Introduction

Significant improvement in mechanical properties such as workability and superplasticity could be achieved by means of grain refinement processes. With this regard, severe plastic deformation (SPD) techniques are well-known operations because of their capabilities for obtaining even nanostructured materials [1]. Aluminum alloys, which have widely been used in aerospace and transportation industries, are usually exposed to high-strain rate loadings. Strike of miscellaneous objects on armaments, flying bodies landing and driving collisions are the cases in which the mechanical components experience high-strain rate loadings, although these components are usually manufactured under quasi-static conditions. Accordingly, it is beneficial to study the material behavior under dynamic loadings. Besides the microstructural characteristics and loading magnitude, flow stresses of metals also depend on the loading rate [2]. Previous investigations have indicated that both the strain rate sensitivity (SRS) and the rate-controlling mechanism would be changed by reducing the grain size of metals [3, 4]. While the materials are subjected to loadings with low and moderate rates, the forest dislocations are believed to be the primary barriers which confine slip procedure. Increasing the loading rate, other flow mechanisms such as viscose drag would be activated within the materials [5–7]. Unlike the body-centered cubic (BCC) metals, reduction in the grain size increases the SRS in face-centered cubic (FCC) materials [8, 9]. Many investigations have been conducted on mechanical behaviors of FCC metals at high strain rates [10, 11]. The effect of equal channel angular extrusion (ECAE) operation on the dynamic response of the materials has been addressed much more than other SPD techniques [12–15]. However, the products of other SPD operations such as high pressure torsion (HPT) [16] and constrained groove pressing (CGP) [17] have also been investigated under dynamic deformations.

In the present research work, for the first time, the mechanical behavior of AA6063 alloy processed via the expansion equal channel angular extrusion (Ex-ECAE) was studied under both dynamic and quasi-static loadings. With this regard, the aluminum alloy was Ex-ECAEd at different temperatures and ram velocities. These process parameters were designed by using response surface method (RSM). Afterwards, processed samples were subjected to compression loading with both the quasi-static and dynamic rates at ambient temperature. Values of SRS and apparent activation volume (AAV) were experimentally determined. Considering the variations of strain rate versus flow stress, plastic deformation mechanisms were also studied. Finally, variations of the SRS and flow stress of the alloy with respect to the temperature and ram velocity of Ex-ECAE experiments were analyzed using RSM.

Experiments

Experiments were carried out using the Al-0.72Mg-0.55Si alloy. The material was purchased in the form of a rod with 15 mm in diameter, then machined into the billets with nominal diameter and length of 15 and 120 mm, respectively. Before the tests, the samples were annealed for 2.5 h at 700 K. Then, they cooled down to 540 K with a rate of 30 K/h and finally, air-cooled to the room temperature by freely convection. According to Table 1, Ex-ECAE operations were conducted at different temperatures and ram velocities. This test schedule was proposed based on the RSM, where temperature and ram velocity of Ex-ECAE process were considered as the design factors. Totally, 9 Ex-ECAE experiments were designed. As Fig. 1 shows, the die set used in the present work involves two perpendicular channels with an identical diameter of 15 mm. These cylindrical channels intersect at a spherical cavity with a diameter of 23 mm. Contact surfaces were lubricated using MoS2. Electrical heaters were employed to elevate the temperature of the forming tools. The temperature was continuously monitored using a thermocouple installed close enough to the deformation zone, and controlled to vary within ±5 °C. In order to attain a thermal equilibrium, the sample was placed into the inlet channel for 10 min prior to running each SPD experiment. For quasi-static compression tests, Ex-ECAEd products and annealed billets were cut and machined into the samples with 6 mm in diameter and a length/diameter ratio of 1.5. Quasi- static compression tests were performed at a strain rate of 0.1 s−1, while MoS2 was utilized to reduce the interfacial friction between the specimen and tools. For dynamic tests, both the Ex-ECAEd and annealed samples were machined into billets with equal length and diameter of 5 mm. In order to conduct the high strain rate experiments, a split Hopkinson pressure bar (SHPB) was employed. As Fig. 2 shows, the main parts of this SHPB involve a gas gun, a striker bar, an incident bar and a transmission bar. The gas gun propels the striker bar towards the incident bar. Therefore, the impact leads to propagation of an elastic compression wave through the incident bar and towards the sample which is placed between the incident and transmission bars. By arriving this wave to the sample, it goes through plastic deformation. Due to an impedance difference between the bars and the sample, a part of the wave is reflected to the incident bar (reflected pulse), while the other part progresses within the transmission bar (transmitted pulse). Each part of the wave is monitored by the strain gauges mounted on the corresponding bars. Assuming a homogeneous deformation and uniform stress state, based on the one-dimensional elastic stress wave theory, the stress, strain and strain rate of the sample would be calculated as follow [18]:

