d.c. erlich and p. chartagnac- determination of dynamic flow curve of metals at ambient and elevated...

8/3/2019 D.C. Erlich and P. Chartagnac- Determination of Dynamic Flow Curve of Metals at Ambient and Elevated Temperat

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JOURNAL DE PHYSIQUEColloqueC5, supplCment au n08,Tome 46, oQt 1985 page C5-455

DE TE RM I N A TI O N O F DY NA M I C FLOW CURVE O F M E TA LS A T A M B I E NT A ND E L E V A TE DTEMPERATURES B Y ROD IMPACT TECHNIQUES*

D.C. Erlich and P. chartagnac**SRI InternationaZ, 333 Ravenswood Avenue, Menlo Park, Ca li fo rni a 94025 ,U.S.A.

~6sum6 On dicrit une approche combinant rgsultats exp&rimentaux etcalculs numgriques pour diterminer la courbe dgformation-contrainte d'unmgtal > tempgrature ambiante ou 'a tempgrature GlevGe pour de randesSe'formations et des vitesses de dgformation GlevGes (lo4 a 10 /s). Unichantillon en forme de barre de section circulaire est percut& k hautevitesse et le profil dgforrng rgsultant de l'impact est photographi; avecune cam6ra k haute vitesse. L'essai est ensuite simulg avec un programmebidimensionneldediff6rences finies pour les calculs de propagation d'onde,en variant les donnges pour la courbe diformation-contrainte, jusqut; ceque les profils expirimentaux et calculgs concordent. On prGsente desrgsultats pour l'acier AISI 4340 et pour un alliage de zinc/aluminium.Abstract - An experimental/computational procedure is described for deter-mining the compressive flow curve of metals at high strains and strain rates(lo4 to lo5/,), at either ambient or elevated temperatures. A cylindricalspecimen rod is impacted at high velocities and the resulting deformationprofiles are recorded with a high-speed framing camera. The experiment isthen simulated using a two-dimensional finite-difference wave propagationcode, varying the input flow curve until the experimental and computationalprofiles agree. Data is presented for AISI 4340 steel and a zinc/aluminumalloy.

Determination of high strain-rate constitutive behavior of materials is ofincteasing interest to researchers in a growing number of fields. However, theavailability of experimental techniques that allow such determinations at highstrain rates and large plastic strains (20%-150%) has been extremely limited, ifnot nonexistent. Recently we have developed the rod impact technique (based uponthe Taylor test for measurement of dynamic yield strengths /1/ to determine thestress-strain flow curve in compression for a material at ambient or elevatedtemperature.I - HISTORICAL PERSPECTIVE AND TECHNIQUE DEVELOPMENTClassic Taylor TestIn 1947, Taylor and Whiffin /1,2/ accelerated cylindrical specimen rods into a"rigid" plate. The plastic deformation at the impact end shortens the rod, and thefractional change in rod length can, by one-dimensional rigid-plastic analysis, besimply related to the dynamic yield strength. The authors showed this relationshipto be independent of both the rod aspect ratio and the impact velocity for a widevariety of materials, including copper, lead, paraffin wax, and various steels.Though appealing in its simplicity, the Taylor test had only a moderate follow-up.Lee and Tupper /3/ in 1953 and Hawkyard et al. /4/ in 1968 attempted to model the

*~esearch artially supported by U.S. Army Research Office.**Current address - ETCA/CEG 465 Gramat, France.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985556
http://www.edpsciences.org/http://dx.doi.org/10.1051/jphyscol:1985556http://dx.doi.org/10.1051/jphyscol:1985556http://www.edpsciences.org/


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C5-456 JOURNAL DE PHYSIQUE

Taylor test using various one-dimensional analyses, but were largely unsuccessful.More recently the use of two-dimensional wave propagation codes allowed betterunderstanding of and renewed interest in this technique. In 1972, Wilkins andGuinan / 5 / , using the HEMP code and an elastic-plastic model with work-hardening,were able to correctly simulate the final shapes, as well as the final lengths, ofTaylor test specimens of several metallic alloys at ambient temperatures. Theirresults showed a good correlation between the dynamic yield strength and thefractional change in rod length for a wide range of impact velocities and rod aspectratios, thus confirming many of the TaylorIWhiffin conclusions.Symmetric Rod Impact TestIn the early 1980s, Erlich et al. /6/ implemented two major modifications to theclassic Taylor technique. The first was to use ultrahigh speed photography tomonitor the deformation history of the specimen rod. This allows intermediate, aswell as final deformations to be compared with the computer simulations, thusimproving the reliability of the flow curve determination.The second modification was to replace the "rigid" plate with another rod of thesame geometry and material as the impacting rod (Fig. la). This arrangement,referred to as the "symmetric rod impact" (SRI) technique, allows the impacting endsof the two specimen rods to deform together symmetrically, thus eliminating boundarycondition uncertainties in the analysis that arise from the unknown frictionconditions at the rod-plate interface and from the deformation of the "rigid" plateadjacent to that interface. By use of the SRI technique, dynamic flow curves atambient temperature were obtained for 6061-T6 aluminum / 6 / and 4340 steel / 7 / .

