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High strain rate behavior of ultrafine-grained Al–1.5 Mg
Materials Science and Engineering A 496 (2008) 308–315
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High strain rate behavior of ultrafine-grained Al–1.5 Mg R. Kapoor ∗ , J.B. Singh, J.K. Chakravartty Materials Group, Bhabha Atomic Research Centre, Mumbai 400085, India
a r t i c l e
i n f o
Article history: Received 29 February 2008 Received in revised form 13 May 2008 Accepted 22 May 2008 Keywords: Ultrafine-grained Al–Mg Equal channel angular pressing Severe plastic deformation High strain rate Hopkinson bar Strain rate sensitivity
a b s t r a c t The high strain rate behavior of ultrafine-grained Al–1.5 Mg alloy produced by the equal channel angular pressing technique is investigated in this work. High strain rate compression tests were performed in a split Hopkinson pressure bar to achieve nominal strain rates of around 2000 s−1 at temperatures ranging from 300 to 523 K. In addition to un-interrupted Hopkinson bar tests, strain rate change tests were carried out using a flange and sleeve arrangement on the incident bar. The results obtained at the high strain rates were compared with those at low strain rates from an earlier study. It was seen that at the strain rate of 2000 s−1 the transition from hardening to softening (with respect to the coarse grained alloy), was shifted to higher temperatures. The strain rate sensitivity for the ultrafine-grained alloy was higher as compared to the coarse grained alloy for the entire range of testing. The increased strain rate sensitivity and the average subgrain size measured after testing at 473 and 523 K, suggest an active role of grain boundaries in the process of deformation. The possible reasons for softening at the low strain rates and its suppression at the high strain rates are discussed. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The effect of grain size on the mechanical properties of polycrystalline materials has been widely studied in the past. These studies have primarily focused on the Hall–Petch (H–P) relation for grain sizes ranging from tens to hundreds of micrometers. It is only in the recent years that the H–P relation has been investigated in the ultrafine (submicron) and nanometer grain size ranges 1 [1,2]. It has been observed that at ambient temperatures the strength of a metal with an ultrafine-grained (UFG) microstructure is higher than that with a coarse grain (CG) one [3–5]. It is also seen that when the grain size is reduced to the tens of nanometer range in fcc metals, the flow stress saturates, or in some cases even decreases with decreasing grain size [1,5]. This later effect is usually referred to as the inverse H–P effect. Although the strength decreases with decreasing grain size in the nano regime, its value still remains higher than that of the CG material, suggesting that a complete cross-over in strength between the CG and UFG has still not occurred. At conditions where grain boundaries act only as barriers to dislocation motion, deformation takes place within grains and UFG is stronger, more so for severely deformed materials where the dislocation density within grains is high to start with. Conversely, at conditions where grain boundaries act as sinks to dislocations or where grain boundary deformation occurs, a UFG structure will be softer than a CG one.
∗ Corresponding author. Tel.: +91 22 25590139; fax: +91 22 25505221. E-mail addresses: [email protected], [email protected] (R. Kapoor). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.05.043
Clearly, lower temperatures and higher strain rates should promote hardening, while higher temperatures and lower strain rates should promote softening. In one study on UFG Cu [6] this transition from hardening to softening was found to occur at 418 K. For UFG Al–1.5 Mg this transition from hardening to softening was found to be dependent on the strain rate and temperature of testing [7,8]. Reducing grain size is also known to affect the strain rate sensi˙ where and ε˙ are the true stress and the tivity m = ln / ln ε, true strain rate, respectively. In general for fcc materials [7–17], and in particular for Al and its alloys [7–11,14,15], refining grains to the UFG level increases m. This increase in m with decrease in grain size has been explained [11] on the basis of the relation between m and the apparent activation volume Va , m = MkT/Va , where M is the Taylor factor, k is the Boltzmann constant and T is temperature. The increase in m occurs due to a drastic decrease in Va caused by a high dislocation density, even though there is a moderate increase in due to grain refinement. Usually m varies with deformation conditions such as ε˙ and T, and since is a function of ε˙ and T, m is also seen to vary with . It has been observed that m decreases with increasing as seen from studies on UFG Cu [6], Ni [18] and Al–1.5 Mg [8]. Also m has been found to increase with increasing T ˙ as in UFG Al [19] and UFG Cu [12]. and decreasing ε, Sufficient experimental evidence exists to suggest that for fcc UFG metals increasing ε˙ (increasing ) reduces m. However, most studies are at low strain rates (≤ 1 s−1 ) and studies at high strain rates (≥ 1000 s−1 ) are few. In one early study [20] on the high strain rate deformation of UFG Cu, Ni and Al–Cu–Zr alloy, the flow behavior was presented and the strain rate sensitivity was estimated by
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Fig. 1. Schematic of Hopkinson bar setup. Also shown is the sleeve on the incident bar and the gap which is adjusted for either trapping the reflected pulse or achieving a strain rate change during the test.
the direct comparison of the flow stresses at the low and high strain rates. There are also some studies at high strain rates on bcc UFG metals emphasizing aspects of strain localization [21,22]. Information on the high strain rate flow behavior of fcc UFG alloys is lacking. This work presents such a study on the high strain rate deformation behavior of UFG Al–1.5 Mg. Here the flow stress, strain rate sensitivity, and temperature sensitivity of this alloy are measured at high strain rates. These are then compared with the corresponding results at low strain rates.
ing the sample is held by a brass sleeve such that it does not touch either bars; the gap being about 10 mm on each side of the sample. This reduces the heating of the bars. The furnace slides over the bars at a position where the sample is at the furnace center. After reaching the desired temperature the sample is held for a minimum of 3–4 min before testing. The bars and sample are brought together within a second prior to firing the striker bar. This procedure is similar to that followed in Ref. [26]. 2.2. Momentum trapping
2. Experiments This study was carried out on Al–1.5 wt% Mg alloy. This was annealed at 770 K for 1 h, which resulted in coarse grains of about 150 m. Billets of annealed Al–1.5 Mg were subjected to severe plastic deformation (SPD) via the equal channel angular pressing (ECAP) technique. The samples were pressed 20 times through an ECAP die with a 120◦ channel intersection angle. This results in a total equivalent strain of 13 (Ref. [23] gives an estimate of equivalent strain due to ECAP). Further details of the ECAP process of Al–Mg alloy used in this study are given in Ref. [8]. The average subgrain size after SPD was measured via TEM micrographs and was found to be 0.25 m [8]. Samples of 4 mm diameter and 5 mm height were machined out from the billet after ECAP, and were tested in a compression split Hopkinson pressure bar (SHPB) at the starting temperatures of 303, 373, 423, 473 and 523 K. These results were compared with those at the low strain rates from Ref. [8].