Table 1 Temperatures and ram velocities of Ex-ECAE experiments selected based on response surface method
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Fig. 1
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One half of the Ex-ECAE die and the processed sample before detaching from the die

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Fig. 2
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The split Hopkinson pressure bar setup employed for dynamic tests. Incident and transmission bars sandwich a cylindrical specimen. A stress wave which is triggered by striker bar impact, propagates through the bars and specimen and then, is conditioned by a set of strain gauges, signal conditioners and oscilloscope

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$$ \left\{\begin{array}{l}\sigma =E\left(\frac{A}{A_s}\right){\varepsilon}_t\\ {}\varepsilon =\frac{2{C}_0}{l_s}{\displaystyle {\int}_0^t{\varepsilon}_td\tau}\\ {}\dot{\varepsilon}=\frac{2{C}_0}{l_s}{\varepsilon}_r\end{array}\right. $$
(1)

It is worth mentioning that the loading direction in the compression tests was parallel to the flow direction in the Ex-ECAE process.

Results and Discussion

Stress–strain curves of Ex-ECAEd and annealed billets, obtained from the compression tests at different strain rates (10−1~3.2 × 103 s−1), are presented in Fig. 3. For each curve, the strain hardening exponent within the strain range of 0.05–0.2 is also plotted in column form. As these diagrams show, Ex-ECAE operation has significantly increased the flow stress compared with the unprocessed annealed condition (Fig. 3(j)). For both the Ex-ECAEd and the annealed samples, the flow stress is enhanced by increasing the compression strain rate. Figure 4 illustrates the variations of the flow stress at a true plastic strain of 0.1 versus the logarithmic strain rate. In this figure, the annealed sample shows the least strength at different strain rates. At various strain rates, as Fig. 4 shows, one can find an improvement in the flow stress by increasing the ram velocity and lowering the temperature of Ex-ECAE operation. It is obvious that by reducing the temperature and rising the ram velocity of the SPD process, the strain rate of the compression tests makes a greater contribution to flow stress development. Among various samples, the annealed rod showed the least improvement in flow stress by increasing the compression strain rate. The product Ex-ECAEd at 373 K and with a ram velocity of 7 mm/min possessed the highest strength at various strain rates of the dynamic tests. On the other hand, doing Ex-ECAE at 523 K and with a ram speed of 7 mm/min has led to the lowest strength for the product. In Ex-ECAE process, the same as the other SPD techniques, increasing the ram velocity (deformation rate) could increase the dislocation generation within the material [19]. Growth in the dislocation density, which is known as the primary obstacle to slip, enhances the flow stresses of various metals. Moreover, reduction in the Ex-ECAE temperature, decelerates the microstructural recovery and dislocation elimination [20] and, consequently, results in material strengthening. The specimen processed at 373 K and with a rate of 7 mm/min, due to the low temperature and high deformation rate (among designed experiments), would involve rather large number of dislocations within its structure. By rising the operation temperature to 523 K, the dislocation density would steeply decrease because of dynamic recrystallization. Results for the sample Ex-ECAEd at 523 K and with a ram velocity of 7 mm/min imply that considerable reduction in the flow stress at different compression strain rates is due to this point. In common, metallic alloys show significant thermal sensitivities [21]. The strength and other mechanical behaviors are considerably affected by the time duration that materials are left at high temperatures. In metal forming process, the ram velocity determines the period of process duration that consequently resulting in the total time for material being exposed at elevated temperature. It could be claimed that during the forming process at elevated temperature, some sort of heat treatment occurs in specimen, which could weaken the product structure. Such the treatment could be kept under control by reducing the process duration. Increasing the ram velocity in Ex-ECAE operation not only, as mentioned before, increased the rate of dislocation generation but also restricted the microstructural recovery and grain growth by limiting process duration. Therefore, as Fig. 3 proves, greater flow stresses could be achieved by increasing the ram velocity.

