in the same place as penetration started which damaged the foam surface 32 A custom hole saw was developed which resolved the problems encountered with standard hole saw
52. ed on the right front leg 1s in the on position 4 Twist the red safety switch on 5 Make sure the load cell signal conditioner the pressure regulator located behind the left monitor and the infrared sensors located in the electronics box are on Emergency Stop I SE Te witcn for electronics 2 Figure B 1 Impactor device and startup switches 110 Fiber Optic Sensors Figure B 2 Electronics box LabView Front Panel Operation 1 Open LabView and select Scott s Impactor vi from the list of recently opened vi s or double click it s icon on the desktop and run it The Controls box is used to set up the impact and is highlighted blue as in Fig B 3 before pressing the Fire button 2 The VI has the ability to either physically fire the cannon or read previously written output files and re process the impact The Data From vertical toggle switch between the Fire and Stop buttons in the Controls box determines which of the two operations is executed when the Fire button is pushed Figure B 4 shows the Controls box changes associated with the vertical toggle switch 111 t Scott s impactos Ele Edt View Project Operate Tool Window Help gt u Controls Dat Er Sample E 0 2300 Y 040 Data Recording C Users Power User Desktop impactor Files New Data EES New Summary tt Time Comment Strain Rete Stress Max V Bar Smplingth lt Smet Dmte COR 5 9 2011 15 AM 2120MPHD 2244 1435 1
53. ellent agreement with experiment across the tested speed range 4 5 5 2 average respectively The flat surface load displacement curves in Fig 6 3 show no decrease in the model s exceptional correlation with experiment when surface geometry was altered 89 7000 6000 5000 34000 Load 1bs 3000 2000 1000 0 0 0 2 0 4 0 6 0 8 Displacement inches Figure 6 3 Flat impact surface comparison of experimental load displacement curves with Mat 57 Shades indicate speed at light 60mph normal 95 mph and dark 120 mph The coefficient of friction between leather and dry metal is approximately 0 5 Engineering Handbook 2006 For Mat 57 adding friction to the contact condition at 120 mph increased force 2 but decreased both COR and displacement by 5 and 2 respectively Friction also lowered CCOR rate dependence by 11 A soft option in the surface to surface contact condition has been previously used in simulating the felt on tennis balls Allen 2008 Interestingly when active the soft option actually reversed the effects of surface geometry causing CCOR to have a higher value than COR 6 3 1 COR Rate Dependence Although lower than experiment the rate dependence of CCOR as shown in Fig 6 4 and COR improved over that of the PU foam sample model The parametric study in Chapter 5 showed that none of the adjustable parameters in Mat 57 improved COR rate dependence A similar parametric study of the s
54. ent by differential model cccoooooooocccnnnnnoo 37 Figure 3 15 Logged temperature during experimental testiOg cccccccnnnnnnnnnnnonnnnnnnnnnnnnos 38 Figure 3 16 Logged humidity during experimental testing cooooooonnnnnnnnncnonononnnnnnnnnnnos 39 Figure 3 17 Compressive stress strain response and master CUIVE ccccccccccnnnnonooocccnnnnnnnnos 40 Figure 3 18 Magnification of load signals at differing SpeedS ccccccccnnnnnnoconanonccnnnnnncnos 41 Figure 3 19 Stress strain response of 0 2 thick samples plotted with master curve 42 Figure 3 20 The effects of striker bar speed on peak strain rate and magnitude 43 Figure 3 21 Peak stress in foam samples impacted with striker bars of varying length 44 Figure 3 22 Peak strain in foam samples impacted with striker bars of varying length 44 Figure 3 23 COR in foam samples impacted with striker bars of varying length 45 Figure 3 24 DS in foam samples impacted with striker bars of varying length 45 Figure 3 25 Strain rates from a 2 inch striker bat oooooonnnnnnncnncccnnnnncnnnnnnnnnnnanonnnnnnnnnncnnos 47 Figure 3 26 Constant strain rate curves derived from impact testing ccccccooooonccccnnnnnos 47 Figure 3 27 Load Frame used to conduct low rate compressive testing cccceeeeeees 48 Figure 3 28 Low rate loading and unloading of samples of differing thickness 49 Figure 3 29 Cons
55. erent speeds for all values of Shape 79 20 4 mph m 41 4 mph COR J LA 0 0 25 0 5 0 Damp Figure 5 10 The lack of an effect on COR rate dependence is indicated by a similar COR at different speeds for all values of Damp 5 4 Mat 83 Fu Chang Foam The previous material model assumed a rate independent compressive response Because rate dependence was shown during experimental testing another foam material designed to incorporate these effects was used Mat 83 utilized multiple loading curves defined as a function of strain rate The model internally applied the appropriate curve depending on the simulated loading conditions 5 4 1 Material Development To define the rate dependent loading response a table was defined which consisted of the stress strain curves from Fig 3 29 and their corresponding strain rate The five curves were adjusted such that no overlapping occurred Each line was extrapolated to higher stresses as experimentation could not produce some strain rates at large strain magnitudes As shown in Fig 3 25 the stress strain curve for the strain rate of 2000 s s only goes to 0 5 e It was assumed that at higher strain magnitudes the curves followed the trends shown at lower strain magnitudes The LS DYNA user s manual made no suggestion regarding the number of curves to use It was found that the simulated loading response changed according to which curves were input 80 Various combi
56. esponse prior to product fabrication The following will discuss the development and simulation of two FEA foam material models with material loading responses derived from experimentation in Chapter 3 and phenomenologically developed unloading responses Simulations of experimental testing from Chapter 3 were performed to allow direct comparison of numerical and experimental results 5 2 FEA Setup The instrumented PU foam sample impacts in Chapter 3 were simulated using the dynamic finite element code LS DYNA Version 971 LSTC Livermore CA Because the foam cell size 0 005 inches was significantly smaller than the specimen diameter 0 42 inches the foam was assumed to be isotropic and homogeneous The PU foam sample shaded black in Fig 5 1 was modeled with 2 772 linear solid elements and two symmetry planes Length and diameter were similar to the actual foam samples 0 3 and 0 42 inches respectively The elastically modeled aluminum striker rod shaded green in Fig 5 1 was modeled with 2 709 elements While the actual striker bar length was 2 inches the simulated rod length was shortened to 0 1 inches to reduce the number of elements Density was correspondingly increased to achieve the correct striker bar mass 70 Figure 5 1 FEA setup of an aluminum striker bar green colliding into a foam sample black using quarter symmetry Besides the symmetry boundary conditions the striker bar was given an initial velocity di
57. ffect of ball variation in bat performance measurements Master s thesis Washington State University 2010 Gibson L Ashby M 1999 Cellular Solids Cambridge MA Cambridge University Press 1999 ISBN 0521499119 Gibson L Ashby M 1999 Cellular Solids Cambridge MA Cambridge University Press 1999 ISBN 0521499119 Goga Vladimir 2010 Measurement of the energy absorption capability of polyurethane foam Portal pre odborne publikovanie ISSN 1338 0087 2010 Goods S H Dentinger P M Whinnery L L 2003 Flashfoam A triboluminescent Polymer Foam for Mechanical Sensing Sandina National Laboratories Report 2003 Hendee S P Greenwald R M and Crisco J J 1998 Static and Dynamic Properties of Various Baseballs Journal of Applied Biomechanics 1998 Vols 14 p 390 400 Hodgkinson E 1835 Rept Brit Assoc Advance of Sci 4th meeting 1833 Instron 2009 Drop Weight Impact Testing Systems Online 2009 Cited October 24 2011 http www instron us wa product Drop Weight Impact Testing S ystems aspx LSTC 2010 LS DYNA Keyword User s Manual Volume II Material Models Version 971 Rev 5 2010 22 Miller S 2006 Modern tennis rackets balls and surfaces J Sports Med 2006 Vol 40 5 p 401 405 Munstone T Sherwood J 2000 Using LS DYNA to develop a baseball bat performance and design tool Detroit MI s n 2000 Russel D A 2005 Physics and Acoustics of Baseball and softball bats Kette
58. i Figure 5 11 Refined stress strain curves used in the Fu Chang Foam model 81 Figure 5 12 COR for Mat 83 showed a nonlinear increase in COR eeens 82 Figure 5 13 Surface penetration for a 41 4 mph impact using Mat 83 assesses 83 Figure 5 14 Foam sample load displacement curves for Mat 83 cccssseeeeeeeeeeees 84 Figure 6 1 Softball model with cylindrical and flat impact surfaces ooooooocononococnnnnnnnns 87 Figure 6 2 Softball load displacement curves for Mat 57 on cylindrical surface 89 Figure 6 3 Softball load displacement curves for Mat 57 on flat surface 90 Fisure 6 4 Matt COOR rate dependencia A E 91 Figure 6 5 Damp factor COR rate dependence ooooccccccccccccnnocccnnnnnnnnnnnonannncnnnnnnnnnnnnnnnnnnnnos 91 Figure 6 6 Hysteretic unloading factor HU COR rate dependence ooooooooooococcccccnncnnnss 92 Figure 6 7 Shape Factor COR rate dependence oocccccccccnonononcccnnnnnonononannnnnnnnonononaninaninnnnnos 92 Figure 6 8 The effect of beta on COR rate dependence ooooooccccccccnnnncncnnnonononannonnnnnnnnccnnos 93 Figure 6 9 Cross sectional strain distribution of Mat 57 i ooooccncnncnnnnnnncnnnnnnnnnnnnonnnnnnnnnnnnnos 94 Figure 6 10 Node segment along which peak strain rate was measured oooooonnnnnnnncncn 94 Figure 6 11 Peak strain rate in a softball as a function of impact speed ooooooocccnnnncc 95 Figure 6 12 Softball load displacement curves for Mat 83 on