In the present SHPB setup, the incident bar is modified to have a flange and a sleeve at the striker bar end, with the primary aim of trapping the reflected pulse; this is referred to as a momentum trap pioneered by Nemat-Nasser’s group [27,25]. The gap between the sleeve and the flange is kept such that after the striker impacts the incident bar and the complete wave passes through to the incident bar, the gap closes. Thus, gap = time of pulse × particle velocity in incident bar. This simplifies to 2LSB εI , where LSB is the length of striker bar and εI is the strain in the incident bar due to the incident pulse. Now when the reflected pulse reaches the striker end of the incident bar, it sees the sleeve. The impedance of the sleeve is same as that of the incident bar and so the reflected pulse goes into the sleeve as a compression pulse. From the free end of the sleeve this compression pulse reflects off as a tension pulse and pulls the sleeve away from the flange. In this way the pulse is ‘trapped’ in the sleeve and does not reload the sample. The sample can thus be recovered for microstructural analysis.
2.1. Uniaxial testing in Hopkinson bar
2.3. Strain rate change tests in SHPB
A schematic of the SHPB used in this work is shown in Fig. 1. Its main components are a gas gun, a striker bar, an incident bar and a transmission bar. The striker bar sits in the barrel at the gas chamber side. The sample to be tested is placed between the incident and transmission bars. The striker bar is propelled by gas pressure towards the incident bar. On impact, an elastic compression wave propagates down the incident bar towards the sample. On reaching the sample, repeated wave propagation within it deforms it plastically. Part of the wave goes through to the transmission bar (transmitted pulse) and part is reflected back into the incident bar (reflected pulse), each of which is picked up by the strain gauges mounted on the corresponding bars. Further details of high strain rate testing using SHPB are given in Refs. [24,25]. The elevated temperature tests were carried out by heating the sample using a small furnace of 30 mm thickness (a disc shaped furnace). During heat-
This sleeve and flange arrangement can also be used to perform strain rate change tests during deformation by keeping the gap about half or less than what is required for momentum trapping. This technique is described in Ref. [25] in section ‘Recovery Hopkinson Bar techniques’. Here the gap closes before all of the wave has passed through to the incident bar. The striker bar now encounters twice the earlier impedance. Initially with the gap open, the particle velocity in the incident bar VI is half the velocity of the striker bar (VSB ), i.e. VSB /2. Once the gap closes, the value of VI in the incident bar becomes VSB /3. Since the strain in the incident bar εI is proportional to VI , the incident pulse is stepped down, falling to 2/3 of its initial value. The sample then sees this stepped down pulse and the stress response, which is proportional to the transmitted pulse, is in accordance with its constitutive behavior. The reflected pulse is also stepped, indicating a step change in strain rate during
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Fig. 2. Strain gauge signals from a SHPB test on UFG Al–1.5 Mg at 303 K. Here the gap is adjusted to produce a stepped incident pulse. The corresponding material response is seen by the kink in the transmitted pulse. The stepped reflected pulse indicates a strain rate change. For clarity, the incident and transmitted signals are shown on different scales. The lines on the transmitted pulse are visual guides to see the changes.
deformation. A typical example of such a strain rate change test is shown in Fig. 2. 3. Results 3.1. Flow behavior Fig. 3 shows the – ε behavior of UFG Al–1.5 Mg tested at ≈ 2000 s−1 and at different temperatures. The tests were carried
Fig. 4. Stress–temperature plot for Al–1.5 Mg both in the UFG and CG conditions and at low and high strain rates.
out using a 400 mm long striker bar with an impact velocity of about 10 m/s. High strain rate tests are adiabatic in nature, as the heat generated during deformation does not have sufficient time to dissipate. This generated heat raises the temperature of the sample. This temperature rise during deformation was calculated and the isothermal flow stress was estimated as given in Appendix A. In an earlier study [28] the isothermal stress of tantalum at high strain rates was estimated in a similar manner and was shown to match well with that obtained through incremental tests. Since for the CG alloy, the magnitude of the temperature sensitivity of stress |∂/∂T | is very low, the isothermal and adiabatic curves match and are not shown separately. From Fig. 3 two points are apparent: one, that
Fig. 3. Stress–strain plots for Al–1.5 Mg at high strain rates and different temperatures. The thin lines are the isothermal curves for the UFG alloy calculated using Eq. (A.4).
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Fig. 5. Stress–strain curves during strain rate change tests of UFG Al–1.5 Mg at 2000 s−1 . The strain rate derived from the reflected pulse is shown on right axis. Shown here is the engineering stress since their changes, due to changes in the strain rate, can be easily identified.
at all temperatures of testing the UFG material has higher strength than the CG one, and second, that although adiabatic curves show strain softening the corrected isothermal ones do not. For the sake of comparison, the flow behavior at low strain rates can be seen in Fig. 2 of Ref. [8]. There it is seen that at 0.002 s−1 and 523 K the UFG alloy becomes softer than the CG one. This –T dependence is better depicted in Fig. 4 for both UFG and CG Al–1.5 Mg and at both 0.002 and 2000 s−1 . It is seen that |∂/∂T | is larger for the UFG alloy as compared to the CG one. Comparing only CG and UFG at the 0.002 s−1 (open circles and triangles in Fig 4), it is clear that at temperatures higher than 510 K, the UFG gets softer than the CG, i.e. there is a transition from hardening to softening. If a similar comparison is made at 2000 s−1 (filled circles and triangles) it appears that even at the higher temperature of 540 K (this includes the temperature rise as estimated by Eq. (A.5)), UFG is still stronger than CG. The transition from hardening to softening at 2000 s−1 can be estimated through visual extrapolation to be about 580 K. The transition temperatures are marked in Fig. 4 as TLR and THR for the low and high strain rates, respectively. 3.2. Strain rate sensitivity
longer in the DSA regime. Strain rate sensitivities (and the corresponding stress exponents n = 1/m) obtained through strain rate change tests at 0.002 and 2000 s−1 are compared in Fig. 6. Tests at 2000 s−1 were performed in the Hopkinson bar at starting temperatures of 303, 473 and 523 K for the UFG material, and 303, 423 and 523 K for the CG material. The results at 0.002 s−1 shown here are at 373, 423, 473 and 523 K for the UFG material, and 423, 473 and 523 K for the CG material. Note that on a given curve the data points correspond to different T; a lower corresponds to higher T. The m– trend is clear: as increases m decreases. For the UFG alloy the m– plot at 0.002 and 2000 s−1 match. However, when compared at a given temperature, m at 2000 s−1 would be lower than that at 0.002 s−1 . 3.3. Stress vs. strain rate trend from low to high strain rates The flow stress at 2000 s−1 is plotted in perspective with the low strain rate data (obtained through stress relaxation) on a – ε˙ plot as shown in Fig. 7. Despite the absence of data at the intermediate strain rates, the values at 2000 s−1 appear to follow the – ε˙ trend for the low strain rates. With increasing strain rate,
Also seen in Fig. 4 is a cross-over in flow stress for the CG alloy when compared at 2000 and 0.002 s−1 . Below 400 K the flow stress at 0.002 s−1 is higher than that at 2000 s−1 ; this is an apparent manifestation of negative strain rate sensitivity. CG dilute Al–Mg alloys are known to exhibit dynamic strain aging (DSA) at ambient temperatures. Negative strain rate sensitivity, which is a manifestation of DSA, has also been observed in UFG Al–Mg alloys at near ambient temperatures and low strain rates [7,15,29]. Although Fig. 4 shows a region of apparent negative strain rate sensitivity, it is possible that for small strain rate changes around 2000 s−1 , m may still be positive. At 2000 s−1 m was determined through strain rate change tests for both CG and UFG materials. Fig. 5 shows two such strain rate change tests in the Hopkinson bar on the UFG material at starting temperatures of 303 and 523 K.1 For both the CG and UFG alloys, m was found to be positive at 2000 s−1 and at all temperatures of testing including ambient temperature. The positive m obtained at ambient temperature and 2000 s−1 shows that Al–1.5 Mg is no
1 The flow stress shown in Fig. 5 has been corrected for dispersion and the high frequency (>100 kHz) electronic noise has been filtered out. The oscillations seen on this expanded scale are only remnants of the filtering process and are not due to any material property. In order to calculate m the change in stress was estimated by drawing a line passing through the mean value of the filtered curve before and after the strain rate change. The deviations in m, shown as error bars in Fig. 6, were estimated taking into account the range of noise in data.
