Impact response of high density flexible polyurethane foam

Impact response of high density ?exible polyurethane foam

E.Zaretsky a ,*,Z.Asaf b ,E.Ran b ,

F.Aizik b

a Department of Mechanical Engineering,Ben Gurion University of the Negev,P.O.Box 653,Beer Sheva 84105,Israel b

Plasan Sasa,Kibbutz Sasa,M.P.Merom Hagalil,13870,Israel

a r t i c l e i n f o

Article history:

Received 13June 2011

Accepted 9September 2011

Available online 16September 2011Keywords:Flexible foam

Shock compression Crush up stress

a b s t r a c t

The impact response of high density ?exible polyurethane-based foam was studied in a series of symmetric (both the impactor and the sample made of the same foam)planar impact experiments,with continuous VISAR monitoring of the velocity of the rear sample surface.The impact velocities in these experiments varied from 43to 605m/s providing a sample compression over the 0.36e 51-MPa pressure range,with the strain rates changing,respectively,from 4Â103to 6Â105s À1.The linear shock velocity-particle velocity Hugomiot of the foam,U S ¼U S 0þsu ¼14.8þ1.318u ,was determined on the basis of the recorded velocity histories.The rise times of the velocity histories allows one to conclude that under shock compression above 3.2MPa,the initial structure of the foam is completely crushed and the foam resistance to the propagation of the shock is determined by the void-free foam material.The dynamic tensile (spall)strength of the foam,determined in a separate impact experiment with 1-mm thick foam impactor was found equal to 0.3MPa.Such unexpectedly low spall strength is possibly the result of substantial damage having taken place in the foam during compression.

Ó2011Elsevier Ltd.All rights reserved.

1.Introduction

The ability of polymeric foams to absorb energy of impact stands behind a wide variety applications in automotive industry,civil engineering,packaging and transportation of fragile goods.The quasi-static mechanical properties of the foams,which belong to a large group of materials with cellular structure,were studied intensely over last ?fty years.The results of these multiple studies were carefully analyzed by Gibson and Ashby [1],who suggested a series of useful phenomenological relations between the densities,moduli,Poisson ’s ratios,and collapse stresses of the foams and the properties of the bulk material the foam was made of.Similar rela-tions for foams ’moduli,yield or collapse stress,etc.,were obtained as the result of the micromechanical study of the struts of the foam skeleton [2].The dynamic response of the foams,essential for their applications,was not addressed in these studies.An important feature of the dynamic response of the polymeric foams is their strong strain rate sensitivity [3].The in ?uence of the strain rate on the mechanical response of foams was revealed in drop-weight [4e 6]and impact sleds [7]experiments and was found to be crucial for their energy absorbing ability.Unfortunately the results of these experiments do not provide data for a constitutive description

of the studied material.This problem was partly solved by use of the SHPB (Split Hopkinson Pressure Bar)[8e 11]study of the dynamic response of the foams.This method allows obtaining the stress-strain relations of the foams at the relevant (102s À1-103s À1)strain rates providing valuable information for the constitutive modeling of the foams and for energy absorption estimates.

Gas gun driven planar impact experiments are widely used for studying the dynamic response of metals,ceramics and polymers up to strain rates of about 106s À1and higher [12].The adjustment technique used in such experiments allows one to create exact uniaxial strain boundary conditions in the impacted sample.As a result,the initial parameters of the shock-induced stress pulse traveling through the studied sample are precisely de ?ned.The response of the impact-loaded sample being monitored by a Velocity Interferometer System for Any Re ?ector (VISAR)[13]provides accurate constitutive information about the studied sample.One motivation for the present work was to explore the possibility of using the VISAR-instrumented gun-driven planar impact experiment for obtaining such constitutive information about ?exible polymeric foam.Another reason was dictated by the need to close the gap between the highest loading rates of SHPB technique,w 103s À1,and the lowest of the planar impact,w 104s À1.Addressing these two issues prompted us to perform a series of planar impact experiments with high density ?exible polyurethane foam,accompanied by VISAR monitoring the velocity w of the free sample surface.

*Corresponding author.Tel.:þ97286477102;fax:þ97286477100.E-mail address:zheka@bgu.ac.il (E.

