OFFICIAL Flit COPY AMMRC TR 82-48 I AD A /J.}~·t5

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ADIABATIC DEFORMATION AND

STRAIN LOCALIZATION

GREGORY B. OLSON, JOHN F. MESCAll, and MORRIS AZRIN

August 1982

Approved for publ ic release; distribution unlimited.

ARMY MATERIALS AND MECHANICS RESEARCH CENTER Watertown, Massachusetts 02172

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Adiaba t i c fl ow HEMP code Plugging Shear flow Compu teri zed s imulation Pene trat i on Ballis t i cs Nonuniform f low

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UNCLASSIFIED

Block No. 20

ABSTRACT

The s tra in loc a iizatio n phenomenon of "adiabatic shea.r'' i s ge nera lly

attributed to a plastic ins tability arising fr om a therma l so f t ening e f fe c t

during adiaba tic or near-adiabatic plastic deformation. High s train-rat e

adiabatic t o r s i on t e sts ind icate that the effective shea r stress- s train

(T- 'Y) r e l a tions for high-strength (rate -insensitive) s tee ls c an be

described by a simple expre ssion of the form:

T ~ T ( l + a y) exp (- By) 0

whe re To is a constant, ~and ~are dimensionless hardening and so ft ening

parameter s . The f l ow stress reaches a maximum at an instabili t y s train,

Yi = p-LQ-1. \v' i t h parameters de rived from the torsion tes ts, this r e l a­

tion has been c.:sed in computer simulations of the development of intens e

shear localization in a simple uniformly loaded body. Strain loca l iza t i on

has been s tudied unde r conditions of both quasistatic and dynami c defo r­

mation. Ap pl ica t ion to the s imulation of ballistic pene tration i s in

progre ss.

Experimental e vidence indicate s the existe nce of a pressure-d~penden t

s tra in soften i ng e ffect attributed to subcritical shear microc racks wh ich

con tributes to she a r instability in mild steels . This phenomenon nay a l s o

ope rate in high-strength steels, giving ri se to a pressure -dependent ~

parameter . Experiments are being designed to de t ermine the r e l a tive i m­portance of t ~ i s effe ct in the adiabatic de formation of high-stre ngt h

steels and its pos sible role in ballistic penetration.

APPROVED:

E. B. KULA Chief Metals Researc h Divis i on

Engineer

APPROVED:

Ac ting Chief Eng ineering Mechanics Di vi s ion

-··- ·- --·-------------------' UNCLASSIFIED

SECURITY CLASSIF1Co1\TION OF THIS Po1\GE(It'llen Data Er~tered)

INTRODUCTION.

BACKGROUND. .

ADIABATIC FLOW RELATIONS.

CONTENTS

COMPUTER SIMULATION OF SHEAR LOCALIZATION

APPLICATION TO BALLISTIC PENETRATION.

PRESSURE-DEPENDENT SHEAR INSTABILITY.

CONCLUSION ............. .

APPENDIX. ADIABATIC STRESS-STRAIN RELATIONS.

ACKNOWLEDGMENTS .

LITERATURE CITED.

Page

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INTRODUCTION

Since the classic work of Zener and Hollomon,! it has been well r ecognized that the temperature rise accompanying plastic deformation under conditions of restricted heat transfer can contribute a destabi liz ing strain-softening contribution to plastic flow behavior. The associated strain localization phenomenon of " adiabat i c shearu is known to play an important role in the dynamic plastic deformat ion encountered in such diverse areas as machining , metalworking, cryogenics, ballistic penetration, and ex­plosive f ragmentation. The conventional view is that the phenomenon can be treated as a continuum plastic instability, provided that the constitutive flow behavior is properly described. We will here examine appropriate constitutive relations for plastic flow under adiabatic conditions, and assess the use of these relations in computer codes allowing an extension from the familiar regime of quasistatic plastic flow to a treatment of strain localization during fully dynamic plastic deformation. With the ultimate objective of unde rs tanding and controlling the ballistic penetrat ion of high-strength steels, we will fo cus largely on the behavior of steels with emphasis on the condit ions for the ini t iation of flow loca lization.

BACKGROUND

The phenomenon of adiabatic she ar as it occurs in ballistic penetration 1s illus­trated in Figure 1.2 Figure la shows t he extensive plastic deformation that occurs when a hard steel projectile impacts a low-strength steel target. As the strength of the target is increased, eventually the l ocal i zed deformation mode of Figure lb occurs, in which plastic flow is concentrated in thin shear bands which appear white after metallo­graphic etching. The localized flow results in a "shear plugging" mode of target failure in which the material ahead of the projectile is ejected as one solid piece with relatively little attendant e ne rgy absorption . This tendency for f l ow localization at high strength levels is also important in the behavior of projectiles. A mixture of fracture and white band formation can be noted in the proj e ctile shown in Figure la.

Recent reviews of the sub ject of adiabatic deformation and f low localization are liste d in Table 1. The r ev i e ws of Ro gers3,4 and Bedford et al. ,5 give an exce llent overview of the general phenome non inc luding the microstructures resulting from local­ized flow . The continuum plasticity theory of ad iabatic flow localization is treated by Clifton,6 and a general survey of strain loca lization, inc luding ad iabatic shear, is given by Argon. 7 A concise treatment of the specific role of adiabatic shear in arma­ments and ballistics can be fo und i n the review of Samuels and Lamborn .8 Table 1 also lists experiment a l measurements relevant to the constitutive rela t ions for adiabatic plastic flow9- 15 which will be discussed later .

Much attention has been directed to the microstructures of the white-etching bands formed in h igh-stre ngth steels.3,8,16-18 The bands are general ly found to be composed of very fine-grained ferrite supersaturated with carbon.l6 As similar microstruc tures are deve loped during cyclic deformation of bearing steels and the wear of surfacesl9-21 where sub stan tial tempera ture rises are less likely, the rel~tive importance of tem­peratur e and high plastic strain in the deve lopment of these bands is not clear . It should be noted that these white- e tching bands ( "transformation bands") as distinct f r om simply bands of concentrated strain ("deformation bands")22 represent an advanced s tage of the localized flow process. Mec hani sms contributing to the development of the white-band microstructures are not necessarily relevant to the conditio ns for the "onset " of the plastic fl ow localizati on. For example, t he experimentally observed conditions for the onset of instability in high-strength stee ls t o be discussed later

l

Table 1. REVIEWS OF ADIABATIC DEFORMATION AND LOCALIZATION

Rogers 1979 (3,4) Bedford et al. 197a (5)

Clifton 1978 (6)

Argon 19 7 3 ( 7)

Samuels and Lamborn 1978 (8)

General phenomenology

Analysis of shear localization

General theory of stability and localization

Role in armaments and ballistics

Shear Stress-Strain Measurements - Steels

Culver 1973 (9) Costin et al. 1979 (10)

Lindholm and Hargreaves 1976 (11,12)

Walker and Shaw 1969 (13)

Luong 1977 (14, 15)

Adiabatic torsion, mild steel

Adiabatic torsion, high strength steel

Isothermal shear and compression, mild steel

Adiabatic shear and compression, mild steel

would be accompanied by a maximum temperature rise of 50°C. Such processes as martensite-austenite reversion,16-23 often invoked in reference to white-band forma­tion, are of little relevance to the initiation of localization at such low temperatur1 From a practical standpoint, it would seem that the most fruitful approach to the control of the adiabatic shear phenomenon would be to delay the onset of localization rather than to search for possible mechanisms of restabilization after intense local­ization has already occurred.

