Metallurgical and Materials Transactions A

, Volume 41, Issue 11, pp 2794–2804

Effect of Strain Rate on Evolution of the Deformation Microstructure and Texture in Polycrystalline Copper and Nickel


  • Nilesh P. Gurao
    • Department of Materials EngineeringIndian Institute of Science
  • Rajeev Kapoor
    • Bhabha Atomic Research Centre
    • Department of Materials EngineeringIndian Institute of Science

DOI: 10.1007/s11661-010-0360-x

Cite this article as:
Gurao, N.P., Kapoor, R. & Suwas, S. Metall and Mat Trans A (2010) 41: 2794. doi:10.1007/s11661-010-0360-x


The evolution of crystallographic texture in polycrystalline copper and nickel has been studied. The deformation texture evolution in these two materials over seven orders of magnitude of strain rate from 3 × 10−4 to ~2.0 × 10+3 s−1 show little dependence on the stacking fault energy (SFE) and the amount of deformation. Higher strain rate deformation in nickel leads to weaker \( \left\langle {101} \right\rangle \) texture because of extensive microband formation and grain fragmentation. This behavior, in turn, causes less plastic spin and hence retards texture evolution. Copper maintains the stable end \( \left\langle {101} \right\rangle \) component over large strain rates (from 3 × 10−4 to 10+2 s−1) because of its higher strain-hardening rate that resists formation of deformation heterogeneities. At higher strain rates of the order of 2 × 10+3 s−1, the adiabatic temperature rise assists in continuous dynamic recrystallization that leads to an increase in the volume fraction of the \( \left\langle {101} \right\rangle \) component. Thus, strain-hardening behavior plays a significant role in the texture evolution of face-centered cubic materials. In addition, factors governing the onset of restoration mechanisms like purity and melting point govern texture evolution at high strain rates. SFE may play a secondary role by governing the propensity of cross slip that in turn helps in the activation of restoration processes.

1 Introduction

Deformation texture evolution in a variety of materials has been studied extensively under different deformation modes such as tension, compression, rolling, and torsion. Most of these studies have been carried out for processing at normal strain rates and temperature.[1] Only a few reports are available that investigate texture evolution under nonambient conditions like very high strain rates (dynamic loading condition) and pressure.[2,3] It is expected that the material response to imposed stress and strain boundary conditions may differ significantly from one under normal conditions. This could be a result of the presence of additional accommodation mechanisms like twinning and even phase transformation in certain cases under these conditions.[4] It is, therefore, expected that texture evolution under nonambient conditions would be substantially different than under normal testing conditions. Of particular interest is the material behavior under dynamic loading conditions, as various crystal-plasticity-based deformation texture evolution models consider slip to be rate insensitive.[5,6]

In the present investigation, a study has been carried out to examine the rate effects on texture evolution for oxygen-free high thermal conductivity (OFHC) copper and nickel over seven orders of magnitude of strain rate ranging from 3 × 10−4 to ~2.0 × 10+3 s−1. The face-centered cubic (fcc) metals are characterized by medium and high stacking fault energy (SFE) with the values γCu = 78 mJ/m2 and γNi = 130 mJ/m2, respectively. However, they possess similar normalized SFE (γ/Gb, where G is the shear modulus and b is the Burger vector) and, therefore, are best suited for high strain rate studies, as additional deformation mechanisms like twinning are not expected to play a dominant role under dynamic loading conditions. This helps in studying the rate effect on texture evolution only caused by slip.