Zaretsky).Contents lists available at SciVerse ScienceDirect

International Journal of Impact Engineering

journal homep age:www.elsevie

/locate/ijimpeng

0734-743X/$e see front matter Ó2011Elsevier Ltd.All rights reserved.doi:10.1016/j.ijimpeng.2011.09.004

International Journal of Impact Engineering 39(2012)1e 7

2.Material and experimental

Planar impact experiments with the polyurethane foam were performed with59-mm bore4-m long gas gun of the Laboratory of Dynamic Behavior of Materials at Ben-Gurion University.The8.9 (Æ0.1)-mm thick sheets of high density(r0¼409Æ4kg=m3,some 65e66%open porosity)?exible polyurethane foam were received from PLASAN Ltd.,Sasa,Israel.The structure of the studied foam,the dense packing of interconnected hollow spheres of100e150-micron diameter,is shown in Fig.1a.Prior the impact experiments,the foam was tested in quasi-static compression using a5587Instron testing machine equipped with the Instron2501150-mm compression platens and an Instron2601de?ection sensor.The results of this test with a55mm thick(6layers of8.9-mm thick)foam sample are shown in Fig.1b.

The presently studied material has a stress-strain diagram that is typical for foams[1],with an in?ection point at approximately 0.13MPa and collapse stress,determined as shown in the insert of Fig.1b,equal to0.07MPa.The initial,straight,segment of the diagram has a slope of about0.78MPa which may be interpreted as the foam’s Young’s modulus.

For8of10planar impact tests(marked as PFA to PFH in Table1) both the samples and the impactors were prepared from60Â60mm2square pieces cut from the foam sheets.The projectiles equipped with the foam impactors were prepared according to the following procedure:the foam square was glued(two-component DEVCON5min epoxy)to the front part of55-mm diameter,11.8-mm thick plane-parallel polymethylmethacrylate(PMMA)disk,and the foam surplus over the55-mm diameter was removed by turning.In order to provide shorting of the velocity and trigger electrical charged pins,the14-m thick aluminum foil ring was glued,using the same epoxy,to the front surface of the foam impactor.The back surface of the PMMA disk was glued with Loctite Super glue to the front edge of the hollow aluminum cylinder sabot.Finally the rear edge of the sabot was closed with a PMMA lid with an O-ring.In these eight tests and in the ninth test PFE1where the sample was made of 5.5-mm(instead of8.9-mm)foam layer,a similar sample assembly was used.The rear surface of the square foam sample was glued on a polyvinyl chloride(PVC)100-mm diameter and5-mm thick disc with a45-mm diameter central hole.In order to provide re?ection of VISAR beam,a piece of14-m aluminum foil was glued on the rear surface of the sample.The disk with the glued sample was?xed on the base ring of the double-tilt sample holder,whose parallel orientation to the front of the projectile had been preliminarily adjusted with an accuracy of0.1mrad.The schematics of these experiments are shown in Fig.2a.In the tenth experiment,aimed at measuring the dynamic tensile(spall)strength of the foam,the impact was produced by a free-of-foam PMMA disk(primary impactor)on the1-mm thick foam sheet(secondary impactor) separated from the sample by a spacer ring of5-mm thickness.As result,the foam sample(Fig.2b)was struck by a thin foam impactor.

The impact velocity,ranged from43.5to605m/s,was controlled by electrical charged pins.The uncertainty of the measurement of the impact velocity did not exceed1%of the measured velocity value.The impactor-sample misalignment controlled by the trigger pins did not exceed1mrad in all experiments.Depending on the impact strength,the velocity of the rear sample surface was moni-tored by VISAR with delay lines providing velocity constants of96.4, 224.0,and407.2m/s per fringe.The parameters of the ten planar impact experiments are listed in Table1.

3.Experimental results

The VISAR-recorded velocity histories obtained after symmetric planar foam e foam impacts are shown in Fig.3a e c.

