Effect of Low-Temperature Shock Compressionmeyersgroup.ucsd.edu/papers/journals/Meyers 247.pdf27 GPa: 248.5 K 30 GPa: 260 K 57 GPa: 508 K 77 GPa: 757 K When performing shock-recovery

METALLURGICAL AND MATERIALS TRANSACTIONS A US GOVERNMENT WORK VOLUME 35A SEPTEMBER 2004mdash2729NOT PROTECTED BY US COPYRIGHT

I INTRODUCTION

THIS contribution honors RW Armstrong and his sem-inal contributions to our understanding of the mechanicalbehavior of materials Of great importance to the dynamicbehavior of materials is the ZerillindashArmstrong equationwhich has found application in computational simulationsworldwide It is anchored in the physical processes occur-ring in a material and has been instrumental in elucidatingnumerous phenomena This is but one example of the broadcontributions of RW Armstrong

Shock-recovery experiments have been used to assess theeffects of shock waves on the postshock microstructure andrelated mechanical behavior of copper and many other mater-ials These experiments are performed such that the impartedshock passes through the test material and is then dissipatedin momentum traps Shock-release waves from free surfacesin the momentum traps can prevent spurious plastic defor-mation from passing through the test material This allowsthe test material to be recovered and then examined to assessonly the effects of the passage of a uniaxial-strain shock-wave rise and release Several types of loading (flyer-plateimpact laser-shock ablation etc) and momentum-traparrangements have been employed

In general shock-recovery investigations performed on Cuand other fcc metals have shown that shock loading results in

an increase in dislocation density and general cellular dislo-cation structures are observed[123] Deformation experimentsperformed on shock-recovered Cu over a wide range of con-ditions have shown ldquoshock hardeningrdquo commensurate with theobserved increase in dislocation density For example Gourdinand Lassila[4] showed that the postshock constitutive behaviorof copper shocked to 10 GPa can be fitted using the mechan-ical threshold stress constitutive model by adjusting the valueof the internal-state variables associated with dislocation den-sity Nevertheless the work-hardening rate in shock-compressedsamples was found to decrease with increasing peak pressureAndrade and co-workers[56] observed a stress-strain curve thatshowed a very low work hardening after shock compression toa pressure of 50 GPa Intriguing results obtained for shock-loaded nickel by Meyers[7] showed clear indication of worksoftening This was interpreted as being due to the breakdownof the loose cellular structure upon quasistatic plastic deform-ation Work softening had earlier been mentioned by Cottrelland Stokes[8] and was obtained by Longo and Reed Hill[91011]

when specimens were first deformed at 77 K and then at ambi-ent temperature Hammad and Nix[12] correlated dislocationdensities with flow stress in Al and observed that dislocationreorganization leads to a decrease in work hardening the ex-treme case would be work softening

The temperature of a material as it is being shocked raisesmonotonically to a peak value (Ts) and then decreases whenthe shock release occurs The temperature of the materials afterthe shock has passed is referred to as the residual shock tempera-ture (Tr) Both Ts and Tr increase with the peak shock pres-sure McQueen et al[13] have predicted a temperature rise fora 300 K initial temperature Figure 1 shows the calculatedshock and residual temperatures as a function of peak shockpressure for both the 90 and 300 K initial temperatures Theshock temperatures were calculated using Eq [544] fromMeyers[3] Since the heat capacity at 90 K (Cv90) is lowerthan the ambient-temperature value Cv300 (above which it is

DAVID H LASSILA and TIEN SHEN Research Scientists are withthe Lawrence Livermore National Laboratory Livermore CA 94550 BUYANG CAO Graduate Student and MARC A MEYERS Professor arewith the University of California San Diego La Jolla CA 92093 Contacte-mail bucaoucsdedu

This article is based on a presentation given in the symposium ldquoDynamicDeformation Constitutive Modeling Grain Size and Other Effects InHonor of Prof Ronald W Armstrongrdquo March 2ndash6 2003 at the 2003TMSASM Annual Meeting San Diego California under the auspices ofthe TMSASM Joint Mechanical Behavior of Materials Committee

Effect of Low-Temperature Shock Compressionon the Microstructure and Strength of Copper

DAVID H LASSILA TIEN SHEN BU YANG CAO and MARC A MEYERS

Copper with two purities (998 and 99995 pct) was subjected to shock compression from an initialtemperature of 90 K Shock compression was carried out by explosively accelerating flyer plates atvelocities generating pressures between 27 and 77 GPa The residual microstructure evolved fromloose dislocation cells to mechanical twins and at the 57 and 77 GPa pressures to complete recrystal-lization with a grain size larger than the initial one The shock-compressed copper was mechanicallytested in compression at a strain rate of 103 s1 and temperature of 300 K the conditions subjectedto lower pressures (27 and 30 GPa) exhibited work softening in contrast to the conventional work-hardening response This work softening is due to the uniformly distributed dislocations and the formationof loose cells evolving upon plastic deformation at low strain rates into well-defined cells with a sizeof approximately 1 m The 99995 pct copper subjected to the higher shock-compression pressures(57 and 77 GPa) exhibited a stress-strain response almost identical to the unshocked condition Thisindicates that the residual temperature rise was sufficient to completely recrystallize the structure andeliminate the hardening due to shock compression Thermodynamic calculations using the HugoniotndashRankine conservation equations predict residual temperatures of 570 and 1000 K for the 57 and 77 GPapeak pressures respectively