Continuum plasticity analyses of the onset of strain localization under adiabatic or near-adiabatic conditions generally ascribe the chief destabilizing influence to a strain softening term given by:

with T the shear flow stress, -y the plastic shear strain, and T the temperature. 24 Thi~ term, often referred to as "thermal softening," is a negative quantity due to the nega­tive temperature dependence ofT. For fully adiabatic conaitions, under which a fraction, £, of the work of plastic deformation, TdY, is not stored as structural defe< and therefore contributes to a temperature rise, the term becomes:

CiT CiT -~ ar aT (l)

2

where p and Cp are the density and spec ific heat . The propor tionality with T i s the principal reason why the therma l ef fect becomes more important in higher strength mate rials. If this term bec ome s large enough t o bring the ne t strain-hardening rate t o zero

d-r = 0 dy •

(2)

de formation in shear becomes unstable, 3nd localizat ion of f low will occur. Analytical treatments of the growth of flow perturbations using elaborate cons titutive models have indicated situations where flow can localize i n s hear while dT/dY i s sti l l sl i ghtly positive, but for the most part Eq. 2 represent s a reasonab ly useful criter ion for the onset of shear localization in the regime of quasistatic p las t ic f low.

The pe rturbation analyses s how tha t heat transfer f r om a deforming vo lume , through r eduction of oT/8Y, can exert a slab ilizing inf l uence on plastic deformation similar to the effect of strain-rate hardening in superplastic flow. Application of a one ­dimensional heat flow solution25 fo r a constant rate of heat input into a region of characteristic d imens ion 1, a s di s cussed by Culve r,9,26 prov ides a useful basi s for assessing the importance of heat flow during plas tic defo r mat ion at h igh strain rates. The temperature profile at time t i s controlled by the parame t er 12 / Kt, wher e K i s the the rmal diffu s ivity. A r ough boundary between the regimes o f " i sothermal" and " ad ia­batic" behavior ~s

~ 1. (3)

The average t empe rature within the region de fined by 1 wil l be 10% and 90% of the fully adiabatic l imit for values o f 12/Kt of ~10~2 and ~102. At .a cons tant strain rate Y , time can be expressed as t ~ Y/Y Use of an appropriate va lue of K for steels indi­cates that for mos t of the conditions for which "adiabatic shear banding" is observed , the deformation preceding locali zation is very nearly fully adiabatic, and heat trans­fer becomes important only after intense localization has occur r e d. This i s particu­larly so in the case of ballistic penetration. One can in f act u se the assumption that restricted heat flow is necessar y to the deve l opment o f whi te-e t ching s hear bands as a means to ca lcula te a l owe r limit to band thickness. For local strain ra tes of 10S to 106s-1 and local strains of 1 to 10, adopting Eq. 3 as a cri terion for signifi­cant heat trans fer gives a band dimension 1 of the order o f 10 ~m in agreement with the white band thicknesses observed in steels.22,23 ,27-29

The analyt ical treatments of strain loca l ization furth er indicate that the most important stabil i zing influence is the intrinsic stru c tural s t r a in hardening r ate (as determined for e xample from the iso thermal flow behavior).30 This i s perhaps the parameter most amenable to mani pu la tion in a t tempt ing to delay the adiabatic insta­b i lity. Mo s t analyses conclude t hat strain-rat e hardening is al so a stabil i zing in­fluence,31 although Clifton6 concludes the o ppos ite ; the physical basis of this result is not obvious. For high strength stee l s , however, strain-rate sensitivity ~s small and its influence can be reasonably neg l e cted.

Estimates of critical stra i no for adiaba t ic instabi l ity have been made based on constitutive r e lations (largely empirical) deve loped origina lly for isotherma l de fol~a­t ion, and compared with result s of high st ra i n-r ate t orsion t es ts .9-12 Conclusions regarding agr eement between theory and experiment are mixed .

3

The flow localization analyses discussed thus far have been based on quasistatic deformation theory. To extend the localization concepts into the regime of dynamic plastic deformation, as is appropriate for problems like ballistic penetration, the concept of "wave trapping" has been proposed.32 In essence, this concept is based on the velocity of a plastic shear wave, v~, expressed by:

VS =~1_ dT • :p p dy (4)

When the net strain hardening rate reaches zero (as in Eq. 2), the plastic wave should cease to propagate, and deformation should localize. This concept will be commented on further when results of dynamic computer code calculations are discussed.

ADIABATIC FLOW RELATIONS

While the temperature T is constant during an isothermal process, the entropy S is the thermodynamic state function which is constant under adiabatic conditions. From the viewpoint of thermodynamics and statistical mechanics, temperature and entropy are equally fundamental quantities, and an equation of state can be formulated with either as an independent variable. Hence, instead of attempting to apply empirical constitutive relations based on isothermal experiments to the case of adiabatic deforma tion, it is equally valid to formulate new empirical constitutive relations for adiabatic (isentropic) plastic flow derived directly from experiments performed under adiabatic conditions. One should note that since the temperature 1s a single-valued function of the state variables under adiabatic conditions, it is no more necessary to determine the temperature during adiabatic deformation than it is to determine the entropy during isothermal deformation, for purposes of describing constitutive flow behavior.

An area where an adiabatic formulation for plastic flow should be particularly use ful is in computer codes designed to treat dynamic deformation involving plastic wave propagation. Constitutive relations so far employed in these codes have generally in­volved either ideal plastic or isothermal work hardening behavior.2 Even in conditions of highly localized flow, the assumption of adiabatic conditions should be a significan improvement over the isothermal assumption, particularly when deformation times are in the microsecond range.

Based on the usual physical assumptions applied to adia~atic plastic deformation, possible anticipated forms forT- Yrelations under constant Y adiabatic conditions are derived in the Appendix. Of these possibilities, an expression which is found to fit the results of adiabatic deformation experiments particularly well is given by:

T = To(l + uy) exp (-By). (5)

Here To 1s a constant representing the shear yield stress, a 1s a dimensionless hardening parameter, and ~ is a dimensionless softening parameter which can be inter­preted in terms of the thermal effect represented in Equation l. In order to generali2 to different stress states, T and Y here represent "effective" or "equivalent" shear stress and shear strain based on a Von Mises or "Jz" flow criterion.

4

The T -Ybehavior given by Eq. 5 is depicted schematically in Figure 2. The true stress is seen to reach a maximum at a shear instability strain, Yi, which is simply determined by the a and {3 parameters:

-1 -1 yi = S -a . (6)

Reliable direct measurements of adiabatic plastic flow behavior can be obtained from torsion and simple shear tests in a relatively narrow range of experimental conditions defined by material properties. The strain-rate must be sufficiently high that condi­tions are reasonably adiabatic, yet sufficiently low that deformation is not dominated by plastic wave propagation, such that stress and strain can no longer be simply inferred from load-displacement information. The boundary between isothermal and adiabatic regimes is expressed in Eq. 3. An approximate boundary between the regimes of 11quasistatic11 and 11dynamic 11 plastic flow in shear deformation is given by the con­dition that the imposed boundary velocity vo produce an initial elastic stress pulse equal to the material flow stress r 0 . This is expressed by

To vo == pvs

e (7)

where v~ is the elastic shear wave velocity given by v~ ='VG/p with G the elastic shear modulus. From Eq. 3 and 7 the range of nominal strain rates corresponding to the regimE of 11quasistatic adiabatic flow" is given by

K

I7 < y < L'VPG (8)

Provided instrumental factors such as "ringing" and inertial loading effects are properl controlled, tests run on steel specimens with convenient L dimensions can fall comfort­ably within this range at strain rates of 102 to 103s-l. Such experiments of course represent a compromise which is neither fully adiabatic nor genuinely static, but from a practical standpoint, the thermal conditions are as close to adiabatic as a convention "isothermal11 test is to isothermal, and the character of the plastic deformation is essentially that described by the static plasticity viewpoint.

