- Email: [email protected]
Microstructure of high-strain, high-strain-rate deformed tantalum
Acta mater. Vol. 46, No. 4, pp. 1307-1325. 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd
Pergamon -
Printed in Great Britain
PII: S1359-6454(97)00746-2
MICROSTRUCTURE RATE
1359-6454/98
$19.00 + 0.00
OF HIGH-STRAIN, HIGH-STRAINDEFORMED TANTALUM
SIA NEMAT-NASSER,
JON B. ISAACS and MINGQI
LIU
Center of Excellence for Advanced Materials, Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA 92093-0416, U.S.A. (Received 28 October 1996; accepted 22 July 1997)
Abstract-Hat-shaped specimens of polycrystalline tantalum are subjected to high plastic shear strains (y = 170-910%) at strain rates exceeding 5 x 104/s in a compression split Hopkinson bar. The dynamic shear tests are performed at room and 600 K initial temperatures, under adiabatic and quasi-isothermal conditions, using UCSD’s recovery Hopkinson technique [l]. The microstructure of the post-test specimens is examined with transmission electron microscopy (TEM). The plastic deformation is highly concentrated, producing a narrow shear-localization region of approximately 200 pm in width. Slip of perfect screw dislocations, on the {110) primary planes along the < 111 > directions, is found to be the dominant deformation mechanism. Dynamic recovery takes place in the shear-localization regions of all adiabatically tested specimens, and evidence of dynamic recrystallization is observed in the specimen deformed to a shear strain of 910% at a 600 K initial temperature. The substructures of the adiabatically tested specimens include well-defined dislocation arrays, grouped dislocations, elongated dislocation cells, subgrains, and recrystallized micron-sized grains. The microstructure of isothermally tested specimens, on the other hand, features high dislocation density and inhomogeneous dislocation distribution. In light of the TEM observations, the relation between the microstructure and shear stress, the causes of strain inhomogeneity, the estimated adiabatic temperature within the shear-localization zone, the rapid quenching of the shearband at the end of the dynamic testing, the slip characteristics of dislocations in tantalum, and the formation mechanisms of dislocation loops, are discussed
1. INTRODUCTION
tor) is much smaller than that for f.c.c. metals (505000b3), resulting in much higher temperature and
Tantalum, a common refractory metal with a bodycentered cubic (b.c.c.) crystalline structure, has been
considered an excellent material for use in shaped charges and explosively forged projectiles (EFPs) due to its high density (16.7 g/cm3), superior strength, and excellent ductility over a wide range of strain rates and temperatures [24]. Tantalum exhibits a high sensitivity to strain rate and temperature, whereas its work-hardening rate is relatively insensitive to these parameters. The yield strength and flow stress of tantalum increase rapidly with increasing strain rate and decreasing temperature, in contrast to the much more modest trends exhibited by many face-centered cubic (f.c.c.) metals. The yield strength of tantalum, for example, increases by more than 400% when tested at strain rates from 10-4/s to 5 x 103/s at room temperature [5]. This type of deformation behavior is shared by a number of b.c.c. metals and has been attributed to a rate-controlling mechanism of the thermal component of the flow stress, i.e. to overcoming the Peierls-Nabarro stress barriers. It has been shown that the activation volume for plastic deformation decreases with plastic strain for f.c.c. metals but is almost constant for b.c.c. metals. Furthermore, the activation volume for b.c.c. metals (5-50b3, where b is the magnitude of Burgers’ vec-
strain-rate sensitivity. Based on the difference of the activation volume between b.c.c. and f.c.c. metals, constitutive equations have been developed [6,7] for use in the computational mechanics modeling of tantalum subjected to high-strain-rate deformation. More recently, similar ideas have been used to develop a physically-based model [l] which can predict the flow stress of tantalum and tantalum-tungsten alloys over a wide range of experimental conditions (strains up to 100%; strain rates up to 4 x 104/s; and temperatures up to approximately 1300 K). Metals used for shaped charges and penetrators must undergo extensive plastic deformation (1000% strain in shaped charges and 500% in EFPs) at strain rates exceeding 104/s. At these high strain rates, the deformation instability often limits the overall performance of the material [8]. It is known that more than 90% of the energy expended in plastic deformation is converted to heat. For plastic deformation at high strain rates, there is no time for appreciable conductive heat flow to occur. Therefore, the deformation can be considered as nearly adiabatic, resulting in significant temperature increase within small localized regions. Reportedly, evidence of dynamic recrystallization has been found in shaped-charge tantalum slugs and
1307
1308
NEMAT-NASSER et al.:
HIGH-STRAIN-RATE DEFORMED Ta
jets [9-111. In recent studies on the high-strain, high-strain-rate deformed tantalum (shear strains up to 550% and strain rates up to 4 x 104/s), a recovered microstructure is observed [12,13]. The dislocation substructure of tantalum deformed at these extreme conditions, on the other hand, has not been fully investigated. The purpose of the present study is to examine the microstructure of the high-strain (shear strains exceeding 900%), high-strain-rate (strain rates exceeding 104/s) deformed tantalum by using transmission electron microscopy (TEM). The emphasis of the research, in particular, is on the dislocation substructure of tantalum deformed under these extreme conditions. The formation mechanisms for the observed microstructure are also discussed. Additionally, the temperature in the shearband is estimated and the time required for the shearband to cool to its original temperature is calculated, showing rapid quenching which preserves the hightemperature microstructure in the small localized deformation zone. 2. EXPERIMENTAL PROCEDURE The material used in the present study was produced and processed by Cabot Corp., Boyertown, PA. It was received as disks with a diameter of 155 mm and a thickness of 8 mm. Tantalum ingots with a height of 300 mm were first forged into 100 mm slabs. These slabs were then cross-rolled to the final thickness with intermediate annealing, in an effort to break up the as-cast columnar structure. The grain size of the as-received tantalum disk, measured by a linear intercept method, was approximately 47 pm. Hat-shaped specimens, developed by Meyer and Manwaring [14], were prepared from the disks by using electrodischarge machining (EDM). The experimental setup and the specimen dimensions are schematically shown in Fig. 1. Five specimens were prepared. The inner diameter at the large end of one specimen (specimen C) was reduced by approximately 3%, in order to sustain a
large amount of shear strain under some normal pressure. The specimens were dynamically compressed using a compression split Hopkinson bar and the displacement 6 of each specimen was controlled by a pulse-shaping method which controls the input energy. A special wave-trapping scheme [15,16] was used in controlling the loading of the specimens. The wave-trapping scheme enables the establishment of a prescribed, well-controlled loading condition, and eliminates repeated loading of the specimens by unwanted reflected waves. The region of concentrated deformation underwent essentially simple shearing. Dynamic shear tests were conducted at strain rates exceeding 5 x 104/s, at the initial ambient temperature and 600 K. For the high-strain-rate compression test conducted at elevated temperatures, it is necessary to heat the specimen to the given temperature while keeping the incident and transmission bars of the Hopkinson construction at suitably low temperatures [l]. During the elevated temperature testing conducted in the present study, the bars are first kept outside the range of the heating unit of the furnace, while keeping the specimen at the furnace center. The bars are then automatically brought into contact with the specimen, microseconds before the stress pulse reaches the end of the incident bar. Once the specimen is loaded, the bars move out and the specimen is recovered without having been subjected to any stresses other than the initial one. The details of experimental setup for the dynamic testing have been described elsewhere [l, 151. In [ 11, in particular, the measured flow stress of the same tantalum which is used for the present study, is reported for strain rates from quasi-static to 4 x 104/s, temperatures from room to 1000 K, and strains exceeding 100%. The high-strain-rate tests were carried out under two conditions: adiabatic and quasi-isothermal. Three adiabatic shear tests were performed: tests A and B were carried out at room temperature with small and moderate shear strains; test C was carried out at 600 K up to a very large plastic strain, com-
Fig. 1. Schematic diagram of the hat-shaped specimen (dimensions in mm) and experimental setup used to generate the high-strain-rate shear deformation.
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
parable to those of shape charges. A method to obtain a quasi-isothermal stress-strain response under high-strain-rate deformation is described in ref. [17]. It consists of conducting incremental tests and allowing the specimen to return to the original testing temperature after each strain increment. The origins of the sequential curves are translated so that the strains are additive. Two quasi-isothermal tests were performed at room temperature by using a two-cycle (test D) and a four-cycle (test E) incremental loading procedure, with moderate shear strains. After dynamic shear testing, the specimens were axially sectioned along the symmetry axis and polished for optical microscopic examination. They were then sliced perpendicular to the shearing direction into semi-circular disks. Three-millimeter TEM samples were cut by EDM through the shear region and ground to a thickness of approximately 200 pm. Electropolishing, using a solution of 93 vol.% methanol + 5 vol.% sulfuric acid + 2 vol.% hydrofluoric acid at 233 K, was followed, when necessary, by ion milling. TEM samples thus obtained were examined with a JEOL-2000FX transmission electron microscope, operated at 200 kV.