Experimental investigations pertaining to texture evolution as a function of strain rate have been sparse. The most profound investigation carried out to date is by Leffers,[7] who reported that rolling texture evolution in Cu-5 pct Zn is rate dependent. Leffers and Pederson[8] showed that a combination of strain rate and temperature can be used to get a particular type of texture in rolling of Cu-5 pct Zn. It was proposed that the activation energy for cross slip that governs the evolution of texture is not only temperature dependent but also strain rate dependent, which was attributed to the dependence of texture evolution on strain rate. Kocks and Mecking[9] showed that the increase in strain rate leads to an increase in flow stress as well as in the strain-hardening rate for an aluminum single crystal. This effect, however, abates as the magnitude of strain rate gets larger. Canova et al.[10] modeled high strain rate deformation by varying the strain rate sensitivity value from 0.01 to 0.3 in a rate-dependent non-Newtonian model proposed by Hutchinson[11] and Asaro.[5] They proposed that at higher strain rates, the number of active slip systems increase as a result of an increase in the rate sensitivity of slip. This increase reduces the plastic spin and subsequently leads to a weaker texture in uniaxial tension and compression, whereas strengthening of texture in simple shear results from the destabilization of grain orientations caused by shear. Asaro and Needleman[5] showed using simulations that if the latent hardening ratio q (ratio of hardening on inactive slip system due because of the active slip system) was changed from 1 to 1.4, then a subsequent change occurs in the deformation texture for axisymmetric compression. However, Bhattacharyya et al.[12,13] recently showed that an appreciable change in texture is found at very high strain rates of the order of 10+3 s−1 in fcc copper, whereas no such change is observed for body-centered cubic iron. This was attributed to the high strain-hardening exponent n of copper compared with iron. They proposed that the relatively higher value of n was likely to increase further with strain rate. Therefore, it may restrict grain rotations that could alter the overall texture, whereas low value of n for iron caused negligible change in texture at higher strain rates.

Fcc metals and alloys show varying strain-hardening behavior depending on the value of SFE. It is known that a deformation mechanism in fcc materials is dependent on the SFE. The variation in the wire drawing texture of fcc materials with SFE was reported by English and Chin,[14] which was attributed to differences in their latent hardening or to the propensity of twinning. However, Stout et al.[15] ruled out this hypothesis by taking account of the initial texture of the material in their simulations for texture evolution during compression. They showed that SFE has a very minor effect on the deformation texture evolution with brass (Cu-30 pct Zn) being an exception. Among other modes of deformation, the work of Hirsch and Lucke,[16] who performed a detailed analysis of the transition of rolling textures from copper to brass type in Cu and Cu-Zn alloys with decreasing SFE, is of paramount importance. They calculated the transition point from copper type to brass type texture as a function of strain and SFE in terms of percentage of Zn (refer to Figure 16 in Reference 16) and found that with a decrease in SFE, the strain required for a transition reduced, indicating that increased Zn (i.e., decreased SFE) and an increased amount of deformation were interchangeable. In a more recent investigation, Hughes et al.[17] reported wide varieties of textures and microstructures as a function of SFE and temperature during torsion deformation. The evolution of different types of textures was attributed to a local slip pattern reflected as grain division into cell blocks, whereas twinning was ruled out. Similarly, Suwas et al.[18] have reported a different texture during equal channel angular extrusion (ECAE) of fcc metals with different SFEs. All these studies used the value of absolute SFE; however, Ray[19] advocated the use of the normalized SFE (γ/Gb) to explain the SFE dependence on texture evolution.

In the present investigation, copper and nickel were chosen as model materials for studying the rate effects on texture evolution in cubic materials. Though copper and nickel have different SFE values, they are close on the normalized SFE scale (6.36 for Cu and γ/Gb = 6.87 for Ni) and show similar rolling texture. Thus, the effect of the strain-hardening exponent on texture evolution at high strain rates in fcc materials can be investigated using copper and nickel isolating additional effects.

2 Experimental

2.1 Materials

To study the effect of strain rate on texture evolution in fcc metals, OFHC copper and nickel that have similar normalized SFE but a different strain-hardening exponent were used as representative materials. The initial grain size of the materials was 60 and 75 μm, respectively. The (111) pole figures obtained from X-ray diffraction (XRD) for the starting material are shown in Figure 1. The starting texture is more diffuse in case of copper, whereas most orientations are concentrated near the center of the (111) pole figure for nickel. The difference in the initial texture is not expected to play an important role in the large strain deformation of copper and nickel as it is very weak in both the materials. Stout et al.[15] have shown that \( \left\langle {101} \right\rangle \) fiber is present irrespective of the SFE under quasistatic compression of fcc materials.
Fig. 1

{111} pole figure for copper and nickel

2.2 Mechanical Testing

Polycrystalline samples of copper and nickel of 6-mm diameter and 9-mm height were compressed uniaxially at strain rates of 3 × 10−4, 10−3, 10−1, 10, and 10+2 s−1 using a servohydraulic testing machine DARTEC. Teflon tape was used as a lubricant for the test to a strain of ~0.7. The high strain rate tests were carried out using a split Hopkinson pressure bar (SHPB) with incident and transmission bars of 13 mm diameter and 1300 mm length. Cylindrical specimens with diameter and height equal to 6 mm were used for the test. A MoS2 lubricant was used between the sample and the bar interfaces. Strain rates of around 2 × 10+3 s−1 were achieved with the speed of the striker bar, at impact being about 20 m/s. For a general description of the test, please refer to Reference 20. At high strain rates, the samples were tested in two steps. After the first deformation step to a strain of 0.4, the samples were machined to a smaller cross section and retested. The samples were deformed to two strain levels of 0.7 and 0.85 under dynamic loading conditions to study the effect of strain.

