1

Effect of Strain-rate in Severe Plastic Deformation on

Microstructure Refinement and Stored Energies

Shashank Shekhar, Jiazhao Cai, Saurabh Basu, Sepideh Abolghasem, M. Ravi Shankar*

School of Engineering, 3700 O‟Hara Street, University of Pittsburgh, Pittsburgh, PA, 15261,

USA

Abstract

The interplay of large strain and large strain-rate during high rate severe plastic deformation

(HR-SPD) leads to dynamic temperature rise in situ that engenders a recovered microstructure

whose characteristics is not just a function of the strain, but also of the strain-rate and the

coupled temperature rise during the deformation. In this paper, we identify three classes of

microstructures characterized by multi-stage recovery phenomena, that take place during the

high strain-rate SPD of Cu. It is found that the first stage of this recovery is similar to the first

stage of static recovery which is characterized mainly by annihilation of dislocations. Second

stage starts around 360K and was characterized by dislocations getting arranged in tight cell

boundaries and eventually into sub-grain. Recovery stages were found to be followed by a stage

of grain growth and recrystallization when the temperature in the deformation zone approaches

480K.

Keywords: ultrafine grained materials, severe plastic deformation (SPD), dynamic recovery,

stored energy, high strain-rate

* Corresponding author (ravishm@pitt.edu)

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I. Introduction

Severe plastic deformation (SPD) in metallic systems is accompanied not only by grain

refinement which endows it with strength [1-4], but also by generation and organization of high

density of crystal defects. The energies stored in various configurations of these defects provide

the driving force for most observed recovery and recrystallization phenomena [5-9]. Dislocations

which contribute to most of this stored energy in severely deformed materials are mostly

integrated into grain boundaries, cell boundaries or complex entanglements that are prone to

annihilation in response to heating, resulting in microstructural transformation.

Most of the work on SPD, till date, has utilized very low strain-rates (~0.1/s to 10/s), except for

few recent works wherein strain-rates of the order of 103 were utilized [10-12] and resulted in

intriguing property combinations. One of these studies (Ref. 10) utilized dynamic plastic

deformation instead of SPD where they obtained high levels of plastic deformation through

repeated compressive deformation at high strain rates. While in the works mentioned in Ref. 11

and 12, we utilized high shear strain rates for SPD where strains of the order 3-5 and strain-rates

of the order of ~103 were obtained in one pass of deformation. The interplay of large shear

strains and high srain-rates and the supplementary effect of temperature rise near the deformation

zone that accompanies the high strain-rates, as modeled in our earlier work, gives rise to novel

microstructures and subsequently, enhanced material properties [11, 12]. We have shown that

high strain-rate SPD can lead to dense dispersion of nanotwins in low SFE material like brass

[11]. In the case of copper, we found that high strain-rate SPD and the accompanying flash

heating leads to bimodal grain size distribution with modes at 500nm and 2000nm [12]. Such

multimodality was shown to lead to a significant increase in ductility of these samples. The flash

3

heating in the deformation zone can, in addition, lead to temperature-induced-dynamic-recovery

which is a microstructural transformation process that takes place by annihilation of defects, and

hence can be expected to alter the stored energy and thus can be related to the changes in

microstructure.

Recovery and recrystallization phenomena have been studied extensively [13-18]. However,

most of these studies, including the ones for dynamic recovery, have focused on very low strain-

rate (~.01 to 1.0) and very high temperatures (> 400°C). In this study, we look at a altogether

different regime of strain, strain-rate and temperature which can induce interplays of recovery

and recrystallization phenomena leading to novel fine grained materials. The difference in the

present study from the earlier studies can be highlighted in following points: this study utilizes

(a) very high strain values – of the order of 3 and higher as compared to a max strain value of 0.5

in the above mentioned references (b) very high strain-rate– in the range of 200 to 4500/s as

compared to highest strain-rate of 20 /s in the earlier studies; (c) we do not heat the samples, but

there is an in situ temperature rise which was calculated to be always less than 300°C. These

parametric differences are also evident from the Z (Zener-Hollomon parameter) values

calculated for various studies (see Table 1). The highest Ln(Z) value for most of these earlier

studies is less than 13, except for the Hasegawa et al, while the lowest Ln(Z) values calculated

for our experiments is above 23, as mentioned in Table 1 and 2. Hasegawa et al. deformed

aluminum samples at room temperature and then studied the recovery ex situ by annealing these

samples at 180°C [14].