Fig. 6. Strain rate sensitivity m (corresponding n) vs. for Al–1.5 Mg both in the UFG and CG conditions and at high and low strain rates [8]. Error bars are shown for the 2000 s−1 data to account for uncertainty in estimation of stress changes. The arrows indicate a drop in m approaching negative values at ambient temperatures and 0.002 s−1 . Note that the data points correspond to different temperatures (see text).
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Fig. 7. Stress vs. strain rate behavior for both CG and UFG alloys covering a wide range of strain rates. The low strain rates are taken from Ref. [8]. The thin lines are visual guides for depicting the trend.
|∂/∂T | decreases and is quite low at 2000 s−1 as seen from the bunching of data in a narrow band for both the CG and UFG alloys. Also, the strain rate sensitivity (slope of – ε˙ curve) decreases with increasing strain rate and decreasing temperature.
Table 1 Average grain sizes intercepts of UFG Al–1.5 Mg after deformation Start temperature (K)
Grain sizes at 0.002 s−1
2000 s−1
0.44 m 1.25 m
0.35 m 0.48 m
3.4. Microstructure
473 523
UFG Al–Mg alloys are known to exhibit grain growth at temperatures beyond 500 K [30]. The TEM microstructures of UFG Al–1.5 Mg after deformation at the higher temperatures of 473 and 523 K at both 0.002 and 2000 s−1 are shown in Fig. 8. The average sub-
grain intercepts determined by the line intersection technique are listed in Table 1 and their cumulative frequency distributions are shown in Fig. 9. The initial microstructure of Al–1.5 Mg after severe plastic deformation can be seen in Ref. [8], the cumulative fre-
Fig. 8. TEM micrographs of UFG Al–1.5 Mg after deformation at (a) 473 K; 0.002 s−1 , (b) 473 K; 2000 s−1 , (c) 523 K; 0.002 s−1 , and (d) 523 K; 2000 s−1 . Micron marker in (c) is same for all.
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Fig. 9. Cumulative frequency distribution of subgrain intercepts for UFG Al–1.5 Mg after being deformed at different test conditions.
quency distribution of which is also shown in Fig. 9. For the UFG alloy, grain growth is largest when deformed at 523 K and 0.002 s−1 , with the average being more than 1 m. For the other deformation conditions the grains have remained in the submicron range. At a given temperature the subgrain size after testing at 0.002 s−1 is higher than that after testing at 2000 s−1 . At 0.002 s−1 , unlike that at 2000 s−1 , the grains are well defined, equiaxed with sharper grain boundaries and cleaner interiors. 4. Discussion The present work brings out the effect of high strain rate on the flow behavior of UFG Al–1.5 Mg and compares it with the CG counterpart. The important observations are: (1) at the high strain rates the UFG alloy is stronger than the CG alloy at all temperatures of testing, (2) m for the UFG alloy is always higher than that for the CG alloy, and (3) for the UFG alloy the variation of m with is similar for both the high and low strain rates. The first point can be compared with the behavior at low strain rates, where the UFG alloy actually becomes softer than the CG alloy at higher temperatures. At both 0.002 and 2000 s−1 , the magnitude of the temperature sensitivity of stress |d/dT | is larger for the UFG alloy (Fig. 4). Thus, although UFG has a higher stress at the lower temperatures, the drop in stress with increasing temperature is steeper than that of the CG alloy, hence the softening effect. It should be noted here that this softening effect is not due to classic thermal softening, but can be indirectly linked to the increase of grain size during deformation. One could suspect that the lack of stability of UFG microstructure at the higher temperatures is the cause for this sharper drop in stress. However this can be ruled out, as seen from Figs. 8 and 9, where at most testing conditions the microstructure is still UFG, and at 523 K for 0.002 s−1 the grains have grown to about 1–2 m, still much smaller than 150 m of the CG alloy. It will be seen later that the increase in grain size is in fact related to the stress response of material. This transition temperature, where UFG becomes softer than the CG alloy, has been shown to be dependent on strain rate; as the strain rate increases the transition temperature increases (Fig. 7 of Ref. [8]). Although at 2000 s−1 , a transition temperature THR from hardening to softening could not be directly determined, THR was
Fig. 10. Depiction of transition from strengthening to softening of UFG compared with CG plotted as (a) transition strain rate ε˙ tr , and (b) transition stress tr vs. transition temperature. The low strain rate data are from Ref. [8]. The lines are visual guides to depict the trend.
estimated through visual extrapolation (Fig. 4). Fig. 10 compares THR with the trend of the transition temperatures at the lower strain rates. If the transition strain rate ε˙ tr (= ε˙ at transition temperature) is plotted as in Fig. 10(a) there appears a deviation at 2000 s−1 from the low strain rate trend. If instead, transition stress tr (= at transition temperature), is plotted as in Fig. 10(b), the trend at the low strain rates matches well with that at 2000 s−1 . This difference between the prediction of ε˙ tr and tr arises because of the low strain rate sensitivity at the higher strain rates. This makes the flow stress at 2000 s−1 only marginally different from that at 0.002 s−1 (Fig. 7), although the ε˙ changes by six orders. Transition from hardening to softening has also been observed in UFG Cu by Blum and co-workers [6,31]. In their work [31] they attribute this softening to the condition when the initial UFG subgrain size w0,UFG becomes smaller than the steady state subgrain size w∞ = kw bG/ [32], where kw is a material constant, G is the shear modulus, and b is the magnitude of the Burgers vector. In the case of CG metals, the grain size dCG w∞ , and thus the mean free path of dislocations is limited by the subgrain size. This makes the flow stress dependent on the subgrain rather than the grain size. However, in the case of UFG metals it is likely that at some value of /G, d0,UFG < w∞ . This would make the mean free path of dislocations equal to d0,UFG , thus making grain boundaries directly contribute to the deformation process. The high angle boundaries in UFG metals would act as sinks for dislocations and would cause a softening effect as proposed in Ref. [6]. The authors of Ref. [6] concluded that the necessary condition for softening is d0,UFG ≈ w0,UFG < w∞ . They showed that testing UFG Cu at 418 K (0.31TM the homologous temperature) satisfies this condition and that the softening which is observed involves the movement of subgrain boundaries to the existing high angle grain boundaries. They also showed in Ti that when w0,UFG < / w∞ , softening did not occur.