2.3 Characterization of Microstructure and Texture

The deformed samples were cut along the compression direction and subjected to the standard grinding and polishing procedure. One half of the disc was subjected to bulk X-ray measurement on the compression plane. The other half was cut further into two and was electropolished using standard electrolyte A2 (for Ni) and D2 (for Cu) provided by M/s Struers before subjecting it to electron back scatter diffraction (EBSD) analysis. The schematics of specimen preparation for EBSD and XRD are shown in Figure 2. EBSD data was analyzed using the commercially available TexSem Laboratory’s (TSL) OIM software and the Reanalysis of EBSD Data at Seoul National University (REDS) software. XRD-based line profile analysis was carried out to estimate the domain size and dislocation density using the multiple whole profile fitting tool.[21,22] Bulk texture was determined by measuring four pole figures namely (111), (002), (113), and (022) on the normal plane by Schulz reflection method using a XRD system on the centre of the compression plane. The measured pole figures were used to calculate the orientation distribution function (ODF) using the arbitrary defined cells approach available in commercially available Labotex software. EBSD was carried out using a field emission gun scanning electron microscope FEI SIRION on the transverse plane to capture microstructural features and for microtexture analysis. Samples deformed to a true strain of 0.85 were analyzed only by EBSD analysis, as the size was too small for X-ray analysis. A step size of 3 μm was used for EBSD scans. The samples deformed at high strain rates also were subjected to small area scans with a step size of 50 nm to check the presence of newly formed recrystallized grains.
Fig. 2

Schematic showing different sections of the sample used for texture measurement by XRD and EBSD

3 Experimental Results

3.1 Mechanical Behavior

The true stress true strain curves for the materials tested at a strain rate of 3 × 10−4 and at 2.0 × 10+3 s−1 are shown in Figure 3. Nickel had higher strength as compared with copper, whereas copper showed a higher strain-hardening rate. Both Cu and Ni exhibited higher flow stresses at 2.0 × 10+3 s−1 as compared with 3 × 10−4 s−1. It is to be mentioned here that the amount of strain that can be achieved in SHPB is limited, and hence, interrupted deformation has to be carried out to achieve higher strains. Therefore, the stress strain curves for the SHPB test in Figure 3 are discontinuous. Samples were deformed to a strain of 0.7 and 0.85 in SHPB in two steps to study the effect of strain in high strain rate deformation. Some recovery seems to have occurred in the Cu from adiabatic heating, as the flow stress on reloading is lower than projected from the initial work hardening (Figure 3). The strain-hardening exponent n was calculated from the stress–strain curves of the tested samples. The values of the strain-hardening exponent at the two extreme strain rates is given in Table I. It was found that copper showed a higher value of n when compared with that of nickel under quasistatic as well as dynamic loading conditions. No substantial change was found in the value of the strain-hardening exponent over seven order of magnitude of strain rate in both the materials.
Fig. 3

Stress–strain curve for nickel and copper samples deformed at a strain rate of 3 × 10−4 and 2 × 10+3 s−1. The high strain rate tests were carried out in two steps with intermediate machining after the first step. The gap in strain between the first and the second step is caused by the small amount of reloading as a result of multiple reflections in the incident bar