The scale of the deformed grain structures examined in this study is also very different from

earlier studies. SPD results in grains of the order of few hundred nanometers as compared to

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polycryststalline and single crystalline samples used in earlier studies. It is important to note here

that the temperature induced microstructural transformation that we observe here, can neither be

classified as static recovery - which is the change in microstructure with time at a particular

temperature after some pre-strain, nor dynamic recovery – which is the change in microstructure

brought upon by increase in strain alone, during deformation process at a given temperature. The

“dynamic recovery” here is instigated by the rise in temperature caused by very high strain and

strain-rate that the material is subjected to, and hence can be termed as temperature-induced-

dynamic-recovery.

In this paper, we investigate the effect of in-situ heating resulting from large strain-rates on

severely deformed microstructures and its effect on the stored energy. We also relate the

microstructures with the variation in stored energy and this in turn enabled us to demarcate

different stages of recovery and recrystallization. To this end, we undertook an exploration of

thermomechanical deformation of copper across a wide-range of strains, strain-rates that involve

varying levels of exposure to in situ heating in the deformation zone in order to realize different

degrees of recovery and recrystallization.

II. Experimental Methods

Chip formation by machining emerged as our choice of method for severe plastic deformation

because of its versatility to impart large range of strain and strain-rate in a single deformation

pass in a range of material systems [19-25]. This allowed us to scan across wide ranges of strain-

rate (~101 – 10

3 /s) and strains while still creating fully-dense bulk samples that were still large

5

enough for reliable thermal and mechanical analysis. The magnitude of strains in the chip during

machining can be controlled by an appropriate choice of the rake angle of the cutting tool (α),

and the strain-rates are determined by the velocity of tool advance or the machining speed (V)

(see figure 1) [22]. The necessary control over strain and strain-rates were achieved through

appropriate choices of these parameters. We used a machining configuration as shown in Figure

1, with a depth of cut (DOC) value, which determines the width of the samples, as 3mm and feed

rate (f), which determines the thickness of the undeformed chip, as 0.17mm. This configuration

where the width is much larger than the undeformed chip thickness offers a plane-strain simple

shear configuration for imposing SPD across a range of strains, strain-rates and temperature

values [19, 22, 26].

A. Material System

We used commercially pure OFHC copper as our material system and annealed it at 700°C for

2hrs and subsequently machined it to create severely deformed chip samples using different rake

angles (0°, 20°) resulting in different shear strains, at three different machining speeds

(low=50mm/s, med=589mm/s and high=1274mm/s). The shear strain values were calculated

using the geometry of the final chip as described in Ref. [26]. The strain-rates can be calculated

directly from shear strain values and the machining speed as explained in Ref. [27]. In all, copper

was machined at 6 different conditions, here on referred to as a-low, a-med, a-high, b-low, b-med

and b-high. The „a‟ and „b‟ refer to two different rake angles used: 0° and 20° respectively. The

„low‟, „med‟ and „high‟ refer to the three different strain-rates utilized to obtain these samples.

The shear strain and strain-rate values for all these samples are listed in Table 2.

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B. Mechanical testing

Hardness tests were conducted on all these samples using a Shimadzu microhardness tester

(HMV-2). The samples were put in epoxy mount and polished till 0.05μ alumina. A force of

490.3 mN was used for measuring the hardness values. A minimum of 10 measurements were

taken to find an average value and the standard deviation. The standard deviation was found to

be less than 6% for all samples.

C. Differential scanning calorimetry (DSC) analysis

For an array of these specimens, the stored energy of the samples was measured by conducting

Differential Scanning Calorimetry (DSC) using Perkin Elmer Diamond DSC system. The DSC

plots for various samples are shown in Figure 2. Samples in the shape of discs were prepared

whose diameter was 3-5mm and the thickness was 1-2mm. The samples were polished on SiC

paper and then stress relieved using an acidic solution composed of a suitable mixture of Nitric

acid, Acetic acid and Phosphoric acid to get rid of any surface deformation which may influence

the total energy released. The weight of most of the samples was between 20 to 40 grams which

was found to be optimum, after conducting several tests on samples of varying weights, for

measuring stored energy which is of the order of 1J/g. Standard aluminum pans were used to

encase the sample and empty aluminum pan was used as reference. In order to determine the

baseline, each sample was reheated at the same condition and the resulting heat flow was

subtracted from the original heat flow. This provided individual baseline for each sample, thus

ensuring high accuracy of the results. A detailed review of use of DSC for calculating stored

energy for SPD materials can be found in Ref. [28].

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D. Electron Microscopy

Small discs of 3mm diameter were cut from the relevant samples to characterize using

transmission electron microscopy (TEM) in a JEOL 200-CX microscope. The samples were

prepared using double-jet electrolytic polishing machine in a Struers Tenupol-5 system.