Experimental arliabatic T -Y curves for steels obtained from thin-walled torsion specimens at a strain rate of 102s-l are shown in Figure 3. The solid curve and open point are from the data of Culver9 for mild steel, the open point estimated from the loa and local strain (from scribe marks) at fracture. Data points from Lindholm and Hargreavesll,l2 for quench-and-tempered HY-TUF steel in both air-melted (AM) and vacuum-arc-remelted (VAR) conditions are also shown. Results very similar to those of t HY-TUF steels have been obtained for 4340 steel tempered to hardness of HRC 45.33

The dotted curves in Figure 3 represent the fit of Eq. 5 using the parameters given in Table 2. Except for the open point for the mild steel estimated from local strain measurement, the data presented are obtained directly from load-displacement measurement as such, the ?Cints beyond the stress maximum are unreliable, since deformation becomes localized, and strain can no longer be directly inferred from the measured displacement. Conditions during localized flow will also be less adiabatic due to the smaller characte istic distance 1.* The deformation preceding the stress maximum, however, is found

*At constant imposed boundary velocity, the L 2 dependence of the thermal behavior is partially compensated by an 1·1 dependence of local strain rate.

5

to be reasonably homogenous, and conditions are fai rly close to adiabatic. The simple relation of Eq. 5 is found to fit the da ta quite well.

Table 2. PARAMETERS DERIVED FROM ADIABATIC TORSION DATA

Mild Steel HY-TUF (VAR) HY-TUF (AM)

'O 31.8 ksi 2

132 ksi 133 ksi (219 MN/m ) (910 MN/m2) (917 MN/m2 )

a 2.56 2 . 36 7.85

8 0.667 1.61 4. 18 -yi 1.11 0.20 0 . 112

T 58.3 ksi 2 141 ksi 157 ksi max (402 MN/m ) (972 MN/m2) (1082 MN/m2)

The adiabatic T- Y data of Figure 3 verify that a shear instability occurs at fairl low strains in the h igh s tre ngth stee l s, consistent with the expec ted gr eater thermal effec t. Having obtained T- Y relations at a strain-ra te of 102s-l, we can now model the deve lopment of shear localization by applying these rel a tions in computer code calculat We will adopt the assumption that these same rela tions apply at higher str ain rates. F the high- s trength steels which are known to be fairly strain-rate insensitive, this app mation seems particularly appropria te.

COMPUTER SIMULATIO N OF SHEAR LOCALIZATION

Computer simulations of adiaba tic plastic deformation have been run using the HEMP code deve loped by Wilkins34 fo r treating dynamic deformation. The code couples conserv tion l aws with an appropriate equation- of-state for dynamic as well as static high pressure conditions, employing a finite-di fference formul at ion, and integrating the equ tions of motion step-by- ste p in time. Problems can be treated which include two spat i a dimensions - plane s train or those involving rota tional symmetry. Virtual l y any e l asti plastic const itutive law can be employed.

Input to the code consists of specif i cation of the problem geometry, a ppropriate i nitial velocities or applied stress fie lds, and the material dynamic f l ow properties. Output cons i sts of a detai l ed space- time hi story of all important physica l quantities such as stress, strai n, displacement, and veloc ity. Thu s it can be a valuable tool foi

providing a dynamic "whole fie ld" analysis r equired to decipher the sequence of events occurring in complex dynamic problems. Numerous comparison s of HEMP code predic tions c exper imental results ind icate excellent ag r eement when materia l properties can be ade­quate l y specified . Further detai l s of the compu tational procedures can be found in Reference 2 .

To treat the development of shear localization, the deformation of the s imple r ec­tangu l ar body depicted in Figure 4 wa s simulated, u sing the plastic f l ow r e lation of Ec with parame t ers s imilar to those of the HY- TUF stee l in Figure 3. The bottom surface • he ld stationary, and a constan t ve l ocity was applied to the top, corresponding to a

Jnstan t i mposed nomi na l strain rate. The developmen t of shear loca lization is illus­Lrated in subsequent figures representing strain profiles along the midplane AA / .

6

Figure 5 shows the development nf the strain profiles at differ ent times for an im­

posed boundary velocity of 1 x 103 cm/s . This ve l oc ity r e presents a lowe r limit for

convenient calcula tion times us ing the HEMP code, and should correspond to condi t ions

of effectively quasistatic plastic deformation. The dashed line de pic ts the ins tability

strain , Yi , and the numbers next to each strain profile represent time in microseconds. It is seen that deformation is initially fairly uniform, but once the instability strain

is e xceeded deformation becomes local ized in accordance wi th the predic tion of contin­

uum plasticity theory.

Two shear band s are fou nd to nuclea t e ; each is only one zone in thicknes s. The

actual positions of the she ar bands are in agreement with the slip-line-field analysis

of Green3 5 for this problem . Such agreement i s appropriate, s ince slip-line- f ield

theory predicts the flow pattern for a material wi th no work-harden ing capacity; this is identical t o the condition which preva ils a t the instability strain . At later times ,

deformation is found to concentrate in t he band near the lowe r stat ionary surface (A').

As shown in Figure 6, very nearly identical deformation behavior i s found fo r an

imposed velocity of 3 x 103 cm/s , just below the threshold of dynami c behavior expressed

by Equation 7 .

The deformat ion behav ior for a velocity of 4 x 103 cm/s, jus t beyond this dynamic thresho l d, is illustrated in Figure 7. The behavior is very s i mi lar to t hat of the lowe1

veloci t i e s, with t he exception that the shear band near the upper (moving) surface is now the one which grows at longe r times, and the band near t he lower surface appears to

be slightly more diffuse. This is i llu s trated more clearly by the behavior of the com­

plete grid pattern with time as shown in Figure 8 .

The influe nce of imposed s train ra t e on the developmen t of flow localization at these veloc itie s i s depicted in Figur e 9, which shows t he maximum s tra i n in the AA' sect ion as a function of imposed bounda r y d isp l acement, vt. As t he imposed veloci t y 1s increased, the deve lopment of localization f or strains beyond the i nstability s train i s

delaye d with r espec t to bound ary displacement. The inf luence of the zone size employed in the HEMP code s imulations was examine d by r unning the lowest veloci t y problem with twice the zone s ize . The overal l de formation pattern was qua litative l y the same, but

as Figure 9 indicat es, the in t e nsificat i on of s tra in wi t h i n the shear band was s ignifi­

can t l y delayed. This effect may be par tly be cause the s train i n a zone resulting from a given r e lative d isplacement across the zone wi ll be inve r sely proportional t o the

zone si ze . However, the ob se rved dif fere nce in strain incr ements during localization is substantial ly grea ter than the zone s i ze ratio . These effec ts sugges t tha t, while

the HEMP code r esults are in excellent agr eement with the qua l i tative behavior expected

in the regime of quasistatic plastic deformation, detai l s of the l ocali zation proce ss,

such as the time scale and intensity of the localization, may be significantly inf lu­enced by the finite zone s i ze employed in the computer code . This cou ld potentially lead to difficulties in the simula tion of some dynamic problems.

Extending the simula t ion well in to the regime of dynamic plast ic deformation, the

strain profiles along AA' fo r an imposed velocity o f 3 x 104 cm/s are shown in F i gure 10

The behavior is radically di fferent f r om that o f Figures 5-7. Rather than a period of

relatively uniform deformat i on fol lowed by localiza tion , the e ffect of the plast ic instability i s s upe r i mposed on the nonunifo rm de formation associa t ed with dynamic flow .