3. RESULTS AND DISCUSSION 3.1.
Shear stress response and shear strain localiz-
ation Figure 2(a) shows the nominal shear stress vs displacement curves for specimens tested under an adiabatic condition. The nominal stress-displacement curve for specimen A displays extensive ringing which sometimes occurs in Hopkinson tests and is not seen in the case of specimen B which was tested under similar conditions. We note that this ringing does not relate to the phenomenon of upper yield limit followed by the yield drop which occurs at certain temperatures and strain rates in tantalum, due to the initial pinning of the dislocations by impurities; indeed the observed peak value of the stress in Fig. 2(a) is much too large to correspond to the upper yield limit. It is noted that the stressdisplacement curves of the two specimens coincide once the ringing portion of the curve of specimen A, is filtered out. We have included the results for specimen A since the final deformed structure is not affected by the ringing phenomenon of the Hopkinson bar. All the stress-displacement curves of the adiabatically tested specimens share a common feature, that is, the shear stress first reaches a peak value, and then decreases with increasing displacement, suggesting that hardening mechanisms are prevailing only at the initial stage of the plastic deformation and then softening mechanisms become dominant. due to the increasing heat accumulation
within
the
DEFORMED
shearing
1309
Ta
region
during
the
high-rate
adiabatic deformation. For specimens tested at room temperature, the peak stress is approximately 390 MPa. whereas for specimens tested at 600 K initial temperature, the peak stress is approximately 295 MPa, which corresponds to about 25% decrease in the nominal shear stress. Considering that the temperature difference (300 K) is less than 0.1 T,,, (melting point of tantalum, 3269 K), this result indicates a high temperature sensitivity for tantalum. This is consistent with our previous experimental results and the model prediction [I] that the temperature, rather than the strain rate, has a significant influence on the response of tantalum. Specimens D and E were subjected at room temperature to two-cycle and four-cycle incremental loading, respectively. The total accumulated displacements for both specimens are similar. For incremental loading tests. the specimens were allowed to cool down to the initial temperature prior to each sequential loading. Therefore, the material yields at a higher nominal yield stress in each sequential loading cycle [Fig. 2(b)]. In general, an ascending curve (positive slope) can be drawn through the initial yield points of the multiple shear stress-strain curves for a given specimen [ 171, representing the corresponding quasi-isothermal flow stress. Figure 3(a)-(c) shows optical micrographs of the deformation localization regions of specimens tested under an adiabatic condition, showing the shearband evolution with increasing displacement 8. It can be seen that the density and tilt angle of the shear markings increase with increased displacement. The deformation is highly localized, leaving the neighboritzg gruim rehtivell intact. The engineering shear strains can be estimated from the micrographs by using the formula. ;’= tan(a)
(1)
7=6/W,
(2)
or
where u is the deflection angle of the shear markings, and W is the width of the shear-localization region. These estimates are not rigorous because the orientations of the shear markings and the width of the shear-localization region vary from one location to another within a specimen. But values of the measured x or W for a given specimen, usually obey a normal statistical distribution with a small standard deviation. A fair agreement between the results of these two approaches, is a good indication of the measurement reliability. The average shear strains for specimens A, B, and C are hence determined to be 170%, 310%. and 910%. To our knowledge, a shear strain of 910% is the highest shear strain ever reported in the literature for dynamically compressed hat-shaped specimens. The spe-
NEMAT-NASSER
1310
ef al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
(a)
600
= I
.
1 -
1 3 1 -
1 .
1 .
1 *
1 -
1 -
1 m
‘1
0.0
0.4
0.2
0.6
0.8
1.0
1.2
Displacement
1.6
1.4
1.8
2.0
2.2
(mm)
w
1
600
--- Specimen 500 z 3 s E 3i $
400
-
D
Specimen E
;r””
Q.#
300
z j *_ E 5 =
200
100
t I
I
I
0.1
0.6 Displacement
.
I
0.7
.
I
0.8
.
0.9
(mm)
Fig. 2. Shear strain vs displacement curves for specimens tested under an adiabatic condition (a) and a quasi-isothermal condition (b). cimen jetted The mens
was fully recovered in this test, it being subto a single controlled stress pulse. shear-localization regions of the two specisubjected to sequential loading are shown in
Fig. 4(a) and (b), respectively. Because their total displacements are similar, no significant differences are observed in their shear-marking angles. The appearance of their shear-localization regions is
1312
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
1313
Ta
Table 1. Shear strains and testing conditions of the hat-shaoed . suecimens examined in the uresent studv 1
A
Specimen Displacement 6 Shear strain y Shear marking angle at Shearband width Wt Testing conditions tAverage
B
0.64 mm 0.36 mm 310% 170% 72.1” 60.3” 210 pm 220 /un Adiabatic at 298 K
c
D
E
2.05 mm 910% X3.2 190 pm Adiabatic at 600 K
0.69 mm 330% 72.9“ 2lO/un Isothermal two-cycle
0.72 mm 340% 73.5’ 210pm Isothermal four-cycle
values
similar to that of the adiabatically tested specimen deformed to a moderate shear strain [Fig. 4(b)], showing continuous shear markings. No evidence of repeated loading is distinguishable from the micrographs. The total shear strains for the two-cycle and the four-cycle tested specimens are determined to be 330 and 340%, respectively. The displacements, shear strains, shear-marking angles, and shearband widths of all specimens employed in the present study are summarized in Table 1. Meyers et al. [13] reported a shear-deformation inhomogeneity phenomenon in tantalum subjected to shear strains of up to 400%. Such a deformation characteristic has been confirmed by the present study in specimens dynamically sheared to low and moderate strains. Figure S(a) shows the central area of the shearband in specimen A (170% strain). Fluctuations in the shear strain can be seen along the length of the shear-localization region, with the maximum amounts of shear occuring at locations adjacent to the edges of the sheared regions. Within the shearband, plastic deformation is inhomogeneous. Some grains exhibit large amounts of shear while others (indicated by the arrows) appear to be essentially strain-free. The deformation inhomogeneity observed in dynamically sheared tantalum is believed to result from the constraints imposed by the grain boundaries. Unlike single crystals, individual grains in a polycrystal specimen have different crystalline orientations and are not necessarily subjected to pure shear stress when the specimen is sheared. In a plastically deformed polycrystal, continuity is maintained across the boundaries between the neighboring grains [18]. Although all grains as a whole deform essentially homogeneously in conformity with the deformation of the specimen, the constraints imposed by the continuity at the grain boundaries cause considerable differences in the deformation between neighboring grains and within each grain. Although the strain may be continuous across the boundary, there could be a steep strain gradient in the grain-boundary vicinity. As the grain size decreases or the strain increases, the plastic deformation is expected to become more homogeneous. This is confirmed by a micrograph [Fig. 5(b)] from specimen C (910% strain). At such a high shear strain, no undeformed grains are seen within the shearband. The shearlocalization region is characterized by the high density of the nearly horizontal shear markings.
Essentially no deformation in the micrograph.
inhomogeneity
is visible
3.2. Shearband substructure specimens
in adiabatically
deformed
Optical microscopy cannot resolve the distinguishing features in the shearbands. TEM was hence employed to elucidate the fine-scale microstructure. The most important characteristic of the shearband microstructure of materials subjected to high-strain-rate shearing is the formation of elongated narrow dislocation cells [12, 13,19-211. Figure 6(a) and (b) shows TEM micrographs taken within the shearbands of the adiabatically deformed specimens A (“r = 170%) and B (y = 310%), showing arrays of elongated dislocation cells. The boundaries between the cells are generally welldefined and straight, with only small curvatures. The dislocation cells in specimen A are approximately 0.7 pm in width and 6-8 pm in length, corresponding to an aspect ratio of approximately 10, while the cells in specimen B are approximately 0.4 pm wide and 4-5 pm long, corresponding to a similar aspect ratio. The micrographs suggest that high-strain-rate shear deformation has a “refining” effect on the dislocation cells, that is, with increased shear strain, the size of the cells decreases. This is most likely due to dislocation interaction and mutilation during plastic deformation. Based on the observations made on planes perpendicular to the shearing direction, it may be surmised that the three-dimensional shape of the elongated dislocation cells is prolate spheroidal. Figure 7 is the corresponding selected-area electron diffraction (SAED) pattern of specimen B, from dislocation cells. The incident beam is along [loo]. It shows that the orientation of the dislocation cell’s long axis is approximately along [l lo]. Cell arrays with the same orientation have been observed by Murr et al. [lo] and Meyers et al. [ 131 in dynamically sheared tantalum, and by Mgbokwere et al. [22] in steel subjected to high-strain-rate torsion, which suggests that the dynamic shearing in b.c.c. metals preferentially occurs on the (110) primary slip planes. The diffraction pattern obtained from the dislocation cells shows a slight separation of ok1 spots, indicative of a small-angle (-6”) misorientation between the neighboring dislocation cells. During TEM examination, it is noted that the degree of misorientation between the dislocation
1314
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
NEMAT-NASSER et al.: HIGH-STRAIN-RATE DEFORMED Ta
Fig. 7. Selected-area electron diffraction (SAED) pattern of specimen B. cells increases with decreasing cell size. As will be shown in the sequel, the degree of cell misorientation reaches a maximum at the shearband center, resulting in ring-like diffraction patterns. A detailed examination was performed on specimen C (y = 910%) to investigate the microstructure evolution at extremely high plastic strains, attained at very high strain rate and a relatively high temperature. As is shown later on, rapid cooling of the shearband by heat conduction preserves the final microstructure. Figure 8(a)-(e) shows a sequence of TEM micrographs, taken with the same magnification, from the shearband edge area to the shearband center. At areas slightly away from the shearband, dislocation arrays tend to be co-planar [Fig. 8(a)], suggesting that a single slip system is dominant in these areas, although many slip systems may have been activated. By using the invisibility criteria [23,24], most dislocations are identified as a/2 < 111 >-type screw dislocations (straight dislocation segments in the micrograph) and the remaining (the curved dislocation segments) are either edge or mixed dislocations. Since most dislocations lie on the { 1IO}-type planes, it is concluded that the high-strain-rate deformation of tantalum in these tests is accomplished preferentially by the movement of the screw-type dislocations on the { 110) perfect slip planes, similarly to the deformation of tantalum which occurs at relatively low strain rates [25-271. At the boundary of the shearband, the highly localized deformation results in a large shear-strain gradient. In this region, a characteristic feature is the increase of dislocation density and the grouping of dislocations into bands, as can be seen in Fig. 8(b). These grouped dislocations are approximately oriented along the same direction. The grouping of dislocations results in an inhomogeneous distribution of dislocations and hence initiates the boundaries of dislocation cells. Within the shearband of specimen C, extensive elongated dislocation cells are observed [Fig. S(c)]. The dislocation cells show a width of approximately 0.25 pm, with aspect ratios varying from 8 to 12.