Samples were also prepared for Orientation Imaging Microscopy (OIM) using EBSD. The

samples were prepared by polishing down to 0.1μ by hand and then put in vibratory polisher

with 0.05μ alumina solution for 1-2 hours for final polishing. OIM was carried out using Phillips

XL-30 system equipped with the EDAX-Ametek EBSD detector featuring a Hikari Camera and

TSL OIM software for data acquisition and analysis. All these images were taken using a step

size of 0.1μ and the scan size was 15μ X 15μ for each sample except for a-high sample for which

the scan size was 25μ X 25μ. We also used the TSL analysis software to measure the length of

regular (15°-180°) grain boundaries and sub-grain boundaries (2°-15°). We then calculated „f’ to

measure the length of sub-grain boundaries as a fraction of the total length of all boundaries.

E. Infrared Thermography

Infrared (IR) thermography was performed to measure the temperature rise and compare the

values with that predicted from our our model. We used a FLIR A325 camera which can

measure temperatures up to 400°C (~675K) for this purpose. The infrared camera was focused

on the middle of the deformation zone ahead of the tool tip in the plane-strain machining

configuration and the resulting images were utilized to calculate the temperature field. A typical

thermograph obtained while machining at 50mm/s using a rake angle of 40° is shown in Figure

3.

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III. Results

The shear strain, strain-rates and the hardness values of all the samples considered are listed in

Table 2. It is also useful to note here that, in general, shear strains decrease with increasing rake

angle and tend to decrease with increasing strain-rate for a given rake angle. Since the shear

strain values are very high, it would be expected that the hardness values would be saturated and

all the samples would show similar hardness. We find an interesting anomaly in a-high and a-

med which show much lower hardness values than the rest of the samples. We will demonstrate

in the ensuing that this can be traced to in-situ flash heating during machining caused by

temperature rise at high strain-rates. Depending on the amount of temperature rise, recovery can

take place up to different stages and if the temperature rise is too high, material may dynamically

undergo sub-grain growth or recrystallization and result in substantial softening.

To examine the effect of this in situ temperature rise on the stored energy, we carried out DSC

on our samples over a temperature range of 50°-300° C. Energy values for all the copper samples

are also listed in Table 2 along with the peak temperature at which this energy was released. To

better visualize the data, we plotted the energy release observed in the various samples as a

function of hardness for the various samples in Figure 4. Here we find that stored energy is

highest for b-low sample, which also showed highest hardness value. The samples a-low, b-med

and b-high show comparable stored energies and comparably high values of hardness, while a-

med show a somewhat lower hardness value and a smaller stored energy. We also note from

Table 2 that stored energy value for a-high sample, which showed low hardness, is almost

negligible.

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TEM images for all the samples are shown in Figure 5. We observe very high level of

refinements for a-low and b-low samples that are consistent with what might be expected from

imposition of high deformation shear strains at the low strain rates. On the contrary, we observe

moderate levels of refinement in a-med, b-med and b-high samples where, we observe

substantial dislocation networks and tangles. To acquire a more statistically significant sampling

of the microstructure across a wider length-scale we performed an EBSD analysis of the samples

(Figure 6). Here, we observe that the scale of the microstructure is generally in agreement with

what was observed in our TEM study. Additionally, we confirm that a-low and b-low samples

are indeed characterized by a preponderance of high-angle grain boundaries intermixed with a

small fraction (f) of low angle boundaries (f~0.3). On the other hand, the samples created at the

higher strain-rates (b-med, b-high and a-med) are characterized by a very high fraction of low

angle boundaries. Yet, we note the rather fine-scale of these low-angle boundaries in these

samples created at the high strain rates. This observation affords some rationalization of the

observed stored energies in the various samples that appears to decline with increasing

deformation rates with b-low > b-med > b-high and a-low > a-med > a-high. Figure 7 illustrates

the rather coarse grain structure in the a-high samples that indicate substantial recovery and even

recrystallization of the sample.

Additionally, we observed a dispersion of twins in the b-high sample that appeared to co-exist

amongst the network of the ultrafine high and low-angle boundaries. A typical HRTEM image

showing twin boundary in this sample is shown in Figure 8a. The inset shows the fast-fourier-

transformation (FFT) pattern obtained for this image and masks were used to obtain inverse-FFT

to reveal the twin boundary as shown in Figure 8b. Note the rather pristine structure of these

twins in this image.