It appear s that strains gr ea t er tha n t he instabi lity strain propaga t e i n a s far as the position where the shear band forms i n t he quasis tatic case (again correspond i ng to the

slip-line-field so lution); there is the n intens e locali zat i on in the first zone a t the surface, while, s imultaneously, strains below the instabil ity strain continue to propaga t e

7

The role of the plastic instability in establishing this deformation pattern is best seen by comparing this result with that of the identical problem run with monotonic work hardening behavior.* This is shown in Figure 11 and illustrates the basic non­uniformity of the dynamic plastic deformation. Note that all strains continue to propagate within the material. Comparing strain profiles at different times, the local plastic strain rate can be calculated. This is plotted as a function of position along AA' at a time of 10 ~s for the results of both the monotonic hardening and adiabatic stress-strain relations in Figure 12. The influence of the adiabatic plastic instability is quite clear. Whereas the local strain rate varies smoothly between 104 and l05s-l in the monotonic hardening case, the shear localization resulting from the adiabatic stress-strain relation causes the local strain rate to approach ro6s-l in the first zone. Adjacent to this zone is a nondeforming "dead" region, followed by ~ region in which strains below the instability strain propagate in a manner very similar to the monotonic hardening case. A comparison of the complete grid patterns at 10 ~s fo the monotonic hardening and adiabatic behavior is shown in Figure 13, emphasizing the intense localization associated with the plastic instability in the adiabatic case.

The observed dynamic plastic deformation behavior is in qualitative agreement with the notion of "plastic wave trapping" mentioned earlier. The position of contours of constant strain, AY(Y), is plotted versus time for the adiabatic problem in Figure 14. The contour for a strain of 1/2 Yi propagates at a fairly constant velocity. This velocity corresponds approximately to the expected velocity of a plastic shear wave; however, lower strain contours propagate much faster, and there is evidence that other types of waves contribute to the deformation through "end effects" associated with the particular geometry chosen. The strain contours of Yi and 2Yi do propagate a certain amount, but after 5 ~s, their velocity is seen to reach zero in accordance with the trapping concept. While the overall behavior is more complex than the simple plane wav€ description, and there is some propagation of strains above Yi, the development of inter localization and an adjacent nondeforming region does appear to be associated with the instability strain Yi, where dT/dY reaches zero.

The observed dependence of the adiabatic deformation behavior on imposed velocity i summarized in Figure 15, which depicts the complete grid patterns at comparable imposed displacements of the upper surface. At the lowest velocities, two shear bands nucleate, but the lower band grows. For an intermediate velocity at the threshold of dynamic flow, two bands nucleate, but the lower band is more diffuse, and the upper band eventu­ally grows. At the highest velocities there is intense locali zation in one band at the upper surface.

For the case of a simple shear deformation, then, the use of the empirical adiabatJ flow relation in the HEMP code allows us to simulate shear localization in agreement wi1 expected behavior under quasistatic conditions, and to examine the manner in which dynar flow conditions modify this behavior. It now becomes of interest to apply this approacl to more complex problems.

APPLICATION TO BALLISTIC PENETRATION

Some preliminary calculations have been run applying the HEMP code with adiabatic flow relations to the impact of 1.0-cm-diamcter steel projectiles against 1.25-cm-thick steel plates. Using the same high-strength steel flow parameters for the projectile as used in the simple shear simulations, and using the mild steel behavior of Figure 3

*Work hardening parameters appropriate to the isothermal deformation of high strength steels were used, keeping initial yield stress constant.

8

for the target, the deformation pattern obtained at a stage of partial penetration is shown in Figure 16. Except for details of projectile fracture which are not treated in the model, the overall behavior is in reasonable agreement with that depicted in Figure Due to the high instability strain in the mild steel, shear banding in the target is not expected.

If the properties of the target are made the same as the projectile, the behavior d picted in Figure 17 is found. While there is no evidence of shear banding in the target there is severe flow localization in the projectile. Such extensive deformation of the projectile is not entirely unexpected, since at equal hardness the target has a geometri advantage over the projectile.

In an effort to simulate shear plugging of the target, the complication of projec­tile deformation was removed from the 'problem by using an extreme flow stress for the projectile. This lead to the deformation pattern depicted in Figure 18. Although these conditions would be expected in practice to lead to the plugging behavior of Figure lb, the simulated projectile is found to burrow through the target by what appears to be a "hydrodynamic flow" mode of target deformation. While each of these simulations allowed frictionless sliding at the target-projectile interface, the addition of complete surface welding in the latter problem did not substantially alter the deformation patter nor did the use of monotonic work hardening behavior for the target material, although the actual stress levels were influenced. It thus appears that the behavior of the simu lation is essentially that of a plastically stable material. Although the instability strain is exceeded, and there is strain softening, the localization of flow in the form of shear bands is suppressed, and an alternate mode of plastic flow ensues.

The velocity and zone-size dependence of the localization process observed in the simple shear simulations implies that the development of shear bands in the ballistic penetration simulation might be delayed by the finite zones employed by the HEMP code. The role of zone size warrants further investigation, but the velocities involved in the ballistic penetration simulations are not greatly different from that of the fully dynamic simple shear simulation in which fairly intense flow localization developed in only a few microseconds.

It is important to note that the stress states encountered in ballistic penetration are radically different from that of the simple shear, involving substantial hydrostatic stresses. The simulations of the high-strength target penetration indicate a compres­sive hydrostatic component in the region ahead of the projectile of the order of 50 kbar (750 ksi) during gross plastic deformation. At the same time, there is a highly deformed region of the target several zones wide near the projectile corners in which a tensile hydrostatic component of -10 kbar (150 ksi) is maintained; it seems very likely that local fracture would occur in this region with an attendant significant modificatio of the pattern of plastic flow. These factors, together with the apparent inadequacy of the simple shear descripcion in simulating ballistic penetration by plugging, raise the interesting question of the possible interrelationships of pressure, fracture, and shear instability.

PRESSURE-DEPENDENT SHEAR INSTABILITY

Of particular concern in the modeling of the high-strain plastic flow behavior of steels are experimental observations indicating that isothermal flow behavior is also describable by the empirical relation developed for adiabatic flow (Eq . 5), and that the

9

instability strain Yi is pressure dependent. Figure 19 represents the results of Walker and Shawl3 from plane-strain linear shear experiments in which a constant uniaxial com­pressive load is superimposed normal to the shear plane. The figure shows effective shear stress-strain curves at different normal stresses for a cold-worked O.IOC mild steel under isothermal conditions. A shear instability was observed at the stress maxi­mum. As Figure 19 shows, the instability strain increases with compressive stress. Walker and Shaw interpret this result in terms of a contribution to high strain plastic flow from the propagation and rewelding of subcritical shear microcracks which introduce a pressure-dependent strain-softening effect. Bridgman36 obtained similar results in combined torsion and compression tests on steels, and reported observing shear cracks which open and close during deformation. The pressure-dependent frictional sliding across shear cracks is known to be an important plastic flow mechanism in brittle mate­rials under high pressure, and the development of shear localizaion for such materials has been treated quantitatively by Rudnicki and Rice.37 The Walker and Shaw results for mild steels were verified in similar experiments by Luong,l4,15 which included a quan­tita-tive scanning electron microscopy ( SEM) study of the development of voids and microcracks during deformation. The defects were observed before the stress maximum an~ were found to increase in number with further straining. Whereas Walker and Shaw suggeE that the strain-softening effect associated with microcrack formation is due to reduced effective cross-sectional area, Luong concludes that this geometric effect can account for only 10% of the observed stress drop, and suggests that local enhancement of slip around voids may be a more important softening contribution. One might also consider tr kinetics of crack growth itself as a deformation mechanism with associated dynamic softening behavior analogous to the "transformation plasticity" effects encountered in strain-induced transformations and mechanical twinning.38,39

Whatever the actual mechani sm, it is clear from the experimental results depicted 1 Figure 19 that a pressure-dependent shear ins tability in s tee ls exists. Analysis of thE Walke r and Shaw data indicates that the observed behavior can be reasonably well rep­resented by Eq. 5 if the~ softening parameter is made a linear function of pressure. Rather than a thermal softening effect, the softening is regarded here as a pressure dependent 11microcrack" so ftening, f3C ( p) expres sed by

(9)

with ~Oc and k constants. The associated behavior of {3c and Yi with pressure P, and the form of the T-y curves for different pressures , are represented schematically in Figure 20. Beyond a critical pressure P* there is no s oftening effect, and strain­hardening is monotonic.