1315
The size of the dislocation cells in specimen C is about 65% smaller than that in specimen A (y = 170%) and is approximately 40% smaller than that in specimen B (y = 310%). It is the smallest among all five specimens examined in the present study, due to the large shear strain (910%) that the specimen had experienced. At regions near the shearband center of specimen C, subgrains are observed [Fig. 8(d)], indicating that a dynamic recovery took place during the high-strain-rate deformation. The boundary structure and geometry of the subgrains are remarkably different from those of the dislocation cells. Because subgrains are formed by the rearrangement of dislocations during dynamic recovery, their boundaries are finer and better defined than those of the dislocation cells. Furthermore, their aspect ratios are significantly smaller than those of the dislocation cells. The subgrains in high-strain-rate sheared tantalum seem to have an olive-like shape with the short and long axes of approximately 0.25 and 0.7 ,um, respectively. Few dislocations are seen in the interior of the subgrains. At the shearband central area, evidence of dynamic recrystallization is observed. Figure 8(e) is a TEM micrograph from the shear region center. Micro-grains as small as 0.15 pm in diameter can be seen. which is more than two orders of magnitude smaller than the initial grain size (47 pm). In contrast to the curved subgrain boundaries, the boundaries of the dynamically recrystallized grains appear relatively straight. Dislocations are observed in the interior of the micro-grains, which is typical for grains formed during dynamic recrystallization. The dislocation density at the boundaries of the recrystallized grains is substantially lower than that observed at the subgrain boundaries. It is interesting to note that the size and morphology of the dislocation cells, subgrains, and recrystallized grains observed in the localized shear region of specimen C are essentially the same as those observed by Murr et al. [lo] in explosively formed tantalum penetrators. Structural analysis of the shearband was performed on specimen C by using a selection-area electron diffraction (SAED) technique. SAED patterns were obtained by translating the specimen along a direction perpendicular to the shearband such that the SAED aperture selected comparable areas at decreasing distances from the center of the band. A sequence of SAED patterns from various regions in specimen C are shown in Fig. 9(a)-(c), which correspond to the areas shown in Fig. 8(a), (c), and (d). This series shows a gradual transition from a sharp spot pattern to a splitting spot pattern, resulting from the small-angle misoriented dislocation cells, and finally to a ring-like pattern from the completely misoriented recrystallized grains. It is widely accepted that the development of a substructure during deformation at elevated tem-
1316
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
Fig. 8. Sequence of TEM micrographs from the shear region of specimen C (y = 910%), showing the microstructure evolution toward the shearband center: (a) area adjacent to the shearband; (b) boundary of the shear region; (c) inside the shearband; (d) approaching the shearband center; (e) shearband center where recrystallization occurs.
Fig. 9. Comparison of SAED patterns obtained from various areas shown in Fig. 8: (a) area adjacent to the shearband; (b) within the shearband; (c) shearband center. With decreasing distance toward the shearband center. The pattern changes from a sharp spot pattern to a ring-like pattern. The incident beam was near [I 111. The same aperture size was used for all patterns.
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
peratures involves two restoration mechanisms, dynamic recovery and dynamic recrystallization, which counteract the strain-hardening resulting from plastic deformation. These two restoration mechanisms can occur concordantly or independently, depending upon the heating rate and temperature. The first process should result in subgrain formation while the second process should result in nucleation and growth of strain-free grains. Thermodynamically, recovery and recrystallization can be considered as a stored-energy releasing process at elevated temperatures. For most metals, recrystallization occurs at temperatures above 0.40.5 T,, which correspond to about 1310-1640 K for tantalum. The temperature of tantalum deformed adiabatically at high strain rates can be calculated assuming that essentially all or a major portion (e.g. 90%) of the work done to deform the metal plastically is used to heat the plastically deformed zones. The rate of change of the temperature is then given by, PC,(T)~ which upon integration,
=
s r0
(3)
yields
T P
7b)i
7
C,(T)dT
=
r(y)dy,
(4)
s0
where T is the adiabatic temperature (K) within the shear-localization zone, T, is the initial testing temperature, p is the density of tantalum (kg/m3), z(y) is the shear stress (N/m* or J/m3) of tantalum as a function of the shear strain, and C, (T) is the temperature-dependent specific heat of tantalum given by WI> C,(T)
= 139.04 + 1.757 x lo-*T + 1.375 x 10-6T2
(5) where temperature is in Kelvin and C, is in J/kg/K. By using this approach, the temperatures in the shear- localization zones of the adiabatically deformed specimens were estimated. The maximum adiabatic for temperature specimen C (y = 910%; T,=600K) is determined to be 1930 K, assuming no heat loss and is 1810 K if a 10% heat loss is assumed. Both are significantly higher than the temperature required for tantalum recrystallization. In order to identify if static recrystallization mechanism is involved in the formation of the micro-size grains observed in the shearband of specimen C, temperature as a function of time in the shearband and the neighboring region of the posttest specimen is estimated as follows. The temperature distribution function, T, of the post-test cylindrical specimen can be expressed by the heat equation; pC,$=K,V*T+r$
(6)
DEFORMED
1319
Ta
where K, is the thermal conductivity and
of tantalum,
(7) Here (r,B) are the polar coordinates. Although a complete analysis of the heat generation and conduction can be made with the aid of equation (6) and suitable boundary conditions, since the shearband is very narrow and axially symmetric, a reasonable estimate can be obtained using a onedimensional calculation which considers a small shearband in an infinite medium. Assuming a constant rate of heat generation in the thin shearing zone, the solution of the heat equation can then be reduced to 1 T(x, t) = d&z
O”f(X)e-(x-f)*/4kfd, s -_oo
(8)
where k is a material constant (k = K&C,)) and Ax) is the temperature distribution within the specimen at the end of the adiabatic deformation, measured relative to the initial temperature T, J‘(x)=TM-To
R;-E
(W
f(x)=o
~-cR~--~orx>Ri+~
(9b)
where TM is the maximum shearband temperature at the end of the deformation; T, is the ambient temperature; E is the (very small) shearband halfwidth (E N 100pm); and Ri is the distance from the center line of the shearband to the center of the cylindrical specimen (Ri = 4.3 18 mm for specimen C). Since e/Rj=0.023< 1 and e/R,=0.016 < 1, where R, is the specimen radius, the estimate in equation (7) is quite adequate. The temperature in the shearband of the post-test specimen is therefore determined by substituting for f(x) from equation (9a) and using the fact that c/Ri is very small. This yields T(x, t) =
2E(TM-Td
e-(x-~,)Z/4kr Rj _
E
VGE
(10)
Figure 10 shows the post-test shearband temperature of specimen C as a function of time. It takes less than 0.1 s for the shearband to cool down from 1930 to 1000 K, which represents very high quench rate at the end of the mechanical testing. The fast cooling rate is due to the very small volume of the deformed zone as well as the high thermal conductivity of tantalum. Therefore, it is concluded that the high-temperature microstructure of specimen C has been preserved, and the micro-grains observed in the shearband are formed by a dynamic recrystallization mechanism during the adiabatic plastic deformation. The adiabatic temperatures for specimens A (y = 170%; T,=298K) and specimen B (y = 310%;
1320
NEMAT-NASSER et al.: HIGH-STRAIN-RATE DEFORMED Ta
'CJ s
looa
e 8
m-
6 600 "'n"""."o""' 0.0 0.1 0.2 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Time (s) Fig. 10. Calculated temperature in the shearband of the post-test specimen C as a function of time. T,=298K), on the other hand, are found to be 580 K and 860 K, respectively, assuming no heat loss. These are substantially lower than the recrystallization temperature for tantalum. This is consistent with the TEM micrographs obtained from the shear-localization regions of specimens A and B, in which signs of dynamic recovery are found but no evidence of dynamic recrystallization is observed. 3.3. Shearband substructure in isothermally deformed specimens
For specimens deformed under quasi-isothermal conditions, two typical substructural features observed are high dislocation density and inhomogeneous dislocation distribution. Both of these are attributed to the sequential loading applied to these specimens. A detailed TEM examination was performed on specimen E, which was subjected to dynamic shearing through four-cycle loading (a1 = b2 = 0.15 mm; &=&=0.21 mm). Figure 11(a) is a TEM micrograph taken from an area near the shearband boundary. Three-dimensional dislocation networks are observed. The dislocation density is approximately 10”/cm2, which is significantly higher than the dislocation density (from 109/cm2 to 10’0/cm2) observed in the comparable areas of the adiabatically tested specimens. The dislocation networks and the high dislocation density observed in the isothermally deformed specimens indicate that different slip systems were activated during dynamic loading. It has been noted in Fig. 7(a) that the slip of screw dislocations on (1 lo} planes is the dominant deformation mechanism in tantalum subjected to high-strain-rate shearing. In tantalum there are six { llO}-type slip planes. Because the line and Burgers vector of a screw dislocation are parallel, they do not define a specific slip plane during the dislocation motion, as they do for an edge dislo-
cation (where the Burgers vector is perpendicular to the dislocation line). For a screw dislocation, all planes containing the dislocation line are potential slip planes, as long as the dislocation moves parallel to its original orientation. The slip plane of a screw dislocation can be any slip plane containing the dislocation, and it can cross-slip from one plane to another, just as long as both planes contain a common slip direction. The movement of dislocations on multiple slip planes causes significant dislocation intersecting, resulting in dislocation forests. Although dislocation intersecting is expected to occur in both the adiabatically and the isothermally deformed specimens, it appears that the dislocation forests in the adiabatically tested specimens are not as dominant as they are in the isothermally deformed specimens. This is mainly attributed to the different deformation temperatures experienced by these two types of specimens. Dynamic recovery occurs in the adiabatically deformed specimens due to their higher deformation temperature, which partially eliminate the dislocation forest and networks formed during the dynamic deformation, resulting in a lower dislocation density. Within the shearband of the isothermally deformed specimens, significant dislocation inhomogeneities are identified. Figure 11(b) is taken from an area adjacent to a dislocation cell boundary in specimen E, showing significant dislocation-density change across the cell boundary. Over a distance of less than 1 pm, the dislocation density changes by a few orders of magnitude, from a density of approximately 101’/cm2 in one cell to greater than 10’2/cmZ in the other. The observations confirm that localized shear strains in each individual dislocation cell are remarkably different during sequential loading. While all cells are expected to deform repeatedly, depending upon their orientation, some cells could experience repeated signz$cant shear strains, while
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
1321
1322
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
others may be subjected to no more than one significant shear straining, resulting in the observed significant differences in the dislocation density between the neighboring cells. Figure 11(c) is a TEM micrograph from an area near the shearband center of specimen E, revealing the elongated dislocation cells. Compared with the micrographs obtained from similar areas in the adiabatically deformed specimens [Fig. 6(a), 6(b), and 8(c)], Fig. 11(c) shows two unique microstructural characteristics. One is the significant variation of the dislocation cell size. The width of the cells varies from 0.3 to 1.5 pm, indicating that the shear deformation was inhomogeneous. Such inhomogeneity is most likely caused by the repeated loading. As mentioned earlier, the shear strain may become concentrated in some preferentially oriented dislocation cells during each sequential loading, resulting in a refinement effect on some cells. The other characteristic observed in the sequentially loaded specimen is the high dislocation density within the dislocation cells. Dislocation density as high as 1013/cm2 has been observed in some cell interior areas, which is similar to the microstructure of large-strain cold-worked metals. Furthermore, fewer subgrains are observed in specimen E than in the adiabatically deformed specimens. The observations suggest that little, if there is any, dynamic recovery occurs in isothermally deformed specimens. In some areas of their shear-localization regions, dynamic recovery may not occur at all. Although each loading cycle applied to specimen E corresponds to an adiabatic testing, the maximum individual displacement is only 0.21 mm, significantly less than those applied to the adiabatically deformed specimens (A, in the present study. B, and C) examined
Fig.