59. impact behavior over changes in impact speed and surface geometry The following will also compare the impact behavior of the current foam material models to the viscoelastic models of previous studies 6 2 FEA Setup The softball and cover were modeled as a single isotropic homogeneous sphere as done elsewhere Duris 2004 Faber 2010 The softball was modeled using 7 168 linear solid elements and quarter symmetry Elastically characterized cylindrical and flat impact surfaces shown in Fig 6 1 were modeled with 4 864 and 2000 nodes respectively The base of each Impact surface was constrained normal to the line of impact and the contact type was surface to surface Penetration between the ball and impact surface was negligible compared to the PU foam sample models Impact force and ball displacement were measured during the simulation and exported to output files which were subsequently used to calculate ball performance and produce load displacement curves The position history of the ball s central node was used to measure both the displacement during impact and the rebounding velocity The ball was given an initial speed in 86 the simulation setup and equation 2 2 was used to calculate COR and CCOR Equation 2 8 was used to calculate impulse Equation 2 7 defines DS as a function of ball mass initial ball velocity and peak impact force Because numerical ball mass and velocity were set equal to experiment percent difference in
60. ison of experiment and FEA softball from Faber 18 Figure 2 10 Force displacement comparison FEA softball from Faber 19 Figure 3 1 Schematic of the new device used to impact softball foam samples 25 Figure 3 2 Instrumentation used to impact foam samples occcccccnnconcnnnnnnnnnnnnonanonnnnnnnnnos 25 Figure 3 3 Visual layout of the impact containment chamber sssseseeeeeeeeeeeeees 26 Figure 5 4 Pressure ROO Ua Oi a taeatadines 27 Figure 3 5 Screen shot of the LabVIEW vi used to operate the device ooooonnnnnnnccnc 29 Figure 3 6 SEM image of softball foam cross section oooonnncncccncnnncncnnnnnononnnnnonnncnnnnnnnnnss 31 Figure 3 7 Step by step machining of a softball to obtain samples ooooonnnnnnnnnnno 32 Figure 3 8 Custom hole saw used to machine foam samples from wafers ooooonccccc 33 Figure 3 9 Standard foam sample used for impact testing occccccoocoonccnnnnnnnnononanonnnnnnnnnos 33 Figure 3 10 Setup for high speed camera Verification ooooonnnnncncccnnnnnnnnnnnnnononnnnnnnnnnnnnnnnnos 34 Figure 3 11 Verification of initial striker bar speed by high speed camera 35 Figure 3 12 Verification of sample displacement by high speed camera 00 3 Figure 3 13 Verification of rebound speed by high speed camera cccccccccnnnnnnnnnnnnooccnnnnnss 36 Figure 3 14 Verification of displacem
61. k strains above 0 3 e To negate the effects of differing impact speeds for a single foam sample COR was divided by impact speed as shown in Fig 3 32 Samples impacted below densification strains showed an increase in COR for a given impact speed This effect diminished with increasing strain such that COR remained constant for the most severel y impacted samples The opposite was shown for DS in Fig 3 33 Samples impacted at lower strains maintained stiffness while increasing the severity of impact also increased sample stiffness 52 00 48 0 008 PA a eo 338 Average 0 018 Strain 3 0 016 Magnitude 3 0 014 00 73 e 00 71 0 012 Bex 00 62 0 01 E as O QU Impact Number Figure 3 32 Change in COR due to repeated impacting as a function of strain magnitude 4000 Average Strain Magnitude 3000 00 73 S 0 71 uN 7 2000 2 00 62 00 48 1000 aa 0 38 Impact number Figure 3 33 Change in DS due to repeated impacting as a function of strain magnitude If a foam structure was damaged less energy could be absorbed by the matrix and the structure would more easily yield to an applied load An increase in both COR and DS indicate the development of damage in the foam samples Increases in COR and DS after a single impact further support the fact that permanent structural damage is caused by compressing the material at the strains tested 53 Strain magnitudes along the cross section of a softball
62. ll was cradled by a polycarbonate sabot Fig 4 3 The sabot was used to center the ball control speed and launch the ball without rotation This allowed testing at specific locations on the ball Figure 4 3 Sabot used to cradle the ball as it travels through the cannon Previous sabot designs were constructed of ultra high molecular weight polyethylene Duris 2004 These would yield upon impact with the arrestor plate and require re shaping It was found that polycarbonate sabots withstood impacts far better Older sabot designs were one solid bowl shaped piece machined from a cylindrical piece of polymer using CNC mills and lathes The solid base had a large mass and cracked quickly A re design included a light weight fiberglass disk to replace the solid base reducing the weight and allowing cheaper replacements The sabot was placed in the breech end of the barrel before firing Pneumatic cylinders closed the breach plate so when air was released the full pressure was behind the sabot ensuring consistent speed After traveling the length of the cannon the sabot was captured by an arrestor plate Fig 4 4 while the ball continued forward to the light gates The arrestor plate consisted of a series of leather foam and aluminum plates bound together Pneumatic cylinders were connected to the arrestor plate that extended out just after the cannon was fired to catch the sabot and lessen its impact 58 Figure 4 4 Arrestor plate u
63. locities can produce variation in strain magnitude while maintaining a constant strain rate Using classical kinematics and neglecting frictional effects the energy of the striker bar can be expressed as 1 z MpVp PA l l 3 8 where vz is bar velocity at the end of the barrel P is constant barrel pressure A is the bar cross sectional area is barrel length and is the bar length Pressure of the barrel is unknown as the striker bar is being fired However the tank pressure which is measured before firing will be slightly higher than barrel pressure and is a good estimate Eq 3 8 was used in comparisons between bar lengths to achieve similar speeds 41 To verify that the master curve was independent of sample dimensions a second round of testing was performed Samples with an average thickness of 0 203 inches were impacted with a 3 inch striker bar at strain rates ranging between 950 and 2600 s The results were plotted along with the master curve developed from impacting 0 3 inch thick samples in Fig 3 19 The master curve closely aligned indicating 1ts independence from foam sample thickness 3500 3000 2500 2000 Master Curve developed from 0 3 thick samples Stress psi 500 ers O 0 4 Strain Figure 3 19 Stress strain response of 0 2 thick samples plotted with the master curve developed from impacting 0 3 thick samples The relationship between striker bar speed and the cor
64. mance to have a much stronger dependence on DS Smith 2008 Hendee Greenwald and Crisco tried unsuccessfully to correlate baseball compression to dynamic properties obtained by firing balls from an air cannon onto a rigidly mounted force plate They found that energy losses during quasi static compression differed from the dynamic energy losses Hendee 1998 Chauvin and Carlson also investigated the correlation between compression and dynamic impact response They used pressure sensitive film to record the impact pressure distribution of baseballs and softballs No correlation between compression and dynamic impact pressure was shown Chauvin 1997 These studies conclude that the dynamic impact behavior of sports balls is best characterized by dynamic properties not static properties For dynamic stiffness and CCOR to effectively describe a bat ball collision the incoming velocity must account for a forward bat swing and backward bat recoil which occurs during play Smith compared the dynamic stiffness of balls impacting a rigid half cylinder and free cylinders of differing mass that recoiled upon impact When the speeds were matched correctly Smith found the force displacement curves to be similar A dynamic stiffness speed of 95 MPH was found to represent the relative speed of a 110 MPH softball bat collision Smith 2008 To calculate dynamic stiffness the ball is assumed to behave like a linear spring with stiffness k according to f t