If the pressure-dependent strain-softening effect occurs under isothermal condi­tions it can also be expected during adiabatic deformation. This has been verified by Luongl4,15 by extending the shear+ compression tests on mild steels to high-strain rates. Flow stresses were higher due to the rate sensitivity of the mild steels, and the shear instability occurred at lower strains , still a func tion of compressive stress . The simplest model of pre s sure-dependent behavior under adiabatic conditions ~s to assume that a fixed thermal softening contribution ~th and the pressure-dependent Lerm {3 C: (p) are additive:

(10)

10

This gives the behavior represented schematically in Figure 21. Beyond the critical pressure P* where ~c ~ 0, ~ becomes ~th and the instability strain reaches the constant value y~h associated with the thermal softening effect alone. This gives the family ofT- Y 2urves de pic ted in Figure 2lc, in which the curve for pressures above P>'< shows the theoretical behavior for the thermal instability in the absence of the pressure­dependent softening contribution.

The flow behavior predicted by Eqs. 5, 9, and 10 and represented in Figure 21 pro­vides us with a model for pressure-dependent adiabatic plastic deformation which could be applied to the computer simulation of dynamic deformation problems. While values of the'parameters can be estimated from the experiments on mild steels, unfortunately no appropriate experimental information is currently available for the high-strength steels for which shear instability is of greatest interest. In order to obtain this information, an instrumented pendulum-type impact machine is being modified at AMMRC tc allow testing of the double-shear specimen illustrated schematically in Figure 22. ThE central portion of the specimen is struck by an instrumented tup at sufficient velocitJ to impose adiabatic strain rates of 102 to ro3s-l while a constant load Pn is maintainE normal to the plane of shear. Should the high strength steels show the same pressure­dependent shear instability behavior found in the mild steels, a better understanding of the mechanisms underlying pressure-dependent softening will be imperative to an understanding of the phenomenon of adiabatic shear.

CONCLUSION

While all the factors underlying the shear instability observed during the adiabal deformation of high strength steels are not well understood, the use of empirical adia· batic flow relations derived from torsion test results has allowed succes sful computer simulation of strain localization in a simply loaded body. The results are in excellet agreement with expected behavior under quasistatic deformation conditions and have al sc allowed an examination of the manner in which dynamic deformation can modify the develc ment of flow localization. While the use of this simple flow relation in preliminary computer calculations for the more complex problem of ballistic penetration has not successfully simulated shear plugging behavior, some available experimental results in· dicate that incorporation of pressure-dependent softening effects may be necessary to correctly model the adiabatic flow behavior of steels under complex loading condi­tions. If further experiments verify that these pressure-dependent effects operate in the high strength steels, this will indicate that an understanding of the role of voids and microcracks in the high strain deformation of steels is essential to an understanding of the adiabatic shear phenomenon. From the viewpoint of a metal­lurgist, this might be a desirable c ircumstance. Rather than the heat capacity, temperature dependence of flow stress, and strain hardening capacity as the only important variables, an essential role of these fracture-related processes would mean that as pects of microstructure more amenable to metallurgical influence could have a decisive influence on the strain loc a lization process.

1 ]

Figure 1. Penetration of 0.22-inch (0.56 em) 4340 steel plates by 0.22-inch-diameter flat-ended steel projectiles. a) H RC 15 target hardness, v = 8.1 X 1 o4 cm/s; b) H RC 52 target hardness, v = 7.3 x 104 cm/s. (2)

Figure 2. Schematic adiabatic stress-strain curve.

12

y

200.---------------------------------~

~ 00 - l ....

50

HY-TUF

.x··x·····~VAR

Mild Steel

... ... ··-... , .. _ ..... .... ... .....

1200

800

400

0 0~----------~~----------~~--------~~ 0 1.0 2.0 3.0

y

Figure 3. Fit of Eq. 5 to adiabatic torsion test results for mild steel and high-strength HY-TU F steel.

v

A

T

1-- .. --··--··- 3 em

Figure 4. Grid pattern of rectangular body deformed in simple shear simulations.

13

N E z :2:

1.4

1.2

1.0

v • l x to3 cmls 250 0.8 1>--

0.6

A A'

Figure 5. Strain profiles along AA' f or v "' 1 x 103 cm/ s.

Time expressed in microseconds.

1.4

1.2

1.0

0.8 V • 3 x Io3 cm/s y

0.6

0.4

A A'

Figure 6. Strain profiles along AA' for v = 3 x 1 Q3 cm/s.

Time expressed in microseconds.

14

1>--

A

v , 4 x 103 cmls

~ . . . . . . . . A'

Figure 7. Strain profiles along AA' for v ~ 4 x 103 cm/s.

a)

b)

cl

Time expressed in microseconds.

t = 50

t = 70

t = 100

Figure 8. Grid pattern development with time (in microseconds), V ~ 4 X 1 Q3 cm/s.

15

X

"' E 1>--

1>-.

V} • l X 10J em/S v2 • 3 x Io3 emls VJ • 4 x 103 cmls

vt, em

Figure 9. Maximum strain in AA' section versus imposed

boundary d isplacement, vt.

(3.51)

1.2 v • 3 x lo4 em/ s

1.0

0.8

A A'

Figure 10. Strain profi les along AA' for v = 3 x 1o4 cm/s.

Time expressed in microseconds.

16

1>-.

...... ' ...,

1.4

1.2

1.0

0.8

0.6

A

A

v • 3 x to4 cm/s Monotonic Hardening

v • 3 x 104 cm/s t = 10 }J.S

/Monotonic Hardening

17

A'

A'

Figure 11. Strain profiles along AA' for v = 3 x 104 cm/s with monotonic work hardening behavior. Time ex­pressed in microseconds.

Figure 12. Local strain rate along AA' at t = 1 0 1J.S for v = 3 x 1 o4 cm/s comparing monotonic hardening and adiabatic flow behavior.

al

b)

al

b)

C)

Figure 13. Comparison of complete grid

patterns at t = 10 J1.S for v "'3 x 104 cm/s.

a) monotonic hardening; b) adiabatic behavior.

v • l x lo3 cmls

v • 4 x lo3 cm/s

v • 3 x 104 cmls

Figure 15. Effect of imposed boundary velocity on

deformation pattern at comparable boundary dis­

placements.

18

E u

j)::. ;;:: <l

0.6

0.4

0.2

10 !, )J-S

Figure 14. Position of constant strain contours

with time for adiabatic flow behavior at

v = 3 x 1o4 cm/s.

Figure 16. Simulation of ballistic penetration

of mild steel plate by flat -ended high-strength

steel projectile using adiabatic flow relations.

Projectile velocity 7.5 x 1o4 cm/s, t = 20 J.lS .

Figure 17. Simulation of impact of high­strength steel projectile on high-strength steel plate, projectile velocity 1.0 X 1 Q5 cm/s, t = 35 IJ.S.

~ ~

m'\1:~

~'IJiitiill ~ ~ N

Figure 18. Simulation of ballistic penetration

of high-strength steel plate by ultra-high strength steel projectile. Projectile velocity 1.0 X 1 Q5 cm/s, t = 12 IJ.S.

90r---------------------------------------------------,

80

I ~

~ 70 .., ... i/)

... ro .., ~60

41.9 ksi 1288.9 MN/m2)

2 3 4 5 6 7

Shear Strai n, Y

Figure 19. Effective shear stress-strain curves at indicated constant

compressive stresses, mild steel.13

19

"' E z ==

400

300

B

al

C)

p• p

20

-th -y Y;

Figure 22. Configuration of adiabatic

double shear + compression test to be

applied t o high-strength steels.