DEFORMED
Ta
Furthermore, after the application of each loading, specimen E is unloaded without being subjected to any additional stress pulses and is allowed to return to room temperature before the application of the next strain increment. There is no continuous heat accumulation within the shearband during the cycled testing. The maximum adiabatic temperature in the shearband of specimen E is estimated to be approximately 450 K, which is slightly below the lower boundary of dynamic recovery temperature for tantalum. The absence of the dynamic recovery in some regions of specimen E is thus expected. Considering that the dynamic recovery is incomplete in the isothermally tested specimens, sequential dynamic loading results in a stronger interaction between dislocations produced during each reloading cycle. Figure 12 is a TEM micrograph from an area in the shear-localization region of specimen D (two-cycle loading; 6i= 0.2 mm and & = 0.49 mm). Numerous dislocation tangles are observed around the dislocation intersecting points. It is known that the intersection of two screw dislocation lines produces jogs with edge orientations in both dislocation lines. Unlike a kink which is a sharp break in the dislocation line remaining in the same slip plane, a jog is a sharp break in the dislocation which is out of the slip plane. The only way that a screw dislocation can slip and take its jog with it is by a non-conservative process under thermal activation. At temperatures where climb cannot occur, the motion of screw dislocations will be significantly impeded by jogs. This should have some contribution, in addition to the dominant temperature effect, to the relatively high shear stress observed in the sequentially loaded specimens.
12. TEM micrograph from an area within the shearband of specimen D (y = 330%, sequential loading) showing numerous dislocation tangles at the intersecting points.
two-cycle
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
1323
1324
NEMAT-NASSER et al.: HIGH-STRAIN-RATE DEFORMED Ta
An important dislocation structure after dynamic testing is the presence of dislocation loops. Dislocation loops have been observed by Murr et al. [lo], Worswick et al. [29], and Qiang et al. [30] in tantalum EFPs, but have not been reported in hat-shaped tantalum specimens subjected to dynamic shear, over a broad range of temperatures. In the present study, a considerable number of dislocation loops are observed in both the adiabatically and isothermally deformed specimens, with the density of loops in the isothermally deformed specimens appearing to be substantially higher. Figure 13(a) and (b) shows TEM images from the adiabatically and isothermally deformed specimens, respectively, showing dislocation loops present in the shear-localization regions. These loops are relatively small. Most of them are under 20 nm. By employing an inside-outside method [31,32] in which the specimen is systematically tilted to determine the orientation of the loop plane, the habit plane and the Burgers vector of the loops are determined. The habit plane of the dislocation loops present in the dynamically sheared specimens, is determined to be { 1 lo}, with a loop Burgers’ vector of < 111 > . Both are consistent with the results obtained in tantalum EFPs [30]. There are two proposed mechanisms for dislocation loop formation [18]. One is the collection of vacancies at elevated temperatures, which is most likely the formation mechanism for the loops observed in the adiabatically deformed specimens. The other is the bowing out of jogged screw dislocations at the edge-oriented jogs, which appear to be the primary source for the loops produced in the isothermally deformed specimens. Wittman et al. [33] have reported the presence of twinning in shocked tantalum. In the present study, however, no evidence of deformation-induced twinning has been observed in the microstructure of dynamically sheared specimens tested under either the adiabatic or the isothermal conditions. Murr et al. [lo] and Worsick et al. [29] also noted the absence of twinning in tantalum penetrators and impactors.
4. SUMMARY In this study, TEM observations were used to investigate the microstructure of shearbands formed in polycrystalline tantalum during high-strain, highstrain-rate shear deformation, at adiabatic and quasi-isothermal testing conditions. The results of the present study can be summarized as follows. The plastic deformation is highly concentrated, producing a narrow shear-localization region with a dimension of approximately 200 pm across the hat-shaped specimen. Deformation inhomogeneity is found within the shearbands of specimens deformed to shear strains of up to 340%. At a shear strain of
3.
4.
5.
6.
7.
8.
910%, no deformation inhomogeneity is observed. Slip of the perfect screw dislocations on (1 lO}type primary planes is the dominant deformation mechanism. Band structure (elongated dislocation cells with small misorientation) is the most predominant microstructural characteristic of the shear-localization region. The size of the dislocation cells decreases with increased shear strain. Dynamic recovery is present in all specimens tested adiabatically at ambient initial temperature. Dynamic recrystallization is observed in a specimen adiabatically deformed to a shear strain of 910%, at 600 K initial temperature. This microstructure is preserved by the rapid cooling which takes place subsequently to the rapid heating (to approximately 1900 K) of the narrow shear zone due to localized plastic work. The microstructural evolution in the high-shearstrain specimen (y = 910%), from the area adjacent to the shearband toward the shearband center, includes arrays of dislocation lines, dislocation groupings, formation of elongated dislocation cells and subgrains, and recrystallized micro-grains (d N 0.15 pm). Compared with the adiabatically deformed specimens, the isothermally deformed specimens exhibit higher dislocation density, a higher degree of inhomogeneous dislocation distribution, and a stronger dislocation interaction, due to the sequential loading and relatively lower adiabatic the shear-localization temperatures within region. Small dislocation loops are extensively observed in the shearbands of both the adiabatically and the isothermally deformed specimens. Formation of the dislocation loops is attributed to the collection of vacancies at elevated temperatures and the bowing out of jogged screw dislocations along the edge-oriented jogs at low temperatures.
Acknowledgements-This work was supported by the Army Research Office (ARO) Contract, DAAL 03-92-G0108 to the University of California, San Diego, and made use of the TEM facilities at the Microscopy and Imaging Resources, Medical Center, University of California, San Diego. The authors would like to thank Dr William Ebihara and Mr Michael Hespos at ARDEC for providing the sample material.
REFERENCES 1. Nemat-Nasser, S. and Isaacs, J. B., Acta Metall., 1997, 45(3), . 907. 2. Bechtold, J. H., Acta Metall., 1955, 3(5), 249. 3. Werner. M.. Phvs. Stat. Sol.. 1987, 104, 63. 4. Steinbeig, b. i. and Lund; C. M., .I. Appl. Phys., 1989, 65(4), 1528. 5. Hoge, K. G. and Mukherjee, A. K., J. Mater. Sci., 1971, 12, 1666.
NEMAT-NASSER 6. 7. 8. 9. 10. 11.
12. 13. 14.
15. 16.
17. 18. 19.
20.
et al.:
HIGH-STRAIN-RATE
Zerilli, F. J. and Armstrong, R. W., J. Appl. Phys., 1987, 61(5), 1816. Zerilli, F. J. and Armstrong, R. W.. J. Appl. Phvs., 1990, 68(4), 1580. Brown, L. M., Met. Trans., 1991, 22A(8), 1693. Shih, H. K., Murr, L. E., Niou, C. S. and Zernow. L., Scripta Metall. Mater., 1993, 29, 1291. Murr, L. E., Niou, C. S. and Feng, F.. Scripta Metall. Mater., 1994, 31(3), 297. Murr, L. E., Niou, C. S., Sanchez. J. C., Shih, H. K., Duplessis, L., Pappu. S. and Zernow, L., J. Matrr. Sci.. 1995, 30, 2747. Vecchio, K. S., J. de Physique, 1994, 4(8), 301. Meyers. M. A., Chen, Y. J.. Marquis, F. D. S. and Kim, D. S., Met. Muter. Trans., 1995. 26A(lO), 2493. Meyer. L. W. and Manwaring, S., Metallurgical Applications of Shock- Wave and High-Strain-Rate Phenomena. ed. L. E. Murr, K. P. Staudhammer and M. A. Meyers. M. Dekker, New York, 1986, 657. Nemat-Nasser, S., Isaacs, J. 8. and Starrett, J. E., Proc. R. Sot. Lond., 1991, 435A, 371. Nemat-Nasser, S., in Shock-Wave and High-Strained. M. A. Meyers, L. Rate Phenomena in Mater& E. Murr and K. P. Staudhammer, M. Dekker, New York 1992, p. 1. Nemat-Nasser, S., Li. Y. F. and Isaacs, J. B., Mech. Muter., 1994, 17, 111. Dieter. G. E., Mechanical Metallurgy 3rd edn., 186 & 170, McGraw-Hill, New York, 1986. Pak, H. R.: Wittman, C. L. and Meyers, M. A., Metallurgical Applications of Shock- Wave and HighStrain-Rate Phenomena. ed. L. E. Murr, K. P. Staudhammer, M. A. Meyers. M. Dekker, New York 1986, 749. Meyers. M. A., Subhash, G., Kad. B. K. and Prasad, L., M&r. Mater., 1994, 17, 175.
21. 22. 23.
24. 25. 26. 27. 28. 29.
30. 31. 32.
33.
DEFORMED
Ta
1325
Chen, R. W. and Vecchio, K. S.. J. de Physique, 1994, 4(9), 459. Mgbokwere, C. O., Nutt, S. R. and Duffy, J., Mech. Mater., 1994, 17, 97. Hirsch, P.. Howie, A., Nicholson, R., Pashley, D. W. and Whelan, M. J., Electron Microscopy qf Thin Crystals 2nd edn.. 181, RE Krieger, Malabar, FL. 1977. Spitzig, W. A. and Mitchell, T. E., Actu Metall.. 1966. 14(10), 1311. Welsch, G., Gibala, R. and Mitchell, T. E., .4cta Metall., 1975, 23(12). 1461. D’Anna, G. and Benoit, W., Muter. Sci. Engr., 1993, A164, 191. Mizubayashi. H., Egashira, H. and Okuda, S., Acta Metall.. 1995, 43(l), 269. Materials Met& Handbook, ASM International. Park, Ohio, U.S.A.. 1990, 799. Worswick. M. J.. Qiang, N., Niessen, P. and Pick, R. J.. in Shock- Wave and High-Strain-Rate Phenomena in Materials ed. M. A. Meyers, L. E. Murr and K. P. Staudhammer, M. Dekker. New York 1992, p. 1. Qiang, N.. Niessen, P. and Pick, R. J.. Mater. Sci. Engr., 1993, A160, 49. Loretto, M. H. and Smallman, R. E.. D&t Analysis in Electron Microscopy, Wiley, New York, 1975, 86. Edington. J. W., Practical Electron Microscopy in New York, Materials Science, Van N Reinhold, 1976, 134. Witman. C. L.. Garrett, R. K.. Clark, J. B. and Lopatin, C. M., in Shock- Wave and High-Strain-Rate Phenomenrr in Materials ed. M. A. Meyers, L. E. Murr and K. P. Staudhammer, M. Dekker, New York 1992, p, 925.