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implies ∝ dp at constant strain rate; the smaller the grain size the lower the stress. Softening in UFG Al–1.5 Mg can be attributed to the process of grain boundary deformation possibly accommodated by grain boundary migration at higher temperatures or lower strain rates, both of which result in a lower stress. A lower stress is in turn linked to a larger w∞ , thus in effect making w0,UFG < w∞ . Higher strain rates result in larger stresses for which the corresponding w∞ is lower. This effectively would avoid the condition for softening. Finally, if the primary benefit of grain refinement is the improvement of both strength and toughness, it is obvious that this benefit is lost beyond the hardening to softening transition temperature. However it is important to note that the UFG alloy still maintains its higher strain rate sensitivity (compared to CG alloy). This feature of reduced and increased m can be put to use in applications of forming/processing. The low would allow easier flowabilty, while the high m would allow good formability. 5. Conclusions Fig. 11. Spacing of subgrain intercepts vs. /G. w∞ is the steady state subgrain size. w0,UFG and d0,CG are the initial measured subgrain and grain size for UFG and CG, respectively. The test temperatures are mentioned next to the individual data points. At 2000 s−1 the test temperatures are after adiabatic correction.
In order to check whether Al–1.5 Mg follows this condition for softening, the measured subgrain intercepts are plotted in Fig. 11 along with w∞ = 28bG/ for dilute Al–Mg alloys [32]. It is seen that at 501 K for 2000 s−1 and 473 K for 0.002 s−1 , where softening is not observed, the measured subgrain spacings are lower than that predicted by the w∞ line. At 523 K for 0.002 s−1 , where softening is observed, the measured subgrain spacing matches with the predicted w∞ line. At 543 K for 2000 s−1 , where softening was not observed, the average subgrain spacing was lower than the w∞ line, although it can still be considered as being close to it. Also, the expected spacing at THR is greater than the average w0,UFG , implying that at the expected point of softening at 2000 s−1 the subgrains would grow. In UFG Cu [33] subgrain growth to the corresponding w∞ was observed after thermomechanical treatment and subsequent testing at a lower /G. In the present study on Al–1.5 Mg, the process of softening has grown the subgrains from w0,UFG to w∞ in accordance with the new steady state stress. Sklenick et al. [34] observed grain boundary sliding in UFG Al deformed in creep at 473 K and 15 MPa. Their data also showed evidence of softening of UFG Al as compared to CG Al at ε˙ ≈ 2 × 10−7 s−1 , T = 473 K and = 15 MPa. From n = 4.8 and an activation energy lower than that of self diffusion they inferred that grain boundary sliding would play an important role in the total deformation process. The process of grain boundary sliding requires an accommodation process which could be provided by grain boundary migration. In the present case for Al–1.5 Mg alloy, since the test temperature is higher than 0.5TM (unlike the case of Cu where it was 0.3TM ), and the stress exponent n is in the range of 3–4 at 523 K and 0.002 s−1 , it is likely that high angle grain boundaries too migrate. It is known that the increase in strength for alloys with finer grains (the Hall–Petch effect) is primarily due to grain boundaries acting as obstacles to dislocation motion. This leads to an increase of dislocation density within grains, which in turn leads to a higher flow stress. Once the grain boundaries become weak, either the dislocations are absorbed at the boundaries or the boundaries themselves deform, e.g. by sliding. As T approaches 0.5TM , grain boundary deformation becomes more probable. Such behavior is a well established phenomenon at high temperatures where non-conservative dislocation motion occurs. The widely used constitutive equation for this is ε˙ ∝ n d−p , where n is the stress exponent, d is the grain size and p is the grain size exponent. This
At high strain rates, UFG Al–1.5 Mg alloy exhibits higher strength than the CG alloy at all test temperatures from 300 to 540 K. For this UFG alloy both the temperature sensitivity and the strain rate sensitivity of stress are found to be lower at the dynamic strain rates compared to the low strain rates. The transition from hardening to softening which was earlier observed at the low strain rates, is not directly observed at the higher strain rate of 2000 s−1 , implying an increase in the transition temperature. However, the strain rate sensitivity of UFG Al–1.5 Mg was found to remain higher than that for the CG alloy. It was inferred that grain boundary deformation appears to play a major role in the process of softening, possibly through grain boundary sliding accommodated by migration, which leads to the observed increase in grain size. High strain rate deformation suppresses this process and thus shifts the softening to higher temperatures. Acknowledgments The authors acknowledge the valuable contribution of Vivek Chavan of Refuelling Technology Division (RTD) BARC, in the setting up of the Hopkinson bar. Thanks are due to Sudhanshu Sharma of RTD BARC, and to Hindol Bandyopadhyay of Indian Institute of Science, Bangalore, for their help in conducting some of the experiments. We also thank Atomic Fuels Division BARC for supply of the Al–Mg alloy used in this work. Appendix A During adiabatic deformation the change in is due to a change in both ε and T, i.e. d =
∂ ∂ dε + dT ∂ε ∂T
d ∂ dT ∂ = − dε ∂ε ∂T dε
(A.1) (A.2)
The total work-hardening rate d/dε is a combination of both the strain effect and the temperature effect due to the adiabatic nature of the test. The isothermal work-hardening rate ∂/∂ε is devoid of temperature changes. Thus the isothermal stress iso is obtained by integrating ∂/∂ε:
iso = adbt − 0
ε
∂ dT dε, ∂T dε
(A.3)
where adbt is the adiabatic measured stress. As a first approximation if temperature sensitivity of stress ∂/∂T is independent of
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strain, iso becomes: iso = adbt −
∂ T ∂T
(A.4)
The temperature rise T at each instant is T = T − T0 =
Cp
ε
dε
(A.5)
0
where and Cp are the material density and the specific heat capacity, respectively, T0 is the initial temperature, and is the fraction of work done converted to heat during plastic deformation. For all practical purposes can be taken as 1 [35]. ∂/∂T in Eq. (A.4) is calculated from vs. T (Fig. 4), where T = T0 + T is the instantaneous temperature. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
High strain rate behavior of ultrafine-grained Al–1.5 Mg R. Kapoor ∗ , J.B. Singh, J.K. Chakravartty Materials Group, Bhabha Atomic Research Centre, Mumbai 400085, India
a r t i c l e
i n f o
Article history: Received 29 February 2008 Received in revised form 13 May 2008 Accepted 22 May 2008 Keywords: Ultrafine-grained Al–Mg Equal channel angular pressing Severe plastic deformation High strain rate Hopkinson bar Strain rate sensitivity