BEFORE IMPACT AFTER IMPACTIdentical Specimen Rods(a ) Symmetric Rod

lmpact Test

Asymmetricl mDact Test

Specimen Rod

FIGURE SCHEMATIC OF TWO ROO IMPACT CONFIGURATIONS

Asymmetric Rod Impact Test For Elevated TemperaturesIn the early 1980s, Gust I81 used a reverse ballistics variation of the classicTaylor test to measure fractional changes in the length of various metallic rods atinitial temperatures up to about 100O0C. In this variation, the "rigid" plate islaunched into a stationary specimen rod preheated to the desired temperature.Concurrently, researchers at SRI International, stymied in their attempts to use thesymmetric rod impact technique to determine dynamic flow curves at elevatedtemperatures (because of the infeasibility of heating the moving specimen rod), wereinvestigating several alternatives. One, impacting a stationary heated rod with anidentical but unheated rod, proved unsatisfactory because the gross difference indeformability of the two rods created large uncertainties in the boundary conditionsat the impact interface.


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A second alternative was to combine the reverse tiallistics impact of a heated rodwith high-speed photographic measurements of the resulting deformation, to form the"asymmetric rod impact" or ASRI technique (Fig. lb). However, the boundarycondition uncertainties inherent in the ASRI technique needed to be examined.Computer simulations of the proposed ASRI test showed that the presence or absenceof friction had a profound effect on the rod deformation, whereas the use of idealrigid or realistic material properties for the impactor plate had a noticeable butminor effect.Identical 4340 specimen rods at room temperature were therefore impacted in twoexperiments: one an SRI test and the other an ASRI test at approximately half theimpact velocity (so as to attain similar stresses). Computer simulations of bothtests yielded identical flow curves to well within the experimental uncertainties,provided that realistic material properties were assigned to the impactor plate anda frictionless rod-plate interface condition was used. Thus it was concluded thatfrictional effects were insufficient to noticeably influence the rod deformationprofiles (future tests are planned to validate this conclusion for a wider range ofspecimen materials), and thus the ASRI technique could be used with confidence toobtain dynamic flow curves.I1 - EXPERIMENTAL TECHNIQUESRI Test at Ambient TemperatureA diagram of the experimental arrangement for the SRI test at ambient temperature isshown in Fig. 2. The specimen rods are identical right circular cylinders, 44.4 mmlong by 9.5 mm in diameter (these dimensions are arbitrary), whose ends are machinedflat and parallel to within about 0.01 mm. The impacting rod is mounted on thefront end of a projectile, which is accelerated by expanding helium in a 6.35-cm-diameter gas gun. The stationary rod is held in place by six ceramic fingersattached to a target mounting fixture, which in turn is affixed to the muzzle of thegun. Alignment of the two rods is critical to ensure that the impacting ends areparallel and coaxial. Misalignment by as little as 0.1 mm can have a noticeableeffect on the deformation profiles.

Hole for Glass

5 cm SIDE VIEW END VIEWFIGURE SYMMETRICRO D IMPACTTESTS T AMBIENT TEMPERATURE

The specimen rods are backlit by a variable-duration fast rise- and fall-time high-intensity xenon flash tube triggered just before impact. The silhouettes of thedeforming rods are recorded by a high-speed framing camera at framing rates betweenone-half and one million frames per second. Selected frames from an SRI test of4340 steel (Rc31) are shown in Fig. 3.