19-E-Symp-03-101Aqxd 63004 738 AM Page 2729

constant) an average value of (Cv90 Cv300)2 was used forthis interval Above room temperature the heat capacity wasassumed to be constant This provides a reasonable approxi-mation to the shock temperature The residual temperature wascalculated by using Eq [545] from Meyers[3] The lower heatcapacity in the temperature range of 90 to 300 K is reflectedin the more rapid increase in the shock and residual tempera-tures in this domain as seen in Figure 1

The residual temperatures for the four pressures with aninitial temperature of 90 K are

27 GPa 2485 K

30 GPa 260 K

57 GPa 508 K

77 GPa 757 K

When performing shock-recovery experiments it is impera-tive that the value of Tr for a given cooling rate associatedwith the experimental setup be less than the temperature thatcan promote static recovery and recrystallization in the studymaterial For this reason the shock-recovery experiments havebeen designed to enhance the cooling rate by projecting therecovery assemblies into water-soaked catch materials

The temperature (or thermal history) which promotes re-crystallization andor ldquorecoveryrdquo of shock-induced internaldislocation structures is very dependent on the microstructuralstate of the material (ie stored elastic and defect energy as-sociated with dislocation structures) For example largeamounts of mechanical work can substantially reduce the re-crystallization temperature of Cu and other metals and alloysAlso the chemical composition of Cu will affect recoveryThus both the shock conditions (Tr and shock-induced dislo-cations) and the chemical composition and impurity concentra-tions of the Cu can affect the ldquoobservedrdquo shock effects in eventhe most carefully executed experiments While these effectshave been known few experimental studies have been con-ducted to assess andor quantify their effect on postshockmicrostructures and mechanical behavior

We present the results of shock-recovery experiments per-formed on Cu at subambient temperature over a range of shockpressures All of the experiments were performed at about 90 Kso that the values of Tr would be reduced relative to the valuesif the experiments were performed at room temperature Thiswas done in an attempt to mitigate static-recovery effects Theeffect of impurity concentration was evaluated by performingexperiments on two grades of commercially available Cu mater-ials The postshock microstructures were examined using opticalmetallography and transmission electron microscopy (TEM)Also the effects of shock-induced microstructures on yieldstrength and work hardening were studied through the use ofuniaxial-stress compression experiments

II EXPERIMENTS

A Shock-Recovery Experiments

The shock-recovery experiments were performed by accelera-ting a flyer plate by an explosive charge as shown schem-atically in Figure 2(a) Two unalloyed polycrystalline Cuconditions were used in this experiment an oxygen flow elec-tronic (OFE) Cu with a nominal purity of 998 pct and a high-purity (HP) Cu which was determined to be 99995 pct Cu Itshould be noted that monocrystalline copper specimens wereshock compressed in the same experiments and are being char-acterized as part of a continuing effort (not reported here) Themomentum traps (spall and lateral) and anvil were made froma Cu-Be alloy known for its enhanced strength relative to un-alloyed Cu Several different methods were employed to attachthe cover plate over the samples including Cu rivets and braz-ing However the best technique was found to be electrode-position of the Cu cover-plate material directly on the anvilsample assembly followed by finish machining to a hightolerance (prior to electrodeposition the Cu samples were pro-tected with a release agent)

The shock-recovery experiments were performed over arange of shock pressures and at low initial temperature bycooling the assembly with liquid nitrogen The flyer-plate ve-locity was determined by using pins located in four positionsequally spaced around the lateral-momentum trap (Figure2(a)) The shock pressures were determined using the flyer-plate velocity in conjunction with the Us-Up Hugoniot[15]

Four shock-recovery experiments were performed withpeak pressures of 27 30 57 and 77 GPa and initial pulseduration of approximately 1 s the values of Tr were esti-mated to be 2485 260 508 and 757 K for these shock pres-

2730mdashVOLUME 35A SEPTEMBER 2004 METALLURGICAL AND MATERIALS TRANSACTIONS A

(a)

(b)

Fig 1mdashCalculated (a) shock and (b) residual temperature for copper as a func-tion of shock compression pressure with initial temperatures of 90 and 300 K


sures respectively (Figure 1) The planarity of the flyer-plateimpact was assessed by analysis of the arrival times as deter-mined by the various pin locations and was found to be ac-ceptable for our experiment (within 10 deg) In general therecovered test materials were found to be in good shape afterthe explosive loading the flatness of the disks was found tobe within 250 m

B Uniaxial-Stress Deformation Experiments

The stress-strain response of the unshocked and shock-recovered materials was determined to evaluate the effects ofshock hardening and also to correlate shock-hardening effectswith shock-induced changes in the microstructure Compressionsamples were manufactured from the shock-recovered disksusing electrodischarge machining Prior to testing the endsof the samples were lapped parallel to within 10 m Uniaxial-compression deformation experiments were performed over arange of strain rates (103 s1 to approximately 5000 s1) usinga conventional screw-driven test machine for the low-strain-rate tests and a split Hopkinson pressure bar for the high-strain-rate experiments The low-strain-rate experiments were performedusing a high-precision subpress with an extensometer attachedto the platens The ends of specimens and platens were lubri-cated with molybdenum disulfide powder