a b s t r a c t The high strain rate behavior of ultrafine-grained Al–1.5 Mg alloy produced by the equal channel angular pressing technique is investigated in this work. High strain rate compression tests were performed in a split Hopkinson pressure bar to achieve nominal strain rates of around 2000 s−1 at temperatures ranging from 300 to 523 K. In addition to un-interrupted Hopkinson bar tests, strain rate change tests were carried out using a flange and sleeve arrangement on the incident bar. The results obtained at the high strain rates were compared with those at low strain rates from an earlier study. It was seen that at the strain rate of 2000 s−1 the transition from hardening to softening (with respect to the coarse grained alloy), was shifted to higher temperatures. The strain rate sensitivity for the ultrafine-grained alloy was higher as compared to the coarse grained alloy for the entire range of testing. The increased strain rate sensitivity and the average subgrain size measured after testing at 473 and 523 K, suggest an active role of grain boundaries in the process of deformation. The possible reasons for softening at the low strain rates and its suppression at the high strain rates are discussed. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The effect of grain size on the mechanical properties of polycrystalline materials has been widely studied in the past. These studies have primarily focused on the Hall–Petch (H–P) relation for grain sizes ranging from tens to hundreds of micrometers. It is only in the recent years that the H–P relation has been investigated in the ultrafine (submicron) and nanometer grain size ranges 1 [1,2]. It has been observed that at ambient temperatures the strength of a metal with an ultrafine-grained (UFG) microstructure is higher than that with a coarse grain (CG) one [3–5]. It is also seen that when the grain size is reduced to the tens of nanometer range in fcc metals, the flow stress saturates, or in some cases even decreases with decreasing grain size [1,5]. This later effect is usually referred to as the inverse H–P effect. Although the strength decreases with decreasing grain size in the nano regime, its value still remains higher than that of the CG material, suggesting that a complete cross-over in strength between the CG and UFG has still not occurred. At conditions where grain boundaries act only as barriers to dislocation motion, deformation takes place within grains and UFG is stronger, more so for severely deformed materials where the dislocation density within grains is high to start with. Conversely, at conditions where grain boundaries act as sinks to dislocations or where grain boundary deformation occurs, a UFG structure will be softer than a CG one.
∗ Corresponding author. Tel.: +91 22 25590139; fax: +91 22 25505221. E-mail addresses: [email protected], [email protected] (R. Kapoor). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.05.043
Clearly, lower temperatures and higher strain rates should promote hardening, while higher temperatures and lower strain rates should promote softening. In one study on UFG Cu [6] this transition from hardening to softening was found to occur at 418 K. For UFG Al–1.5 Mg this transition from hardening to softening was found to be dependent on the strain rate and temperature of testing [7,8]. Reducing grain size is also known to affect the strain rate sensi˙ where and ε˙ are the true stress and the tivity m = ln / ln ε, true strain rate, respectively. In general for fcc materials [7–17], and in particular for Al and its alloys [7–11,14,15], refining grains to the UFG level increases m. This increase in m with decrease in grain size has been explained [11] on the basis of the relation between m and the apparent activation volume Va , m = MkT/Va , where M is the Taylor factor, k is the Boltzmann constant and T is temperature. The increase in m occurs due to a drastic decrease in Va caused by a high dislocation density, even though there is a moderate increase in due to grain refinement. Usually m varies with deformation conditions such as ε˙ and T, and since is a function of ε˙ and T, m is also seen to vary with . It has been observed that m decreases with increasing as seen from studies on UFG Cu [6], Ni [18] and Al–1.5 Mg [8]. Also m has been found to increase with increasing T ˙ as in UFG Al [19] and UFG Cu [12]. and decreasing ε, Sufficient experimental evidence exists to suggest that for fcc UFG metals increasing ε˙ (increasing ) reduces m. However, most studies are at low strain rates (≤ 1 s−1 ) and studies at high strain rates (≥ 1000 s−1 ) are few. In one early study [20] on the high strain rate deformation of UFG Cu, Ni and Al–Cu–Zr alloy, the flow behavior was presented and the strain rate sensitivity was estimated by
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Fig. 1. Schematic of Hopkinson bar setup. Also shown is the sleeve on the incident bar and the gap which is adjusted for either trapping the reflected pulse or achieving a strain rate change during the test.
the direct comparison of the flow stresses at the low and high strain rates. There are also some studies at high strain rates on bcc UFG metals emphasizing aspects of strain localization [21,22]. Information on the high strain rate flow behavior of fcc UFG alloys is lacking. This work presents such a study on the high strain rate deformation behavior of UFG Al–1.5 Mg. Here the flow stress, strain rate sensitivity, and temperature sensitivity of this alloy are measured at high strain rates. These are then compared with the corresponding results at low strain rates.
ing the sample is held by a brass sleeve such that it does not touch either bars; the gap being about 10 mm on each side of the sample. This reduces the heating of the bars. The furnace slides over the bars at a position where the sample is at the furnace center. After reaching the desired temperature the sample is held for a minimum of 3–4 min before testing. The bars and sample are brought together within a second prior to firing the striker bar. This procedure is similar to that followed in Ref. [26]. 2.2. Momentum trapping
2. Experiments This study was carried out on Al–1.5 wt% Mg alloy. This was annealed at 770 K for 1 h, which resulted in coarse grains of about 150 m. Billets of annealed Al–1.5 Mg were subjected to severe plastic deformation (SPD) via the equal channel angular pressing (ECAP) technique. The samples were pressed 20 times through an ECAP die with a 120◦ channel intersection angle. This results in a total equivalent strain of 13 (Ref. [23] gives an estimate of equivalent strain due to ECAP). Further details of the ECAP process of Al–Mg alloy used in this study are given in Ref. [8]. The average subgrain size after SPD was measured via TEM micrographs and was found to be 0.25 m [8]. Samples of 4 mm diameter and 5 mm height were machined out from the billet after ECAP, and were tested in a compression split Hopkinson pressure bar (SHPB) at the starting temperatures of 303, 373, 423, 473 and 523 K. These results were compared with those at the low strain rates from Ref. [8].