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IV. Discussion

The behavior of plastic deformation systems for a given material and prior microstructure is

expected to be controlled by the interactive effects of shear strain, strain-rate and the temperature

in the primary deformation zone ahead of the tool tip. In this study, we examined SPD at a range

of strain rates in samples that were nominally deformed at room temperatures, even though the

temperature in the deformation zone is expected to be elevated. Here, the temperature in the

deformation zone is not an independent variable, but a function of the shear strain and the strain

rate. And, we can intuitively foresee that higher the shear strain and the strain-rate, higher the

temperature in the deformation zone and vice-versa. However, the temperature in the

deformation zone also modifies the constitutive behavior, thus interacting with the

accommodation of the shear strain and the strain-rates, and manifesting the myriad of resulting

deformed microstructures and associated thermomechanical property combinations.

Capturing these interactions is crucial for rationalizing our experimental results. To this end, we

utilized a machining model due to Weiner that is based on the moving heat source principles

[26]. The deformation zone temperature in machining depends primarily on (a) ratio of primary

flow stress to heat capacity, (b) deformation shear strain and (c) thermal number „α‟, which is

defined as *4/)tan..( fV where „ f ‟ is the feed rate (or the undeformed chip thickness) in

machining, is the primary shear plane angle, is the thermal diffusivity of the material and

V is the speed of machining that is also directly proportional to the strain rate in machining. It

has been shown that temperature rise in the deformation zone ΔT is given by Ref. [26]:

)/(*)1( ckT , where is the partition parameter that determines fraction of heat taken

away by the bulk work piece, k the shear-flow stress, the deformation shear strain imposed

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during machining and )( c is the heat capacity of the work material. Heat capacity )( c , of

copper was taken as 3.45 MJ/m3 [29]. can be estimated using equation given by Weiner [30]:

)2

1()1(

4

1

e

erfcerf , where is the thermal number. Shear flow

stress, k , can be calculated from 3/k , where is the tensile strength. However, this flow

strength is itself a function of shear strain and strain-rate and also the temperature in the

deformation zone. This effect is reasonably captured by material models such as the Johnson and

Cook (JC) equation [29]: ]1][ln1][[ ** mn TCBA , where 0

* / is the

dimensionless plastic strain rate, 1

0 0.1 s and T* is defined as 293293* mpTTT . A, B, n,

C and m are five material constants which were obtained empirically and their values are

A=90MPa, B=292MPa, n=0.31, C=0.025 and m=1.09 for copper [29]. JC model provides good

strain-rate dependence of stress at moderately high temperatures and high strain-rates, which is

where our experimental results are expected to lie. These two models (Weiner model for

temperature calculation [30] and JC model [29] for stress calculation) setup a

thermomechanically coupled problem where we need to know the temperature rise to calculate

the shear strength values, which in turn is required to calculate the temperature rise. The

equations for ΔT(σ, ε, ε ) and σ(ΔT, ε, ε ) can be solved using recursive iteration, the flowchart for

which is shown in Figure 9. The first run of the iteration begins with an initial guess of the

temperature rise. Then we use this temperature rise to calculate the homologous temperature and

then used the JC model to calculate the shear stress and subsequently the temperature rise using

the moving heat source model. This temperature rise is then used to compute the error between

the guessed temperature rise and the calculated temperature rise. Subsequently, regression is

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used to improve the guess until the error between the temperature rise input into the Johnson-

Cook model and that calculated from the moving heat source model converge to a sufficiently

small value. Using this approach we calculated the temperature rise (ΔTJC) and the shear flow

stress in the deformation zone ( k ) for the various SPD conditions in Table 2. Note that much of

this temperature rise primarily occurs in the deformation zone and during the transit through the

deformation zone, the material is subjected to this flash heating following which it cools very

rapidly. ΔTJC value was also calculated for the machining condition for which infrared

thermography was done (rake =40°; speed = 50mm/sec) and was found to be 40.5° C, hence the

expected temperature in the deformation zone would be T=293 + ΔTJC = 333.5 K. In the

thermograph shown in Figure 3, we see that the temperature in the deformation zone is 324 K

which is very close to the calculated value. This result reinforces our expectation that this

methodology can be used to accurately model the temperature rise and shear strength for a given

machining condition.

We note that we are considering the strain-rate and temperature rise due to the primary

deformation zone alone and the secondary effect due to frictional heating at the tool-chip

interface has been ignored. It has been demonstrated that the effect of frictional heating scales

with the cutting speed (V) and that it is has an effect on the deformation zone temperature at

speeds much higher than those considered here [26]. It is important to point out that for the

temperature field in Figure 3, the camera is focused on the deformation zone, ahead of the tool-

tip and the comparison between the model and the measurement is valid exclusively for this

zone. Further away from the deformation zone, outside the focal region of the camera, it may be

misleading to interpret the results to elucidate the characteristics of the thermomechanical

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deformation field. Still, it is noteworthy that even in the vicinity of the focused zone ahead of

the tool we do not observe any significant “hot spots” due to secondary frictional heating at the

tool-chip that approach the temperature rise due to the SPD. This is in line with the expectation

that for the deformation speeds considered here, the contribution from frictional heating is small.