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After the deformation is complete (from 40 to 100 ps after impact, depending on thematerial), the specimen rods fly into a recovery pipe filled with rags and otherenergy-absorbing materials that minimize additional deformation. The pipe is narrowenough to prevent the projectile from entering and reimpacting the specimen. Therecovered rods are then sectioned along the axis and examined metallographically toascertain the extent of internal damage. The impact velocity must be low enough tosuppress the formation of tensile voids (which may occur at early times by thefocusing of the radial release waves on the rod axis) or shear bands (which mayoccur at later times as a result of large plastic deformation near the impactend). ~ 1 t h o u ~ h . amall amount of incipient damage can be tolerated, any significantamount of damage will affect the shape of the deforming rod profiles or cause rodfailure.ASRI Test at Elevated TemperatureThe ASRI technique for specimens at elevated temperatures differs only slightly fromthe SRI technique. The impactor is a 5-cm-wide, 1-cm-thick disk of ultrahighstrength maraging steel backed by a thicker aluminum projectile head. Thestationary specimen rod needs to be aligned parallel to the direction of impact, butthe co-axiality condition critical to the SRI test is not necessary here, since therod can impact anywhere near the middle of the disk.The specimen is heated before impact by three infrared line heaters arranged aroundthe rod (at a distance of 15 cm) so that radiation from the linear filaments isfocused by elliptical reflectors onto the rod. The temperature of the specimen rodis monitored by a Chromel-Alumel thermocouple attached to the nonimpacted end. Byuse of a variable 280-V, 100-A power.supply for the heaters, a temperature of 1000Ccan be attained in about 150 s. Thermal uniformity of the rod is quite good becauseof the relatively short thermal equilibrium times (a couple of seconds) for metallicrods of this diameter.Specimen rods from ASRI tests are usually recovered with negligible additionaldamage and with the impact interface very nearly perpendicular to the rod axis. Suchis not the case with specimens recovered from SRI tests, where the two rodsdecelerating together can re-impact, causing further deformations, and where slightmisalignments in co-axiality can skew the impact interface.111 - ANALYTICAL TECHNIQUESMeasurement of Rod Deformation ProfilesThe first step in the analysis is to digitize and plot the rod profiles forcomparison with computer simulations at various times during the deformation. ForSRI tests, the profiles are obtained exclusively from the framing camera records.For ASRI tests, however, in addition to the photographic records, we can measure,with a far greater accuracy, the recovered specimens and obtain the finaldeformation profile.For the framing camera records, errors may be caused by photographic aberrations andnonlinearities, target misalignments (SRI tests only), and parallax errors, butmostly by the fuzziness of the image. If we assume that the error band has aconstant width, M y , independent of axial position (Fig. 4), we can estimate themagnitude of the uncertainty in radial expansion AylAR, both for the photographicand the recovered rod measurements.The results, shown in the table in Fig. 4, show that the error in radial expansion,for a particular axial position, can vary from 2% for the sharpest photographs oflarge deformations (100% AR/R ) , to 25% for the poorest quality photographs ofsmaller deformations (20% A R / ~ . For the same two deformations, measurements ofthe recovered rod profiles woufd yield radial expansion uncertainties of 0.3% and1.5%, respectively.


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FIGURE 3 SILHOUETTES OF 4340 STEEL(Rc31) RODS DURING SYMMETRIClMPACT AT 456 m/s

(b) +1 IU (f ) +15IU -I5 0.5naQ

Times shown are approximate times fromimpact.

-\--:: 'lnitial Contour0 - I0 1 .O 2 O 3.0 4.0(c) +4m-6 AXIAL DISTANCE (cm)FIGURE 5 DEFORM ATION CONTOURS 2 5 ~ sFTER 4340(h) +30@ STEEL SYMMETRIC ROD IMPACTS AT 457 m/s(d l +7 paFIGURE 4 UNCERTAINTIES IN OBTAINING DIGITIZ ED ROD PROFILES

FramingCameraSilhouettes

RecoveredRodProfiles

Computer Simulations of Rod Impact TestsThe dynamic flow curve of a material is determined from a rod impact test bycomputationally simulating the experiment and varying the input flow curve until thecomputed profiles agree with those determined experimentally at various times duringthe deformation history. The computer code we have used for these simulations isthe recently developed C-HEMP /9/, a two-dimensional finite-difference code fortreating stress wave propagation, in either planar or axisymmetric flow, caused byimpacts or explosive detonations.

AY(mm)

0.1 - 0.25

0.015

The specimen rods (and the impactor, for ASRI test simulations) are divided into aseries of rectangular zones, or computational cells, each of which, in theaxisymmetric geometry appropriate to the rod impact test, represents an annulus ofrevolution about the rod axis. The corners, or nodes, of the cells are given anappropriate initial velocity. Then the subsequent node velocities and the resultingdeformations are determined for successive small time increments by solving theLagrangian equations of motion for a continuous medium.A standard Mie-Gruneisen formulation relates the pressure to the specific volume andinternal energy, and a rate-independent elastic-plastic model with work hardening is