Except for the waveform obtained after the weakest impact,the waveforms shown in Fig.3are characterized by a two-wave structure marked as P1and P2in Fig.3a.The PFE1test was per-formed in order to show that the presence of the P2wave is caused by interaction of the unloading wave generated at the rear surface of the sample,with the reloading wave generated at the interface between the foam impactor and the PMMA backing.The stress s-particle velocity u diagram and the time t-distance(Lagrangian)h diagram of Fig.4are to illustrate such interaction in the case of the PFE and PFE1tests.Since both the samples and the impactors are made of the same foam,the particle velocity u1behind the shock fronts P1propagating through both the sample and impactor with velocity U S is equal to one half of the impact velocity.Accepting for both shocks the same impact velocity equal to v0¼312m/s,yields for the particle velocity u1¼156m/s.The amplitude of this impact-generated shock is s1(Fig.4a).At the arrival of the shock at the sample free surface it acquires velocity equal to196m/s.In the absence of the PMMA backing,the rear surface of the foam impactor should be decelerated from312m/s to106m/s.The presence of the PMMA backing results in the reloading of the impactor material from state with stress s1to state with stress s2

.

Fig.1.SEM image of the cross-section of the studied polyurethane foam(a),and stress-strain diagram obtained after quasi-static compression tests performed with a55-mm initial thickness foam sample.The strain rate in the test was_ε¼1:5Â10À3sÀ1.The insert shows the determination of the collapse stress.

E.Zaretsky et al./International Journal of Impact Engineering39(2012)1e7

2

The reshock R of the amplitude s 2travelling towards the sample rear surface meets the unloading wave U1,generated at the rear surface of the 5.5-mm sample or U2generated at the rear surface of the 8.9-mm sample.As a result,the partially unloaded shocks R1and R2(for 5.5-mm and 8.9-mm samples,respectively)with amplitude s 3arrive at the sample rear surface,accelerating it from w 1¼196m/s (the free surface velocity corresponding to the P1wave amplitude)to w 2¼354m/s (the free surface velocity corre-sponding to the P2wave amplitude).The later arrival of the P2wave (Fig.4b)at the rear surface of the 5.5-mm sample,47.1m s with respect to 44.1m s in the case of the 8.9-mm sample,is the result of certain relations between the speeds of unloading (U 1,U 2)and reloading (R ,R 1,R 2)waves.It is apparent from Fig.4,that for accu-rate description of the second,P2,wave knowledge of the s 1Às 2,s 2Às 3,and s 3À0paths is required.Since reliable data are avail-able only for the description of the s 1Às 2path,the analysis in the next section will be limited to the shock states s 1behind the P1wave and to those produced by unloading from the s 1states.

The waveform recorded after a single spall-oriented impact is shown in Fig.5.Since the foam impactor used in this experiment was very thin,a part of the waveform amplitude is eliminated by hydrodynamic decay.(The 355-m/s velocity of the primary PMMA impactor corresponds to some 600-m/s impact of the secondary foam impactor on the foam sample.)Although the spall signature (the velocity pull-back D w )at the waveform of Fig.4is very small,of about 3m/s,the post-spall oscillations of the free surface suggest that the foam sample was fractured by the tensile pulse caused by collision of the rarefaction waves generated at the free surfaces of the sample and the secondary impactor.4.Impact response of the foam 4.1.Hugoniot of the foam

In order to obtain the Hugoniot states at the top of the P1wave from the free surface velocity histories shown in Fig.3,the velocity

U S of the propagation of the wave front should be determined.Since the wave fronts are not step-like,we assume U S for the velocity of propagation of the wave half-height.The wave leading edge trav-elling with velocity U LE higher than U S gives rise to the multiple wave re ?ections,as it is shown in Fig.6a.These re ?ections distort the timing of the arrival of the wave half-height at the sample surface.Accounting in that the U LE is the velocity of propagation of low-stress perturbations,we assume that all the multiple re ?ec-tions shown in Fig.6a propagate with the same velocity equal to U LE .In such case,the Lagrangian velocity U S is determined by the times t 1and t 2of the arrival of,respectively,the wave leading edge and the re ?ection from the wave half-height at the free surface of the sample of thickness d .