Table I

Strain-Hardening Exponent n for Copper and Nickel at Different Strain Rates

Strain Rate

3 × 10−4 s−1

2.0 × 10+3 s−1










3.2 Texture Evolution

The experimentally measured X-ray pole figures were used to calculate ODF using the commercially available Labotex software. The texture evolution in uniaxial deformation is well depicted using an inverse pole figure, and hence, these values were obtained from the calculated ODF for the deformed samples. The inverse pole figures computed on the compression plane of the samples deformed to a strain of 0.7 are shown in Figure 4. The Cu and Ni samples show clustering of orientations near \( \left\langle {101} \right\rangle \) in the inverse pole figure. The effect of SFE is not that apparent at the lowest strain rate (3 × 10−4 s−1), as both Cu and Ni show qualitatively a similar texture evolution under these conditions. However, the \( \left\langle {101} \right\rangle \) component is stronger for nickel compared with copper at \( \dot{\varepsilon } = 10^{ - 3} \,{\text{s}}^{ - 1} . \) At an intermediate strain rate of 10+2 s−1, the \( \left\langle {101} \right\rangle \) component weakens in nickel, whereas it is more or less unaffected in copper. At higher strain rates, orientation is spread for nickel, whereas copper maintains a strong \( \left\langle {101} \right\rangle \) component.
Fig. 4

\( \left\langle {00 1} \right\rangle \) Inverse pole figure (a) initial, (b) έ = 3 × 10−4 s−1, (c) έ = 10+2 s−1, and (d) έ = 2 × 10+3 s−1 samples for copper and (e) initial, (f) έ = 3 × 10−4 s−1, (g) έ = 10+2 s−1, and (h) έ = 2 × 10+3 s−1 samples for nickel deformed to ε = 0.7

To get a quantitative estimate of texture evolution with strain rate, the volume fraction of the \( \left\langle {101} \right\rangle \) component for samples tested at \( \dot{\varepsilon } = 10^{ - 3} , \) 10+2, and ~2.0 × 10+3 s−1 was plotted (Figure 5). It is observed that the volume fraction of the \( \left\langle {101} \right\rangle \) fiber component, which is the major component in compression of fcc materials, shows a different response with an increase in strain rate for copper and nickel. For nickel, the volume fraction of the \( \left\langle {101} \right\rangle \) fiber decreases with an increase in strain rate and saturates at \( \dot{\varepsilon } = 10^{ + 2} \,{\text{s}}^{ - 1} . \) However, for copper the volume fraction of the \( \left\langle {101} \right\rangle \) component was almost constant until \( \dot{\varepsilon } = 10^{ + 2} \,{\text{s}}^{ - 1} \); after which it showed an increase at 2.0 × 10+3 s−1. A significant decrease was observed in the \( \left\langle {101} \right\rangle \) component for the nickel sample deformed at \( \dot{\varepsilon } = 10^{ + 2} \,{\text{s}}^{ - 1} \) as against the one deformed at 10−3 s−1. On the contrary, a reduction in the \( \left\langle {101} \right\rangle \) fiber component in copper was very little over this range, comprising six orders of magnitude of the strain rate. In addition to the volume fraction of different texture components, the strength of texture can be estimated by a scalar parameter such as “texture index” that is proportional to F2, where F is the ODF. To have a clearer idea of textural changes, the texture index gives a quantitative estimate of the strength of the texture and was plotted with strain rate for copper and nickel (Figure 6). The texture index was reduced in the case of nickel from strain rate \( \dot{\varepsilon } = 10^{ - 3} \) to 10+2 s−1, whereas it was almost constant for copper. However, at a higher strain rate \( \dot{\varepsilon } = 2 \times 10^{ + 3} \,{\text{s}}^{ - 1} , \) the texture index increased only slightly for nickel, whereas a substantial increase was observed for copper.
Fig. 5

Variation in the volume fraction of \( \left\langle {101} \right\rangle \) component for samples deformed to a strain of 0.85 at different strain rates
Fig. 6

Variation of texture index for samples deformed to a strain of 0.7 at different strain rates