The stress-strain responses of the unshocked and shock-recovered materials are shown in Figure 3 There are at least

two major conclusions from looking at the data first exten-sive shock-hardening effects are seen in the specimens sub-jected to 27 and 30 GPa In the high-pressure experiments(57 and 77 GPa) recovery is apparent For the 99995 pctCu the stress-strain curves are below the initial conditionThis is consistent with the larger grain size observed aftershock loading (Section IIndashC) For the 998 pct Cu the stress-strain curve for the 57 GPa condition shows less hardeningthan the lower pressures This can only be due to the recoveryof the substructure since it has undergone greater shock hard-ening at the higher pressure The 57 GPa curve falls belowthe one for the unshocked condition for the 999995 pct CuThese results are consistent with the lower recrystallizationtemperature for this purity level

The second notable finding is that some of the shock-recovered materials exhibit significant work softening in theirstress-strain response similar to that observed in shock-recoverednickel[7] Figure 4 shows the results from shock-loaded nickel

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 35A SEPTEMBER 2004mdash2731

(a)

(b)

Fig 2mdash(a) Schematic of shock recovery experiments performed by accel-eration of a flyer plate by an explosive charge (b) Anvil with OFE HP andsingle-crystal test samples (the postshock microstructures and mechanicalbehavior have not been studied)

(a)

(b)

Fig 3mdashStress-strain curves of shock-recovered Cu samples under com-pression test (a) OFE Cu tested at 300 K and (b) HP Cu tested at 300 K


The shocked nickel (20 GPa) tested at ambient temperatureundergoes work softening It can be seen that the postshockedmaterial tested at 77 K shows the conventional work hardeningMeyers et al[16] also observed work softening in an Fe-345 pctNi alloy shocked to a pressure of 75 GPa The interpretation

given by Meyers[7] was that the substructure generated by shockwas closer to the low-temperature low-strain rate deformationsubstructure This natural work hardening occurs during low-temperature mechanical deformation The shocked substruc-ture underwent collapse when tested at ambient temperatureThe TEM analysis carried out by Meyers et al[17] confirmed thebreakup of the loose dislocation cell structure after postshockdeformation It is important to note that the earlier results byMeyers were obtained in tension This leaves open the ques-tion whether the work softening observed was truly due tomicrostructural reorganization or whether it was due to an earlytensile instability (necking) The present results in compres-sion show incontrovertibly that the microstructure is ldquosoften-ingrdquo A discussion of these results and correlation with the ob-served shock-induced microstructural effects are given inSection IIndashD

Figure 5 shows the effect of temperature and strain rate onthe stress-strain response of the shock-recovered Cu (30 GPa)Figure 5(a) refers to OFE copper while Figure 5(c) refers toHP copper The stress-strain response at 77 K shows the classicalhardening behavior for the two cases while the ambient-temperature response is characterized by a yield point followedby softening A compression test carried out in a Hopkinsonbar (strain rate of 5000 s1) reveals a situation intermediarybetween work softening and work hardening The high strain


Fig 4mdashStress-strain curves for shock-recovered nickel samples undertension (adapted from Ref 7)

Fig 5mdashShock-recovered Cu samples under low-temperature compression test (a) stress-strain curves of OFE (b) TEM of Cu sample after 30 GPaand 77 K compression test and (c) stress-strain curves of HP Cu

(b)(a)

(c)


rate at ambient teperature partially suppresses the dynamic recovery

The results presented in Figure 5 are consistent with theearly results by Meyers[7] Figure 5(b) is the TEM micrographfor the OFE copper after being subjected to quasistatic com-pression the dynamic recovery observed after ambient-temperature testing is suppressed The fact that work softeningwas observed in compression testing is incontrovertible proofof this phenomenon

C Microstructural Analyses

Optical metallography was performed on the OFE and HPCu in the unshocked and shock-recovered conditions Sampleswere prepared by etching a polished surface normal to the shock-propagation direction with a solution of ammonium persulfate(20 pct) and water Photographs of the etched surfaces are shownFigure 6 In the unshocked condition the grain structure wasfound to be equal to grain sizes of 10 and 8 m for the OFE


Fig 6mdashGrain structures of OFE and HP Cu in unshocked and postshock conditions In unshocked condition both Cu samples contain annealing twins in grainstructure The amount of deformation twins increases (not shown) as shock pressure increases from 27 to 30 GPa As the shocked pressure further increasd to57 and 77 GPa the Cu samples either slightly recovered (OFE) or fully recrystallized (HP) The 77 GPa postshock samples exhibit a larger grain size



and HP materials respectively A standard line-intercept methodwas used for these grain-size determinations and annealing twinswere accounted for in the analysis