AY-o

2-5%

0.3%

AY/AR forAR- 20%Ro

10-25%

1.5%

AR-= 50%0

4-1 0%

0.6%

A - 100%-R

2-5%

0.3%


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used to describe the plastic deformations in each cell. Bulk and shear moduli areobtained from Hugoniot data, if available, but computations have shown that thedeformation profiles are sensitive to variations in the flow parameters only, andnot the elastic moduli.The flow curve is inputted in terms of a flow stress (Y), equal to the yieldstrength in a uniaxial stress test, as a function of the equivalent plastic strain,which is defined as the square root of two-thirds the sum of the squares ofdifferences of the three principal strains. A quasi-static compressive or tensileflow curve is often used as the first trial flow curve (since there are few dynamiccurves to be found in the literature), and the flow curve is then modified insubsequent computations until the computed deformation profiles agree with theexperimental results to within the experimental error. This process may take fromtwo to more than twenty computational iterations.Considerations of Strain Rate and TemperatureComputer simulations have shown that the equivalent plastic strains (as defined inthe previous section) and strain rates vary as a function of time and of axial andradial position within the specimen rod. For positions near the impact interface,the average strain rate along the rod axis is two to three times higher than thatnear the edge. For positions along the rod axis, the average strain rate near theimpact interface is about four times higher than that one rod radius distant.It is thus important to note that the experimentally measured radial rod expansionat a particular axial position is not the result of a region of material undergoingdeformation at a specific strain rate, but rather the result of various regions ofmaterial deforming over a moderate range of strain rates. Therefore, the rod impacttechnique should not be viewed as a method for accurately determining the strainrate sensitivity of the flow curve within the range of strain rate observed in thetest (most of the deformation occurs between lo4 and 5 x 104/s), but rather as ameans of determining the average flow curve over that range.Furthermore, if a material's flow stress exhibits a very large strain ratesensitivity within the observed strain rate range, then no matter what flow curve wewould try in our rate-independent simulation, we could not match the experimentalprofiles throughout the deformation history, and in fact, we might not be able tomatch the profiles well at any time much after impact. So conversely, if we areable, by using a particular flow curve, to match the experimental profiles wellthroughout the deformation history, then theathe material exhibits no significantstrain rate sensitivity within the range noted above.The computer simulations have also shown that large temperature increases caused byplastic work are created in the highly deformed regions of the specimen rods. Thisis as expected for any high-strain-rate process, where the deformation is too rapidto allow temperature equilibration throughout the specimen. For the 4340 steel SRItest discussed previously, temperatures in the region near the impact interfaceincreased by as much as 430C during the deformation process.The rod impact test is thus an adiabatic, rather than an isothermal process, andthere is no way to separate the temperature effect on the flow curve (thermalsoftening) from the plastic strain effect (work hardening). This makes it difficultto compare the flow curve obtained from rod impact tests with those obtained at aspecific temperature from other tests. We do not consider this a seriouslimitation, however, because the flow curve we obtain is appropriate for a materialundergoing high strain and strain rate deformations, which are always accompanied bya large temperature increase.IV - ROD IMPACT TEST RESULTSResults are presented for some SRI and ASRI tests at ambient and elevated


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temperatures. Space limitations prevent comparisons with other data or detaileddiscussion of the metallurgical significance of these results.SRI Tests on 4340 Steel at Ambient TemperaturesAmbient temperature SRI tests at identical impact velocity (457 m/s) were made using4340 steel specimens of three initial hardnesses: Rb94, Rc31, and Rc39. The late-time profiles (approximately 28 ys after impact) for all three of these tests arecompared in Fig. 5. Although the three profiles do not precisely coincide, they alllie within the band of experimental uncertainty, M y .Computer simulations were performed, first using the Rb94 and Rc39 static flowcurves obtained in the literature /10,11/, and then varying the input flow curvesuntil the computed rod profiles matched the experimental data to within +9y. Fig. 6shows the various flow curves used in these calculations and compares theirresultant late-time profiles with the experimental rod profiles (an average from thethree tests). The static curves provide a very poor match to the data. Elastic-perfectly plastic curves at flow stresses (Y) of 13 and 14 kbar (Case 1 and 2,respectively) are significantly better. A flow curve that work hardens from Y = 11kbar at zero strain to Y = 13 kbar at a 0.2 strain and is perfectly plastic atfurther strains (Case 3) provides the desired match. To further substantiate thisresult, we compared the Case 3 simulated profiles at several intermediate times withthe corresponding experimental profiles. Results for the Rc31 case (Fig. 7 ) ,indicate good agreement throughout the deformation history.

t\=+a; I II + - xperimental 1Static (RB94)