65. mpact energy Hysteresis or energy lost during impact 1s represented as the area under the load displacement curve Increasing hysteresis in a softball model will decrease COR After maximum compression a softball continues recovering to 1ts original shape even after the ball has separated contact By the time a softball leaves contact with the bat 1t has recovered only about half of the deformation Faber 2010 Minimal displacement recovery is shown after peak deformation and throughout the unloading phase The slow recovery is caused by the creep response of the viscoelastic PU matrix 2 5 Instrumentation Experimental foam impacts must occur at strain rates representative of play The peak strain rate during an impact occurs just as the collision begins which for bat ball impacts is between 1000 and 2500 s Bryson 2009 Few devices exist which are capable of measuring foam properties at these rates Universal testing machines UTM have peak strain rates well below this range 25 s Drop towers have been used to characterize polymeric foams but not for the purpose of sports ball modeling Goods 2003 Serifi 2003 Maximum speed ranges of a typical drop tower are around 15 ft s which is well below the speed of a bat ball collision Instron 2009 Optional features such as springs can be added to increase the potential energy of the drop weight to achieve strain rates similar to play The cost of a specialized drop tower however
66. nations of curves were simulated and 1t was found that the best experimental agreement occurred when all five curves shown in Fig 5 11 were used 4000 gt 3500 3000 2500 2 2000 Stre a 1500 1000 500 0 0 0 2 0 4 0 6 0 8 Strain Figure 5 11 Refined stress strain curves used in the Fu Chang Foam model The Fu Chang model had parameters of density Young s modulus damp shape and a hysteretic unloading factor HU damp and shape were adjusted to best match experiment Similar to Mat 57 the lowest value of HU maximum energy loss did not sufficiently account for energy loss so shape was adjusted to match experimental COR Parameter values are listed in Table 5 2 The strain rate flag for this material was set to engineering strain rate to match the experimental engineering strain measurements Table 5 2 Mat 83 parameters which optimized agreement with experiment p E Model lb s in ksi HU Shape Damp Mat 83 PU Foam Sample 3 90E 05 20 0 01 7 5 0 5 5 4 2 Results The model was run at various speeds between 20 4 and 41 4 mph to capture strain rates typical of play COR increased nonlinearly with impact speed which was contrary to experimental behavior as shown in Fig 5 12 Interestingly at low impact speeds COR behaved 81 correctly but deviation with experiment increased with impact speed Theoretically as impact speed increases so will the stiffness of the viscous material Increased ma
67. nd 120 mph 64 7000 O Flat 120 mph 6000 e Flat 95 mph Load Ibs a SO ao 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 COM Displacement in Figure 4 12 Load displacement curves for flat surface impacts at 60 95 and 120 mph As discussed in Chapter 2 impulse can be calculated by integrating the load signal Eq 2 8 or by performing a momentum balance Eq 2 10 The two impulse measurements were denoted as Lr and L respectively The ratio of the impulse values K Ly Lf is an indication of measurement accuracy which according to Fig 4 13 slightly decreased as speed increased for both surface types 98 apa Flat E Cylinder 97 x 96 95 94 T T 50 65 80 95 110 125 Ball Speed mph Figure 4 13 The ratio of impulse measurements as a function of ball speed Trends indicate a decrease in instrumentation accuracy as speed increased 65 4 4 Damage Effects Limited work has been done to quantify the effect of repeated impacts on softball performance As discussed in Chapter 2 Duris found that ball COR and peak force remained constant through 100 impacts Duris 2004 This however applies to the entire ball and not to a single impact location Current softball bat performance testing methods do not stipulate a limit on the number hits a softball can take ASTM F1890 2009 However softballs used for Amateur Softball Association ASA certification testing are limited to ten im
68. ndix 6000 5000 4000 3000 Load Ibs 2000 1000 0 0 2 0 4 0 6 0 8 l Displacement inches Figure 6 12 Cylindrical surface load displacement curves for Mat 83 Shades indicate speed at light 60mph normal 95 mph and dark 120 mph 96 7000 e Experiment 6000 H fat 83 5000 4000 E E 3000 2000 1000 0 0 2 0 4 0 6 0 8 Displacement inches Figure 6 13 Flat surface load displacement curves for Mat 83 Shades indicate speed at light 60 mph normal 95 mph and dark 120 mph Mat 83 showed excellent agreement with experimental COR value and rate dependence On both flat and cylindrical surfaces COR was consistently within 2 of experiment while the CCOR rate dependence the slope in Fig 6 14 was 2 lower than experiment COR rate dependence was 4 lower than experiment 60 15 90 105 120 Speed mph Figure 6 14 Comparison of experimental and numerical CCOR for Mat 83 97 Implementing friction into the contact condition for Mat 83 increased peak force 12 at 120 mph but lowered 1t 2 at 60 mph Friction decreased COR rate dependence by 4 6 5 Linear Viscoelastic Model Comparison Previous work by Duris Faber and Bryson produced finite element models of softballs in LS DYNA using the standard viscoelastic material model Duris 2004 Faber 2010 Bryson 2009 The authors each published material parameters for their models as summarized in Table 6 3 Each viscoel
69. ning behavior at lower strain rates Faber s single objective for his model was to accurately emulate CCOR and DS on a cylindrical surface at 95 mph Faber 2009 While his model had the most accurate cylindrical DS at 95 mph the model had the poorest match with experimental DS on a flat surface 101 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 95 mph DS Ibn Experiment Mat 57 Mat 83 Viscoelastic Viscoelastic Viscoelastic 1 2 3 Figure 6 19 Comparison of dynamic stiffness Viscoelastic models are from 1 Duris 2 Faber and 3 Bryson A comparison of DS rate dependence is shown in Fig 6 20 Mat 57 was the only model to correctly emulate a lower rate dependence of DS on a flat surface compared to a cylindrical surface Mat 57 also best matched DS rate dependence on both impact surfaces E Cylinder E Flat mi On O O DS slope ib mph yin 30 20 10 0 Experiment Mat 57 Mat 83 Viscoelastic Viscoelastic Viscoelastic 1 2 3 Figure 6 20 DS rate dependence as a function of surface geometry Viscoelastic models are from 1 Duris 2 Faber and 3 Bryson 102 6 6 Summary The two foam material models developed in Chapter 3 were used in simulated softball impacts on flat and cylindrical surfaces Speeds identical to experiment in Chapter 3 were used to directly compare load displacement curves Surface penetration and hour glassing were found to affect the simulation
70. oftball simulation revealed that damp HU shape and f each affected COR rate dependence Fig 6 5 8 HU shape and non zero values of improved COR rate dependence at the cost of increasing COR value 90 e Experiment o Mat 57 60 15 105 120 90 Speed mph Figure 6 4 Mat 57 CCOR rate dependence was lower than experiment 0 5 60 mph E 120mph 0 44 5 i O 0 38 0 32 0 0 0 5 l 1 5 Damp Figure 6 5 The effect of damping factor damp on COR rate dependence Black markers indicate values used in the model 91 60 mph 0 7 E 20mph 0 6 pe O 0 5 0 4 0 3 0 0 2 0 4 0 6 0 8 l Hysteretic Unloading Factor HU Figure 6 6 The effect of Hysteretic Unloading Factor HU on COR rate dependence Black markers indicate values used in the model e 60 mph E 20mph 0 1 l 10 100 1000 Shape Figure 6 7 The effect of Shape Factor on COR rate dependence Black markers indicate values used in the model 92 0 8 60 mph 0 7 4 E 120mph Inactive Non Zero Beta Figure 6 8 The effect of beta on COR rate dependence 6 3 2 Strain Magnitude and Rate Strain within the numerical softball was investigated for Mat 57 as it showed good agreement with experimental load displacement curves Figure 6 9 shows an increase in both peak strain and the area of the ball with strain magnitudes above the elastic region gt 0 1 e for increasing impact speed Interestingly peak s
71. ole maintains a positive volume LS DYNA 2003 It was found that using 1 point elements as well as reducing the timestep scale factor below the default value of 0 9 prevented the numerical instabilities and allowed adjustment of the damping values to best match experiment Adjustment of damp and shape improved cylindrical performance significantly Impulse force displacement and CCOR of the modified ball model were on average within 3 3 4 and 4 of experiment respectively Load displacement curves of Mat 57 shows excellent experimental correlation with respect to curve shape and loading stiffness as shown in Fig 6 2 Parameters of both the PU foam sample model and softball model are summarized in Table 6 1 Performance values for Mat 57 are listed in Tables A 1 and A 2 in the appendix 88 6000 e Experiment 4000 3000 Load Ibs 2000 1000 0 0 0 2 0 4 0 6 0 8 l Displacement inches Figure 6 2 Cylindrical impact surface comparison of experimental load displacement curves with Mat 57 Shades indicate speed at light 60mph normal 95 mph and dark 120 mph Table 6 1 FEA material model parameters for Mat 57 Density p Young s modulus E hysteretic unloading factor HU shape factor and damp factor p E Model lb s in ksi HU Shape Damp PU Foam Sample 3 90E 05 20 0 01 30 0 75 Softball 3 90E 05 20 0 01 6 1 8 On a flat surface peak force COR impulse and displacement all maintained exc