In the present SHPB setup, the incident bar is modified to have a flange and a sleeve at the striker bar end, with the primary aim of trapping the reflected pulse; this is referred to as a momentum trap pioneered by Nemat-Nasser’s group [27,25]. The gap between the sleeve and the flange is kept such that after the striker impacts the incident bar and the complete wave passes through to the incident bar, the gap closes. Thus, gap = time of pulse × particle velocity in incident bar. This simplifies to 2LSB εI , where LSB is the length of striker bar and εI is the strain in the incident bar due to the incident pulse. Now when the reflected pulse reaches the striker end of the incident bar, it sees the sleeve. The impedance of the sleeve is same as that of the incident bar and so the reflected pulse goes into the sleeve as a compression pulse. From the free end of the sleeve this compression pulse reflects off as a tension pulse and pulls the sleeve away from the flange. In this way the pulse is ‘trapped’ in the sleeve and does not reload the sample. The sample can thus be recovered for microstructural analysis.
2.1. Uniaxial testing in Hopkinson bar
2.3. Strain rate change tests in SHPB
A schematic of the SHPB used in this work is shown in Fig. 1. Its main components are a gas gun, a striker bar, an incident bar and a transmission bar. The striker bar sits in the barrel at the gas chamber side. The sample to be tested is placed between the incident and transmission bars. The striker bar is propelled by gas pressure towards the incident bar. On impact, an elastic compression wave propagates down the incident bar towards the sample. On reaching the sample, repeated wave propagation within it deforms it plastically. Part of the wave goes through to the transmission bar (transmitted pulse) and part is reflected back into the incident bar (reflected pulse), each of which is picked up by the strain gauges mounted on the corresponding bars. Further details of high strain rate testing using SHPB are given in Refs. [24,25]. The elevated temperature tests were carried out by heating the sample using a small furnace of 30 mm thickness (a disc shaped furnace). During heat-
This sleeve and flange arrangement can also be used to perform strain rate change tests during deformation by keeping the gap about half or less than what is required for momentum trapping. This technique is described in Ref. [25] in section ‘Recovery Hopkinson Bar techniques’. Here the gap closes before all of the wave has passed through to the incident bar. The striker bar now encounters twice the earlier impedance. Initially with the gap open, the particle velocity in the incident bar VI is half the velocity of the striker bar (VSB ), i.e. VSB /2. Once the gap closes, the value of VI in the incident bar becomes VSB /3. Since the strain in the incident bar εI is proportional to VI , the incident pulse is stepped down, falling to 2/3 of its initial value. The sample then sees this stepped down pulse and the stress response, which is proportional to the transmitted pulse, is in accordance with its constitutive behavior. The reflected pulse is also stepped, indicating a step change in strain rate during
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Fig. 2. Strain gauge signals from a SHPB test on UFG Al–1.5 Mg at 303 K. Here the gap is adjusted to produce a stepped incident pulse. The corresponding material response is seen by the kink in the transmitted pulse. The stepped reflected pulse indicates a strain rate change. For clarity, the incident and transmitted signals are shown on different scales. The lines on the transmitted pulse are visual guides to see the changes.
deformation. A typical example of such a strain rate change test is shown in Fig. 2. 3. Results 3.1. Flow behavior Fig. 3 shows the – ε behavior of UFG Al–1.5 Mg tested at ≈ 2000 s−1 and at different temperatures. The tests were carried
Fig. 4. Stress–temperature plot for Al–1.5 Mg both in the UFG and CG conditions and at low and high strain rates.
out using a 400 mm long striker bar with an impact velocity of about 10 m/s. High strain rate tests are adiabatic in nature, as the heat generated during deformation does not have sufficient time to dissipate. This generated heat raises the temperature of the sample. This temperature rise during deformation was calculated and the isothermal flow stress was estimated as given in Appendix A. In an earlier study [28] the isothermal stress of tantalum at high strain rates was estimated in a similar manner and was shown to match well with that obtained through incremental tests. Since for the CG alloy, the magnitude of the temperature sensitivity of stress |∂/∂T | is very low, the isothermal and adiabatic curves match and are not shown separately. From Fig. 3 two points are apparent: one, that
Fig. 3. Stress–strain plots for Al–1.5 Mg at high strain rates and different temperatures. The thin lines are the isothermal curves for the UFG alloy calculated using Eq. (A.4).
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Fig. 5. Stress–strain curves during strain rate change tests of UFG Al–1.5 Mg at 2000 s−1 . The strain rate derived from the reflected pulse is shown on right axis. Shown here is the engineering stress since their changes, due to changes in the strain rate, can be easily identified.
at all temperatures of testing the UFG material has higher strength than the CG one, and second, that although adiabatic curves show strain softening the corrected isothermal ones do not. For the sake of comparison, the flow behavior at low strain rates can be seen in Fig. 2 of Ref. [8]. There it is seen that at 0.002 s−1 and 523 K the UFG alloy becomes softer than the CG one. This –T dependence is better depicted in Fig. 4 for both UFG and CG Al–1.5 Mg and at both 0.002 and 2000 s−1 . It is seen that |∂/∂T | is larger for the UFG alloy as compared to the CG one. Comparing only CG and UFG at the 0.002 s−1 (open circles and triangles in Fig 4), it is clear that at temperatures higher than 510 K, the UFG gets softer than the CG, i.e. there is a transition from hardening to softening. If a similar comparison is made at 2000 s−1 (filled circles and triangles) it appears that even at the higher temperature of 540 K (this includes the temperature rise as estimated by Eq. (A.5)), UFG is still stronger than CG. The transition from hardening to softening at 2000 s−1 can be estimated through visual extrapolation to be about 580 K. The transition temperatures are marked in Fig. 4 as TLR and THR for the low and high strain rates, respectively. 3.2. Strain rate sensitivity
longer in the DSA regime. Strain rate sensitivities (and the corresponding stress exponents n = 1/m) obtained through strain rate change tests at 0.002 and 2000 s−1 are compared in Fig. 6. Tests at 2000 s−1 were performed in the Hopkinson bar at starting temperatures of 303, 473 and 523 K for the UFG material, and 303, 423 and 523 K for the CG material. The results at 0.002 s−1 shown here are at 373, 423, 473 and 523 K for the UFG material, and 423, 473 and 523 K for the CG material. Note that on a given curve the data points correspond to different T; a lower corresponds to higher T. The m– trend is clear: as increases m decreases. For the UFG alloy the m– plot at 0.002 and 2000 s−1 match. However, when compared at a given temperature, m at 2000 s−1 would be lower than that at 0.002 s−1 . 3.3. Stress vs. strain rate trend from low to high strain rates The flow stress at 2000 s−1 is plotted in perspective with the low strain rate data (obtained through stress relaxation) on a – ε˙ plot as shown in Fig. 7. Despite the absence of data at the intermediate strain rates, the values at 2000 s−1 appear to follow the – ε˙ trend for the low strain rates. With increasing strain rate,
Also seen in Fig. 4 is a cross-over in flow stress for the CG alloy when compared at 2000 and 0.002 s−1 . Below 400 K the flow stress at 0.002 s−1 is higher than that at 2000 s−1 ; this is an apparent manifestation of negative strain rate sensitivity. CG dilute Al–Mg alloys are known to exhibit dynamic strain aging (DSA) at ambient temperatures. Negative strain rate sensitivity, which is a manifestation of DSA, has also been observed in UFG Al–Mg alloys at near ambient temperatures and low strain rates [7,15,29]. Although Fig. 4 shows a region of apparent negative strain rate sensitivity, it is possible that for small strain rate changes around 2000 s−1 , m may still be positive. At 2000 s−1 m was determined through strain rate change tests for both CG and UFG materials. Fig. 5 shows two such strain rate change tests in the Hopkinson bar on the UFG material at starting temperatures of 303 and 523 K.1 For both the CG and UFG alloys, m was found to be positive at 2000 s−1 and at all temperatures of testing including ambient temperature. The positive m obtained at ambient temperature and 2000 s−1 shows that Al–1.5 Mg is no
1 The flow stress shown in Fig. 5 has been corrected for dispersion and the high frequency (>100 kHz) electronic noise has been filtered out. The oscillations seen on this expanded scale are only remnants of the filtering process and are not due to any material property. In order to calculate m the change in stress was estimated by drawing a line passing through the mean value of the filtered curve before and after the strain rate change. The deviations in m, shown as error bars in Fig. 6, were estimated taking into account the range of noise in data.