This model now enables us to calculate deformation zone temperature for a range of shear strain

and strain-rates in machining to then identify the regions to which the various samples belonged

to (Figure 10). The horizontal axis is the strain-rate plotted on a logarithmic scale in order to

cover a large range of strain-rates and the vertical axis represents the shear strain values. The six

sample conditions that were used in our experiments are also shown on the plot. Colored bands

depict expected temperature in the deformation zone for the given shear strain and strain-rate

conditions and these values increase monotonically as we go towards top-right corner of the map

where both shear strain and strain-rates are high. The various stages in this figure are demarcated

in the context of the DSC results as delineated subsequently.

In order to understand temperature rise of the various samples in context of the stored energy, we

plotted stored energy as a function of temperature rise (Figure 11). It is immediately apparent

that the variation of the stored energy with the deformation zone flash heating temperature

collapses to a single curve, which has been drawn schematically and superimposed on this figure.

Further, in order to find the extent of the different stages of recovery on this plot, we looked at

the stored energy, hardness values and temperature rise of these samples as listed in Table 1. We

see that sample „a-high‟ which showed a very low hardness value and a very high temperature

rise has almost negligible stored energy. The negligible energy value implies that this sample

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underwent complete recovery process and experienced full microstructural transformation. This

was confirmed by OIM micrograph obtained for this sample (Figure 7) which showed very

coarse grains, which is in contrast to the ultra-fine grains expected at the shear strain values to

which this sample was subjected. The temperature rise for this sample that was calculated from

our iterative method is indicated in Table 1 as ~263° C, the highest among all the samples. We

therefore conclude that this sample was subjected to a high dynamic temperature rise in the

deformation zone that entailed its nearly complete recrystallization and hence the observed

softening, despite the otherwise high level of SPD. This corresponds to the stage III in Figures 10

and 11.

We note from Table 2 and Figure 4 that hardness values of „b-low‟ is high and so is the stored

energy. Moreover, the calculated temperature rise in the deformation zone from Table 1, for this

sample is quite modest ( ~75°C). Under the slow strain rate conditions, it is thus unlikely that

these samples have undergone any significant recovery. Hence, it can be interpreted that this

sample is in the first stage of recovery process which is similar to the first stage of static recovery

where nominal annihilation of dislocations occur due to thermal agitation. This level of recovery

is demarcated as Stage I in Figures 10 and 11. This would also imply that the deformation of this

sample is similar to other slow strain-rate SPD of Cu, like ECAP and we find evidence of this in

the stored energy observed for SPD of Cu obtained by other slow strain-rate processes which

were comparable to that in the present study [10, 31, 32, 33]. The „a-low‟ sample shows a

relatively higher temperature rise (~101°C) than „b-low‟ sample and also has lower energy

compared to it. It can be extrapolated that this sample condition is in Stage-II of the recovery

process. Furthermore, we see from Table 2 that „b-med‟ sample shows very high strength and

moderate temperature rise (~165°C), however, the stored energy in this sample (1.1 J/g) is still

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comparable to the „a-low‟ sample (1.1 J/g), implying that the in situ thermal agitation in „b-med‟

sample is insufficient for causing rampant recovery or coarsening. So, we can surmise that this

sample is likely in stage-II of recovery. The „b-high‟ and „a-med‟ samples show a relatively high

temperature rise (~201°C and ~223°C respectively) in Table 1, however, the hardness values of

„a-med‟ is significantly lower than the hardness value of „b-high‟, even though the shear strain

values of „a-med‟ is about twice that of „b-high‟. The energy stored in sample „a-med‟ (0.8J/g) is

also significantly lower than the energy stored in sample „b-high‟ (1.0J/g). It can be extrapolated

from these values that the dynamic recovery of „b-high‟ sample is somewhere in the vicinity of

end of stage-II while recovery for „a-med‟ went past stage-II and into the grain-growth regime

leading to its softening. Based on these arguments we demarcate the expected range of the

different recovery stages, which is superimposed on Figures 10 and 11.