3.3 Microstructural Evolution

The optical micrographs of the samples deformed at \( \dot{\varepsilon } = 2 \times 10^{ + 3} \,{\text{s}}^{ - 1} \) (Figure 7) indicated evidence of grain fragmentation in copper and nickel. It was observed that the grains in nickel were full of deformation bands, whereas no such features were seen in copper. Microstructural investigation using EBSD was carried out for analyzing the stronger texture observed in copper at high strain rates. Figure 8 shows the inverse pole figure (IPF) map for the samples deformed to a strain of 0.85 from EBSD analysis. The EBSD-generated microstructures were analyzed further using parameters like the grain orientation spread (GOS) and grain average misorientation (GAM), which indicate long-range and short-range intragranular misorientations, respectively, and were developed for geometrically necessary dislocations during plastic deformation. The values of these parameters averaged with the area of the grain are shown in Table II. It is observed that GAM and GOS values per unit area are higher for the nickel samples deformed at a higher strain rate than for those deformed under quasistatic (3 × 10−4 s−1) conditions to the same amount of strain. This outcome is expected, as the entire grain cannot reorient completely because of short time scales involved, leading to grain fragmentation under dynamic loading condition. However, for copper samples, a decrease was observed in the intragranular misorientations. The grain boundary character distribution (GBCD) for the samples deformed to strains of 0.7 and 0.85 by SHPB and samples deformed at 3 × 10−4 s−1 to a strain of 0.85 is shown in Figure 9. A decrease in the low-angle grain boundary (LAGB θ ≤ 15 deg) and a corresponding increase in the high-angle grain boundary (HAGB θ > 15 deg) was observed at a higher strain rate and a higher strain in copper and nickel with the effect being dominant in the former case. The fraction of coincident site lattice (CSL) boundaries is plotted in Figure 9 for a copper and nickel sample deformed at different strain rates and up to different strains at a high strain rate. It was observed that the CSL fraction increased at a higher strain rate in copper, whereas no significant change in the fraction was noticed for nickel. The misorientation profile in copper and nickel deformed to a strain of 0.85 by SHPB test is shown in Figure 10 with the McKenzie plot for random distribution. A bimodal distribution of misorientations is clearly observed in copper.
Fig. 7

Optical micrograph for copper and nickel samples deformed to a strain of 0.85 at strain rate of 2 × 10+3 s−1 using SHPB test
Fig. 8

IPF maps obtained from EBSD for copper and nickel samples deformed to a strain of 0.85 at strain rate of 2 × 10+3 s−1 using SHPB test

Table II

Average Normalized GAM and GOS Values for Sample Deformed to a Strain of 0.85 at Quasistatic and Dynamic Loading Conditions

Strain Rate


3 × 10−4 s−1 (deg/μm2)

2.0 × 10+3 s−1 (deg/μm2)














Fig. 9

GBCD of samples deformed to a strain of 0.85 at low and high strain rates and the sample deformed to a strain of 0.7 at strain rate of 2 × 10+3 for (a) copper and (b) nickel, respectively. An increase in strain rate and an increase in strain at high strain rates have a similar effect
Fig. 10

GBCD for copper and nickel samples deformed to a strain of 0.85 using SHPB test

The increase in amount of HAGB in copper with strain rate and strain could be attributed to the formation of new grains by recrystallization. To verify this, a high-resolution EBSD scan with a step size of 50 nm was carried out on the sample deformed to strain of 0.85. The inverse pole figure and image quality (IPF + IQ) map for the copper and nickel sample shown in Figure 11(a) clearly indicates the presence of smaller grains in copper, whereas a microband is observed in nickel. The transmission electron micrograph (TEM) image (Figure 11(b)) of the copper sample clearly shows the presence of <100 nm grains as a result of recrystallization.
Fig. 11

IPF + IQ map with a step size of 50 nm for (a) copper and nickel deformed at a high strain rate obtained from EBSD, (b) TEM micrograph of a copper sample showing the presence of sub 500 nm grains

3.4 Crystal Plasticity Modeling

The microstructural observation of grain fragmentation was incorporated in a crystal plasticity code to model texture evolution. The Los Alamos polycrystalline plasticity (LApp) code,[15] based on the Taylor Rate sensitive theory, was used to model quasistatic and dynamic compression test. A full constraint Taylor’s approach with Bishop Hill criterion was adopted that activates slip systems at the single crystal yield surface. The maximum work principle was used to select the vertex that fulfills the strain increment. We used rate sensitivity of 0.05 that ensures a unique determination of shears on the activated slip systems. Once the activity of the slip systems is obtained, grain rotation could be obtained that leads to texture evolution.