Pergamon -
Printed in Great Britain
PII: S1359-6454(97)00746-2
MICROSTRUCTURE RATE
1359-6454/98
$19.00 + 0.00
OF HIGH-STRAIN, HIGH-STRAINDEFORMED TANTALUM
SIA NEMAT-NASSER,
JON B. ISAACS and MINGQI
LIU
Center of Excellence for Advanced Materials, Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA 92093-0416, U.S.A. (Received 28 October 1996; accepted 22 July 1997)
Abstract-Hat-shaped specimens of polycrystalline tantalum are subjected to high plastic shear strains (y = 170-910%) at strain rates exceeding 5 x 104/s in a compression split Hopkinson bar. The dynamic shear tests are performed at room and 600 K initial temperatures, under adiabatic and quasi-isothermal conditions, using UCSD’s recovery Hopkinson technique [l]. The microstructure of the post-test specimens is examined with transmission electron microscopy (TEM). The plastic deformation is highly concentrated, producing a narrow shear-localization region of approximately 200 pm in width. Slip of perfect screw dislocations, on the {110) primary planes along the < 111 > directions, is found to be the dominant deformation mechanism. Dynamic recovery takes place in the shear-localization regions of all adiabatically tested specimens, and evidence of dynamic recrystallization is observed in the specimen deformed to a shear strain of 910% at a 600 K initial temperature. The substructures of the adiabatically tested specimens include well-defined dislocation arrays, grouped dislocations, elongated dislocation cells, subgrains, and recrystallized micron-sized grains. The microstructure of isothermally tested specimens, on the other hand, features high dislocation density and inhomogeneous dislocation distribution. In light of the TEM observations, the relation between the microstructure and shear stress, the causes of strain inhomogeneity, the estimated adiabatic temperature within the shear-localization zone, the rapid quenching of the shearband at the end of the dynamic testing, the slip characteristics of dislocations in tantalum, and the formation mechanisms of dislocation loops, are discussed
1. INTRODUCTION
tor) is much smaller than that for f.c.c. metals (505000b3), resulting in much higher temperature and
Tantalum, a common refractory metal with a bodycentered cubic (b.c.c.) crystalline structure, has been
considered an excellent material for use in shaped charges and explosively forged projectiles (EFPs) due to its high density (16.7 g/cm3), superior strength, and excellent ductility over a wide range of strain rates and temperatures [24]. Tantalum exhibits a high sensitivity to strain rate and temperature, whereas its work-hardening rate is relatively insensitive to these parameters. The yield strength and flow stress of tantalum increase rapidly with increasing strain rate and decreasing temperature, in contrast to the much more modest trends exhibited by many face-centered cubic (f.c.c.) metals. The yield strength of tantalum, for example, increases by more than 400% when tested at strain rates from 10-4/s to 5 x 103/s at room temperature [5]. This type of deformation behavior is shared by a number of b.c.c. metals and has been attributed to a rate-controlling mechanism of the thermal component of the flow stress, i.e. to overcoming the Peierls-Nabarro stress barriers. It has been shown that the activation volume for plastic deformation decreases with plastic strain for f.c.c. metals but is almost constant for b.c.c. metals. Furthermore, the activation volume for b.c.c. metals (5-50b3, where b is the magnitude of Burgers’ vec-
strain-rate sensitivity. Based on the difference of the activation volume between b.c.c. and f.c.c. metals, constitutive equations have been developed [6,7] for use in the computational mechanics modeling of tantalum subjected to high-strain-rate deformation. More recently, similar ideas have been used to develop a physically-based model [l] which can predict the flow stress of tantalum and tantalum-tungsten alloys over a wide range of experimental conditions (strains up to 100%; strain rates up to 4 x 104/s; and temperatures up to approximately 1300 K). Metals used for shaped charges and penetrators must undergo extensive plastic deformation (1000% strain in shaped charges and 500% in EFPs) at strain rates exceeding 104/s. At these high strain rates, the deformation instability often limits the overall performance of the material [8]. It is known that more than 90% of the energy expended in plastic deformation is converted to heat. For plastic deformation at high strain rates, there is no time for appreciable conductive heat flow to occur. Therefore, the deformation can be considered as nearly adiabatic, resulting in significant temperature increase within small localized regions. Reportedly, evidence of dynamic recrystallization has been found in shaped-charge tantalum slugs and
1307
1308
NEMAT-NASSER et al.:
HIGH-STRAIN-RATE DEFORMED Ta
jets [9-111. In recent studies on the high-strain, high-strain-rate deformed tantalum (shear strains up to 550% and strain rates up to 4 x 104/s), a recovered microstructure is observed [12,13]. The dislocation substructure of tantalum deformed at these extreme conditions, on the other hand, has not been fully investigated. The purpose of the present study is to examine the microstructure of the high-strain (shear strains exceeding 900%), high-strain-rate (strain rates exceeding 104/s) deformed tantalum by using transmission electron microscopy (TEM). The emphasis of the research, in particular, is on the dislocation substructure of tantalum deformed under these extreme conditions. The formation mechanisms for the observed microstructure are also discussed. Additionally, the temperature in the shearband is estimated and the time required for the shearband to cool to its original temperature is calculated, showing rapid quenching which preserves the hightemperature microstructure in the small localized deformation zone. 2. EXPERIMENTAL PROCEDURE The material used in the present study was produced and processed by Cabot Corp., Boyertown, PA. It was received as disks with a diameter of 155 mm and a thickness of 8 mm. Tantalum ingots with a height of 300 mm were first forged into 100 mm slabs. These slabs were then cross-rolled to the final thickness with intermediate annealing, in an effort to break up the as-cast columnar structure. The grain size of the as-received tantalum disk, measured by a linear intercept method, was approximately 47 pm. Hat-shaped specimens, developed by Meyer and Manwaring [14], were prepared from the disks by using electrodischarge machining (EDM). The experimental setup and the specimen dimensions are schematically shown in Fig. 1. Five specimens were prepared. The inner diameter at the large end of one specimen (specimen C) was reduced by approximately 3%, in order to sustain a
large amount of shear strain under some normal pressure. The specimens were dynamically compressed using a compression split Hopkinson bar and the displacement 6 of each specimen was controlled by a pulse-shaping method which controls the input energy. A special wave-trapping scheme [15,16] was used in controlling the loading of the specimens. The wave-trapping scheme enables the establishment of a prescribed, well-controlled loading condition, and eliminates repeated loading of the specimens by unwanted reflected waves. The region of concentrated deformation underwent essentially simple shearing. Dynamic shear tests were conducted at strain rates exceeding 5 x 104/s, at the initial ambient temperature and 600 K. For the high-strain-rate compression test conducted at elevated temperatures, it is necessary to heat the specimen to the given temperature while keeping the incident and transmission bars of the Hopkinson construction at suitably low temperatures [l]. During the elevated temperature testing conducted in the present study, the bars are first kept outside the range of the heating unit of the furnace, while keeping the specimen at the furnace center. The bars are then automatically brought into contact with the specimen, microseconds before the stress pulse reaches the end of the incident bar. Once the specimen is loaded, the bars move out and the specimen is recovered without having been subjected to any stresses other than the initial one. The details of experimental setup for the dynamic testing have been described elsewhere [l, 151. In [ 11, in particular, the measured flow stress of the same tantalum which is used for the present study, is reported for strain rates from quasi-static to 4 x 104/s, temperatures from room to 1000 K, and strains exceeding 100%. The high-strain-rate tests were carried out under two conditions: adiabatic and quasi-isothermal. Three adiabatic shear tests were performed: tests A and B were carried out at room temperature with small and moderate shear strains; test C was carried out at 600 K up to a very large plastic strain, com-
Fig. 1. Schematic diagram of the hat-shaped specimen (dimensions in mm) and experimental setup used to generate the high-strain-rate shear deformation.
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
parable to those of shape charges. A method to obtain a quasi-isothermal stress-strain response under high-strain-rate deformation is described in ref. [17]. It consists of conducting incremental tests and allowing the specimen to return to the original testing temperature after each strain increment. The origins of the sequential curves are translated so that the strains are additive. Two quasi-isothermal tests were performed at room temperature by using a two-cycle (test D) and a four-cycle (test E) incremental loading procedure, with moderate shear strains. After dynamic shear testing, the specimens were axially sectioned along the symmetry axis and polished for optical microscopic examination. They were then sliced perpendicular to the shearing direction into semi-circular disks. Three-millimeter TEM samples were cut by EDM through the shear region and ground to a thickness of approximately 200 pm. Electropolishing, using a solution of 93 vol.% methanol + 5 vol.% sulfuric acid + 2 vol.% hydrofluoric acid at 233 K, was followed, when necessary, by ion milling. TEM samples thus obtained were examined with a JEOL-2000FX transmission electron microscope, operated at 200 kV.
3. RESULTS AND DISCUSSION 3.1.
Shear stress response and shear strain localiz-
ation Figure 2(a) shows the nominal shear stress vs displacement curves for specimens tested under an adiabatic condition. The nominal stress-displacement curve for specimen A displays extensive ringing which sometimes occurs in Hopkinson tests and is not seen in the case of specimen B which was tested under similar conditions. We note that this ringing does not relate to the phenomenon of upper yield limit followed by the yield drop which occurs at certain temperatures and strain rates in tantalum, due to the initial pinning of the dislocations by impurities; indeed the observed peak value of the stress in Fig. 2(a) is much too large to correspond to the upper yield limit. It is noted that the stressdisplacement curves of the two specimens coincide once the ringing portion of the curve of specimen A, is filtered out. We have included the results for specimen A since the final deformed structure is not affected by the ringing phenomenon of the Hopkinson bar. All the stress-displacement curves of the adiabatically tested specimens share a common feature, that is, the shear stress first reaches a peak value, and then decreases with increasing displacement, suggesting that hardening mechanisms are prevailing only at the initial stage of the plastic deformation and then softening mechanisms become dominant. due to the increasing heat accumulation
within
the
DEFORMED
shearing
1309
Ta
region
during
the
high-rate
adiabatic deformation. For specimens tested at room temperature, the peak stress is approximately 390 MPa. whereas for specimens tested at 600 K initial temperature, the peak stress is approximately 295 MPa, which corresponds to about 25% decrease in the nominal shear stress. Considering that the temperature difference (300 K) is less than 0.1 T,,, (melting point of tantalum, 3269 K), this result indicates a high temperature sensitivity for tantalum. This is consistent with our previous experimental results and the model prediction [I] that the temperature, rather than the strain rate, has a significant influence on the response of tantalum. Specimens D and E were subjected at room temperature to two-cycle and four-cycle incremental loading, respectively. The total accumulated displacements for both specimens are similar. For incremental loading tests. the specimens were allowed to cool down to the initial temperature prior to each sequential loading. Therefore, the material yields at a higher nominal yield stress in each sequential loading cycle [Fig. 2(b)]. In general, an ascending curve (positive slope) can be drawn through the initial yield points of the multiple shear stress-strain curves for a given specimen [ 171, representing the corresponding quasi-isothermal flow stress. Figure 3(a)-(c) shows optical micrographs of the deformation localization regions of specimens tested under an adiabatic condition, showing the shearband evolution with increasing displacement 8. It can be seen that the density and tilt angle of the shear markings increase with increased displacement. The deformation is highly localized, leaving the neighboritzg gruim rehtivell intact. The engineering shear strains can be estimated from the micrographs by using the formula. ;’= tan(a)
(1)
7=6/W,
(2)
or
where u is the deflection angle of the shear markings, and W is the width of the shear-localization region. These estimates are not rigorous because the orientations of the shear markings and the width of the shear-localization region vary from one location to another within a specimen. But values of the measured x or W for a given specimen, usually obey a normal statistical distribution with a small standard deviation. A fair agreement between the results of these two approaches, is a good indication of the measurement reliability. The average shear strains for specimens A, B, and C are hence determined to be 170%, 310%. and 910%. To our knowledge, a shear strain of 910% is the highest shear strain ever reported in the literature for dynamically compressed hat-shaped specimens. The spe-
NEMAT-NASSER
1310
ef al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
(a)
600
= I
.