APPENDIX. ADIABATIC STRESS-STRAIN RELATIONS

The thermal softening effect represented by Eq . 1 can be expressed as :

ar a:r -= - 13 T

()y ar

with {3 given by

f ()T

- cat· p p

Taking B as a cons tant, the form of the adiabatic T - y curve at depend on the form of the struc tural strain hardening behavior. employed t o de s cribe isothermal strain hardening behavior is the harde ning r ela tion:

- -n T = Ky

(A-I)

(A-2)

constant y will A form commonly simple power law

(A-3)

with K and n constants. This harde n i ng be havior can be expressed ~n diffe r ential form as:

dT -n-1 nKy

or, by subs titution of Equation A-3 ,

T n-.

y

(A-4)

(A-5)

While Eq. A-5 i s perhaps l e ss physica lly me aningful than Eq . A-4 as a basic harden­ing law , it is mathemati c3lly mor e convenient; adopting Eq. A-5 and adding the thermal s oft ening term of Eq. A-1 yields a simple separable di ffere nt ia l equation f or adiabatic flow:

T • (A-6)

Integration y ields the relation

- -n -T = Ky exp (- 13Y)• (A-7)

21

Similarly, adopting other simple forms for the structural hardening behavior, and ex­pressing the hardening rate as a function of stress, leads to the simple relations given in Table A-1. Some properties of these relations are also given in the table. Expressing the equivalent uniaxial tensile stress and strain as CF = V3r and E = Y I VJ, the associated tensile necking strain (n is also included.

Table A-1. ADIABATIC STRESS-STRAIN RELATIONS

-n exp(-By) K(y+y )n exp(-BY) - n

exp(-BY) Stress-strain relation: 1 .. Ky T 1 1 (Hay) 0 0

Differential form: d'T (~-B)

- dr ( n ) - d1 _ ~ na ~-1 dy "'y+yo -B T dy dy - Ho::Y -e

1 ,

Yield stress: - n

'y Ky T "' 1 0 y 0

Tensile necking strain: n n Yo n 1 £ .. {36+1 £ "'V3s+l- {j £

)l!e+l ~ n n n

Shear instability strain: n n n -1 yi B yi "'B -yo yi =.:s-a

Maximum flow stress: 1 K(~e)n K(~e) nexp ~:Yo) - (ina) n (B) 1 T 1 o Be exp\a m m m

Comparison with experimental results as in Figure 3 suggests that the third relation in Table A-1, with n = 1, is adequate for describing the behavior of high strength stee ls. This gives the relation of Eq. 5. Ther0 ,a , and~ parameters can be determined from the stress maximum point Tm (Yi) and one other point. Using the yield point, the ratio r = ~/a can be obtained from

T

ln ~ + 1 = r - lnr. (A-8)

To

This is most easily determined from a plot of the function x-lnx versus x, as g~ven ~n Figure A-1. From this r value, ~ and a are simply obtained by the relations

and

1-r s =-

yi

S/r.

(A-9)

(A-10)

22

X c: I X

X

Figure A-1 . Plot of x-1 nx versus x for fitting of Equation 5.

If the yield point is not well defined, another flow stress point Tl(yl) can be used through the relation

with

T

ln ~+ 1 = n-lnn Tl

n -yl

yi r = ------------

1 yl

and a and ~are again determined from r and Yi through Equations A-9 and A-10 .

23

(A-ll)

(A-12)

ACKNOWLEDGMENTS

The authors are grateful to Ms. Anna M. Hansen for her assistance in runn~ng the computer simulations. Helpful discussion with Professor F. A. McClintock of M.l.T., particularly regarding slip-line-field solutions, is also appreciated. This work was performed at the Army Materials and Mechanics Research Center (AMMRC) as part of an ongoing program on adiabatic deformation and ballistic penetration.

24

LITERATURE CITED

1. ZENER, C., and HOLLOMON, J. H. f:jji•ct of Strain Rate Upon Plastic F7ow of Srec/. J. Appl. Phys., v. 15. 1944, P- 22-32. 2. MESCALL, J. , and PAP!RNO, R. Spallation in Cylindcr-l'latc Impact. Lxp. Mech., v. 14, no. 7, 1974. p. 257-266. 3. ROGERS, H. C. Adiabatic Shearing: A Review. Drexel University Report prepared for U.S. Army Research Office. 1974. 4. ROGERS, H. C. Adiabatic Plastic Deformation. Ann. Rev. Mater. Sci., v. 9, 1979, P- 283-311. 5. BEDFORD, A. J., WINGROVE, A. L, and T HOMPSON. K. R. L J. Aust. lnst. Metals, v. 19, no. I, 1974. p. 61-74. 6. CLIFTON, R. J. Adiabatic Shear Banding in Materials Response to Ultra High Loading Rates, Chap. 8, National Materials Advisory

Board Committee, Rep. No. NMAB-356, 1980, p. 129-142. 7. ARGON, A. S. Stability of Plastic Deformarion in The I nhomogcncity o r Plastic Deformation, Chap. 7, ASM. Metals Park. OH.

1973, p. 161-189. 8. SAMUELS, L E., and LAMBORN, I. R. Failure Analysis o} Armamenr Hardware in Metallography in Failure Analysis. J. L.. McCall

and P.M. French, ed., Plenum Press, NY, 1978, p. 167-190. 9. CULVER, R. S. Thermal In stability Strain in Dynamic PlaHic Dej(Hmalion in Metallurgical Effects at High Strain Rates, R. W. Rohde.

B. M. Butcher, J. R. Holland, and C. H. Karnes, ed., Plenum Press, NY, 1973. p. 519-5 30. 10. COSTIN, L S., CRISMAN, E. E., HAWLEY, R. H., and DUFFY, J. On the Localization of Plastic Flow in Mild Steel Tubes Under

Dynamic Torsional Loading_ Brown University, Rep. No. NSF I 8532/7, 1979. II. LINDHOLM, U. S., and HARGREAVES, C. R. Dynamic Testing of High Strength Steels and Their Susceptibility to brhomogeneous

Shear in Proc. Second Int'L Conf. on Mech. Beh. of Materials, ASM, Metals Park, OH, 1976, p. 1463-1467. 12. IIARGREA VES, C. R., and /IOEGFELDT, J. M. The Hfjcc/ of Strain Rate (Thermal Feedback) on the Dej(Jrmation and Fracture

Processes in Proc. Second lnt'L Conf. on Mech. Beh. of Mat~rials, ASM. Metals Park, OH, 1976, p. 1806-1810. 13. WALKER, 'L J., and SHAW, M. C. On Deformation at I.argc' Strains in Advances in Machine Tool Design and Research, S. A. Tobias,

and F. Kocnigsberger, ed., Pergamon Press, NY, 1969, p. 241-252. 14. LUONG, H. S. A Study of Microvoid Formation in Metal Cutting. PhD Thesis, Monash University, Victoria, Australia, 1977. 15. LUONG, H. S. Discontinuities and Their Effects on Work Material in Chip Formation in Proc. of Australian Conf. on Manufacturing.

Engineering, Monash University, Victoria, Australia, 1977, p. 122-126. 16. WOODWARD, R. L., and AGHAM, R. L The Structure o{ a White t'tching Band in an t:xplosively Fractured Steel. Metals Forum,

v. 1, no. 4,1978, p. 180·184. 17. TURLEY, D. M. The Nature of the White Erching Surface Layers Produced During Reaming Ulrra-High Strength Steel. Mater. Sci.

Engr., v. 19, 1975, p. 79-86. 18. WINGROVE, A. L. A Note on the Structure of Adiabatic Shear Bands in Steel. J. Aust. Ins!. Metals, v. 16, no. 1, 1971, p. 67-70. 19. TRENT, E. M. The Formation and Properties of Martensite on the Surface of Rope Wire. J. Iron and Steel Inst., v. 143, no. I,

1941, p. 401-419. 20. DeMORTON, M. E., and WOODWARD, R. L The Effect of Fricrion on tire Stmcture of Surfaces Produced During Ballistic Tesrs.