72. out After measuring striker bar speed and impact force impact properties were calculated and logged along with tabulated load displacement and stress strain data 28 F Scott s impactos Ele Edt Yiew Project Operste Tools Window Help CUses Power User Desktop impactor Files New Data New Summary bt E Time Comment Strain Rate Stress Max V Bar Smpl Lagth Smpl Dmte COR 5 9 2011 11 3445 AM 2120MPHD 2244 1435 17388075 7112217 03170 04180 9 2011 113513 AM 2 120MPH D 2298 31 1770 7673 730 7078 0318 loam 10 259 ONL S 9 2011 11 37 34 AM S2120MPH D 23446365 18831486 752 6064 0321 04180 5 9 2011 11 3848 AM 02 1200MPH O 24435688 21281929 801814803280 04180 Figure 3 5 Screen shot of the LabVIEW vi used to operate the impactor device Plots of strain center load time top right and a stress strain curve lower right were output for each impact Calculations of foam sample impact properties performed in LabVIEW were very similar to the equations used for softball impact testing discussed in Chapter 2 The initial bar velocity v23 and user defined mass m of the striker bar along with the load signal were used to calculate the displacement of the striker bar COM during impact Eq 2 6 Foam sample displacement was assumed to be equal to the striker bar displacement Because rebound speed was not measured COR was calculated from Eq 2 2 where rebound speed was calculated as Vy vi f FO de 3 1 0 Mp
73. ow Select the appropriate Load Cell 500 lbs default Select Length for the Impact Bar section Bar weight is automatically assigned according to bar length and can only be changed in the rear panel Load the striker bar into the end of the barrel and use a rod to push it to the back of the barrel Set the desired Line Pressure suggested between 4 10 psi Overly high pressures will max out and damage the load cell Define the Length and Diameter in the Sample section Apply a thin layer of grease to the sample and mount it to the load cell Close the clear protection lid The DAQ Parameters section control how the load cell is read After the cannon is fired the program waits a period of time set by Delay and then records a number of Samples at the specified Frequency In the Data Recording section the directory for a Summary file can be set The summary file saves impact results including date comment strain rate max strain COR impulse bar velocity and sample diameter and length The summary file content is displayed in the table below the Controls box The Wave Out indicator shows the directory and filename of the last saved output file which includes time load and sample displacement Make a comment in the Note text box if desired The Count number is an automated increment for repeated impacts with the same Note If you want an incremented number to follow the note set Count to 1 and 1t will
74. pacts on each ear Regarding the recovery time allowed between impacts Duris suggested that balls be impacted no more than 10 times in one hour or more than one impact per minute He also suggested that balls which are to be reused should be given a minimum of one hour in standard laboratory conditions to recover following a sequence of impacts before re use In ASA bat certification testing impact frequency is no more than one impact per minute per ball while all four ears of the ball are sequentially impacted To better understand changes in impact performance due to repeated testing a durability test was performed Three balls were repeatedly impacted 50 times on the same ear at 95 mph While monitoring surface temperature it was found that a single 95 mph impact raised the ball surface temperature by 2 F To keep ball temperature within the ASTM F2845 limit of 4 F only two hits were made on each ball before allowing temperature to stabilize for an hour Five minutes was allowed between the two hits to allow foam structure recovery 66 0 365 5 15 25 35 45 55 Impact Number Figure 4 14 CCOR as a function of repeated impacts 8500 7500 DS 6500 5500 0 0 5 15 25 35 45 55 Impact Number Figure 4 15 DS as a function of repeated impacts The results in Fig 4 14 show a 2 decrease in CCOR for balls 1 and 3 and a 3 decrease for ball 2 The change in CCOR was likely due to the repeated impacting
75. parameter Mat 83 was better able to describe rate effects in load displacement curves as the material allowed for rate dependent loading characterization Contact surface penetration was greater compared to Mat 57 causing COR to non linearly increase with impact speed which was not typical of experiment 84 5 6 References Duris J G 2004 Experimental and numerical characterization of softballs Master s Thesis Washington State University 2004 Gibson L Ashby M 1999 Cellular Solids Cambridge MA Cambridge University Press 1999 ISBN 0521499119 LS DYNA 2001 LS DYNA Support Online 2001 Cited February 15 2012 Online http www dynasupport com tutorial contact modeling in Is dyna contact types LSTC 2010 LS DYNA Keyword User s Manual Volume II Material Models Version 971 Rev 5 Sambamoorthy B Halder T 2001 Characterization and component level correlation of energy absorbing EA polyurethane foams PU using LS DYNA material models LS DYNA Eurpoean Conference 85 6 Ball Modeling 6 1 Introduction To allow direct comparison with experimental results from Chapter 4 softball impacts on cylindrical and flat impact surfaces were simulated in LS DYNA The following will discusses results from implementing both foam material models from Chapter 5 In past research softball models have been modeled using a linear viscoelastic material Shortcomings in these models were shown when characterizing
76. perimentally e Experiment 0 15 o Mat 57 20 24 28 32 36 40 44 Bar Speed mph Figure 5 6 Comparison of experimental and numerical COR rate dependence for Mat 57 5 3 3 COR Rate Dependence Parametric Study Additional material parameters not listed in Table 5 1 but included in the MAT 57 material model were designed to control rate effects Young s relaxation modulus and a decay constant B were adjusted but the same effect was produced for all non zero values As shown in Fig 5 7 COR rate dependence slightly increased but hysteresis was reduced to almost zero dd 0 9 0 7 COR Inactive Non Zero Beta Figure 5 7 Beta designed to control rate effects did not significantly improve COR rate dependence A parametric study was performed to determine 1f other parameters affected COR rate dependence HU Shape and Damp were separately adjusted within their respective value ranges and simulated at low 20 4 mph and high 41 4 mph speeds to compare COR values at differing rates As shown in Fig 5 8 5 10 none of the parameters changed the COR rate dependence Results were similar for Young s modulus 78 0 0 2 0 4 0 6 0 8 l Hysteretic Unloading HU Figure 5 8 The lack of an effect on COR rate dependence is indicated by a similar COR at different speeds for all values of HU COR 0 1 10 100 1000 Shape Figure 5 9 The lack of an effect on COR rate dependence is indicated by a similar COR at diff
77. r impulse I mp vi v 2 10 and applying the instrumented velocity measurements where rebound speed is negative An ideal collision will result in identical impulse values from Eq 2 8 and 2 10 2 3 Conditioning Polyurethane being a viscoelastic polymer 1s sensitive to temperature and humidity Experimental testing which minimizes variation in environmental variables will enhance accuracy in measuring dynamic ball response ASTM standards for measuring ball properties requires softballs to be conditioned at 50 10 relative humidity RH at 72 F 4 F for a minimum of 14 days prior to testing ASTM F1887 2009 ASTM F1888 2009 ASTM F2845 2010 Duris monitored the weight gain of softballs transitioning from 30 to 50 RH and found the moisture saturation to be reached at 14 days Duris 2004 He also found the difference in COR of a ball conditioned at 30 RH and 55 RH to be less than 1 whereas the static compression decreased 21 over the same humidity range This suggests that rate effects may depend on moisture content Drane investigated the effects of temperature on baseball COR Baseballs which were conditioned at 25 40 70 and 120 F and then impacted at 60mph were found to have statistically significant differences in COR For 100 mph impacts more representative of play conditions the COR was unaffected by temperatures above freezing The subfreezing temperature however significantly reduced the ball COR Drane
78. rected normal to the contact surface while the foam sample face opposite of the impact was constrained in plane A surface to surface contact type was used where friction was neglected as the impact had no obliquity The addition of frictional effects was found to have no effect on impact performance An alternate surface to surface soft contact option also caused no change in results Impact force and sample displacement were measured during the simulation and exported to output files which were subsequently used to quantify foam behavior and produce load displacement curves The position history of the striker bar s central node was used to measure both the sample displacement during impact and the rebounding striker bar velocity Equation 2 2 was used to calculate COR and Eq 2 8 was used to calculate impulse To determine if the simulation results were independent of mesh density the foam sample was re meshed with 4864 elements Simulations with peak strain rates near 2500 s 41 4 71 mph were compared to that of the 2772 element sample COR impulse and maximum displacement all changed by less than 1 The coarse mesh was used to shorten solving time 5 2 1 Simulation Challenges Various simulating issues were caused by the large deformation of the foam sample Especially at higher speeds the model experienced hourglassing as shown in Fig 5 2 By assigning fully integrated elements to both the striker bar and foam sample ho