Rationalizing the levels of dynamic recovery in the various samples becomes clearer once the

resulting microstructure is also considered. The TEM micrograph for „b-low‟ sample, shown in

Figure 5a, clearly reveals the presence of disorganized dislocation accumulation inside numerous

grains and is pointed out by the arrows. The low temperature rise in this sample does not allow

much mobility to these dislocations and hence a random distribution. The „b-med‟ samples, on

the other hand, which were exposed to a moderately high temperature-rise, would be expected to

have some cell-wall formation from increased mobility of these dislocations and we do see

evidence for this in the TEM micrograph of this sample shown in Figure 5c. Clearly, the

increased temperature causes some re-ordering of the dislocations into more organized cell-

walls. The „a-low‟ samples (in Figure 5b) show a mix of dislocation and some cell-wall

formation, confirming the suggestion that the recovery of this sample just went past Stage-I into

Stage-II. The „b-high‟ sample shows the formation of relatively sharp sub-grain boundaries in the

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micrograph shown in Figure 5d. The „a-med‟ sample which experienced a little higher

temperature than „b-high‟ shows a distinctively recovered microstructure, accompanied by

moderate grain growth. These micrographs, in effect, show the evolution of a microstructure

through different stages of recovery.

The progress through various recovery stages can also be followed in the Image Quality (IQ)

map obtained by EBSD, as shown in Figure 6, for five different samples (b-low, a-low, b-med,

b-high, a-med), which lie in three different stages of the recovery process and the eventual grain-

growth regime. The dark lines (black) in the figures depict regular grain boundaries which have

misorientation >15° while the light lines (green) depict sub-grain boundaries for which we used a

misorientation between 2° and 15°. With increasing recovery, more and more dislocations

rearrange to form cell-walls and sub-grains, so we expect to see an increase in low angle

boundaries from Stage-I through Stage-II which is clearly evident in images from Figure 6a

(Stage-I) through Figure 6d (end of Stage-II) by increasing density of green lines. Furthermore,

beyond this stage, grains start to grow, and here we expect to see a decrease in the density of

these sub-grain boundaries. In Figure 6e which shows IQ map for a-med sample, which

purportedly lies in Stage-III of grain growth and recrystallization, we observe significantly fewer

of these green lines compared to Figure 6d. We found that there was a monotonous increase in f -

the fraction of low angle boundaries, from Figure 6a and b through Figure 6d which represent

Stage-I through Stage-II of recovery. The relatively lower value of f for sample b-low in Figure

6b can be understood from the fact that this sample is very close to the beginning of Stage-II and

hence significant cell-wall formation has not taken place, yet. We also saw a significant drop in

this ‘f’-value for „a-med‟ sample in Figure 6e, which again goes on to show that recovery in this

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sample went past Stage-II and entered into the grain-growth regime, thereby reducing the density

of sub-grain boundaries.

The b-high sample shows a relatively high strength for a sample which purportedly lies near the

end of Stage-II, where we expect grain growth to begin and hence softening to set in. This higher

strength of the b-high sample-condition can also be attributed to the presence of twins as

revealed by HRTEM analysis, shown earlier in Figure 8. Dense dispersion of twins is known to

provide improved multifunctional characteristics to the material, from improved strength to

enhanced ductility [34-40]. Initially, we were surprised to observe the presence of twins even

amongst the rampant presence of dislocation structures in the moderately high SFE Cu,

particularly at high temperature expected in the deformation zone. To rationalize this

observation, we utilized the constitutive model for slip-twinning transition formulated by Meyers

et al. which shows that twins can be formed in Cu, albeit, at relatively large shear strains and

high strain-rates [41].

In order to confirm this, we plotted (see Figure 12) the stresses required for twin formation and

that for slip-dislocations for different shear strain values and used the strain-rate found for

sample b-high, i.e. 3300/s. We also ensured that we calculate the temperature for each

combination of shear strain and strain-rate considered in this plot using our iterative approach,

instead of using a constant temperature as used in the plots in Ref [41]. This is crucial because

the stress required for slip is given by [41]: 2/1

432 )lnexp( dkCTCC s

n

G , where

G =46.5MPa, C2=890MPa, C3=0.28 X 10-3

K-1

, C4=1.15 X 10-4

K-1

, n=0.5 and ks=5 MPa.mm1/2

.

And, this contains a strong thermal component, which in our thermomechanically coupled

machining framework varies with shear strain and strain-rate and hence needs to be explicitly

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considered. Since the twin formation is an athermal process, it was plotted as a horizontal line in

the Figure 12 depending only on the grain-size with a grain size dependent twinning stress given

by [41]: 2

1

0

dkTTT , where T0 =300MPa and kt=21.6MPa.mm1/2

. The stress values for

yielding and twinning was found to be strongly dependent on the grain size, hence we drew plots

for various initial grain sizes varying from 1.25µ to 0.5µ (see Figure 12). We observe a grain size

dependent stress for thermally activated slip which is generally smaller than the stress required

for twinning at the smaller shear strain levels. As the shear strain values increase, we find a

transition point beyond which twinning stress becomes smaller than the stress for slip and under

these conditions, twinning can become feasible.