In the shock-recovered condition the microstructure of theOFE and HP Cu shocked to peak pressures of 27 and 30 GParespectively exhibited significant amounts of what are believedto be shock-induced deformation twins (TEM analysis givenin the following section confirmed this) Examples of twinnedgrains are marked by the arrows labeled as ldquoArdquo A micrographtaken at a higher magnification shown in Figure 7 shows thecrystallographic nature of the deformation twins We notehere that not all of the grains showed deformation twins andin particular there appears to be an absence of twins in thelarger grains (also shown in Figure 7) These grains are markedby the arrows labeled as ldquoBrdquo This is inconsistent with the re-sults by Andrade et al[6] who observed a considerable grain-size dependence of mechanical twinning induced by shockloading with large grains having a greater propensity for twinformation Profuse twinning was observed after shock loadingof 50 GPa for specimens with grain sizes of 117 to 315 mSpecimens with grain size of 95 m did not twin It is there-fore suggested that these large twin-free grains are the resultof local recrystallization In addition to deformation twinsmany of the areas exhibited a ldquomottledrdquo appearance suggestiveof a highly dislocated structure If indeed these grains arerecrystallized then the predicted residual temperature is un-derestimated Section IIndashE addresses the possible contribu-tion of frictional heat to this effect

The OFE Cu shocked to a pressure of 57 GPa shows a simi-lar structure to the materials shocked to 27 GPa and 30 GPa(ie significant amounts of deformation twins and dislocatedstructures) However both the OFE and HP Cu shocked to apressure of 77 GPa exhibited a recrystallized microstructureand in the case of the HP Cu the grain size of the shock-recoveredmaterial was slightly increased relative to the unshocked mater-ial This is a clear indication that the magnitude of Tr wassignificantly higher than the recrystallization temperature Also

there appears to be a significant difference in the recrystallizationtemperature of the OFE vs that of the HP materials becauseat the shock pressure of 57 GPa the HP Cu was recrystallizedwhile as indicated earlier the OFE Cu was not

Separate annealing experiments were carried out on HP cop-per shocked to 303 GPa at 393 K for durations between 3 and600 minutes (Figure 8) The time corresponding to the onsetin the drop of hardness (square symbols designate the aver-age reading at each time) is approximately 20 minutes Thusthe materials shocked to this pressure probably did not exhibitsignificant static recovery after shock loading consistent withthe mechanical-test data shown in Figure 3 Chojnowski andCahn[14] determined the recrystallization temperatures for cop-per (OFE) shocked to 155 and 41 GPa They obtained activ-ation energies of 29 and 355 Kcalmole respectively For thecopper shocked at 41 GPa they obtained a drop in mechanicalproperties (hardness and yield point) after a 15-minute annealat 250 degC (523 K) Thus this can be considered a safe estimateof the recrystallization temperature of copper shocked to thisamplitude The recrystallization temperature after the 155 GPashock was higher 400 degC (673 K)

D The TEM Characterization

The effects of shock loading on the internal structure ofthe unshocked and shock-recovered materials were observedby TEM A JEOL 200CX microscope operating at 200 kV

JEOL is a trademark of Japan Electron Optics Ltd Tokyo

was used for the characterization All images were recordeddirectly with a Gatan MultiScan close-coupled device cam-era The TEM study focuses on the OFE Cu in the unshockedand shocked (30 GPa) conditions Various samples were se-lected for TEM study based on our interest in the effects ofstrong shocks on the microstructure and also the effect ofpostshock deformation of the shock-induced microstructure

1 Unshocked OFE CuThe microstructure of unshocked OFE Cu contains a low

density of dislocations and the typical 111 annealing twinsWhen this unshocked material was subjected to deformationin compression to 36 pct strain at 300 K and at a strain rateof 103 s1 the TEM microstructure showed the accumula-tion of glide dislocations and the development of slip(111)

Fig 7mdashMicrograph showing shock-induced deformation twins (OFE Cu27 GPa) (selected examples indicated by arrows A) regions that appearrecrystallized are marked by arrows B

Fig 8mdashMicrohardness of HP Cu vs time at annealing temperature 393 Kand shock pressure 30 GPa (average value square)


bands The 111 annealing-twin orientation was again iden-tified by its diffraction pattern

2 Shock-Recovered OFE Cu (30 GPa)The shock-recovered OFE Cu was found to have a high

density of forest dislocations (Figure 9(a)) and many finedeformation twins (Figure 9(b)) Also fine elongated cellstructures were observed (Figure 8(c)) reminiscent of tran-sition bands The thickness of these elongated cells was meas-ured to be around 01 m This structure suggests that thedynamic recovery may have taken place in certain regionsin the shocked OFE Cu sample due to adiabatic heating

Quasistatic deformation (300 K 037) of the OFE Cushocked to 30 GPa resulted in significant dislocation cell-structure

development relative to the shock-induced substructure Asshown in Figure 10 distinct dislocation cell structures wereobserved with an average cell diameter of approximately 1 min diameter The scale of the cell is much larger than thatobserved in the postshock condition (01 m) This microstruc-ture reorganization produced by postshock quasistatic deform-ation has been observed previously by Meyers et al[16] uponplastically deforming shock-loaded Ni One with much largercells replaced the shock-induced microstructure As discussedpreviously the stress-strain curve showed a work-softeningphenomenon (an indication of dynamic recovery) which seemsconsistent with the evolution of a relatively uniform distributionof dislocations in the shock-recovered condition to a lower-energy cell structure during postshock quasistatic deformation