1 -
1 3 1 -
1 .
1 .
1 *
1 -
1 -
1 m
‘1
0.0
0.4
0.2
0.6
0.8
1.0
1.2
Displacement
1.6
1.4
1.8
2.0
2.2
(mm)
w
1
600
--- Specimen 500 z 3 s E 3i $
400
-
D
Specimen E
;r””
Q.#
300
z j *_ E 5 =
200
100
t I
I
I
0.1
0.6 Displacement
.
I
0.7
.
I
0.8
.
0.9
(mm)
Fig. 2. Shear strain vs displacement curves for specimens tested under an adiabatic condition (a) and a quasi-isothermal condition (b). cimen jetted The mens
was fully recovered in this test, it being subto a single controlled stress pulse. shear-localization regions of the two specisubjected to sequential loading are shown in
Fig. 4(a) and (b), respectively. Because their total displacements are similar, no significant differences are observed in their shear-marking angles. The appearance of their shear-localization regions is
1312
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
1313
Ta
Table 1. Shear strains and testing conditions of the hat-shaoed . suecimens examined in the uresent studv 1
A
Specimen Displacement 6 Shear strain y Shear marking angle at Shearband width Wt Testing conditions tAverage
B
0.64 mm 0.36 mm 310% 170% 72.1” 60.3” 210 pm 220 /un Adiabatic at 298 K
c
D
E
2.05 mm 910% X3.2 190 pm Adiabatic at 600 K
0.69 mm 330% 72.9“ 2lO/un Isothermal two-cycle
0.72 mm 340% 73.5’ 210pm Isothermal four-cycle
values
similar to that of the adiabatically tested specimen deformed to a moderate shear strain [Fig. 4(b)], showing continuous shear markings. No evidence of repeated loading is distinguishable from the micrographs. The total shear strains for the two-cycle and the four-cycle tested specimens are determined to be 330 and 340%, respectively. The displacements, shear strains, shear-marking angles, and shearband widths of all specimens employed in the present study are summarized in Table 1. Meyers et al. [13] reported a shear-deformation inhomogeneity phenomenon in tantalum subjected to shear strains of up to 400%. Such a deformation characteristic has been confirmed by the present study in specimens dynamically sheared to low and moderate strains. Figure S(a) shows the central area of the shearband in specimen A (170% strain). Fluctuations in the shear strain can be seen along the length of the shear-localization region, with the maximum amounts of shear occuring at locations adjacent to the edges of the sheared regions. Within the shearband, plastic deformation is inhomogeneous. Some grains exhibit large amounts of shear while others (indicated by the arrows) appear to be essentially strain-free. The deformation inhomogeneity observed in dynamically sheared tantalum is believed to result from the constraints imposed by the grain boundaries. Unlike single crystals, individual grains in a polycrystal specimen have different crystalline orientations and are not necessarily subjected to pure shear stress when the specimen is sheared. In a plastically deformed polycrystal, continuity is maintained across the boundaries between the neighboring grains [18]. Although all grains as a whole deform essentially homogeneously in conformity with the deformation of the specimen, the constraints imposed by the continuity at the grain boundaries cause considerable differences in the deformation between neighboring grains and within each grain. Although the strain may be continuous across the boundary, there could be a steep strain gradient in the grain-boundary vicinity. As the grain size decreases or the strain increases, the plastic deformation is expected to become more homogeneous. This is confirmed by a micrograph [Fig. 5(b)] from specimen C (910% strain). At such a high shear strain, no undeformed grains are seen within the shearband. The shearlocalization region is characterized by the high density of the nearly horizontal shear markings.
Essentially no deformation in the micrograph.
inhomogeneity
is visible
3.2. Shearband substructure specimens
in adiabatically
deformed
Optical microscopy cannot resolve the distinguishing features in the shearbands. TEM was hence employed to elucidate the fine-scale microstructure. The most important characteristic of the shearband microstructure of materials subjected to high-strain-rate shearing is the formation of elongated narrow dislocation cells [12, 13,19-211. Figure 6(a) and (b) shows TEM micrographs taken within the shearbands of the adiabatically deformed specimens A (“r = 170%) and B (y = 310%), showing arrays of elongated dislocation cells. The boundaries between the cells are generally welldefined and straight, with only small curvatures. The dislocation cells in specimen A are approximately 0.7 pm in width and 6-8 pm in length, corresponding to an aspect ratio of approximately 10, while the cells in specimen B are approximately 0.4 pm wide and 4-5 pm long, corresponding to a similar aspect ratio. The micrographs suggest that high-strain-rate shear deformation has a “refining” effect on the dislocation cells, that is, with increased shear strain, the size of the cells decreases. This is most likely due to dislocation interaction and mutilation during plastic deformation. Based on the observations made on planes perpendicular to the shearing direction, it may be surmised that the three-dimensional shape of the elongated dislocation cells is prolate spheroidal. Figure 7 is the corresponding selected-area electron diffraction (SAED) pattern of specimen B, from dislocation cells. The incident beam is along [loo]. It shows that the orientation of the dislocation cell’s long axis is approximately along [l lo]. Cell arrays with the same orientation have been observed by Murr et al. [lo] and Meyers et al. [ 131 in dynamically sheared tantalum, and by Mgbokwere et al. [22] in steel subjected to high-strain-rate torsion, which suggests that the dynamic shearing in b.c.c. metals preferentially occurs on the (110) primary slip planes. The diffraction pattern obtained from the dislocation cells shows a slight separation of ok1 spots, indicative of a small-angle (-6”) misorientation between the neighboring dislocation cells. During TEM examination, it is noted that the degree of misorientation between the dislocation
1314
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
NEMAT-NASSER et al.: HIGH-STRAIN-RATE DEFORMED Ta
Fig. 7. Selected-area electron diffraction (SAED) pattern of specimen B. cells increases with decreasing cell size. As will be shown in the sequel, the degree of cell misorientation reaches a maximum at the shearband center, resulting in ring-like diffraction patterns. A detailed examination was performed on specimen C (y = 910%) to investigate the microstructure evolution at extremely high plastic strains, attained at very high strain rate and a relatively high temperature. As is shown later on, rapid cooling of the shearband by heat conduction preserves the final microstructure. Figure 8(a)-(e) shows a sequence of TEM micrographs, taken with the same magnification, from the shearband edge area to the shearband center. At areas slightly away from the shearband, dislocation arrays tend to be co-planar [Fig. 8(a)], suggesting that a single slip system is dominant in these areas, although many slip systems may have been activated. By using the invisibility criteria [23,24], most dislocations are identified as a/2 < 111 >-type screw dislocations (straight dislocation segments in the micrograph) and the remaining (the curved dislocation segments) are either edge or mixed dislocations. Since most dislocations lie on the { 1IO}-type planes, it is concluded that the high-strain-rate deformation of tantalum in these tests is accomplished preferentially by the movement of the screw-type dislocations on the { 110) perfect slip planes, similarly to the deformation of tantalum which occurs at relatively low strain rates [25-271. At the boundary of the shearband, the highly localized deformation results in a large shear-strain gradient. In this region, a characteristic feature is the increase of dislocation density and the grouping of dislocations into bands, as can be seen in Fig. 8(b). These grouped dislocations are approximately oriented along the same direction. The grouping of dislocations results in an inhomogeneous distribution of dislocations and hence initiates the boundaries of dislocation cells. Within the shearband of specimen C, extensive elongated dislocation cells are observed [Fig. S(c)]. The dislocation cells show a width of approximately 0.25 pm, with aspect ratios varying from 8 to 12.
1315
The size of the dislocation cells in specimen C is about 65% smaller than that in specimen A (y = 170%) and is approximately 40% smaller than that in specimen B (y = 310%). It is the smallest among all five specimens examined in the present study, due to the large shear strain (910%) that the specimen had experienced. At regions near the shearband center of specimen C, subgrains are observed [Fig. 8(d)], indicating that a dynamic recovery took place during the high-strain-rate deformation. The boundary structure and geometry of the subgrains are remarkably different from those of the dislocation cells. Because subgrains are formed by the rearrangement of dislocations during dynamic recovery, their boundaries are finer and better defined than those of the dislocation cells. Furthermore, their aspect ratios are significantly smaller than those of the dislocation cells. The subgrains in high-strain-rate sheared tantalum seem to have an olive-like shape with the short and long axes of approximately 0.25 and 0.7 ,um, respectively. Few dislocations are seen in the interior of the subgrains. At the shearband central area, evidence of dynamic recrystallization is observed. Figure 8(e) is a TEM micrograph from the shear region center. Micro-grains as small as 0.15 pm in diameter can be seen. which is more than two orders of magnitude smaller than the initial grain size (47 pm). In contrast to the curved subgrain boundaries, the boundaries of the dynamically recrystallized grains appear relatively straight. Dislocations are observed in the interior of the micro-grains, which is typical for grains formed during dynamic recrystallization. The dislocation density at the boundaries of the recrystallized grains is substantially lower than that observed at the subgrain boundaries. It is interesting to note that the size and morphology of the dislocation cells, subgrains, and recrystallized grains observed in the localized shear region of specimen C are essentially the same as those observed by Murr et al. [lo] in explosively formed tantalum penetrators. Structural analysis of the shearband was performed on specimen C by using a selection-area electron diffraction (SAED) technique. SAED patterns were obtained by translating the specimen along a direction perpendicular to the shearband such that the SAED aperture selected comparable areas at decreasing distances from the center of the band. A sequence of SAED patterns from various regions in specimen C are shown in Fig. 9(a)-(c), which correspond to the areas shown in Fig. 8(a), (c), and (d). This series shows a gradual transition from a sharp spot pattern to a splitting spot pattern, resulting from the small-angle misoriented dislocation cells, and finally to a ring-like pattern from the completely misoriented recrystallized grains. It is widely accepted that the development of a substructure during deformation at elevated tem-
1316
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
Fig. 8. Sequence of TEM micrographs from the shear region of specimen C (y = 910%), showing the microstructure evolution toward the shearband center: (a) area adjacent to the shearband; (b) boundary of the shear region; (c) inside the shearband; (d) approaching the shearband center; (e) shearband center where recrystallization occurs.