U S ¼2

d Àðt 2Àt 1ÞU LE =2

t 2þt 1

(1)

The principal Hugoniot of the foam,namely the stress s 1and the speci ?c volume V 1at the top of the P1wave,may be obtained by applying the mass and momentum conservation laws to the wave front propagating with the velocity U S :

V 1V 0

¼ðU S Àu 1Þ

U S ;

s 1¼

U S u 1

V 0

(2)

where V 0¼1=r 0¼2:44Â10À3m 3=kg is the initial speci ?c volume of the ing conservation of mass and momentum across the unloading wave (path u 1w 1in Fig.4a),yields the esti-mates of the average velocity of the unloading wave U UL and of the speci ?c volume V UL of the foam unloaded after loading up to the stress s 1.The corresponding estimates are given in Table 2.

The velocities U LE ,U S ,and U UL and the difference U LE ÀU S are shown in Fig.6b as a functions of the particle velocity u 1¼v 0/2at the top of P1wave.

The linear expression U S ¼14.8þ1.318u (dashed line in Fig.6)?ts the data on the velocity of the propagation of the wave half-

Table 1

Parameters of the planar impact experiments performed with dense ?exible polyurethane foam.Test impactor a sample a imp.velocity,m/s Test impactor a sample a imp.velocity,m/s PFA foam foam 43.5PFE1b

foam foam 314PFB foam foam 72.5PFF foam foam 384PFC foam foam 141PFG foam foam 499PFD foam foam 235PFH foam foam 605PFE

foam

foam

311

PFAS c

foam

foam

355

a Thickness of both foam impactors and samples was 8.9Æ0.1mm.The impactor diameter is 55mm,the samples were 60mm Â60mm squares.

b The foam sample was a 60mm Â60mm square of 5.5(Æ0.1)-mm thick.

c

The thickness of the primary PMMA impactor and of the secondary foam impactor were 11.80Æ0.01mm and 1Æ0.1mm,respectively.

impactor

b

the sample holder

a

Fig.2.Schematics of the symmetric planar impact tests with primary foam impactor (a),and of the spall-oriented experiment with the secondary foam impactor (b).In both cases the velocity of the free rear surface of the foam sample was monitored by VISAR.

E.Zaretsky et al./International Journal of Impact Engineering 39(2012)1e 7

3

height with Pearson correlation coef ?cient p ¼0.9998implying

more than four-fold compression of the foam at strong shocks.It is

apparent from Fig.6b that the difference between U LE and U S

decreases with the strength of the impact and for the particle

velocities higher than 200m/s,it becomes negligibly small,2e 3m/

s.The rise times of the waveform fronts (the time intervals between

0.1w 1and 0.9w 1)decrease from approximately t rt ¼126m s for the

weakest,43.5-m/s,impact to less than t rt ¼0.43m s for the strongest,605-m/s,one.The rise time of the shock front is usually associated with the material strength [14].It is plausible to assume that in the tests with relatively low impact velocity the rise time is controlled by the foam crush up,while at the stronger impacts the steepness of the shock front is controlled by the dynamic viscosity of the crushed (free of voids)foam.The linear dependence of U S on u yields the foam ’s principal

Hugoniot on the stress s -particle velocity u

plane Fig.3.Experimentally recorded waveforms obtained after "strong"(a)and "weak"(b)impacts.The corresponding impact velocities are shown along the waveforms.The waveforms recorded after stronger (72.5m/s and higher)impacts have a two-wave structure containing P1and P2waves propagating with different velocities.The 141-m/s waveform is shown in both (a)and (b)as a scale.The 311-m/s waveform (PFE test)of (a)is shown in (c)together with the velocity history recorded after impacts of similar velocity (314m/s,PFE1test)on the sample of 5.5-mm thickness.The values of the sample thickness are shown near the bottom part of the waveforms.

E.Zaretsky et al./International Journal of Impact Engineering 39(2012)1e 7

4

s ¼ð6:053u þ0:539u 2ÞÂ10À3MPa,where the particle velocity units are m/s.The foam Hugoniot in stress s -relative volume V /V 0

coordinates is shown in Fig.7along with the static compression curve of Fig.1b.The departure of the Hugoniot data from the isothermal compression curve,Fig.7,seems to be caused by large irreversible heating of the shocked foam.An accurate estimate of the temperature caused by this heating is,however,hardly possible.Within assump-tion of constant speci ?c heat C V and constant ratio of Gruneisen parameter to speci ?c volume G /V ,the temperature T H behind the shock front is related to the temperature T 0ahead of the shock as [15]

T H

¼T 0exp G ε 1þ1þs 6T 0a

ε2

þ.