In the present study, the experimentally measured texture of copper and nickel was discretized into 200 single orientations that were used as input to the code. A normal full constraint Taylor model with \( \left\{ { 1 1 1} \right\}\left\langle { 1 10} \right\rangle \) slip system activity was used to model compression texture evolution under quasistatic condition. Both copper and nickel showed a strong \( \left\langle {101} \right\rangle \) texture, which is in accordance with the experimental observations. The high strain rate response of copper was different from that of nickel. For copper, the microstructure was characterized by lesser grain fragmentation and by the presence of recrystallization. Though it is not possible to model recrystallization by LApp code, we developed a unique scheme to account for grain fragmentation. A scheme depicting grain fragmentation is shown in Figure 12. It is shown clearly that with deformation, a gradual change occurs in orientation within the grain as a result of the generation of dislocations. Because of shorter time scales involved in high strain rate deformation, an entire region of the grain cannot reorient itself, leading to grain fragmentation. The schematic of grain fragmentation shown in Figure 12 is a simplified model that has been used in the present work to simulate a high strain rate deformation. The actual situation is much more complex and hence is difficult to model. In this investigation, grain fragmentation was captured by adding misorientation to the existing grain orientations on deformation. A normal distribution with a mean of 0 deg and standard deviation (Δ) of 5 deg and 15 deg was added and subtracted from the existing grain orientations (φ1 Φ φ2). This was implemented after the deformation to half the strain for copper and nickel, respectively. The results ensured a higher intragranular misorientation for nickel than for copper. The new set of grains with the older one formed the input for deformation to the final strain. For nickel, the higher intragranular misorientation was modeled by adding a higher misorientation (Δ = 15 deg) to the grains, whereas less misorientation (Δ = 5 deg) was incorporated in copper to model lesser intragranular misorientation. This scheme is valid even in the presence of continuous dynamic recrystallization (cDRX) as the recrystallized grains have the same orientation as the parent grains. The simulated texture shows qualitative similarity with the experimentally measured texture with a weakening of texture in nickel, whereas little effect is noted on copper with strain rate (Figure 13).
Fig. 12

Schematic of the grain fragmentation mechanism proposed in the present investigation. A change in orientation with deformation leads to misorientation within the grain and subsequent grain fragmentation
Fig. 13

Simulated [001] IPF for samples deformed to a strain of 0.85 under quasistatic condition for nickel and copper (a) and (b) and under dynamic deformation conditions for nickel and copper (c) and (d)

4 Discussion

Results of the present investigation indicate a unique behavior of copper under dynamic loading conditions. The stronger and qualitatively similar texture observed in copper in the present investigation seems to contradict the observations at high strain rate as reported by Bhattacharya et al.[12] However, it should be noted that their investigation involved the deformation of copper in shear mode as against compression in the present investigation. Canova et al.[10] had predicted that the higher rate sensitivity at a large strain rate will lead to an accelerated texture evolution in shear, whereas a retardation of texture would occur in compression or tension. In the present investigation, a high strain rate deformation of copper presents a unique case with a stronger texture evolution in compression. Various factors that lead to this unique behavior of copper will be discussed in detail.

4.1 Effect of Strain-Hardening Exponent

Bhattacharya et al.[12,13] had attributed the stronger texture evolution in copper compared with that in iron to the higher strain-hardening value in the former case. It was proposed that at higher strain rates, a further increase occurs in the n value that leads to a unique texture evolution in copper. To examine the effect of strain-hardening characteristics on texture evolution at different strain rates, the corresponding strain-hardening exponent was calculated from the stress–strain curves. It was observed that although the yield strength of nickel is higher than that of copper, the strain-hardening exponents are in the opposite order (i.e., nNi < nCu at a lower strain rate). The calculated value of the strain-hardening exponent was 0.4 and 0.146 for Cu and Ni, respectively, at the lowest strain rate. The increase in stress with the increase in strain rate was apparent in both the cases. The strain-hardening coefficient increased very little for copper as well as for nickel to 0.42 and 0.148, respectively, at the highest strain rate. This is also in accordance with the fact that the effect of the strain rate on the hardening behavior for fcc materials is negligible. The decrease in the volume fraction of \( \left\langle {101} \right\rangle \) fiber in Ni can be attributed to a randomization of texture at a higher strain rate. Nickel, because of its low strain-hardening exponent, is vulnerable to deformation instabilities like deformation banding. This finding could be the reason for a weaker texture evolution in nickel at high strain rates. However, copper with a higher strain-hardening exponent is more resistant to these instabilities and maintains a strong \( \left\langle {101} \right\rangle \) component until strain rate \( \dot{\varepsilon } = 10^{ + 2} \,{\text{s}}^{ - 1} . \) This proposition is supported by the observation that higher intragranular misorientations are developed in nickel (Table I) when compared with copper. Another important observation was the evolution of a higher HAGB fraction in copper when compared with that in nickel at a higher strain rate. However, the strengthening of the \( \left\langle {101} \right\rangle \) fiber in copper at strain rate \( \dot{\varepsilon } = 2 \times 10^{ + 3} \,{\text{s}}^{ - 1} \) cannot be explained completely based on these arguments. To understand the discrepancy shown by copper, a detailed microstructural investigation was carried out using EBSD. The effect of microstructural evolution on texture will be discussed in the latter section.