Fig. 9. Comparison of SAED patterns obtained from various areas shown in Fig. 8: (a) area adjacent to the shearband; (b) within the shearband; (c) shearband center. With decreasing distance toward the shearband center. The pattern changes from a sharp spot pattern to a ring-like pattern. The incident beam was near [I 111. The same aperture size was used for all patterns.
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
peratures involves two restoration mechanisms, dynamic recovery and dynamic recrystallization, which counteract the strain-hardening resulting from plastic deformation. These two restoration mechanisms can occur concordantly or independently, depending upon the heating rate and temperature. The first process should result in subgrain formation while the second process should result in nucleation and growth of strain-free grains. Thermodynamically, recovery and recrystallization can be considered as a stored-energy releasing process at elevated temperatures. For most metals, recrystallization occurs at temperatures above 0.40.5 T,, which correspond to about 1310-1640 K for tantalum. The temperature of tantalum deformed adiabatically at high strain rates can be calculated assuming that essentially all or a major portion (e.g. 90%) of the work done to deform the metal plastically is used to heat the plastically deformed zones. The rate of change of the temperature is then given by, PC,(T)~ which upon integration,
=
s r0
(3)
yields
T P
7b)i
7
C,(T)dT
=
r(y)dy,
(4)
s0
where T is the adiabatic temperature (K) within the shear-localization zone, T, is the initial testing temperature, p is the density of tantalum (kg/m3), z(y) is the shear stress (N/m* or J/m3) of tantalum as a function of the shear strain, and C, (T) is the temperature-dependent specific heat of tantalum given by WI> C,(T)
= 139.04 + 1.757 x lo-*T + 1.375 x 10-6T2
(5) where temperature is in Kelvin and C, is in J/kg/K. By using this approach, the temperatures in the shear- localization zones of the adiabatically deformed specimens were estimated. The maximum adiabatic for temperature specimen C (y = 910%; T,=600K) is determined to be 1930 K, assuming no heat loss and is 1810 K if a 10% heat loss is assumed. Both are significantly higher than the temperature required for tantalum recrystallization. In order to identify if static recrystallization mechanism is involved in the formation of the micro-size grains observed in the shearband of specimen C, temperature as a function of time in the shearband and the neighboring region of the posttest specimen is estimated as follows. The temperature distribution function, T, of the post-test cylindrical specimen can be expressed by the heat equation; pC,$=K,V*T+r$
(6)
DEFORMED
1319
Ta
where K, is the thermal conductivity and
of tantalum,
(7) Here (r,B) are the polar coordinates. Although a complete analysis of the heat generation and conduction can be made with the aid of equation (6) and suitable boundary conditions, since the shearband is very narrow and axially symmetric, a reasonable estimate can be obtained using a onedimensional calculation which considers a small shearband in an infinite medium. Assuming a constant rate of heat generation in the thin shearing zone, the solution of the heat equation can then be reduced to 1 T(x, t) = d&z
O”f(X)e-(x-f)*/4kfd, s -_oo
(8)
where k is a material constant (k = K&C,)) and Ax) is the temperature distribution within the specimen at the end of the adiabatic deformation, measured relative to the initial temperature T, J‘(x)=TM-To
R;-E
(W
f(x)=o
~-cR~--~orx>Ri+~
(9b)
where TM is the maximum shearband temperature at the end of the deformation; T, is the ambient temperature; E is the (very small) shearband halfwidth (E N 100pm); and Ri is the distance from the center line of the shearband to the center of the cylindrical specimen (Ri = 4.3 18 mm for specimen C). Since e/Rj=0.023< 1 and e/R,=0.016 < 1, where R, is the specimen radius, the estimate in equation (7) is quite adequate. The temperature in the shearband of the post-test specimen is therefore determined by substituting for f(x) from equation (9a) and using the fact that c/Ri is very small. This yields T(x, t) =
2E(TM-Td
e-(x-~,)Z/4kr Rj _
E
VGE
(10)
Figure 10 shows the post-test shearband temperature of specimen C as a function of time. It takes less than 0.1 s for the shearband to cool down from 1930 to 1000 K, which represents very high quench rate at the end of the mechanical testing. The fast cooling rate is due to the very small volume of the deformed zone as well as the high thermal conductivity of tantalum. Therefore, it is concluded that the high-temperature microstructure of specimen C has been preserved, and the micro-grains observed in the shearband are formed by a dynamic recrystallization mechanism during the adiabatic plastic deformation. The adiabatic temperatures for specimens A (y = 170%; T,=298K) and specimen B (y = 310%;
1320
NEMAT-NASSER et al.: HIGH-STRAIN-RATE DEFORMED Ta
'CJ s
looa
e 8
m-
6 600 "'n"""."o""' 0.0 0.1 0.2 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Time (s) Fig. 10. Calculated temperature in the shearband of the post-test specimen C as a function of time. T,=298K), on the other hand, are found to be 580 K and 860 K, respectively, assuming no heat loss. These are substantially lower than the recrystallization temperature for tantalum. This is consistent with the TEM micrographs obtained from the shear-localization regions of specimens A and B, in which signs of dynamic recovery are found but no evidence of dynamic recrystallization is observed. 3.3. Shearband substructure in isothermally deformed specimens
For specimens deformed under quasi-isothermal conditions, two typical substructural features observed are high dislocation density and inhomogeneous dislocation distribution. Both of these are attributed to the sequential loading applied to these specimens. A detailed TEM examination was performed on specimen E, which was subjected to dynamic shearing through four-cycle loading (a1 = b2 = 0.15 mm; &=&=0.21 mm). Figure 11(a) is a TEM micrograph taken from an area near the shearband boundary. Three-dimensional dislocation networks are observed. The dislocation density is approximately 10”/cm2, which is significantly higher than the dislocation density (from 109/cm2 to 10’0/cm2) observed in the comparable areas of the adiabatically tested specimens. The dislocation networks and the high dislocation density observed in the isothermally deformed specimens indicate that different slip systems were activated during dynamic loading. It has been noted in Fig. 7(a) that the slip of screw dislocations on (1 lo} planes is the dominant deformation mechanism in tantalum subjected to high-strain-rate shearing. In tantalum there are six { llO}-type slip planes. Because the line and Burgers vector of a screw dislocation are parallel, they do not define a specific slip plane during the dislocation motion, as they do for an edge dislo-
cation (where the Burgers vector is perpendicular to the dislocation line). For a screw dislocation, all planes containing the dislocation line are potential slip planes, as long as the dislocation moves parallel to its original orientation. The slip plane of a screw dislocation can be any slip plane containing the dislocation, and it can cross-slip from one plane to another, just as long as both planes contain a common slip direction. The movement of dislocations on multiple slip planes causes significant dislocation intersecting, resulting in dislocation forests. Although dislocation intersecting is expected to occur in both the adiabatically and the isothermally deformed specimens, it appears that the dislocation forests in the adiabatically tested specimens are not as dominant as they are in the isothermally deformed specimens. This is mainly attributed to the different deformation temperatures experienced by these two types of specimens. Dynamic recovery occurs in the adiabatically deformed specimens due to their higher deformation temperature, which partially eliminate the dislocation forest and networks formed during the dynamic deformation, resulting in a lower dislocation density. Within the shearband of the isothermally deformed specimens, significant dislocation inhomogeneities are identified. Figure 11(b) is taken from an area adjacent to a dislocation cell boundary in specimen E, showing significant dislocation-density change across the cell boundary. Over a distance of less than 1 pm, the dislocation density changes by a few orders of magnitude, from a density of approximately 101’/cm2 in one cell to greater than 10’2/cmZ in the other. The observations confirm that localized shear strains in each individual dislocation cell are remarkably different during sequential loading. While all cells are expected to deform repeatedly, depending upon their orientation, some cells could experience repeated signz$cant shear strains, while
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
1321
1322
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
others may be subjected to no more than one significant shear straining, resulting in the observed significant differences in the dislocation density between the neighboring cells. Figure 11(c) is a TEM micrograph from an area near the shearband center of specimen E, revealing the elongated dislocation cells. Compared with the micrographs obtained from similar areas in the adiabatically deformed specimens [Fig. 6(a), 6(b), and 8(c)], Fig. 11(c) shows two unique microstructural characteristics. One is the significant variation of the dislocation cell size. The width of the cells varies from 0.3 to 1.5 pm, indicating that the shear deformation was inhomogeneous. Such inhomogeneity is most likely caused by the repeated loading. As mentioned earlier, the shear strain may become concentrated in some preferentially oriented dislocation cells during each sequential loading, resulting in a refinement effect on some cells. The other characteristic observed in the sequentially loaded specimen is the high dislocation density within the dislocation cells. Dislocation density as high as 1013/cm2 has been observed in some cell interior areas, which is similar to the microstructure of large-strain cold-worked metals. Furthermore, fewer subgrains are observed in specimen E than in the adiabatically deformed specimens. The observations suggest that little, if there is any, dynamic recovery occurs in isothermally deformed specimens. In some areas of their shear-localization regions, dynamic recovery may not occur at all. Although each loading cycle applied to specimen E corresponds to an adiabatic testing, the maximum individual displacement is only 0.21 mm, significantly less than those applied to the adiabatically deformed specimens (A, in the present study. B, and C) examined
Fig.