Fig. 3
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Compressive stress–strain curves and strain hardening exponents for AA6063 at various strain rates (a–i) Ex-ECAEd at different temperatures and ram velocities, and (j) for annealed (initial) condition

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Fig. 4
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Flow stresses at 0.1 plastic strain vs. logarithmic strain rate for products Ex-ECAEd under various conditions and the annealed billet

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In most of the stress–strain diagrams, as Fig. 3 illustrates, the strain hardening exponent is decreased by increasing the strain rate towards 3200 s−1. Quite the same results are reported for the ECAE process [2]. During the compression tests, rising the strain rate has led to an increase in dislocation generation [2]. On the other hand, a greater dislocation generation is coupled with an intensive dynamic recovery [22, 23]. This phenomenon causes a balance between generation and annihilation of dislocations, which eventually results in reduction in strain hardening behavior at higher strain rates. In Fig. 5, flow stresses at different compression strain rates (102~3.2 × 103 s−1) are plotted versus the temperature and ram velocity of Ex-ECAE operation. With this regard, RMS technique incorporated in Minitab 16 statistical software [24] was employed. Accordingly, by using the coefficient of determination (R 2), precision of both the linear and quadratic surface fittings were examined. R 2 for linear, linear-interactions and full quadratic fittings were measured to be 94.6, 95.4 and 99.9 %, respectively. Hence, the full quadratic surface fitting was utilized.

Fig. 5
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Contour plots of the flow stress vs. temperature and ram velocity of Ex-ECAE experiments, obtained from the compression tests at strain rates of (a) 100 s−1, (b) 1200 s−1, (c) 2000 s−1 and (d) 3200 s−1

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As mentioned before, lowering the temperature and rising the ram velocity of the Ex-ECAE process, generally improved the strength of the product. By rising the Ex-ECAE temperature, the influence of this parameter on flow stress was slightly decreased. In Fig. 5, one can find that by reducing the temperature and increasing the ram velocity of the SPD process, contour lines tend to lie on the vertical direction. This situation is more evident at higher compression strain rates. In other words, at lower Ex-ECAE temperatures, increasing the ram velocity does not significantly affect the product strength. As a result, considering limited forming power of the equipment, the Ex-ECAE technique could be performed with lower ram velocities without considerable reduction in the product strength.

Mechanical behavior of metals, besides the microstructural features, depends on the loading rate and temperature. In fact, the flow stress can be formulated as [2]:

$$ \sigma =f\left(\varepsilon, \dot{\varepsilon},T\right) $$
(2)

In turn, the SRS exponent can be defined as:

$$ m={\left(\frac{\partial \ln \sigma }{\partial \ln \dot{\varepsilon}}\right)}_{T,\varepsilon } $$
(3)

Based on this equation, the SRS can be measured at a specific plastic strain and temperature, i.e. for a specified microstructural state. Therefore, the approaches such as strain rate jumping and stress relaxation are generally employed to determine the m value [25, 26]. In the present study, using the logarithmic stress-logarithmic strain rate diagrams at a plastic strain of 0.1, m was measured as the slope of a linear fitting [27, 28]. For FCC materials similar to aluminum alloys, a reduction in the grain size usually rises the SRS of the material [29, 30, 9]. This phenomenon could be explained by studying the parameter of AAV [19]. Based on the thermal activation theory, the stress required for plastic deformation under uniaxial loading can be expressed as [2]:

$$ \sigma ={\sigma}_a+\sqrt{3}\left[\varDelta F-KT \ln \frac{{\dot{\varepsilon}}_0}{\dot{\varepsilon}}\right]/{V}_a $$
(4)

Taking the partial derivative of equation (4) with respect to \( \ln \dot{\varepsilon} \) results in [2]:

$$ \frac{\partial \sigma }{\partial \ln \dot{\varepsilon}}=\frac{\sqrt{3}KT}{V_a} $$
(5)

Accordingly, AAV can be derived as the slope of linear fitting on the logarithmic strain rate versus stress diagram. Figure 6(a) shows the calculated SRS and AAV at a plastic strain of 0.1 for both the Ex-ECAEd and the annealed samples. The value of m for the annealed billets was measured to be 0.024. After Ex-ECAE at 373 K and with a ram velocity of 7 mm/min, this parameter increased to 0.108, denoting more than four times improvement. The growth of dislocation density through the Ex-ECAE operation could cause this considerable development in SRS. The investigations carried out on the ECAE process have reported quite the same results [31, 20]. Ex-ECAE process dramatically decreased AAV. This parameter is about \( {10}^2\sim {10}^3{b}^3 \) for coarse-grained FCC metals [4], where b = 2.85 × 10−10 m is the Burger’s vector for aluminum. By refining the grains, the AAV is noticeably reduced [13, 2, 23]. For coarse-grained metals, with plastic deformation mechanism of dislocation movement, reduction in the grain size causes other flow mechanisms with considerably lower activation volume [23]. Prior to Ex-ECAE operation, the AAV was determined to be 125b 3. By performing Ex-ECAE at 373 K and with a rate of 7 mm/min, the AAV of the AA6063 aluminum alloy was reduced to 7.2b 3.