79. responding strain rate and magnitude induced in the foam sample is shown for the 3 inch bar in Fig 3 20 Strain rate increased linearly with striker bar speed Strain magnitude also increased but with decreasing gains at higher speeds 42 3000 0 9 0 8 2500 0 7 E E 2000 0 6 3 E 1500 os amp 14 i z 042 E 5 1000 0 3 gi O Peak Strain Rate 0 2 500 Peak Strain Magnitude 0 1 8 13 14 18 212224262730 32 35 3738 4041 Impact Speed mph Figure 3 20 The effect of striker bar speed peak strain rate and magnitude in the foam sample An investigation was conducted to reveal whether impact response was dependent on the the mass of the striker bar Aluminum striker bars 2 3 6 and 9 inches in length with weights of 0 645 0 955 1 83 and 2 76 oz respectively were used to impact foam samples over the range of operable speeds up to the maximum load cell range of 500 Ibs for each bar Results comparing impact properties for differing bar lengths are shown in Figs 3 21 24 43 A000 o Inch Bar 3500 o 3 Inch Bar 3000 6 Inch Bar 2500 e 9Inch Bar 2000 1500 Peak Stress psi 1000 500 0 10 20 30 40 Bar Kinetic Energy ft 1b Figure 3 21 Comparison of peak stress in foam samples impacted with striker bars of varying length gt gt F eE A oo GO MA E Peak Strain Inch Bar P 3 Inch Bar 6 Inch Bar e 9 Inch Bar T o ba O 0 1
80. revious viscoelastic models are compared to the foam models developed in this study Viscoelastic models are from 1 Duris 2 Faber and 3 Bryson The dependence of COR and CCOR on impact speed was observed to be linear in Table 4 2 The slope of numerical COR and CCOR as a function impact speed is compared with experiment in Figure 6 18 Mat 83 better matched experimental COR and CCOR rate dependence than any other model Interestingly all models correctly described the higher rate dependence of the flat surface impacts over the cylindrical impacts The lack of sensitivity to time dependence in Mat 57 has been manifest throughout this study and Fig 6 18 is no exception 100 0 0016 E Cylinder 0 0014 a Flat 0 0012 0 001 0 0008 0 0006 0 0004 COR Slope 1 mph 0 0002 y To Experiment Mat 57 Mat 83 Viscoelastic Viscoelastic Viscoelastic 1 2 3 Figure 6 18 COR rate dependence as a function of surface geometry Previous viscoelastic models are compared to the current foam models Viscoelastic models are from 1 Duris 2 Faber and 3 Bryson eZ Dynamic stiffness was compared for each material model at 95 mph in Fig 6 19 While Mat 57 did not best match either flat or cylindrical DS it outperformed all models when both cylindrical and flat DS were considered across all speeds 11 average DS for Mat 83 was lower than most models which was due to the previously discussed softe
81. rfaces which led to nonlinear rebounding trends Both foam material models were implemented into a simulated softball which impacted flat and cylindrical surfaces at speeds between 60 and 120 mph Mat 57 showed excellent correlation with both the shape and magnitude of experimental load displacement curves predicting softball deformation mechanisms better than previous linear viscoelastic models both as a function of speed and surface geometry Mat 83 characterized rebound behavior on both flat and cylindrical impact surfaces within 2 of experiment which was better than any comparable model Table of Contents A E A A ee eee l ak A 55 555 ov ce case Gee ae aaa ce case cee aac cca cca eee nee l 2 MACK STOW A AA erst eetuaiene 3 ZE SONDAE COMPOSI Msi ni cian 3 22 A a aed va ee eee anes 4 ZN A tease Mss aad hanes E A eaesuiena st hee cate 4 Za COR ai CC OR cette raid io iii die ie 4 225 tato COMPTE inici 5 Zeze IIA MO SUM Sii 6 229 TO 9 A A O RN 10 2A POLyMErC DM iii 11 23 SAA O T E 14 20 A a a 15 Z A O A S 20 o RE CW NCC a E 21 RS AAA a a N A O 24 ES 24 Dal APPI asii 24 OZ Device AA oo loa 24 A DEVICE OPEO statcaat ays ba vadsittveat neluua sie deieadand Gavadoudsnead teva edeeunneed 28 Vl See MAO Anis AMPc oiia 30 I N A aa ticte E E eae ete etsuenlens 34 A SUNS her ene E 38 6 am 01 Bo 1 Gre BF ee em ee ee 48 O A c whic 6 Koger rere mrerere nr 50 A ees aries assented ieaeureareceascane se taed
82. riment o Vat 57 3000 o Nat 783 Load Ibs 1000 0 0 0 2 0 4 0 6 Displacement inches Figure 6 15 Cylindrical surface load displacement curves at 95 mph Viscoelastic models from previous studies are compared to the foam models developed in this study Viscoelastic models are from 1 Duris 2 Faber and 3 Bryson 6000 Viscoelastic 1 Viscoelastic 2 5009 a Viscoelastic 3 O Experiment Mat 57 4000 Nat 83 Load 1bs D 2000 1000 0 0 2 0 4 0 6 Displacement inches Figure 6 16 Flat surface load displacement curves at 95 mph Viscoelastic models from previous studies are compared to the foam models developed in this study Viscoelastic models are from 1 Duris 2 Faber and 3 Bryson 99 95 mph COR and CCOR from the FEA models is compared with experiment in Figure 6 17 Since impacts on a flat surface have less ball deformation and less energy loss the COR should be greater than the CCOR Both foam models correctly reflected the effect of surface geometry on COR whereas all three viscoelastic models show CCOR greater than COR The magnitude of COR and CCOR of both foam modes were closer to experiment than any of the viscoelastic models Si i E Cylinder i E Flat 95 mph COR Lu gt J gt Wn pe CAN O La Experiment Mat 57 Mat 83 Viscoelastic Viscoelastic Viscoelastic 1 2 3 Figure 6 17 COR value as a function of surface geometry P
83. ring University Website Online 2005 Cited 8 26 201 1 http www kettering edu physics drussell bats new nonlinear ball html Sambamoorthy B Halder T 2001 Characterization and Component Level Correlation of Energy Absorbing EA Polyurethane Foams PU using LS DYNA Material Models LS_DYNA Eurpoean Conference 2001 Sandmeyer B J 1994 Simulation of bat ball impacts using finite element analysis Master s Thesis Oregon State University 1994 Serifi E Hirth A Matthaei S Mullershon H 2003 Modelling of Foams using MAT 83 Preparation and Evaluation of Experimental Data 4th European LS Dyna Users Conference 2003 Shenoy M M 2000 Numerical simulation of baseball bat performance Master s Thesis Washington State University 2000 Smith L V 2008 Measuring the hardness of softballs IMAC XXVI Orlando FL s n 2008 Traeger R K 1967 Physical Properties of Rigid Polyurethane Foams s l Journal of Cellular plastics 1967 Vol 3 405 23 3 Foam Testing 3 1 Introduction The FEA foam material models used in this study required experimentally developed compressive loading curves to govern the model s compressive response Obtaining compressive foam properties at rates typical of play is not trivial Limitations and disadvantages in established instrumentation has led to the development of a new device ideally suited to measure the impact response of soft materials over a wide range in strain rates Th
84. s A section of aluminum tubing with an outside diameter of 0 5 inches was sanded on the inside to a custom diameter of just over 0 4 inches Square teeth were cut into the end to prevent the foam from ripping The teeth were tapered as shown in Fig 3 8 to decrease the initial contact surface area which increased hole saw stability as penetration started When mounted in a drill press the hole saw produced straight and square samples with excellent surface smoothness Fig 3 9 The nominal dimensions of the foam samples used in this study were 0 42 inches in diameter and 0 3 inches long with 1 tolerance Figure 3 8 Custom hole saw used to machine foam samples from wafers Yo INCH Prk Figure 3 9 Standard foam sample used for impact testing 33 3 4 Verification To verify velocity and displacement measurements for the new device a Phantom V711 high speed camera was placed directly above the foam sample as shown in Fig 3 10 Videos of ten impacts at high gt 40 mph and low lt 23 mph speeds were taken at 60 000 frames per second ProAnalyst motion tracking software was used to measure initial and rebounding striker bar velocities as well as foam sample displacement Figure 3 10 Setup for velocity and displacement verification using a high speed camera Figures 3 11 3 13 show the comparison of measurement methods at the lower impact speed Incoming velocity was quite accurate with an average difference of 1 6 at