DEFORMED
Ta
Furthermore, after the application of each loading, specimen E is unloaded without being subjected to any additional stress pulses and is allowed to return to room temperature before the application of the next strain increment. There is no continuous heat accumulation within the shearband during the cycled testing. The maximum adiabatic temperature in the shearband of specimen E is estimated to be approximately 450 K, which is slightly below the lower boundary of dynamic recovery temperature for tantalum. The absence of the dynamic recovery in some regions of specimen E is thus expected. Considering that the dynamic recovery is incomplete in the isothermally tested specimens, sequential dynamic loading results in a stronger interaction between dislocations produced during each reloading cycle. Figure 12 is a TEM micrograph from an area in the shear-localization region of specimen D (two-cycle loading; 6i= 0.2 mm and & = 0.49 mm). Numerous dislocation tangles are observed around the dislocation intersecting points. It is known that the intersection of two screw dislocation lines produces jogs with edge orientations in both dislocation lines. Unlike a kink which is a sharp break in the dislocation line remaining in the same slip plane, a jog is a sharp break in the dislocation which is out of the slip plane. The only way that a screw dislocation can slip and take its jog with it is by a non-conservative process under thermal activation. At temperatures where climb cannot occur, the motion of screw dislocations will be significantly impeded by jogs. This should have some contribution, in addition to the dominant temperature effect, to the relatively high shear stress observed in the sequentially loaded specimens.
12. TEM micrograph from an area within the shearband of specimen D (y = 330%, sequential loading) showing numerous dislocation tangles at the intersecting points.
two-cycle
NEMAT-NASSER
et al.:
HIGH-STRAIN-RATE
DEFORMED
Ta
1323
1324
NEMAT-NASSER et al.: HIGH-STRAIN-RATE DEFORMED Ta
An important dislocation structure after dynamic testing is the presence of dislocation loops. Dislocation loops have been observed by Murr et al. [lo], Worswick et al. [29], and Qiang et al. [30] in tantalum EFPs, but have not been reported in hat-shaped tantalum specimens subjected to dynamic shear, over a broad range of temperatures. In the present study, a considerable number of dislocation loops are observed in both the adiabatically and isothermally deformed specimens, with the density of loops in the isothermally deformed specimens appearing to be substantially higher. Figure 13(a) and (b) shows TEM images from the adiabatically and isothermally deformed specimens, respectively, showing dislocation loops present in the shear-localization regions. These loops are relatively small. Most of them are under 20 nm. By employing an inside-outside method [31,32] in which the specimen is systematically tilted to determine the orientation of the loop plane, the habit plane and the Burgers vector of the loops are determined. The habit plane of the dislocation loops present in the dynamically sheared specimens, is determined to be { 1 lo}, with a loop Burgers’ vector of < 111 > . Both are consistent with the results obtained in tantalum EFPs [30]. There are two proposed mechanisms for dislocation loop formation [18]. One is the collection of vacancies at elevated temperatures, which is most likely the formation mechanism for the loops observed in the adiabatically deformed specimens. The other is the bowing out of jogged screw dislocations at the edge-oriented jogs, which appear to be the primary source for the loops produced in the isothermally deformed specimens. Wittman et al. [33] have reported the presence of twinning in shocked tantalum. In the present study, however, no evidence of deformation-induced twinning has been observed in the microstructure of dynamically sheared specimens tested under either the adiabatic or the isothermal conditions. Murr et al. [lo] and Worsick et al. [29] also noted the absence of twinning in tantalum penetrators and impactors.
4. SUMMARY In this study, TEM observations were used to investigate the microstructure of shearbands formed in polycrystalline tantalum during high-strain, highstrain-rate shear deformation, at adiabatic and quasi-isothermal testing conditions. The results of the present study can be summarized as follows. The plastic deformation is highly concentrated, producing a narrow shear-localization region with a dimension of approximately 200 pm across the hat-shaped specimen. Deformation inhomogeneity is found within the shearbands of specimens deformed to shear strains of up to 340%. At a shear strain of
3.
4.
5.
6.
7.
8.
910%, no deformation inhomogeneity is observed. Slip of the perfect screw dislocations on (1 lO}type primary planes is the dominant deformation mechanism. Band structure (elongated dislocation cells with small misorientation) is the most predominant microstructural characteristic of the shear-localization region. The size of the dislocation cells decreases with increased shear strain. Dynamic recovery is present in all specimens tested adiabatically at ambient initial temperature. Dynamic recrystallization is observed in a specimen adiabatically deformed to a shear strain of 910%, at 600 K initial temperature. This microstructure is preserved by the rapid cooling which takes place subsequently to the rapid heating (to approximately 1900 K) of the narrow shear zone due to localized plastic work. The microstructural evolution in the high-shearstrain specimen (y = 910%), from the area adjacent to the shearband toward the shearband center, includes arrays of dislocation lines, dislocation groupings, formation of elongated dislocation cells and subgrains, and recrystallized micro-grains (d N 0.15 pm). Compared with the adiabatically deformed specimens, the isothermally deformed specimens exhibit higher dislocation density, a higher degree of inhomogeneous dislocation distribution, and a stronger dislocation interaction, due to the sequential loading and relatively lower adiabatic the shear-localization temperatures within region. Small dislocation loops are extensively observed in the shearbands of both the adiabatically and the isothermally deformed specimens. Formation of the dislocation loops is attributed to the collection of vacancies at elevated temperatures and the bowing out of jogged screw dislocations along the edge-oriented jogs at low temperatures.
Acknowledgements-This work was supported by the Army Research Office (ARO) Contract, DAAL 03-92-G0108 to the University of California, San Diego, and made use of the TEM facilities at the Microscopy and Imaging Resources, Medical Center, University of California, San Diego. The authors would like to thank Dr William Ebihara and Mr Michael Hespos at ARDEC for providing the sample material.
REFERENCES 1. Nemat-Nasser, S. and Isaacs, J. B., Acta Metall., 1997, 45(3), . 907. 2. Bechtold, J. H., Acta Metall., 1955, 3(5), 249. 3. Werner. M.. Phvs. Stat. Sol.. 1987, 104, 63. 4. Steinbeig, b. i. and Lund; C. M., .I. Appl. Phys., 1989, 65(4), 1528. 5. Hoge, K. G. and Mukherjee, A. K., J. Mater. Sci., 1971, 12, 1666.
NEMAT-NASSER 6. 7. 8. 9. 10. 11.
12. 13. 14.
15. 16.
17. 18. 19.
20.
et al.:
HIGH-STRAIN-RATE
Zerilli, F. J. and Armstrong, R. W., J. Appl. Phys., 1987, 61(5), 1816. Zerilli, F. J. and Armstrong, R. W.. J. Appl. Phvs., 1990, 68(4), 1580. Brown, L. M., Met. Trans., 1991, 22A(8), 1693. Shih, H. K., Murr, L. E., Niou, C. S. and Zernow. L., Scripta Metall. Mater., 1993, 29, 1291. Murr, L. E., Niou, C. S. and Feng, F.. Scripta Metall. Mater., 1994, 31(3), 297. Murr, L. E., Niou, C. S., Sanchez. J. C., Shih, H. K., Duplessis, L., Pappu. S. and Zernow, L., J. Matrr. Sci.. 1995, 30, 2747. Vecchio, K. S., J. de Physique, 1994, 4(8), 301. Meyers. M. A., Chen, Y. J.. Marquis, F. D. S. and Kim, D. S., Met. Muter. Trans., 1995. 26A(lO), 2493. Meyer. L. W. and Manwaring, S., Metallurgical Applications of Shock- Wave and High-Strain-Rate Phenomena. ed. L. E. Murr, K. P. Staudhammer and M. A. Meyers. M. Dekker, New York, 1986, 657. Nemat-Nasser, S., Isaacs, J. 8. and Starrett, J. E., Proc. R. Sot. Lond., 1991, 435A, 371. Nemat-Nasser, S., in Shock-Wave and High-Strained. M. A. Meyers, L. Rate Phenomena in Mater& E. Murr and K. P. Staudhammer, M. Dekker, New York 1992, p. 1. Nemat-Nasser, S., Li. Y. F. and Isaacs, J. B., Mech. Muter., 1994, 17, 111. Dieter. G. E., Mechanical Metallurgy 3rd edn., 186 & 170, McGraw-Hill, New York, 1986. Pak, H. R.: Wittman, C. L. and Meyers, M. A., Metallurgical Applications of Shock- Wave and HighStrain-Rate Phenomena. ed. L. E. Murr, K. P. Staudhammer, M. A. Meyers. M. Dekker, New York 1986, 749. Meyers. M. A., Subhash, G., Kad. B. K. and Prasad, L., M&r. Mater., 1994, 17, 175.
21. 22. 23.
24. 25. 26. 27. 28. 29.
30. 31. 32.
33.
DEFORMED
Ta
1325
Chen, R. W. and Vecchio, K. S.. J. de Physique, 1994, 4(9), 459. Mgbokwere, C. O., Nutt, S. R. and Duffy, J., Mech. Mater., 1994, 17, 97. Hirsch, P.. Howie, A., Nicholson, R., Pashley, D. W. and Whelan, M. J., Electron Microscopy qf Thin Crystals 2nd edn.. 181, RE Krieger, Malabar, FL. 1977. Spitzig, W. A. and Mitchell, T. E., Actu Metall.. 1966. 14(10), 1311. Welsch, G., Gibala, R. and Mitchell, T. E., .4cta Metall., 1975, 23(12). 1461. D’Anna, G. and Benoit, W., Muter. Sci. Engr., 1993, A164, 191. Mizubayashi. H., Egashira, H. and Okuda, S., Acta Metall.. 1995, 43(l), 269. Materials Met& Handbook, ASM International. Park, Ohio, U.S.A.. 1990, 799. Worswick. M. J.. Qiang, N., Niessen, P. and Pick, R. J.. in Shock- Wave and High-Strain-Rate Phenomena in Materials ed. M. A. Meyers, L. E. Murr and K. P. Staudhammer, M. Dekker. New York 1992, p. 1. Qiang, N.. Niessen, P. and Pick, R. J.. Mater. Sci. Engr., 1993, A160, 49. Loretto, M. H. and Smallman, R. E.. D&t Analysis in Electron Microscopy, Wiley, New York, 1975, 86. Edington. J. W., Practical Electron Microscopy in New York, Materials Science, Van N Reinhold, 1976, 134. Witman. C. L.. Garrett, R. K.. Clark, J. B. and Lopatin, C. M., in Shock- Wave and High-Strain-Rate Phenomenrr in Materials ed. M. A. Meyers, L. E. Murr and K. P. Staudhammer, M. Dekker, New York 1992, p, 925.