In chip formation by machining, microstructure refinement occurs gradually across the

deformation zone wherein the microcrystalline material is transformed into a nanostructured

material in a single deformation pass. It has been shown that the deformation zone wherein this

transformation occurs is fan-shaped wherein the material is incrementally subjected to increasing

levels of shear strain [22]. It has also been demonstrated that in the initial parts of this fan shaped

deformation zone, the strain-rates are smaller and the strain rates become progressively more

intense.

In the initial parts of the fan shaped deformation zone, the accumulated shear strain values are

smaller and the level of refinement of the microstructure is also expected to be marginal. In this

early stage of deformation, suppose the microstructure was already refined to a grain size of 0.5

microns, no amount of shear strain can result in twin formation (Figure 12). However, if the

grain sizes in the initial sections of the deformation zone are only refined to say ~1.0 micrometer

in size, then from Figure 12, only a shear strain close to 3.2 is required to produce twins. Now,

19

past the initial marginal levels of deformation, the progressive straining in the b-high sample can

certainly reach these levels of shear strain in the more intense regions of the deformation zone

where the strain rates are also much higher. Thus, enabling the transition from slip to twinning in

accordance with the calculation illustrated in Figure 12. In our earlier work, we have shown that

sample condition b-high results in bimodal grain size distribution and a number of grains which

are greater than 1.0 microns were observed in the chip microstructure. It is plausible that

twinning occurred in these larger grains [12]. Additionally, it is likely that the twins also

contribute to the increased strength in the b-high sample.

V. Conclusions

Chip formation in machining was used to subject Cu to an array of large plastic shear strains at a

range of strain rates with an objective of understanding the effect of strain rate on the stored

energy of the system and its microstructure. The resulting materials were found to possess stored

energies that were found to be a function of the in situ dynamic heating that occurs in the

deformation zone as an outcome of the applied shear strain and strain-rate. Samples which

experienced low temperature rise were found to lie in the first stage of recovery which resulted in

nominal change in microstructure and stored energy. Second stage of recovery was found to start

around 360K and samples in this stage were characterized by formation of cell walls and sub-

grain boundaries with a slight decrease in stored energy. Third stage of the recovery was found

to start near 480K and was characterized by grain growth for samples very close to this

temperature while those subjected to much higher temperature were found to show signs of

complete recovery or recrystallization. The b-high sample which lies near the end of Stage-II

20

retained its hardness even though the samples just-into Stage-III showed substantial softening.

This was rationalized by the presence of twins along with the dislocation structures, which can

also contribute to the higher strength in this sample condition.

VI. Acknowledgements

We would like to acknowledge support from the National Science Foundation (Awards 0826010,

0856626, 0927410) and the Nuclear Regulatory Commission (Faculty Development Grant). We

also thank the Department of Mechanical Engineering and Materials Science for the provision of

access to the electron microscopy instrumentation and for assistance with the execution of this

part of our research.

21

Table 1: Zener Hollomon parameter for earlier studies on recovery and recrystallization of

copper.

T(K) Q/RT LnZ

Hasegawa et al. 2.20E-04 -8.42188 293 29.76019079 21.33831

Petkovic et al. 1.80E-03 -6.31997 723 12.06049226 5.740524

1.80E-02 -4.01738 773 11.2803828 7.262999

8.00E-02 -2.52573 813 10.72538241 8.199654

Sample et al. 5.00E-03 -5.29832 973 8.961701851 3.663384

1.58E-01 -1.84516 973 8.961701851 7.116542

5.00E-03 -5.29832 1073 8.126501306 2.828184

5.00E-02 -2.99573 873 9.988242728 6.99251

2.00E-02 -3.91202 873 9.988242728 6.07622

2.00E-01 -1.60944 873 9.988242728 8.378805

2.00E+00 0.693147 873 9.988242728 10.68139

2.00E+01 2.995732 873 9.988242728 12.98398

2.00E-01 -1.60944 723 12.06049226 10.45105

2.00E-01 -1.60944 668 13.05349686 11.44406

2.00E-02 -3.91202 773 11.2803828 7.36836

2.00E+00 0.693147 873 9.988242728 10.68139

2.00E-01 -1.60944 973 8.961701851 7.352264

Gottstein et al 5.00E-04 -7.6009 673 12.95651694 5.355614

Luton et al. 1.80E-02 -4.01738 773 11.2803828 7.262999

1.80E-03 -6.31997 723 12.06049226 5.740524

8.00E-02 -2.52573 813 10.72538241 8.199654

22

Table 2: SPD shear strain (γ), strain-rate, resulting hardness values, stored energy from

differential scanning calorimetry (ΔH), temperature value for peak energy release during

differential scanning calorimetry, and dynamic temperature rise in the deformation zone (ΔTJC)

and shear flow stress in the deformation zone (κ) calculated using Johnson and Cook model by

recursive iteration for various samples that were examined. (“a” samples were obtained using a

rake angle of 0° while “b” samples were obtained using a rake angle of 20°)