4.2 Origin of HAGB at a High Strain Rate

Grain-boundary analysis was carried out using the data obtained from EBSD. The volume fraction of LAGB with misorientation angle θ ≤ 15 deg, HAGB with θ > 15 deg, and CSL Σ3 boundaries is shown in Figure 8. The high amount of LAGB in copper and nickel under quasistatic deformation to a strain of 0.85 is a characteristic of heavily deformed metals and alloys. However, the sample deformed by SHPB to a strain of 0.7 and 0.85 show a higher amount of HAGB accompanied with a decrease in LAGB for copper and nickel. Thus, an increase in the strain rate and the strain at a higher strain rate has the similar effect in copper and nickel. In both copper and nickel, HAGB increased at the expense of LAGB with an increase in the strain rate (for equal strain) and the strain (at the same strain rate). The GBCD of copper and nickel samples deformed by SHPB to a strain of 0.85 does not follow the random McKenzie distribution but shows contrasting behavior. Nickel shows a large amount of LAGB fraction and a very low amount of HAGB. On the other hand, copper shows a bimodal distribution of misorientation with a higher amount of LAGB accompanied by a sufficient amount of HAGB. A bimodal distribution of grain misorientation (Figure 10) present in copper is attributed to the continuous conversion of LAGB to HAGB. The increase in HAGB at the expense of LAGB can be attributed to grain subdivision or to the formation of new grains as a result of recrystallization. Copper because of its high strain-hardening rate is resistant to shear band formation and hence maintains the characteristic \( \left\langle {101} \right\rangle \) deformation texture. However, nickel has a low strain-hardening exponent that leads to extensive microbanding, which contributes to the scatter in the texture. Although no shear bands were observed in the deformed samples, the nickel sample was characterized by grain fragmentation and microband formation, which were absent in the copper sample. This finding explains the continuous weakening of texture with the strain rate for nickel and the relative little change in copper that is resistant to any kind of deformation heterogeneity like microbands. It is to be mentioned here that the velocity of dislocations in copper is an order of magnitude higher than that in nickel under the experimental conditions.[4] This situation accounts for the faster conversion from LAGB to HAGB in copper.

To investigate the anomalous increase in HAGB, a small region in the scan with larger step size (3 μm) was subjected to a scan with a smaller step size (50 nm) to check for recrystallized grains (Figure 11). A microstructural investigation from high-resolution EBSD shows the presence of submicron grains in copper, whereas no such features are found in nickel. Moreover, grains are found with a range of aspect ratio between 0.6 and 0.8, but very few grains are found with aspect ratio of 1, indicating that copper does not undergo dynamic recrystallization completely. These submicron-sized grains are the newly formed recrystallized grains that contribute to the high amount of HAGB and lead to bimodal misorientation distribution for the copper. The anomalous behavior of copper is a result of the self-organization of microstructure[23] leading to cDRX, which is attributed to its lower melting point and higher strain hardening rate.