85. s The load displacement response of the numerical model is compared with experiment in Fig 5 4 and shows good agreement A notable departure between the model and experiment occurs near the peak strain of each test The model shows no evidence of viscous softening in this region which suggests an insensitivity to time dependence Oscillations in the numerical results at small strain magnitudes indicate the presence of elastic waves propagating through the sample The deformation caused by compression waves which is typical of dynamic crushing in cellular solids Gibson 1999 1s shown in Fig 5 5 75 350 cm Vat 57 300 e Experiment N N Nn Load Ibs 7 D 0 00 0 05 0 10 0 15 0 20 Displacement inches Figure 5 4 Comparison of experimental and numerical load displacement curves of foam sample impacts at the low medium and upper strain rates typical of play conditions I 20 4 mph II 29 7 mph and III 41 4 mph Fringe Levels 0 000e 00 6 250e 03 1 250e 02_ 1 875e 02_ 2 500e 02_ 3 125e 02 Figure 5 5 Shaded strain magnitudes highlight the localization of deformation initiated just after contact The impulse peak displacement and peak force of the model agreed with experiment on average within 5 6 and 4 respectively The COR from the FEA model is compared with 76 experiment in Fig 5 6 and shows numerical COR changing less as a function of speed than was observed ex
86. s in o between the quasi static and high rate 2780 s stress strain response of PU softball foam have been shown both experimentally and numerically by Bryson Bryson 2009 Even more so than strain rate the behavior of foam is dependent on temperature Compressive strength of rigid PU foam has shown a strong decreasing correlation with increasing temperature Traeger 1967 Compressive Young s modulus of the same foam was also shown to depend on temperature The compressibility of the gas inside closed cell foams is dependent on temperature As the gas temperature lowers its molecules vibrate slower and the gas is more easily compressed It is clear that the properties of a foam softball core will change 12 with temperature Environmental conditioning 1s necessary to acquire consistent and accurate impact data Foam density contributes heavily to compressive response Gibson defines relative density as the density of the cellular material divided by that of the solid from which the cell walls are made Gibson 1999 Increasing the relative density of foam increases Young s modulus raises the plateau stress and reduces the strain at which densification starts As relative density increases the cell walls thicken and the pore spaces shrink Gibson also stated that foams above a relative density of 0 3 are considered to be more of a solid which contains isolated pores This distinction is highlighted in other experimentation Chen 2001
87. scoelastic material model was applied to a modeled dynamic stiffness test Fig 2 4 Numerical force time and force displacement curves were compared to experiment and are shown in Fig 2 9 and 2 10 5000 4500 mmm FEA 4000 7 A9044ASAWR 3500 3000 2500 2000 Force Ibs 1500 1000 500 0 0 0005 0 001 0 0015 Time sec Figure 2 9 Force time curve comparison of experiment and FEA softball impacts at 95 mph from Faber 18 5000 4500 mmr FEA 4000 a ASOA4ASAWR 3500 3000 2500 2000 1500 1000 500 Force Ibs 0 0 2 0 4 0 6 0 8 1 Displacement in Figure 2 10 Force displacement curve comparison of experiment and FEA softball impacts at 95 mph from Faber FEA ball stiffness was shown to be greater than experiment which resulted in a lower displacement A difference in load displacement curve shape in Fig 2 10 suggests an incorrect material characterization Despite the difference in load curves the model did agree with experimental CCOR and DS for a 95 mph impact with viscoelastic material parameters of Go 20 ksi G 1 0 ksi and B 6 8 x 10 from Eq 2 11 A split Hopkinson pressure bar SHPB device was used by Bryson in an effort to characterize PU softball foam at high strain rates Bryson 2009 Stress strain curves from experimental testing were compared to mathematical viscoelastic models defined by equations 2 13 and 2 14 o t 2R 1 v
88. sed to catch the sabot after exiting the barrel The ball traveled past light gates Fig 4 5 impacted the control surface and then rebounded back through the light gates Two sets of ADC Beam light gates measured ball speed similar to the device in Chapter 3 Ball speed was adjusted such that only shots within 1 mph were accepted as valid test shots A diagonal pair of light gates determined ball rebound angle Vertical cannon alignment with respect to the impact surface was adjusted so that only rebounds within 10 of the inbound path were considered valid shots Ball rebound trajectory was verified using high speed videos operating at 250 fps Interestingly the distance between the light gates and impact surface was previously found to be measureable due to the effects of drag Smith 2006 Figure 4 5 Light gates red and cylindrical impact surface mounted to the rigid surface right 59 The impact surfaces were mounted to three load cells designed for dynamic loading applications and rated to 5 kips each PCB model 208C05 The load cells were arranged in a two inch equilateral triangle and were mounted to a massive support from behind Fig 4 6 Load measurements were taken at a sample rate of 100 kHz Figure 4 6 Maximum deformation of a softball impacting a cylindrical surface at 100 mph 4 3 Results Various authors have conducted experimental testing on softballs Biesen impacted 42 softballs at speeds of 60 80 9
89. sively high stresses or degradation As the cells fully collapse stiffness rapidly increases in a densification region where the foam behaves much like the matrix material Rate insensitive compressive response is often represented as a single master curve Densification Cells fully Compress Plateau Region Elastic Cell Buckling Compressive Stress O nl A Elastic Region Linear Cell Stretching Compressive Strain Figure 2 6 Typical Stress strain loading response of polymeric foam under compression Because PU foam is viscoelastic the compressive response is rate dependent The plastic collapse strength of a foam o or the stress at which cell collapse begins is directly 11 proportional to the yield strength of the solid of which it is made Gibson 1999 Increasing strain rate causes a slight increase in yield strength Multiple studies listed by Gibson have shown a linear increase in yield strength with increasing log This behavior is shown for rigid polystyrene foam in Fig 2 7 STRAIN RATE 10 1 04 m 1 0 s AA lt T6x10 s 7156x1075 0 8r E 1 6x107S _ 2 6 6 x 10 5 gt 06 1 6 x107s S wn Y W 04 Y 0 2 POLYSTYRENE DATA RINDE amp HOGE Pyp 01 1971 j 0 2 L 6 8 10 12 STRAIN Figure 2 7 Rate dependent compressive stress strain response of rigid Polystyrene foam at strain rates between 10 and 10 s from Gibson Difference
90. splacements were calculated for six impacts at low speeds 10 mph The results in Fig 3 14 show good agreement with an average displacement difference of 2 The device measured COR an average of 10 8 lower than the model 36 0 5 0 45 E Experiment 0 35 0 3 0 25 0 2 MEN 0 1 0 05 Displacement inches Sample Figure 3 14 Displacement Comparison between the device and differential model Both external methods of measurement verification showed that the device measured COR between 10 and 14 low This error in device measurement was either due to errors in the infrared sensors or the load cell Because the high speed video verified correct speed measurements from the infrared sensors the load cell likely caused the low COR values Theoretical force of impact was calculated by differentiating Eq 3 6 twice to get acceleration and then multiplying by striker bar mass f m a A comparison with the load cell measurements showed the load cells measuring 9 8 low on average Measurements of static loads on the load cell could not be done because as time elapsed the force value decreased This behavior was described in the load cell operation manual as the discharge time constant The decay of load value was found to have a half life of approximately 6 seconds Using the equation for half life decay O fo py a where tiz is the half life f is the actual force and f t is the measured force at time t the measure
91. ss did not sufficiently account for energy loss so the shape factor was adjusted to increase energy loss by further shifting the unloading curve down Shape factor values ranged from zero inactive to 1000 above which hysteresis did not change Viscous effects were controlled by a damp factor Increasing damp values tended to lower displacement analogous to adding a material damper The suggested range of damp was between 0 05 and 0 5 LSTC 2010 While the damp value which best matched experiment was outside this range 0 75 using values higher than this resulted in elements with negative volumes within the sample which caused the solver to abort These negative volumes were likely 74 due to numerical instabilities which are discussed in section 6 3 The non dimensional values of HU damp and shape factors were iteratively adjusted to align the model s load displacement curves with experiment The foam material parameters are summarized in Table 5 1 while all other parameters were left as default Table 5 1 Parameters used for the Material 57 Low Density Foam material model p E Model lb s in ksi HU Shape Damp Mat 57 PU Foam Sample 3 90E 05 20 0 01 30 0 75 5 3 2 Results The model was run with initial striker bar speeds of 20 4 29 7 and 41 4 mph to capture the low mid range and upper strain rates typical of play Selection of these specific speeds also enabled direct comparison with previously instrumented impact