Fig. 6. Strain rate sensitivity m (corresponding n) vs. for Al–1.5 Mg both in the UFG and CG conditions and at high and low strain rates [8]. Error bars are shown for the 2000 s−1 data to account for uncertainty in estimation of stress changes. The arrows indicate a drop in m approaching negative values at ambient temperatures and 0.002 s−1 . Note that the data points correspond to different temperatures (see text).
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Fig. 7. Stress vs. strain rate behavior for both CG and UFG alloys covering a wide range of strain rates. The low strain rates are taken from Ref. [8]. The thin lines are visual guides for depicting the trend.
|∂/∂T | decreases and is quite low at 2000 s−1 as seen from the bunching of data in a narrow band for both the CG and UFG alloys. Also, the strain rate sensitivity (slope of – ε˙ curve) decreases with increasing strain rate and decreasing temperature.
Table 1 Average grain sizes intercepts of UFG Al–1.5 Mg after deformation Start temperature (K)
Grain sizes at 0.002 s−1
2000 s−1
0.44 m 1.25 m
0.35 m 0.48 m
3.4. Microstructure
473 523
UFG Al–Mg alloys are known to exhibit grain growth at temperatures beyond 500 K [30]. The TEM microstructures of UFG Al–1.5 Mg after deformation at the higher temperatures of 473 and 523 K at both 0.002 and 2000 s−1 are shown in Fig. 8. The average sub-
grain intercepts determined by the line intersection technique are listed in Table 1 and their cumulative frequency distributions are shown in Fig. 9. The initial microstructure of Al–1.5 Mg after severe plastic deformation can be seen in Ref. [8], the cumulative fre-
Fig. 8. TEM micrographs of UFG Al–1.5 Mg after deformation at (a) 473 K; 0.002 s−1 , (b) 473 K; 2000 s−1 , (c) 523 K; 0.002 s−1 , and (d) 523 K; 2000 s−1 . Micron marker in (c) is same for all.
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Fig. 9. Cumulative frequency distribution of subgrain intercepts for UFG Al–1.5 Mg after being deformed at different test conditions.
quency distribution of which is also shown in Fig. 9. For the UFG alloy, grain growth is largest when deformed at 523 K and 0.002 s−1 , with the average being more than 1 m. For the other deformation conditions the grains have remained in the submicron range. At a given temperature the subgrain size after testing at 0.002 s−1 is higher than that after testing at 2000 s−1 . At 0.002 s−1 , unlike that at 2000 s−1 , the grains are well defined, equiaxed with sharper grain boundaries and cleaner interiors. 4. Discussion The present work brings out the effect of high strain rate on the flow behavior of UFG Al–1.5 Mg and compares it with the CG counterpart. The important observations are: (1) at the high strain rates the UFG alloy is stronger than the CG alloy at all temperatures of testing, (2) m for the UFG alloy is always higher than that for the CG alloy, and (3) for the UFG alloy the variation of m with is similar for both the high and low strain rates. The first point can be compared with the behavior at low strain rates, where the UFG alloy actually becomes softer than the CG alloy at higher temperatures. At both 0.002 and 2000 s−1 , the magnitude of the temperature sensitivity of stress |d/dT | is larger for the UFG alloy (Fig. 4). Thus, although UFG has a higher stress at the lower temperatures, the drop in stress with increasing temperature is steeper than that of the CG alloy, hence the softening effect. It should be noted here that this softening effect is not due to classic thermal softening, but can be indirectly linked to the increase of grain size during deformation. One could suspect that the lack of stability of UFG microstructure at the higher temperatures is the cause for this sharper drop in stress. However this can be ruled out, as seen from Figs. 8 and 9, where at most testing conditions the microstructure is still UFG, and at 523 K for 0.002 s−1 the grains have grown to about 1–2 m, still much smaller than 150 m of the CG alloy. It will be seen later that the increase in grain size is in fact related to the stress response of material. This transition temperature, where UFG becomes softer than the CG alloy, has been shown to be dependent on strain rate; as the strain rate increases the transition temperature increases (Fig. 7 of Ref. [8]). Although at 2000 s−1 , a transition temperature THR from hardening to softening could not be directly determined, THR was
Fig. 10. Depiction of transition from strengthening to softening of UFG compared with CG plotted as (a) transition strain rate ε˙ tr , and (b) transition stress tr vs. transition temperature. The low strain rate data are from Ref. [8]. The lines are visual guides to depict the trend.
estimated through visual extrapolation (Fig. 4). Fig. 10 compares THR with the trend of the transition temperatures at the lower strain rates. If the transition strain rate ε˙ tr (= ε˙ at transition temperature) is plotted as in Fig. 10(a) there appears a deviation at 2000 s−1 from the low strain rate trend. If instead, transition stress tr (= at transition temperature), is plotted as in Fig. 10(b), the trend at the low strain rates matches well with that at 2000 s−1 . This difference between the prediction of ε˙ tr and tr arises because of the low strain rate sensitivity at the higher strain rates. This makes the flow stress at 2000 s−1 only marginally different from that at 0.002 s−1 (Fig. 7), although the ε˙ changes by six orders. Transition from hardening to softening has also been observed in UFG Cu by Blum and co-workers [6,31]. In their work [31] they attribute this softening to the condition when the initial UFG subgrain size w0,UFG becomes smaller than the steady state subgrain size w∞ = kw bG/ [32], where kw is a material constant, G is the shear modulus, and b is the magnitude of the Burgers vector. In the case of CG metals, the grain size dCG w∞ , and thus the mean free path of dislocations is limited by the subgrain size. This makes the flow stress dependent on the subgrain rather than the grain size. However, in the case of UFG metals it is likely that at some value of /G, d0,UFG < w∞ . This would make the mean free path of dislocations equal to d0,UFG , thus making grain boundaries directly contribute to the deformation process. The high angle boundaries in UFG metals would act as sinks for dislocations and would cause a softening effect as proposed in Ref. [6]. The authors of Ref. [6] concluded that the necessary condition for softening is d0,UFG ≈ w0,UFG < w∞ . They showed that testing UFG Cu at 418 K (0.31TM the homologous temperature) satisfies this condition and that the softening which is observed involves the movement of subgrain boundaries to the existing high angle grain boundaries. They also showed in Ti that when w0,UFG < / w∞ , softening did not occur.