4.3 Restoration Mechanism

At high strain rates, deformation is expected to be heterogeneous because of the formation of shear bands or by the activation of more slip systems as proposed by Canova.[10] All these factors contribute to a randomization of texture as observed in nickel. However, to maintain strain compatibility between various heterogeneously strained regions of the same sample, geometrically necessary boundaries (GNBs) are needed. In addition to this, the statistically stored dislocations within the grain contribute to the formation of LAGB within the grains. As the amount of strain increases, the misorientation of both the boundaries increases because of an accumulation of dislocations. This effect is more pronounced for the GNBs, and they contribute to the higher volume fraction of HAGBs at higher strains. Because of the lower melting point of copper accompanied with its higher purity, grain-boundary movement is expected, whereas a higher melting point of nickel abates the possibility of such a process at room temperature (or about 70 K to 80 K (70 °C to 80 °C) in SHPB test). A steady state therefore may be achieved in copper, wherein the grain boundary moves at a rate comparable with that of the formation of new boundaries. This in turn leads to the continuous increase in HAGB with the amount of strain at a higher strain rate and for a higher strain rate at equal strain. For nickel, however, the migration of dislocations as well as that of boundaries is sluggish because of the higher melting point. Nevertheless, the higher SFE of nickel leads to an extensive cross slip, and the conversion of LAGB to HAGB is accelerated with the amount of strain at a higher strain rate and for a higher strain rate at equal strain. At the same time, new HAGBs are created by grain and microband formation in nickel. However, this effect is not as dominant as in copper. The dislocation density values measured from the Multiple Whole Profile fitting tool yielded a value of 2.36 and 2.0 × 1016/m2 for nickel and copper, respectively. The slightly smaller dislocation density value for copper indicates the absence of conventional recrystallization or geometric dynamic recrystallization (gDRX) that involves large grain-boundary migration. Therefore, a steady state is reached in copper, and the grain refinement as shown in Figure 10 is attributed to cDRX. SFE thus plays a secondary role in the evolution of deformation texture under dynamic conditions by controlling the onset of relaxation mechanism if possible. The presence of cDRX in ECAE of copper has been reported by Skrotzki et al.,[24] and it was shown that it does not change the texture significantly. Meyers et al.[25] had proposed that the microstructural breakdown mechanism that dominates a high strain rate deformation is also relevant in materials processed by severe plastic deformation. It is therefore expected that the operation of cDRX helps in maintaining the strong \( \left\langle {101} \right\rangle \) in compression of copper even under dynamic loading conditions. Bhattacharya et al.[13] had attributed the sharper texture evolution at a high strain rate deformation to the moderate rise in temperature that led to dynamic recovery. Also, Meyers et al.[26] have shown that \( \left\langle {101} \right\rangle \) fiber texture forms near shear bands in stainless steels deformed at strain rate of 10+4 s −1 to accommodate deformation and that the shear bands consist of newly recrystallized grains of the order of 100 to 200 nm. This is accordance with the \( \left\langle {101} \right\rangle \) fiber and submicron grains that are observed in copper.

5 Conclusions

The objective of the present investigation was to study texture evolution in copper and nickel at extreme strain rates ranging seven orders of magnitude from 3 × 10−4 to ~2.0 × 10+3 s−1. The results of the investigation led to the following conclusions:
  1. 1.

    Texture evolution in compression of fcc Cu and Ni shows \( \left\langle {101} \right\rangle \) as the major deformation texture fiber component, and only the strengthening or weakening of this fiber is observed over a wide strain rate range.

  2. 2.

    Copper maintains the strong \( \left\langle {101} \right\rangle \) fiber at higher strain rates more than six orders of magnitude (from 10−4 to 10+2 s−1), whereas texture evolution is retarded in nickel as the strain rate increases. This is attributed to the higher strain-hardening coefficient of copper that prevents the formation of deformation heterogeneities like shear bands or microbands that are prevalent in nickel, which contribute to weakening of texture.

  3. 3.

    There is an increase in the strength of texture for copper while it weakend for nickel when deformed under dynamic loading conditions. This effect is more pronounced in copper because of the onset of a restoration mechanism like cDRX as a result of its lower melting point compared with nickel.

  4. 4.

    The strain-hardening exponent n decides the texture evolution in fcc materials at a higher strain rate, whereas SFE plays little role in the deformation texture evolution at higher strain rates. Instead, various parameters like purity, temperature, and so on, influence restoration mechanisms in materials and might play an important role in determining texture evolution under dynamic loading conditions.



The authors acknowledge the X-ray equipment support from the national facility (DST-IRPHA) at I.I.T. Bombay. Thanks are due to Professor I. Samajdar for providing this facility. The authors are also thankful to Dr. D.-I. Kim (KIST, Seoul) and to Professor K.H. Oh (SNU, Seoul) for providing the REDS software. The authors thank Mr. S. Sasidhara for help in carrying out the compression tests using DARTEC. The authors thank DST for the microscopy facility at the Institute of Nano Science Initiative in Indian Institute of Science, Bangalore. The authors are grateful to Professors G. Ravichandran and R.K. Ray for discussion on various aspects of the present study.

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2010