Wear, v. 47, 1978, p. 195-209. 21. DOBROVOL'SKAYA, G. V., LEBEDEVA, I. L., and LYUHARASKTY, L M. Peculiarities of Friction Austenite. Phys. Met. and

Metal!., v. 42, no. 5, 1976, p. 76-81. 22. BACKMAN, M. E., and I'INNEGAN, S. A. The Propagation of Adiabatic Shear in Metallurgical Effects at High Strain Rates,

R. W. Rohde, B. M. Butcher, J. R. Holland, and C. H. Karnes, ed., Plenum Press, NY, 1973, p. 531-543. 23. RUSSELL. R. J., and WINCHELL, P. G. Re~-ersal of Fe-Ni-C Martensite by Rapid Large Shear. Met. Trans., v. 3, 1972, p. 2403-2409. 24. RECHT, R. f7. Catastrophic Thermoplastic Shear. J. Appl. Mech., v. 86E, 1964, p. 189·193. 25. CARSLAW, H. S., and JAEGER, J. C. Conduction of Hear in Solids. Clarendon Press, Oxford, 1947. 26. CULVER, R. S. Adiabatic Heating Ejj('cts in Dynamic Deformation in Proc. Third lnt'L Conf. of Center for lligh Energy hHmin!!,

U. of Denver, CO, 1971, p. 4.3 .1-4.3.38. 27. J EGLIC, L S., and PACKWOOD, R. H. lmpact-Dcposited White Layer on X65 Stec:l. Metallography, v. 11, 1978, p. 43-50. 28. MANION, S. A., and STOCK, T. A. C. The Measuremenr of Srrain in Adiabatic Shear Bands. J. Aust. lnst. Metals, v. 14, 1969.

p. 190·191. 29. LEMAIRE, J. C., and BACKOFEN, W. A. Adiabatic Insrability in the Orth<wonal Cutting o{ Steel. MeL Trans., v. 3, 1972, p. 4 77-4H I. 30. YELLUP, J. M., and WOODWARD, R. L. [la•esti!(ations inro rhe Prel'r't1lion of Adiaharic Shear Failure in High Strength Armour

Materials. Res. Mcchanica, v. 1. 1980, p. 41-57. 31. STOCK, T. A. C'., and WINGROVE, A. L. The Fncrg_F Rc(tuired j(Jr lhf!.h Speed Shearin?, of Steel. J. Mcch. 1-:ng. Sci., v. 13. no. 2.

1971. p. 11f', l4. 32. ERLICH, D. C., 'UH.RAN, D. R., and SEAM, L. l,.urlhcr IJc•vclopmc!ll o j a Computational Shear Band Mudd AMMRC TK

80-3. March 1980, SRI International Report prepared for Army Materials and Mechanics Research Center, Watertown, MA. 33. TSANGARAKLS, N. Unpublished Research. Army Materials and Mechanics Research Center, Watertown, MA. 34. WILKINS, M. L Calculation of t.'lastic-Plastic Flow. Lawrence Radiation Lah., Livermore, CA. Rep. No. UCRL-7322, Rev. I, 1969. 35. (;REEN, A. P. The Plastic Yielding of Metal Junctions Due to Combined Shear aod Pressure. J. Mcc h. Phys. Solids, v. 2, 1954.

p. 197-211. 36. BRIDGMAN, 1'. W. Studies in Large Plastic Flo w and Frac!ure. Chap. 15, Harvard University Press, Cambrid~l', \1A . 1964. p. 247-27H. 3 7. RUDNICKI. J. W .. and RICL, J. R. Cowiitio11s _I(Jr til e l. rJ< ali: atio 11 oj Dcj(!fmatirm in l'r<'SS!Ir<'·Scllsitirc /Jilata11t Mal<'riall

J. Mcch. l'hys. Solids. v. 23 . J 9 75. p. 37 1-394. 38. OLSON. G. ll .. and AZR!N, M. Tramjonna tion B<'lwrior o / TR/1' Stcd1·. Met. Trans. , v. 9A, !97!l, p. 7 13-721. 39. OLSON. G. B., and COHFN. ~\. Str. ·ss-As.>istcd lw tltcmwl .·'vtartcm·itic Tram}ormatiott a11d Trans.f(.>mrarimt l'la>rh ill in !'roc.

US/ Japan s~rninar on Mechanical Behavior o r Metal s and i\0\oys Associated wirh Displacivc Phase Transrurmatiom, R. P. 1., Troy. NY, 1979. p. 7.

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; - -,-- --, .... "·• r Nater i d l s J;,d HeChdn ics Re searctt :..ente r ,

Wa tertown. Massachusetts 02112 ADIABATIC O(FORHATIOH AN D STRA !t• LOCALIZATIO~ - Gregory B. Ol son, John F. Mescal !, and 1-lorri s Azr rn

'cchn•cal Report AMMRC TR 82-48, August I98Z. 2." ~P ­i l l us-tables , OiA Pr oject l LI61102AH42 , AHCMS Code 611I01. ~4200 l i

AD_----·---··-UNCLASSIF l EO

UNLIHIT£0 OISTRI8UT ION

Key Words

Adiabatic flow Shear fl ow BaliJstics

The strain !ocaitzat1on phenomenon of ''acHabati c shear" is gener<~lly attributed to a pla~t1c ins tability ari~inl) from a ther~al !.Ofteni r\9 effect dudn~ ad·i"bati c or near-ad 1abiJ tic plastic deformat; on. High s tra in~rdte adidbdt i r. torslon tests ind;c.ate tha~ the effect lve shear stress.-strdi n ( f - Y) re l ations for tngh-strenqth ( r ate -insens itive ) ~tee l s can be described by d s lmpT e expr ession of tfle form;

; , ; (1 + o1) exp (-B1 ) 0

whe,-e r-·0 i 'S J conSt J nt , a· and .3 ~re d lmensio~?css h~rdeni ng J nd sQftenfng p~rameters. The f low s tres!> l(~a c.h f' s d ma.-imum Jt i\11 iostat.ility s t r a i n, Y; ·. tJ-1-a-1 . k'it h pdr tmle t ers de r ivPd from t t1e to r sion t£'sts, this re l ati o n has bee, used i n c omputer ~1mulations of t he deve lopmen t of inte nse shear loc.:al ; za tion in <t ~ imp ,e.uR Hormly loaded body. St ratn loc a H zaUon has. been 'itudied under' conditions

•) f ba th quas ; su .tH· dod dyn amic def ormation. Appl ic a tion to the s imulat ion o f bal l i ~ t i c pene t ration 1 s f11 pr· ogr-Ps s. bperlme, lt al ev idence ind ic dt e>:. the e xis t ence of d pressur-e-(lependent s trai n so f t ening ef fect attr" ibutfd t o s:,bcrit ic a l s he ar microcr dc. ks whic h contrib:JtE's t o shear i nst abl ll ty in r"'l il d s tt>e l s. TtP ':' phe!~omenon n ay a lso oper ate in hi gh-strpngt h ster 1s . q hlnq r ise to a pressu,.e · de~cndt? l':t a fhV' ame~cr. £,-pcri"'leNo;. ar~ hein9 rlC!-.igf'ed t c deter~ • f'E' the r e i at 1ve imoort dnce of t hn ~ffect in t t--r. ad !~t. a: t;c defor ma tior of hlyh-strP.ngth <> t ee ls dnd i t 3 poss i hk role 1n ball i!. t H v~net rdt ion .