Sample γ Strain-rate (s-1)

κ (JC shear flow stress) [MPa]

ΔTJC

(°C) Hardness (kgf/mm2)

Δ H (J/g)

Peak Temp (°C) Ln(Z)

a-low 15.1 60 451 101 154 1.1 191.7 26.2

a-med 10.2 1000 382 223 147 0.8 215.4 23.8

a-high 8.5 2500 355 263 109 ~0 207.5 23.5

b-low 10.3 80 418 75 163 1.2 198.8 28.1

b-med 6.7 1350 365 165 161 1.1 215.3 26.2

b-high 5.8 3300 345 201 159 1.0 217.7 25.8

Br40H

23

Figure 1: Machining configuration and various parameters associated with machining. The „chip‟

coming out of machining makes the sample.

24

Figure 2: DSC plots for various samples (a) a-low, a-med and a-high samples (b) b-low, b-med

and b-high samples. [The various plots were shifted by 1J/g unit on y-axis to display various

samples on one plot]

25

Figure 3: Infrared thermograph for machining of copper on a linear setup using a rake angle of

40° at a speed of 50mm/sec Most of the temperature rise is concentrated in the region ahead of

the tool tip which underscores the fact that primary deformation zone is the main contributor to

temperature rise in the material and the chip.

26

Figure 4: Hardness plotted against the stored energy for various copper samples. The top left

quadrant designates materials with high strength and low stored energy. Top Right quadrant

shows materials with high strength, but high stored energy, eg nanostructured materials. Bottom

left quadrant shows material with low strength and low stored energy, eg. the usual

polycrystalline materials. Bottom right quadrant is for materials with low strength and high

stored energy.

27

Figure 5: TEM micrographs for (a) b-low: arrows point to random distribution of dislocations

indicating stage-I of recovery; (b) a-low: arrows indicate to the presence of dislocations and cell

walls that start to form in this samples are also visible (c) b-med: arrows point to cell walls

indicating stage-II of recovery; (d) b-high; arrows point to sub-grain walls indicating later stages

of stage-II of recovery; (e) a-med: illustrating much larger grains indicating grain growth

occurring in stage-III.

28

29

Figure 6: Image Quality maps obtained by EBSD to show the variation in fraction of low angle

boundaries along various stages of recovery (a) b-low sample in stage-I; (b) a-low sample which

has just entered stage-II; (c) b-med sample in stage-II; (d) b-high sample near the end of stage-II;

(e) a-med sample in stage-III. The black lines indicate the regular grain boundary (>15°), while

the green lines indicate the low angle boundaries (2°-15°). f is fraction of low angle boundaries.

[step size = 0.1μ] There is a gradual increase in the low-angle boundary fraction f from a-low and

b-low sample through b-med and finally to b-high sample. However, there is a sudden drop in

the f-value for a-med sample.

30

31

Figure 7: OIM of „a-high‟ sample showing coarse grain structure indicating recrystallization. The

inset shows the color scheme for the orientation of the grains. This micrograph clearly shows the

recrystallized microstructure that is obtained for „a-high‟ sample. (Black lines indicate the high

angle grain boundaries and the green lines show the low angle boundaries)

32

Figure 8: HRTEM image of sample b-high, showing twin boundary. (a) bright field image along

with the FFT pattern in the inset; (b) Inverse FFT image obtained from the FFT-diffraction

pattern, using the mask shown in the inset.

33

Figure 9: Flowchart to show the calculation of temperature rise (ΔT) and shear stress (σ) by

recursive iteration process.

34

35

Figure 10: Color-coded map showing the various parameters that influence the final

microstructure: shear strain, strain-rate and the temperature in the deformation zone (293 + ΔT),

where ΔT was calculated using recursive iteration. Various samples used in the study are shown

on the plot. (The temperature values are in Kelvin.)

36

Figure 11: Variation of stored energy with respect to temperature rise ΔT is plotted along with a

schematic depiction of three stages of recovery and eventual sub-grain growth regime.

37

Figure 12: Stresses required for twin formation and slip-dislocation and their transition point as a

function of shear strain, for various initial grain sizes. The solid lines describe the stress required

for yielding and the dashed lines describe the stress required for twinning for a given initial-grain

size. The circles mark the transition point from slip-dislocation to twin formation. (strain-rate =

4500 s-1

, same as that for sample b-high.)

38

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