92. strain magnitudes yet no damage occurs because the polymer is flexible and air easily penetrates the open celled structure Some crushable foams are designed to have no recovery If a foam is composed of a brittle matrix fracture will occur at large strains and permanently damage the structure 3M produces a crushable foam with voids created by soda lime glass bubbles which act as a mechanical fuse to collapse at specific pressures 3M 2011 Bubble wrap when excessively compressed also suffers catastrophic and irrecoverable damage To study the effects of damage in softball foam both 0 2 and 0 3 inch thick samples were compressed at a quasi static strain rate 0 01 s with strain magnitudes ranging from 0 2 to 0 8 50 e The thickness of each sample was then monitored to see how the samples recovered over time It was found that the sample thickness did not change after one week of recovering Figure 3 30 shows the permanent residual strain after allowing sufficient time for recovery Damage to the foam structure increased with strain magnitude Full recovery was shown for samples compressed up to 0 3 e 4 5 4 0 00 2 inch thick samples 3 5 4 503 inch thick samples a 3 0 5 2 2 5 E 3 2 0 3 1 5 1 0 0 5 lt gt 0 0 Go 0 0 0 2 0 8 2 0 4 0 6 Initial Strain Applied to the Sample Figure 3 30 Structural foam damage indicated by permanent residual strain from quasi static loading When comparing the effec
93. t of deformation on softballs Smith observed that quasi static loading was more severe than impact loading Smith 2008 To determine how a dynamic impact induces structural damage in softball foam permanent residual strain was monitored for 0 3 inch samples impacted over a range of strain magnitudes Sample recovery stopped after one week The results in Fig 3 31 are comparable to quasi static loading with samples strained up to 0 3 e showing full recovery While an exponential increase in residual strain was shown for increasing initial strain residual strains from impact were approximately half that of quasi static loading 51 Residual Strain 0 0 2 0 4 0 6 0 8 Initial Dynamic Strain Figure 3 31 Damage to the foam structure indicated by permanent residual strain for high rate impacts While 1t was shown that structural damage occurs to softball foam during both quasi static and dynamic loading the effect of damage on impact performance was still unknown Six foam samples were impacted repeatedly at differing speeds while an effort was made to keep peak strain for each sample relatively constant Repeating specific strain magnitudes was difficult on the impactor device because a constant tank pressure produced striker bar speeds ranging an average of 3 6 mph Sufficient time was allowed between impacts for sample recovery According to Fig 3 22 and 3 23 the relationship between COR and impact speed was linear for impacts with pea
94. t strain rates typical of play 1000 to 2500 s Softball performance is typically characterized by stiffness and liveliness which can be measured by standardized procedures Performance however changes according to the ball speed and the geometry of the surface impacted Accuracy of numerical ball models can be quantified by comparison with experimental impact performance The objective of this study was to develop a FEA softball model which could accuratel y emulate instrumented ball impact behavior both as a function of speed and surface geometry New instrumentation was developed to characterize the PU foam at rates typical of play Two numerical foam material models were developed with experimentally derived material loading responses and phenomenologically developed unloading responses These materials were then applied to softball simulations and compared to previous material models to show performance improvement 2 Background 2 1 Softball Composition Predominantly modern softballs consist of a rigid polyurethane PU foam core wrapped in a stitched leather cover which is colored either white or yellow Fig 2 1 ASTM standards for softballs used in bat certification testing limit the ball weight to between 6 25 oz and 6 75 oz Circumference is also restricted to between 12 0 and 12 25 in ASTM F1890 2009 Figure 2 1 Softball cross section showing the PU foam core The rigid polyurethane foam core is made by the reac
95. tant strain rate curves from the load frame and impactor device 50 Figure 3 30 Foam damage indicated by residual strain from quasi static loading 51 Figure 3 31 Foam damage indicated by residual strain for high rate impacts 92 Figure 3 32 Change in COR due to repeated impacting oooccccncncccncnnnonnnnnnnnnnnnonanannnnnnnnnos 53 Figure 3 33 Change in DS due to repeated impacting ooooonccnnnncncnnnnnnnnnnnnnnnnnnonanannnnnnnnnos 53 Figure 4 1 Setup of the dynamic stiffness test apparatus occcccccccnonononnnnnnnnnnnnnnnannnnnnnnnnos 57 Figure 4 2 Air cannon used to fire softballs and baseballs ooooooocononnnnnnnnnnnnos 57 Xi Figure 4 3 Sabot used to cradle the ball as it travels through the cannon 58 Figure 4 4 Arrestor plate used to catch the sabot after exiting the barrel 59 Figure 4 5 Light gates and cylindrical impact surface mounted to the rigid surface 59 Figure 4 6 Maximum deformation of a softball impact at 100 mph ooooooccnnnncc 60 Figure 4 7 Load curves from 100 different DeMarini A9044 softballs 61 Figure 4 8 Load displacement curves on differing surface geometry cccceeeeeeeeees 63 Figure 4 9 Load vs time for softball impacts at speeds of 60 93 and 120 mph 63 Figure 4 10 Impulse as a function of both speed and surface geometry
96. ted of a viscoelastic material an increase in stiffness at higher loading rates was shown The high rate curves merged well with slower constant rate curves obtained from a load frame Permanent damage to the foam structure was shown to occur at strains above 0 3 e at both low and high compression rates Repeatedly impacting the samples caused an increase in both COR and DS 54 3 9 References 3M 2011 Crushable Foam Online 2011 Cited Dec 22 2011 http solutions 3m co uk wps portal 3M en_GB O1lGas Industry Solutions Drilling CrushableFo am Bryson A J 2009 Impact response of polyurethane Master s thesis Washington State University 2009 Chen W Lu F Winfree N 2001 p 65 73 High strain rate compressive behavior of a rigid polyurethane foam with various densities Experimental Mechanics 2001 p 65 73 Duris J G 2004 Experimental and numerical characterization of softballs Master s Thesis Washington State University 2004 Smith L V 2008 Measuring the Hardness of Softballs IMAC XXVI Orlando FL Society of Experimental Mechanics Bethal CT 2008 55 4 Ball Testing 4 1 Introduction Instrumented softball performance data was needed for both development and validation of the numerical softball models Performance measured as a function of speed and impact surface geometry was of primary interest The following will discuss the methods and results of experimentally measuring dynamic softb
97. terial stiffness will lower sample displacement thereby reducing energy loss and increasing COR This effect was not shown in experiment but 1t could possibly explain the increase in COR with impact speed 0 40 0 35 az 0 30 Y O Experiment OO gt o e 0 25 4 Mat 83 4 Mat 83 with Tied Contact 20 25 30 35 40 Impact Speed mph Figure 5 12 COR for Mat 83 showed an uncharacteristic nonlinear increase in COR with impact speed As discussed earlier mesh density mesh alignment and the contact option all affect the contact surface penetration Re meshing the PU foam sample from 2772 to 9765 elements resulted in the striker bar penetrating further through the foam sample Including the second row of nodes in the contact condition also resulted in more surface penetration Surface penetration was minimal at low impact speeds but as seen in Fig 5 13 increased considerably at higher speeds compared to Mat 57 in Fig 5 3 LS DYNA s built in Tied Surface to Surface contact option constrains the slave nodes to move with the master surface thus eliminating surface penetration At the beginning of the simulation the nearest master segment for each slave node is located based on an orthogonal projection of the slave node to the master segment LS DYNA 2001 Moving the striker bar closer to the foam sample gap of 0 001 82 inches and using the tied contact option eliminated surface penetration and reduced the non
98. tion of polyisocyanates and polyols in the presence of catalysts surfactants and blowing agents Softballs are constructed by mixing the polyisocyanates and polyols in a large mixing tank The batter in the consistency of pancake mix is poured into the molds and then rotated while it cures over three minutes Variation in cure time chemical composition and temperature all lead to differences in foam properties Bryson 2009 2 2 Ball Properties 2 2 1 Introduction In an effort to keep the offense and defense sides of play fair regulating agencies have placed limits on how well softball bats and balls can perform Bats with high performance and balls with extra liveliness will shift the game balance in favor of the offense This puts the defense at a disadvantage increases the number of home runs and reduces the skill required to excel in the sport Because properties of both bat and ball contribute to the resultant batted ball speed BBS certification testing methods have been implemented to regulate bat and ball performance The following will discuss the calculations tolerances and methods associated with softball performance properties 2 2 2 COR and CCOR The coefficient of restitution COR or e which 1s a measure of the elasticity of an impact 1s defined as the ratio of the relative normal velocity of two objects after impact to that before impact as V y e a 2 1 where v and vz are the post impact rebound speeds and V