(a)

(c)

(b)

Fig 9mdashThree types of microstructure observed in OFE Cu sample shocked at 30 GPa (a) high density of forest dislocations (b) fine deformation twinsand (c) formation of transition-band-like fine elongated cell structure


resulted in little change in the dislocation structure relative tothe shock-recovered state Instead a further increase in thedensity of forest dislocations was observed with no significantcell evolution This observation is consistent with the observedmechanical behavior shown in Figure 4 for nickel in that theshock-recovered material was observed to have significantwork hardening during the straining at 77 K The results shownin Figure 5 for copper shock compressed to 30 GPa and testedat 77 K and 104 s1 are in full agreement with the TEMobservations The shock-compressed copper work hardenstherefore one would not expect a breakup of the dislocationsubstructure produced by shock compression Clearly the ef-fects of thermal activation on the structure evolution of theshock-induced dislocation structure are important

E Characterization and Quantification of Shock-InducedDeformation Twins

The metallographic examination of the OFE Cu shockedat 57 GPa suggested that this material developed extensivetwinning within the grain structure To obtain solid evidenceof shock-induced deformation twinning TEM analyses ofmicrostructure of this material were performed Figures 11and 12 show the TEM bright- and dark-field images of deform-ation twins in OFE Cu shocked to 57 GPa In Figure 11 thedeformation twins were identified from the (011) diffractionpattern By tilting the foil to align the twin plane closely paral-lel to the electron beam the twin reflections in the diffraction


Fig 10mdashMicrostructure of 30 GPa postshock OFE Cu sample compres-sion tested at 300 K to 037 with

103 s1

Fig 11mdashOFE Cu shocked at 57 GPa showing the formation of (111) deformation twins as identified by (011) diffraction pattern

In contrast to the dislocation-structure evolution resultingfrom quasistatic deformation of shock-recovered 30 GPa Cuat 300 K the same extent of quasistatic deformation at 77 K


pattern can be obtained and easily identified by a simple180-deg rotation around the 111 twin axis In the currentcase the twin plane is and the twin reflections are13244 and 13511 as a result of twinning from the 200and 111 planes respectively The dark-field image wastaken from the twin reflection

Figure 12 shows deformation twins from the (001) dif-fraction pattern The beam direction is not parallel with anytwin plane and twin reflections overlapped with the matrixdiffraction spots The dark-field image was taken from the

twin reflection which overlapped with the matrix reflection Based on the TEM observation the widthof the deformation twins observed in the OFE Cu shocked at57 GPa varied from 01 to 1 m and the occurrence of deform-ation twins varied from place to place

Deformation-twin boundaries which are similar in natureto annealing-twin boundaries act essentially to refine thegrain size of material Zerilli and Armstrong[18] expressedthe spacing of twin boundaries in terms of a HallndashPetch-typerelationship and applied it to Armco iron The incorporationof the strengthening due to twin boundaries into the ZerillindashArmstrong equation improved the match between predictedand experimentally observed deformation profiles in Tayloranvil specimens significantly To estimate the possible ldquograin-

(200)13 (4 24)

13 (2 4 4)

(111)

refinementrdquo effect of shock loading we performed detailedmetallography using Normarski interference contrast at amagnification of 500 times on samples that were etched ina solution of ammonium persulfate (20 pct) and water Aline-intercept method was used to determine the averagenumber of intercepts counting both high-angle grain bound-aries and annealing and deformation twins The data sum-marized in Table I indicate that the shock-recovered materialshave a grain size approximately one-half that of the grainsizes in the unshocked condition due to the presence of de-formation twins In other words the effect of shock loadingat pressures of about 30 GPa resulted in a grain-size refine-ment of about a factor of 2 As the pressure is increased atand above 57 GPa this grain refinement disappears and isreplaced by an increase in grain size This is a direct resultof recrystallization and is evident in Table I



Table I Effective Grain Sizes (in m) of Unshockedand Shocked Cu (m)

Materials Unshocked 27 GPa 30 GPa 57 GPa 76 GPa

HP Cu 8 5 3 15 15OFE Cu 10 2 5 5 15


F Additional Heating Term Due to Plastic Deformation

It is instructive to estimate the effect of plastic deformationin the release portion of the wave on the residual temperatureThe residual temperatures listed in Figure 1 are obtained fromthe shock temperature (Ts) assuming an isentropic releaseThis isentropic release is given by

[1]

where 0 is the MiendashGruneisen parameter V0 is the initialspecific volume and Vs is the specific volume at the shockedstate In the case of the decompression of a solid with finitestrength one would need to add a heat component due toplastic deformation

The temperature increase due to plastic deformation inthe release portion of the wave can be expressed as

[2]

where is the density Cp is the heat capacity and is theTaylor factor For the shock-compression case the strain1 is a function of V and V0

[3]

The strength of the material () has to be estimated underthe specified condition This material has been shock hardenedby the shock front that introduced a dense array of disloca-tions andor twins Zerilli and Armstrong[1920] proposed a con-stitutive equation for incorporating the effects of strain strainrate and temperature This ZerillindashArmstrong equation has thefollowing form for fcc metals