(3)

Here a is the coef ?cient of the volumetric thermal expansion,s is the slope of the material Hugoniot,and ε¼ðV 0ÀV Þ=V 0.The thermal expansion coef ?cient a of polyurethane is of about 2Â10À4K À1[16],For the polyurethane foam of close,300kg/m 3,density Maw et al.[17]suggest the value G z ing such values of G and a yields even for modest,V =V 0z 0:6,compression T H z 1000K.Another approach based on the direct thermodynamic

de ?nition G ¼a C 2b =C p

with characteristic for polyurethane speci ?c heat C p z 500J =kg [18]seems to underestimate the T H ;for the strongest,V =V 0z 0:27,foam compression in the 605-m/s test it yields T H z 500K with G ¼0.064.4.2.Foam ’s compressive strength

As mentioned above the material strength mechanisms are responsible of the shock front rise time t rt .The latter may be quanti ?ed through the assessment of the average strain rate

during

a Fig.4.Stress-particle velocity (a)and time-distance (b)diagrams of the tests PFE and PFE1corresponding to the waveforms shown in Fig.3c.The impact velocity is assumed to be equal to 312m/s in both tests.Waves ’timing (b)corresponds to the arrival of the leading wave edge at the sample rear

surface.

Fig.5.The waveform recorded after impact of 1-mm foam impactor on the 8.9-mm foam sample (shot PFAS of Table 1).The insert shows vertical magni ?cation of the spall-related signal with the velocity pull-back D w pb z 3m =s.

100200300

400

L a g r a n g i a n v e l o c i t i e s U S ,U L E a n d U U L , m /s

particle velocity u , m/s

V e l o c i t y d i f f e r e n c e U L E - U S , m /s

U S

U LE

U LE

U LE t 2

t 18.9

time

h,mm

a

b

Fig.6.Time t -Lgrangian distance h diagram of the propagation of the spread shock front through the foam sample of 8.9-mm thickness (a)and velocities of propagation of the leading edge U LE (?lled circles),of the wave half-height U S (open circles),and of the release wave U UL (open triangles)as a function of the particle velocity at the top of P1wave (b).The dashed line is the linear approximation U S ¼U S 0þsu .The crosses show the difference U LE ÀU S (right ordinate).

Table 2

Foam states behind compressive and unloading waves.Test

u1,m/s U LE ,m/s US,m/s s 1,

MPa V 1/V 0w1,m/s U UL ,m/s V UL /V 0

00 1.0PFA 21.75104.740.70.360.46543.540.7 1.0PFB 36.25129.061.20.910.4085370.70.534PFC 70.50157.8109.5 3.160.35699124.90.461PFD 117.5192.6174.08.360.325152226.90.383PFE 155.5236.1222.714.20.302198288.30.354PFE1157.0236.1219.414.20.295199275.40.348PFF 192.0270.5266.420.90.279240345.80.325PFG 249.5345.0342.334.90.271315419.00.321PFH 302.5

415.9

413.0

51.0

0.266

384

488.0

0.319

E.Zaretsky et al./International Journal of Impact Engineering 39(2012)1e 75

the foam compression:h _ε

i ¼ðV 0ÀV 1Þ=V 0t rt ,where V 1is the foam speci ?c volume at the top of P1wave.The average strain rates h _ε

i ,estimated on the basis of the recorded waveforms are shown in Fig.8as a function of the Hugoniot stress (coordinates are loga-rithmic).It is apparent that the point with s ¼3.2MPa marks a boundary between two modes of the foam impact response.Below this point the foam structure participates in the establish-ment of the shock front form.Beyond the 3.2-MPa stress the foam structure is completely crushed and the shape of the wave front is maintained by the viscosity and the thermal conductivity of the crushed material.While the stress s ¼3.2MPa marks apparently the point beyond which the voids cease to exist in the compressed foam,it is hardly possible to ?x the stress of the onset of the foam ’s crush up.Recalling that in the weakest test,PFA test of Table 1,the impact velocity,v 0¼43.5m/s,and the maximum waveform velocity coincide,and that the departure of the corresponding