Case 1 (13 kb)Case 2 (14 kb)........ Case 3 11-13 kb)

Initial Contour

AXI AL DISTANCE (crn)

IL 54 0 0.2 0.4 0.6 0.8 1.0

EQUI VALE NT PLASTIC STRAINFIGURE6 COMPARISON OF EXPERIMENTALPROFILE 2 8 ~ sFTER SYMMETRIC IMPACTOF 4340 STEEL RODS WITH COMPUTEDPROFILES, SING DIFFERENT FLO W CURVES

FIGURE 7 CALCULATED (SOLID INE) NDEXPERIMENTAL (DASHED INE) PROFILESAT INTERMEDIATE IMES AFTER IMPACTAT 457 mls OF 4340 STEEL (Rc31) OD


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Considering the large variation in the static flow data as a function of initialhardness, the insensitivity of the dynamic flow curve was at first surprising.However, hardness tests on the recovered rods indicated that the material from theR 94 and R 31 specimens hardened to nearly the Rc39 level at rather low strains(gelow 20%$. So, for most of the deformation history, the three materials behavedsimilarly.ASRI Tests on Zinc/Alumimum AlloySix ASRI tests were performed using Zn-22%A1 alloy at two grain sizes: fine-grained(FG) and coarse-grained (CG), with mean grain diameters of 0.6 and 3.3 ym,respectively. Tests on both FG and CG specimens were conducted at ambienttemperature, 150C, and 250C. Flow curves that provided an accurate match betweenthe final computational profiles and the recovered specimen rod profiles are shownin Fig. 8. Comparisons of computational profiles and framing camera profiles atearlier times in the deformation histories (as, for example, in Fig. 5) showedagreement within the larger experimental uncertainty. The dynamic flow curves seemto indicate that, for the CG specimens, work hardening dominates over thermalsoftening, whereas for the FG specimens, the reverse is true.

I I I I I I I I I / J ] I ,- 211-22 Al Alloy -CG- - FG = Fine Grained------ FG CG = Coarse Grained -.: -- 0c -

CG - 50c----

- -.I - - - - - - - -

-->--------- '.- -_A -._CG -'--,_FG, - 0

l Denotes Maximum Strain Level -Reached by C-HEMP SimulationI , I I I I I I I I I l I

A X I A L A X I A LDISTANCE (cm) DISTANCE (crn)(a ) 25 s After Impact (b ) 60 i s After Impact

1 .o6 0.5-U1

O -Q0.5

00P02 0.5

0 0.4 0.8 1.2 1.6 2.0 2.4 2.8E Q UI V A LE NT P LAS T IC S TRA I N FIGURE 9 COMPARISON OF CALCULATED ANDEXPERIMENTAL (FROM PHOTOGRAPHS) FG

FIGURE 8 FLOW CURVES OBTAINED Zn-22AI ALLOY ROD PROFILES AT TWO TIMESFROM ASRl TESTS OF Zn-22AI ALLOY DURING ASRl TESTS

-.

-

-

REFERENCESTaylor, G. I., Proc. Roy. Soc. A 194 (1948) 289-299.Whiffin, A. C., Proc. Roy. Soc.A-E1948) 200-232.Lee, E. H. and Tupper, S. J., J. Appl. Mech.Z(I954) 63-70.Hawkyard, J . B., Eaton, D. and Johnson, W., Intl. J . Mech. Sci. E(1968) 929-948.Wilkins, M. L., and Guinan, M. W., J. Appl. Phys.a(l973) 1200-1206.Frlich, D. C., Shockey, D. A., and Seaman, L., AIP Conf. Proc. 78, 2nd TopicalConf. on Shock Waves in Condensed Matter (1981) 402-406.Erlich, D. C., and Shockey, D. A., Proc. APS Topical Conf., Shock Waves inCondensed Matter (1583) 129-132.Gust, W. H., J. Appl. Phys. 53(5) (1982) 3566-3575.Seaman, , Cooper, T. and Erlich, D. C., "User's Manual for C-HEMP, a Two-Dimensional Wave Propagation Code," SRI International Final Report forBallistic Research Laboratory, Aberdeen Proving Ground, M) (1984).Metals Handbook, Amer. Soc. for Metals, 9th Edition (1978).Idarson, . R. and Nunes, J., ASM Trans. -53 (1960) 663-682.

-Measured Profile ..\-rom Photographs---C-HEMP 20c-.Simulated Profile

20% .\L ~ Ab

15Ooc..

250% ..T

250"~.

d.c. erlich and p. chartagnac- determination of dynamic flow curve of metals at ambient and elevated...

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