Army Hater i a 1 s aod Meehan ic s Research Cent er, Watertown , Massachusetts 02 172 AOIABATIC OEFORHATIOH ANO STRAIN LOCALI ZATION - Gregory 8. Olson, John F. 11esca ll , and Horr l~ Azrl n

Te<:hn1cal R•port AMP>IR C TR 82- 48, Augus t 1982 , i ll us - tables, 0/A Projct t lli61102A~42 , AMCMS Code 611102. H4200ll

ZB PP -

AD ·-·---- ·· I UHCLASSI F lEO

UNLJMI T£0 OI STRIBUTION

Key Words

Adiabatic flow Shear flow Balli s tic s

The s train locali zation phenor~~~enon of Madiabati c shea ,-n i s genera lly at tr ibuted to a p ldc;t )c ins.tabi l Hy aris i ng from a thermal soft enlng effe ct durln9 adiaba ti c or near-ad1d bat ic plas tic deformation. Ht gh strain-rate ad i dba t. i r. t orsion test s indi c ate tha t t ne effe ctive ll hear lltress-str-ain ~ T -Y j re lations for high-s tre ngth ( rate · itlsenosit ive) s t ee l s can be descr ibed by a slmpl e express ion of the form:

1 : ;0

(1 + >1) exp (-By)

where T0 l s a co ns t ant, a and (j are d"imcnsio_::!.1e ss ha r-de n ing dnd s.ofte ni n9 pa rdlneters . The now s t res s r"Paches a m<l.x Jmum at a n i ns tabi ti t y stra in. Y; ~ a - La- 1. , i th par ameter" s deri ved from t he t ors ion tests , th ~ s re l ~Uon nas bePn used i n computer c; imul a. t i ons of the devel opment o f i nteo(,e she ar loca l i zd t ion i n a s imp1e u,.ifor ml y loaded body. Strdln 1oc a l i za t i on has been s t udied unde r conrlftjons of b!Jth quasistat k and dynannc de f ormati on. Appl icdt i on to the ~ im u l dt ion of bJ. ll istic pefle t rati on 1 s 1n p,.-og r- ess . Expe,.-i me nt a l ev idence indl c Jtes t he ex i stenc e of a pressure - dependent strain so f t~n ing pffe-ct .attr itwt ed t o SlJhcn tica J she-ar microcracks whic h contr jbutPs t o shea r Jns tab ilit y in rrn ld stee ls. T~i s phen~enon may also operate 1n h igh- strength s tee l s , gi ving rise to a pressu1e · dependef" l a ;>aratncter . ~xpe~ :ments arl? bei ng dt:s.\gocd to dete~ml ne t he r clat1ve i trtpo r t aoce of t h•s effect in t he dd l a bdt it" deformat •on o t h1qh-s~rcngth s t ee l'> dnd its possi b l e r ole in ball 1st 1<. pen~;>tr at 10n.

- -~ I .!_· 1;;y Ha~_ er i J!~ Jn\! :"'.e-cndr. it:s Pes\?dr-c tt ':'enle"',

Watertown, Mossathusett• 0211 2 ."DI ABAT!C :J[FORMAT !ON ANO STRAIN lOCALJ ZAf!ON - Gregory 8. Olson,

-;).0 __ ------ ·---·· -· .-

UNCLASS IF ![0 UNLIMI T£0 DI STRIBUTION

-+ I Ar"my Mdterid f s aod Meenan i cs RE-search Cent er,

Wat erto-.n, Masso<husetts 02112 ADIABATI C OEFORMAT!ON AND STRA !It LOCAli ZATION - Gregory B. Ol son,

AD

UNCLASS IF lCD UNLIMITED OI ST~IBUTION

i I

,John F. Mesull, and Morri s Azrin

Tec hni cal Report AMMRC TR B2-4U, August 1982, >llu>- t ab le, , 0/A Project IL16 1102AH4 2, 'MCMS Code 61 i IO:! . H4 W0ll

?8 PP -

Key words

AOiabati c f low Shear flo w Bal l ist iCI

The stra i" loca li zat i on phenomenon of "ddiahat.i c shear " is g ~:~ nerilJl~ a ttri t>ut ~d t o a plas ti~ lns tab; JH y dr ~sing from a tt1er mal softeni119 ef fec t during ad l ab~tic or- net}r·ad u bd tic pl as ti c de t ormatlon. Hi gh s trdi n· rate ad~abatic to r sion tes t s ind icate that the eff ec tive shear s t r e ss-strai n { f - Y} r e lat ions for high-streogth (rat e-i nsensi tive ) st eels can he desc r ibed by a s imple expression of the form:

; : ;0

( 1 + >Y ) exp ( -By )

wher e T 0 is <1 const an t , a a nd tJ are dirnensi o.!!_less har den ing and sof teni ng paramet ers. The f l ow s t ress reaches a ma )l lmt.m at an ins t ab1li t y s t r ai n, Y; .,_ !)- L a - l . With pardmeters derived f r om the t ors ion tes t s, t h is rel ation has been used in c omputer s imul a tions of t he devel opment o f intense shear l oca ll z<ltion in a s1mple uMifo rmly loaded body. Strd in loc allzdtlon he~s been stud ied under coodltions of bot t. Ql:asi sta.ti c and dynamic def o-rmation. App lication to the s imo h tion of balli s t i c penet rat1on 1s 111 progress. h .per iment a l evi dence 1ndic .nes the ex is t e nce of a pressure-de pe ndent strain soften ing e f f ect dttr ibuted t o subcr t tica l she ar m1cn.>cracks whic h contr ibu t e s to shea r instabll lt y in mlld s tee ls . Th is pheOOfllenon Play dl so oper ate in hl gh -strength stee ls, giving ri se to a pressur e-depende~ t (J par ame ter . EKoenments are be i nc] des igned to determine t he r elat 1ve impar· t dnce of t his effec t ir. the ad iabatl c de formati on o f high·strength. s t eel s and H s poss i bl e role 1n ball1stic nene trdt ion.

John F. Mescall , and Morri s Azr>n

Tec hnJcal Report AMMRC TR 82 -48, Augu s t 1982, >llus - tab les , 0/A Project 1Ll6 11D2A~42 , AM CMS Code 6ll l02. H4 200ll

?8 pp .

Key Words

Adiabatic flow \ hear fl ow Ba I I i s tic s

The st r ai n loc() li z() t i or1 phenomenorJ o f "ad i abati c s hedr " i s gener a l :y attn but ed t o "- p l as tic i ns tabi l ity dris i ng from a tt1erma l softeni nq effec t dur ing ddiaba t i c or near - adiabat i c pl a s t i c deforma ti on. t-Hgh st r a in- rate a dlabat !c tor s ton t es t. ~ ln(n cate f. hat thtl' e f fec t i·..-e ~hear stress-strain ( f -· Y ) reht ions for h igh-strength ( ra t e - i nsensi ti ve ) s teels can he descr i bed by a simple expression o f t ne for m:

t, ;0

( 1 + •Y) e.p ( - By)

where T'0

i s a. cons t ant, a a nd :J a re dimensio~less harde nlng dnd softe ni ng pa rameters. The f low s tre 'is r e ac hes a ma.dmum a. t an ins tability s tra in . Yi ~ o· l-a-1 . With parameter s det-ived from the t ors i on tes t s , t h is r e l at ion has been used In comput er s imu lati ons of t he development of int ense shear local i zdt ioo io a s imple .I.IAifor m\ y loaded bod y. Str a in loca li zat ion has been s t ud1ed und("r cond i tlons of both quas i s~at ic ond dynanic de f-or mdt i on . App l i cation t o the s imt~ l at ion c f ba ll is tic pene tration i ~ 'in progres~- f.xperime ntd l e vidence indic ates the exi stence of a pressure- dependent \tra in so ft en ing effect attr" ibuted t o suberiti c al shear microcrac ks which con t r ibutes tc. shear inst ab i11 t y i n mi ld steels . n-.;.s. phenomenon may dlSo operate i n high -stre ngth s t eels. . g l ., iog ri s e t o a p ,-essure· dependent fJ paramet er. Experiment -s are being designed to de-term ine the rei a t 1ve- iflllpa r t ance of th is e f f ec t ln UJe adiabat ic deformat ion o f h1gh · s trength s t eeh dnd i ts poss i b l e ro le t n ball i sti c penetr atton .

L j_ - _j