Hugoniot point from the isothermal compression curve is negli-gibly small,we can conclude that the foam deformation during this test is still reversible.Respectively,the Hugoniot stress in this test,s ¼0.36MPa,may be considered as the stress of the onset of the foam ’s crush up under shock loading.4.3.Dynamic tensile behavior

The experimentally measured value of the velocity pull-back D w pb allows estimating the dynamic tensile (spall)strength s sp of the foam [19]

s sp ¼12

r 0C D w pb

(4)

where r 0¼409kg/m 3is the initial foam density,and C is the slope of the Raleigh line connecting (on the s Àu plane)the unloaded after loading state of the foam with that corresponding to the collision of the two release waves,generated,respectively,at the free surfaces of the foam impactor and the foam sample.The slope C is determined by the compressibility of the foam under negative stress.Since the latter is unknown,the value of the P1wave propagation velocity U 1z 540m =s corresponding to the impact velocity 355m/s (the impact velocity in the spall-oriented experi-ment),was used as the C estimate.This yields for the dynamic tensile strength of the foam s sp z 0:3MPa.The tensile strength of bulk ?exible polyurethanes is within 8e 40MPa [20e 22].It is plausible to assume that the tensile strength of the polyurethane foam with some 65-%porosity should not be lower than 2.8MPa.The measured value of the foam dynamic tensile strength,0.3MPa,is tenfold lower.The difference seems to be related to serious damaging of the foam during the compressive part of the loading cycle.

5.Conclusion

A ?exible polyurethane foam with initial density r 0¼409kg/m 3was tested in a series of gun-driven planar impact experiments accompanied by VISAR monitoring of the free surface of foam samples.The velocity of symmetrical (foam e foam)impact in these experiments was varied between 43.5and 600m/s.The average compressive strain rate in these experiments ranged from 3.6Â103s À1to 6.2Â105s À1.

The recorded velocity histories made it possible to establish the principal Hugoniot of the foam in a linear form U S ¼U S 0þsu ¼14.8þ1.318u ,where U S is the velocity of propagation of the wave half-height and u is the particle velocity behind the wave front.Such Hugoniot implies that under strong shock loading maximum,the foam compression is V /V 0¼0.241.The velocity of the release (unloading)wave U UL ,determined from the same velocity histories are found to be some 25%higher than the corresponding U S values.The experiments show that under impact with velocity higher than 43m/s (the shock stress s 1¼0.36MPa),the loading of the foam is accompanied by the foam crush up and by an irreversible heating.A reliable assessment of this heating requires,however,more accurate,than available at present,information on the foam Gruneisen parameter.

Based on the rise times of the recorded velocity histories,one can conclude that under impact with velocity higher than 141m/s (s 1z 3:2MPa),the foam is completely crushed and the foam structure ceases to participate in the establishment of the wave-form front.Starting from this point,the structure of the wave front is controlled by the viscosity and thermal conductivity of the bulk foam

material.

Fig.7.Hugoniot of the foam on the s ÀV /V 0plane.The dashed line is the maximum foam compression V /V 0¼(s À1)/s ¼0.241.The insert shows the low pressure Hugoniot data together with the static compression curve of Fig.1

.

Fig.8.The P1wave rise time (from 0.1u 1to 0.9u 1)as a function of the P1amplitude s 1in logarithmic coordinates.The 3.2-MPa point marks the change of the foam response.

E.Zaretsky et al./International Journal of Impact Engineering 39(2012)1e 7

6

The dynamic tensile(spall)strength of the studied foam was found to be very low,w0.3MPa,some10times lower than expected for such foam under quasi-static tension.Such low resistance of the foam to the tensile stress may be caused by the considerable damage suffered by the foam under shock compression.

To summarize,the VISAR-instrumented gun-driven planar impact experiment is a useful tool for obtaining constitutive information about low-impedance materials under strain rates ranging from103to106sÀ1.

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