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implies ∝ dp at constant strain rate; the smaller the grain size the lower the stress. Softening in UFG Al–1.5 Mg can be attributed to the process of grain boundary deformation possibly accommodated by grain boundary migration at higher temperatures or lower strain rates, both of which result in a lower stress. A lower stress is in turn linked to a larger w∞ , thus in effect making w0,UFG < w∞ . Higher strain rates result in larger stresses for which the corresponding w∞ is lower. This effectively would avoid the condition for softening. Finally, if the primary benefit of grain refinement is the improvement of both strength and toughness, it is obvious that this benefit is lost beyond the hardening to softening transition temperature. However it is important to note that the UFG alloy still maintains its higher strain rate sensitivity (compared to CG alloy). This feature of reduced and increased m can be put to use in applications of forming/processing. The low would allow easier flowabilty, while the high m would allow good formability. 5. Conclusions Fig. 11. Spacing of subgrain intercepts vs. /G. w∞ is the steady state subgrain size. w0,UFG and d0,CG are the initial measured subgrain and grain size for UFG and CG, respectively. The test temperatures are mentioned next to the individual data points. At 2000 s−1 the test temperatures are after adiabatic correction.
In order to check whether Al–1.5 Mg follows this condition for softening, the measured subgrain intercepts are plotted in Fig. 11 along with w∞ = 28bG/ for dilute Al–Mg alloys [32]. It is seen that at 501 K for 2000 s−1 and 473 K for 0.002 s−1 , where softening is not observed, the measured subgrain spacings are lower than that predicted by the w∞ line. At 523 K for 0.002 s−1 , where softening is observed, the measured subgrain spacing matches with the predicted w∞ line. At 543 K for 2000 s−1 , where softening was not observed, the average subgrain spacing was lower than the w∞ line, although it can still be considered as being close to it. Also, the expected spacing at THR is greater than the average w0,UFG , implying that at the expected point of softening at 2000 s−1 the subgrains would grow. In UFG Cu [33] subgrain growth to the corresponding w∞ was observed after thermomechanical treatment and subsequent testing at a lower /G. In the present study on Al–1.5 Mg, the process of softening has grown the subgrains from w0,UFG to w∞ in accordance with the new steady state stress. Sklenick et al. [34] observed grain boundary sliding in UFG Al deformed in creep at 473 K and 15 MPa. Their data also showed evidence of softening of UFG Al as compared to CG Al at ε˙ ≈ 2 × 10−7 s−1 , T = 473 K and = 15 MPa. From n = 4.8 and an activation energy lower than that of self diffusion they inferred that grain boundary sliding would play an important role in the total deformation process. The process of grain boundary sliding requires an accommodation process which could be provided by grain boundary migration. In the present case for Al–1.5 Mg alloy, since the test temperature is higher than 0.5TM (unlike the case of Cu where it was 0.3TM ), and the stress exponent n is in the range of 3–4 at 523 K and 0.002 s−1 , it is likely that high angle grain boundaries too migrate. It is known that the increase in strength for alloys with finer grains (the Hall–Petch effect) is primarily due to grain boundaries acting as obstacles to dislocation motion. This leads to an increase of dislocation density within grains, which in turn leads to a higher flow stress. Once the grain boundaries become weak, either the dislocations are absorbed at the boundaries or the boundaries themselves deform, e.g. by sliding. As T approaches 0.5TM , grain boundary deformation becomes more probable. Such behavior is a well established phenomenon at high temperatures where non-conservative dislocation motion occurs. The widely used constitutive equation for this is ε˙ ∝ n d−p , where n is the stress exponent, d is the grain size and p is the grain size exponent. This
At high strain rates, UFG Al–1.5 Mg alloy exhibits higher strength than the CG alloy at all test temperatures from 300 to 540 K. For this UFG alloy both the temperature sensitivity and the strain rate sensitivity of stress are found to be lower at the dynamic strain rates compared to the low strain rates. The transition from hardening to softening which was earlier observed at the low strain rates, is not directly observed at the higher strain rate of 2000 s−1 , implying an increase in the transition temperature. However, the strain rate sensitivity of UFG Al–1.5 Mg was found to remain higher than that for the CG alloy. It was inferred that grain boundary deformation appears to play a major role in the process of softening, possibly through grain boundary sliding accommodated by migration, which leads to the observed increase in grain size. High strain rate deformation suppresses this process and thus shifts the softening to higher temperatures. Acknowledgments The authors acknowledge the valuable contribution of Vivek Chavan of Refuelling Technology Division (RTD) BARC, in the setting up of the Hopkinson bar. Thanks are due to Sudhanshu Sharma of RTD BARC, and to Hindol Bandyopadhyay of Indian Institute of Science, Bangalore, for their help in conducting some of the experiments. We also thank Atomic Fuels Division BARC for supply of the Al–Mg alloy used in this work. Appendix A During adiabatic deformation the change in is due to a change in both ε and T, i.e. d =
∂ ∂ dε + dT ∂ε ∂T
d ∂ dT ∂ = − dε ∂ε ∂T dε
(A.1) (A.2)
The total work-hardening rate d/dε is a combination of both the strain effect and the temperature effect due to the adiabatic nature of the test. The isothermal work-hardening rate ∂/∂ε is devoid of temperature changes. Thus the isothermal stress iso is obtained by integrating ∂/∂ε:
iso = adbt − 0
ε
∂ dT dε, ∂T dε
(A.3)
where adbt is the adiabatic measured stress. As a first approximation if temperature sensitivity of stress ∂/∂T is independent of
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strain, iso becomes: iso = adbt −
∂ T ∂T
(A.4)
The temperature rise T at each instant is T = T − T0 =
Cp
ε
dε
(A.5)
0
where and Cp are the material density and the specific heat capacity, respectively, T0 is the initial temperature, and is the fraction of work done converted to heat during plastic deformation. For all practical purposes can be taken as 1 [35]. ∂/∂T in Eq. (A.4) is calculated from vs. T (Fig. 4), where T = T0 + T is the instantaneous temperature. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
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