[4]

The parameters obtained by ZerillindashArmstrong for copperare

0 00028 K1

1 0000115 K1

B 890 MPa

The term G kd12 incorporates all the athermal com-ponents of the flow stress In our case we approximate thisterm as 350 MPa The strain rate at the release portion of thewave is on the order of 105 to 106 s1 Substituting the pre-vious parameters into the ZerillindashArmstrong equation [Eq [4])and assuming a perfectly plastic response (n 0) and constanttemperature (T 300 K) we obtain

Applying an average value of 9452 MPa to Eq [2]we obtain the increase in temperature due to plastic workFigure 13 shows the temperature increase due to plastic de-formation This increase is modest and cannot account fordifferences in the recrystallization temperature observed Theexperiments reported herein show a gap in pressure (the 30to 57 GPa region) It would be necessary to carry out shock-

s 9689 MPa (

106 s1)

s 9216 MPa ( 105 s1)

s sG kd12 B exp (b0T b1T ln )

1 2

3 ln

Vs

V0

Td b

rCp1

0

sd

Tr Ts exp c g0

V0 (Vs V0) d

compression experiments in this region to verify whetherthe residual temperature is indeed higher than the predic-tions from a simple isentropic release (without consideringplastic dissipation processes in the release portion of thewave)

III SUMMARY AND CONCLUSIONS

Shock-recovery experiments were performed on OFE andHP Cu at subambient temperature (90 K) in an attempt tolower the postshock residual temperature and enable success-ful shock-recovery experiments at high pressures The followingis a summary of our findings

1 Optical microscopy was performed to examine the effectof shock loading on the microstructure Significant extentsof deformation twinning (confirmed by TEM analyses)were observed in the shock-recovered materials that werenot recrystallized Our analyses suggest that the grain-size refinement due to shock loading at pressures of 27and 30 GPa in the OFE and HP Cu materials is about afactor of 2

2 Recrystallization occurred in the HP Cu after a 57 GPashock the expected residual shock temperature is 508 KAlso we found that both OFE and HP Cu materials werefully recrystallized after recovery from a 77 GPa shock(expected residual temperature of 757 K) The residualtemperature of the specimen is rapidly decreased due topostquenching of the fixture in water-soaked catch mater-ials Parallel recrystallization experiments carried out inthe specimen subjected to 30 GPa shock (Figure 7) reveala reduction in average microhardness number between20 and 60 minutes for a temperature of 393 K Chojnowskiand Cahn[14] report a recrystallization temperature (15-minute anneal) of 573 K after a 40 GPa shock Their cop-per (oxygen-free high conductivity) is similar to OFEboth have a higher impurity level than our HP Cu

3 Uniaxial stress-compression deformation experimentswere performed to investigate the postshock mechanicalbehavior of the shock-recovered materials Under deform-ation conditions where thermally activated processes are


Fig 13mdashIncrease in residual temperature due to plastic deformation inthe release portion of the wave


minimal (ie 77 K) the shocked and recovered materialexhibited a gradual transition to plastic behavior and pos-itive work hardening However the postshock mechanicalbehavior was found to be substantially different when test-ing was carried out at ambient temperature showing ayield point work softening and almost no indication ofpositive work hardening out to a strain of 35 pct or moreThis work softening had been detected earlier for shock-loaded Ni[717] and Fe-34 pct Ni[16]

4 Transmission electron microscopy of shock-recoveredOFE Cu (30 GPa) indicated that the shock-release processresulted in a fairly uniform dislocation structure This isin contrast to dislocation cell structures observed in othershock-recovered copper materials notably those shockedat ambient temperature Upon subsequent quasistaticstraining at room temperature a cell structure evolved fromthe ldquouniformrdquo structure to a cellular structure (1 m)and this correlated with the yield phenomena and worksoftening observed in the mechanical behavior

ACKNOWLEDGMENTS

The authors thank Mr Fred Sandstrom for assembly ofthe shock recovery experiments and for their execution Thiswas carried out at the Energetic Materials Research and Tech-nology Center New Mexico Institute of Mining and Tech-nology Also we thank Robert P Kershaw for performingthe optical light metallographic examinations of the materialsand Mary M LeBlanc and Scott Preuss for performing themechanical testing of the shockrecovered materials The helpof Mr Anuj Mishra with manuscript preparation is gratefullyacknowledged

REFERENCES1 O Johari and G Thomas Acta Metall 1964 vol 12 pp 1153-592 RL Nolder and G Thomas Acta Metall 1964 vol 12 pp 227-403 MA Meyers Dynamic Behavior of Materials John Wiley amp Sons

Inc New York NY 1994 pp 382-4474 WH Gourdin and DH Lassila Mater Sci Eng A 1992 vol 151

pp 11-185 UR Andrade MA Meyers KS Vecchio and AH Chokshi Acta

Metall 1994 vol 42 (9) pp 3183-1956 MA Meyers UR Andrade and AH Chokshi Metall Mater Trans A