99. train in the model increased 21 between impacts of 60 and 95 mph but only 3 between impacts of 95 and 120 mph According to the foam structural damage results from chapter 3 regions of the ball shaded green through red in Fig 6 9 should experience permanent residual strain Impacts at 95 mph clearly have densification strains however experimental testing in chapter 4 showed no significant change in impact performance for repeated testing at this speed 93 Fringe Levels 1 388e 16 1 000e 01 2 000e 01 3 000e 01 4 000e 01 5 000e 01 60 mph 95 mph 120 mph Max Strain 0 525 Max Strain 0 637 _ Max Strain 0 655 Figure 6 9 Cross sectional strain distribution of Mat 57 at the three instrumented speeds Bryson defined the highest strain rate experienced in a 95 mph softball collision to be about 2500 s Bryson 2009 In his FEA model this value was measured where the ball first contacted the impact surface Using a similar location shown in Fig 6 10 strain rates were measured for Mat 57 and are plotted in Fig 6 11 Figure 6 10 Node segment along which peak strain rate was measured 94 Peak Strain Rate 60 70 80 90 100 110 120 Impact Speed mph Figure 6 11 Peak strain rate in a softball as a function of impact speed As expected a linear correlation with impact speed was shown While the peak strain rate at 95 mph matched closely with Bryson s definition the lower strain rate typical of play listed
100. und in the power law models which were developed phenomenologically Ten models with differing power law parameters were found to fit experimental COR and maximum impact force data for a 60 mph impact Two of those showed fair agreement with experimental force time curves at speeds ranging between 60 and 110 mph None of the models however were able to fit experimental cylindrical impact data A high Poisson s ratio 0 5 was observed in the model which is uncharacteristic of an actual ball 0 1 as stated by Duris It was suggested that future work focus on a different material model which could better capture the low Poisson effect and improve response to varied impact surface geometry 17 A numerical bat ball collision was developed by Biesen to describe the plastic deformation of aluminum softball bats Biesen 2006 The softball was modeled in LS DYNA as a solid isotropic sphere Tuning of the model was accomplished by simulating a dynamic stiffness test and comparing the results to instrumented measurements of softball CCOR and DS at speeds between 60 and 130 mph Viscoelastic parameters from Eq 2 11 were adjusted at each speed to produce good agreement The model was able to accurately describe ball hardness and energy loss for a number of speeds however the desired accuracy was only achieved by tailoring the ball s parameters at each impact speed Faber developed an FEA bat ball collision in LS DYNA Faber 2010 A power law vi
101. urglassing was minimized at the cost of an increased solve time Figure 5 3 shows the well stabilized node structure for the fully integrated foam sample black during maximum deflection at the highest simulated speed of 41 4 mph Figure 5 2 Hourglassing caused by high deformations Another effect of the large deformation was a tendency of the striker bar to penetrate the foam sample surface during contact Two variables affecting this was mesh density and mesh alignment Using the same mesh density and diameter for both striker bar and foam sample 72 caused the surface penetration to increase Mesh densities of the striker bar and sample were adjusted such that penetration was minimized as shown in Fig 5 3 Surface penetration was also found to be affected by the contact option Selecting the entire foam sample and striker bar in defining the surface to surface contact option produced the poorest results with the striker bar passing far into the foam sample Penetration was minimized when the single row of surface nodes was selected for the contact option Figure 5 3 Contact penetration between the striker bar green and foam sample black during peak displacement at the highest simulated speed 41 4 mph using Mat 57 5 3 Mat 57 Low Density Foam Mat 57 was the first of two LS DYNA foam material models selected to characterize the PU softball foam Sambamoorthy investigated numerical simulations of dynamically loaded
102. urves consistent with elastic wave propagation may be observed at low strain magnitudes in Fig 3 17 The oscillation in the stress strain response is a result of measuring load at the fixed end of the sample and deriving strain from the displacement at the free end of the sample Fortunately the magnitude of the oscillations is relatively small so that the average material stress strain response could be readily discerned Elastic wave propagations were also observed in numeric simulations discussed in Chapter 5 The speed of a wave in any medium is dependent on the medium s density While the foam structure will increase density during compression due to cell collapse the PU matrix which transmits the compression wave maintains a constant density As further verification that 40 elastic wave propagation was the source of the oscillations in Fig 3 17 the load signals of three impacts at differing speeds were magnified in Fig 3 18 The alignment of the oscillations indicates a constant compression wave speed which is independent of collision conditions 900 800 700 600 2 500 3 400 Strain Rate 300 1127 200 1864 100 2588 0 0 0E 0 5 0E 5 1 0E 4 1 SE 4 2 0E 4 Time s Figure 3 18 Magnification of load signals at differing speeds shows similar oscillatory behavior One advantage of the device was the ability to use striker bars of varying mass Testing bars of differing mass at similar ve
103. with measured ball response compared to previous viscoelastic models Optimal agreement was only achieved however when the foam material parameters were tailored to the measured ball response Mat 57 was able to describe the time and surface geometry dependence of load displacement curves as well as the dynamic stiffness response better than any other material model Both foam models correctly emulated the effect of a changing impact surface on COR as well as a softball s linear loading behavior Mat 83 better emulated COR and CCOR rate dependence than any other material model 7 1 Future Work Obtaining an appropriate description of the ball remains the primary impediment to modeling sports ball impacts with high energy dissipation While progress in this area continues to be made the models have not evolved to the point where they can be used ubiquitously in product development or design Although Mat 57 was able to describe load and displacement well on both flat and cylindrical surfaces its lack of rate dependent formulation weakened the material s overall robustness Future work could be done to investigate other foam material models which incorporate rate effects A potential foam model in LS DYNA is Mat 73 which uses one stress strain loading curve similar to Mat 57 but incorporates a relaxation curve for rate effects An improved description of time dependence will be key to future improvements of solid ball impacts using fo
104. ylinder 95 mph A000 J 9 Flat 95 mph A 3000 T T 3 2000 1000 0 0 0 2 0 4 0 6 COM Displacement in Figure 4 8 Load displacement curves highlighting the impact behavioral differences between a cylinder and flat plate 6000 O Cylinder 120 mph Flat 120 mph 5000 ECylinder 95 mph Flat 95 mph A 4000 Cylinder 60 mph Flat 60 mph 3 3000 2000 1000 E 0 0 5 1 1 5 Time ms Figure 4 9 Load vs time measurements of softball impacts at speeds of 60 95 and 120 mph Comparison of flat and cylindrical impact surfaces highlight the differences in impact response caused by the surface geometry 63 Impulse Ib s bo tb A td ka Ln 50 65 80 95 110 125 Ball Speed mph Figure 4 10 Impulse as a function of both speed and surface geometry The effect of speed on impact properties was significant for both cylindrical and flat impact surfaces as shown in Fig 4 11 and 4 12 respectively COR was observed to linearly decrease with increasing ball speed while impulse peak force and peak displacement increased with speed DS behaved similarly to peak force although showing a smaller dependence on ball speed and a greater dependence on surface geometry Cylinder 120 mph 6000 e Cylinder 95 mph 5000 Cylinder 60 mph Load Ibs ta T SS 3000 2000 1000 O z 0 0 2 0 4 0 6 0 8 COM Displacement in Figure 4 11 Load displacement curves for cylindrical impacts at 60 95 a

DYNAMIC CHARACTERIZATION OF RIGID POLYURETHANE

Contents

Download Pdf Manuals

Related Search

Related Contents