Fig. 6
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(a) Strain rate sensitivities and apparent activation volumes at strain of 0.1 for products Ex-ECAEd under various conditions (Table 1), and (b) contour plot of strain rate sensitivity vs. temperature and ram velocity of the Ex-ECAE process

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RSM analysis for variations of SRS with temperature and ram velocity of SPD experiments is presented in Fig. 6(b). As shown in this figure, SRS of the alloy is increased by rising the ram velocity and lowering the temperature of the Ex-ECAE operation. By reducing the Ex-ECAE temperature, the bandwidth of the contour lines slightly decreased. This means that at lower temperatures, this parameter affects SRS more strongly than higher temperatures. For instance, at a temperature of 373 K, by rising the ram velocity from 7 to 11 mm/min, the SRS improved nearly 14 %. However, at 525 K with a similar rise in the ram velocity, the SRS did not vary notably. Increasing the Ex-ECAE temperature could accelerate microstructural recovery and dislocation annihilation. Hence contribution of dislocation generation caused by rising the ram velocity would be reduced. Nevertheless, at lower temperatures and higher ram velocities, the dislocations play more effective role in improving the flow stress. Therefore, increasing the ram velocity at higher temperatures did not affect the SRS as much as that at lower temperatures.

As materials, especially fine-grained ones flow with relatively low strain rates (less than 103 s−1), the dislocation transmission is disrupted by barriers such as other dislocations and grain boundaries [7]. Consequently, the time consumed by a moving dislocation for passing through the obstacles is negligible compared with that for staying inside such barriers. In this regime of strain rate, a large amount of activation energy is required for dislocation slip and start of plastic deformation [2]. At higher ranges of strain rate, other flow mechanisms would be active. The viscous drag is a mechanism which plays an important role in material flow under dynamic loadings [6]. As the strain rate exceeds 103 s−1, the necessary time for a dislocation to travel between consecutive obstacles is almost equal to the waiting time within the barriers. In this case, the viscous drag caused by the stress wave propagation, lattice vibration and electron conduction strongly influences the flow stress. Lattice vibration and electron movements elevate the energy level of dislocations and in turn, diffuse them [32]. This procedure finally dissipates the lattice energy and reduces the activation energy required for dislocation movement [32]. When the viscous drag operates, one can find a linear relation between the flow stress and strain rate [6, 7]. For Ex-ECAEd products, flow stress variations versus the strain rate are illustrated in Fig. 7. In this figure, a linear behavior can be observed at high strain rates. This evidence implies that the viscous drag is the major flow mechanism for plastic deformation at high strain rates.

Fig. 7
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Strain rate variations with the flow stress at 0.1 plastic strain for AA6063 samples processed under different conditions as well as for the annealed billet

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Conclusions

In the present investigation AA6063 alloy was subjected to SPD via the Ex-ECAE operation. By conducting several compression tests, the mechanical behavior of Ex-ECAEd products was studied at various strain rates (10−1~3.2 × 103 s−1). Afterwards, strain rate sensitivity (SRS) and apparent activation volume (AAV) were experimentally determined and analyzed using response surface method (RSM). The Ex-ECAE process considerably improved the flow stress of the specimens. Strengths of both the Ex-ECAEd and the annealed billets also showed a growing trend by increasing the compression strain rate. Increasing the ram velocity and lowering the temperature in the preliminary Ex-ECAE experiments enhanced the flow stress of the products. This improvement, observed almost at all the strain rates, could be due to increased dislocation density through the Ex-ECAE process. The strain hardening of products was reduced by rising the strain rate of compression tests to 3200 s−1, which is probably caused by a balance between dislocation generation and dynamic recovery. The RSM analyses demonstrated that at higher Ex-ECAE temperatures, this parameter negligibly affected the product strength. At lower Ex-ECAE temperatures, on the other hand, the flow stress did not show noteworthy variation by increasing the ram velocity more than a particular value. By conducting the Ex-ECAE operation at 373 K and with a rate of 7 mm/min, the SRS of product showed remarkable growth compared with the annealed condition. Moreover, performing Ex-ECAE under such condition, significantly reduced the AAV, namely from 125b 3 to 7.2b 3. The experimental findings indicated that SRS proportionally varied with the ram velocity, while rising the Ex-ECAE temperature decreased the value of this parameter. At high levels of strain rate, a linear relation between the flow stress and strain rate suggested that the flow mechanism during the dynamic compression tests changed to viscous drag.