1995 vol 26A pp 2881-937 MA Meyers Metall Mater Trans A 1977 vol 8A pp 1581-838 AH Cottrell and RJ Stokes Proc R Soc A 1955 vol 233

pp 17-349 WP Longo and RE Reed Hill Scripta Metall 1970 vol 4


pp 833-3611 WP Longo and RE Reed Hill Metallography 1974 vol 7

pp 181-20112 FH Hammad and WD Nix Trans ASM 1966 vol 59 pp 94-10413 RG McQueen SP Marsh JM Taylor JN Frits and WJ Carter

in High-Velocity Impact Phenomena R Kinslow ed Academic PressNew York NY 1970 pp 293-317

14 EA Chojnowski and RW Cahn in Metallurgical Effects at HighStrain Rates TW Rohde BM Butcher JT Holland and CH Karneseds Plenum New York NY 1973 pp 631-44

15 Shock Waves and High Strain Rate Phenomena in Metals MA Meyersand LE Murr eds Plenum Press New York NY 1981

16 MA Meyers LE Murr CY Hsu and GA Stone Mater Sci Eng1983 vol 57 pp 113-26

17 MA Meyers K-C Hsu and K Couch-Robino Mater Sci Eng1983 vol 59 pp 235-49

18 FJ Zerilli and RW Armstrong in Shock Waves in Condensed MatterSC Schmid and NC Holmes eds Elsevier Science Publishers BVAmsterdam 1988 pp 273-76

19 FJ Zerilli and RW Armstrong J Appl Phys 1987 vol 61 pp 1816-25




constant) an average value of (Cv90 Cv300)2 was used forthis interval Above room temperature the heat capacity wasassumed to be constant This provides a reasonable approxi-mation to the shock temperature The residual temperature wascalculated by using Eq [545] from Meyers[3] The lower heatcapacity in the temperature range of 90 to 300 K is reflectedin the more rapid increase in the shock and residual tempera-tures in this domain as seen in Figure 1

The residual temperatures for the four pressures with aninitial temperature of 90 K are

27 GPa 2485 K

30 GPa 260 K

57 GPa 508 K

77 GPa 757 K

When performing shock-recovery experiments it is impera-tive that the value of Tr for a given cooling rate associatedwith the experimental setup be less than the temperature thatcan promote static recovery and recrystallization in the studymaterial For this reason the shock-recovery experiments havebeen designed to enhance the cooling rate by projecting therecovery assemblies into water-soaked catch materials

The temperature (or thermal history) which promotes re-crystallization andor ldquorecoveryrdquo of shock-induced internaldislocation structures is very dependent on the microstructuralstate of the material (ie stored elastic and defect energy as-sociated with dislocation structures) For example largeamounts of mechanical work can substantially reduce the re-crystallization temperature of Cu and other metals and alloysAlso the chemical composition of Cu will affect recoveryThus both the shock conditions (Tr and shock-induced dislo-cations) and the chemical composition and impurity concentra-tions of the Cu can affect the ldquoobservedrdquo shock effects in eventhe most carefully executed experiments While these effectshave been known few experimental studies have been con-ducted to assess andor quantify their effect on postshockmicrostructures and mechanical behavior

We present the results of shock-recovery experiments per-formed on Cu at subambient temperature over a range of shockpressures All of the experiments were performed at about 90 Kso that the values of Tr would be reduced relative to the valuesif the experiments were performed at room temperature Thiswas done in an attempt to mitigate static-recovery effects Theeffect of impurity concentration was evaluated by performingexperiments on two grades of commercially available Cu mater-ials The postshock microstructures were examined using opticalmetallography and transmission electron microscopy (TEM)Also the effects of shock-induced microstructures on yieldstrength and work hardening were studied through the use ofuniaxial-stress compression experiments

II EXPERIMENTS

A Shock-Recovery Experiments

The shock-recovery experiments were performed by accelera-ting a flyer plate by an explosive charge as shown schem-atically in Figure 2(a) Two unalloyed polycrystalline Cuconditions were used in this experiment an oxygen flow elec-tronic (OFE) Cu with a nominal purity of 998 pct and a high-purity (HP) Cu which was determined to be 99995 pct Cu Itshould be noted that monocrystalline copper specimens wereshock compressed in the same experiments and are being char-acterized as part of a continuing effort (not reported here) Themomentum traps (spall and lateral) and anvil were made froma Cu-Be alloy known for its enhanced strength relative to un-alloyed Cu Several different methods were employed to attachthe cover plate over the samples including Cu rivets and braz-ing However the best technique was found to be electrode-position of the Cu cover-plate material directly on the anvilsample assembly followed by finish machining to a hightolerance (prior to electrodeposition the Cu samples were pro-tected with a release agent)

The shock-recovery experiments were performed over arange of shock pressures and at low initial temperature bycooling the assembly with liquid nitrogen The flyer-plate ve-locity was determined by using pins located in four positionsequally spaced around the lateral-momentum trap (Figure2(a)) The shock pressures were determined using the flyer-plate velocity in conjunction with the Us-Up Hugoniot[15]

Four shock-recovery experiments were performed withpeak pressures of 27 30 57 and 77 GPa and initial pulseduration of approximately 1 s the values of Tr were esti-mated to be 2485 260 508 and 757 K for these shock pres-


(a)

(b)

Fig 1mdashCalculated (a) shock and (b) residual temperature for copper as a func-tion of shock compression pressure with initial temperatures of 90 and 300 K









(a)

(b)


(a)

(b)









(b)(a)

(c)






























(a)

(c)

(b)








103 s1








(200)13 (4 24)

13 (2 4 4)

(111)






HP Cu 8 5 3 15 15OFE Cu 10 2 5 5 15




[1]



[2]


[3]


[4]


0 00028 K1

1 0000115 K1

B 890 MPa



s 9689 MPa (

106 s1)

s 9216 MPa ( 105 s1)


1 2

3 ln

Vs

V0

Td b

rCp1

0

sd

Tr Ts exp c g0

V0 (Vs V0) d












ACKNOWLEDGMENTS




























(a)

(b)


(a)

(b)









(b)(a)

(c)






























(a)

(c)

(b)








103 s1








(200)13 (4 24)

13 (2 4 4)

(111)






HP Cu 8 5 3 15 15OFE Cu 10 2 5 5 15




[1]



[2]


[3]


[4]


0 00028 K1

1 0000115 K1

B 890 MPa



s 9689 MPa (

106 s1)

s 9216 MPa ( 105 s1)


1 2

3 ln

Vs

V0

Td b

rCp1

0

sd

Tr Ts exp c g0

V0 (Vs V0) d












ACKNOWLEDGMENTS



























(b)(a)

(c)






























(a)

(c)

(b)








103 s1








(200)13 (4 24)

13 (2 4 4)

(111)






HP Cu 8 5 3 15 15OFE Cu 10 2 5 5 15




[1]



[2]


[3]


[4]


0 00028 K1

1 0000115 K1

B 890 MPa



s 9689 MPa (

106 s1)

s 9216 MPa ( 105 s1)


1 2

3 ln

Vs

V0

Td b

rCp1

0

sd

Tr Ts exp c g0

V0 (Vs V0) d












ACKNOWLEDGMENTS

















































(a)

(c)

(b)








103 s1








(200)13 (4 24)

13 (2 4 4)

(111)






HP Cu 8 5 3 15 15OFE Cu 10 2 5 5 15




[1]



[2]


[3]


[4]


0 00028 K1

1 0000115 K1

B 890 MPa



s 9689 MPa (

106 s1)

s 9216 MPa ( 105 s1)


1 2

3 ln

Vs

V0

Td b

rCp1

0

sd

Tr Ts exp c g0

V0 (Vs V0) d












ACKNOWLEDGMENTS










































(a)

(c)

(b)








103 s1








(200)13 (4 24)

13 (2 4 4)

(111)






HP Cu 8 5 3 15 15OFE Cu 10 2 5 5 15




[1]



[2]


[3]


[4]


0 00028 K1

1 0000115 K1

B 890 MPa



s 9689 MPa (

106 s1)

s 9216 MPa ( 105 s1)


1 2

3 ln

Vs

V0

Td b

rCp1

0

sd

Tr Ts exp c g0

V0 (Vs V0) d












ACKNOWLEDGMENTS



























(a)

(c)

(b)








103 s1








(200)13 (4 24)

13 (2 4 4)

(111)






HP Cu 8 5 3 15 15OFE Cu 10 2 5 5 15




[1]



[2]


[3]


[4]


0 00028 K1

1 0000115 K1

B 890 MPa



s 9689 MPa (

106 s1)

s 9216 MPa ( 105 s1)


1 2

3 ln

Vs

V0

Td b

rCp1

0

sd

Tr Ts exp c g0

V0 (Vs V0) d












ACKNOWLEDGMENTS


























103 s1








(200)13 (4 24)

13 (2 4 4)

(111)






HP Cu 8 5 3 15 15OFE Cu 10 2 5 5 15




[1]



[2]


[3]


[4]


0 00028 K1

1 0000115 K1

B 890 MPa



s 9689 MPa (

106 s1)

s 9216 MPa ( 105 s1)


1 2

3 ln

Vs

V0

Td b

rCp1

0

sd

Tr Ts exp c g0

V0 (Vs V0) d












ACKNOWLEDGMENTS

























(200)13 (4 24)

13 (2 4 4)

(111)






HP Cu 8 5 3 15 15OFE Cu 10 2 5 5 15




[1]



[2]


[3]


[4]


0 00028 K1

1 0000115 K1

B 890 MPa



s 9689 MPa (

106 s1)

s 9216 MPa ( 105 s1)


1 2

3 ln

Vs

V0

Td b

rCp1

0

sd

Tr Ts exp c g0

V0 (Vs V0) d












ACKNOWLEDGMENTS























[1]



[2]


[3]


[4]


0 00028 K1

1 0000115 K1

B 890 MPa



s 9689 MPa (

106 s1)

s 9216 MPa ( 105 s1)


1 2

3 ln

Vs

V0

Td b

rCp1

0

sd

Tr Ts exp c g0

V0 (Vs V0) d












ACKNOWLEDGMENTS























ACKNOWLEDGMENTS





















Documents

Effect of Low-Temperature Shock Compressionmeyersgroup.ucsd.edu/papers/journals/Meyers 247.pdf27 GPa: 248.5 K 30 GPa: 260 K 57 GPa: 508 K 77 GPa: 757 K When performing shock-recovery