Keywords

1 Introduction

Severe plastic deformation (SPD) is a technique in which a large plastic strain is imposed on a bulk metal to produce an ultrafine-grained structure. A finer grain size increases the strength and fracture toughness of the material [1, 2]. Due to the ability to produce grains with diameters of several hundred nanometers, SPD processes such as equal channel angular pressing (ECAP), constrained groove pressing (CGP), accumulative roll bonding (ARB), and high-pressure torsion (HPT) drew the interest of researchers in the 1990s. Among the SPD techniques, multi-axial forging (MAF) is of particular interest for its potential to be scaled up to relatively large samples [3, 4]. Figure 1 demonstrates the multi-axial forging principle.

Fig. 1
figure 1

Schematic diagram of multi-axial forging process

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In MAF, a workpiece is subjected to a specific strain in each pass several times on different axes using the same die; this leads to the accumulation of a large plastic strain in the material [5, 6]. The disadvantage of multi-axial forging is that the strain distribution along the specimen’s cross-section is not uniform; however, this can be avoided through proper lubrication. Even though multi-axial forging produces less inhomogeneous strain than ECAP and HPT, it can be used to refine grain sizes for all metals [7, 8].

Qing Feng Zhu et al. studied the impact of forging passes on the refining of high purity aluminum during multi-axial forging [8]. The structural uniformity was focused due to deformation non-uniformity. When the forging passes reached 6, an X-shaped fine grain zone (Fig. 2) was initially formed. With further increases in the passes, this X-shaped zone started to spread the whole sample. Limitation in the structural refinement was observed with increasing strain during the multi-forging process at room temperature. The grain size in the center was refined to a certain extent as the forging passes reached 12, and there was no further grain refinement in the center after increasing the forging passes to 24. However, the sizes of the coarse grains near the surface continuously decreased with increasing forging passes [8].

Fig. 2
figure 2

Schematic diagram of three deformation zones in free forging process [8]

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Saeed Khani Moghanaki et al. [9] investigated the effect of initial heat treatment on mechanical properties and texture evolution during the multi-axial forging of an Al-Cu-Mg alloy. Under both solution-treated and over-aged conditions, the compressive stress during MAF increased up to the second pass; by further straining, the flow-stress decreased in the third pass. The deformation mode was a plane strain, and the equivalent strain per pass was approximately 0.4 (with a total strain of 1.2).

Multi-axial forging involves subjecting a material to complex loading conditions by applying sequential compression in all three principal directions. This process significantly alters the microstructure and enhances the mechanical properties of aluminum alloys, making them suitable for high-strength applications. A few researchers [10,11,12,13] have worked on microstructural changes during MAF and its effect on the mechanical properties of aluminum and its alloys; however, the published literature on the flow-stress modeling and finite element simulation of MAF on aluminum alloys is limited. Simulations that use suitable flow-stress models and their validation by using experimental results can lead to accurate predictions of required loads in MAF and the strain and stress distributions in the deformed samples. In view of this, finite element simulation of the multi-axial forging of the AA6082 alloy has been carried out in the present work. Reliable predictions from FE simulations could help engineers choose optimum choices of process parameters to reduce costly real-life experiments. A three-dimensional model of the tools and workpiece was created using CAD software. Isotropic hardening with a Voce flow-stress model has been used for numerical simulations. Also, the strain distributions that were obtained from our finite element simulations have been correlated with hardness distributions in order to validate the predicted variations through the cross-section.

2 Materials and Methods

2.1 Material

6XXX-series alloys have better strength and forgeability than other wrought Al alloys, and AA 6082 can provide better strength after heat treatment as compared to the other alloys of this series [14]. In this study, AA6082 has been used for multi-axial forging experiments. The nominal chemical composition of AA6082 is listed in Table 1 [15].

Table 1 Chemical composition of AA6082 [15]
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2.2 Experimental Work

Uniaxial Compression Tests

Uniaxial compression tests of AA6082 were carried out as per ASTM Standard E9 on an Instron 5900R/5582 machine (capacity—10 kN) at a constant cross-head speed of 1 mm/min. Specimens with an L/D ratio of 3 were generally used for determining the compressive properties of metallic materials as per ASTM E9. So, samples with a diameter of 13 mm and a height of 38 mm were prepared by wire electric discharge machining, and these samples were tested until the first load drop with the help of the load–displacement data that was obtained from the machine.

It is well-known that, during plastic deformation, a number of changes occur in the microstructure of a material that affects its properties. Work hardening (a phenomenon in which strength increases and plasticity decreases) is a consequence of increased deformation extent and cannot be ignored [16]; this must be incorporated into a flow-stress model to accurately predict the flow curve in finite element simulation.

The flow-stress curve of as-cast AA6082 that was obtained from uniaxial compression testing was compared to four flow-stress models (namely, Hollomon, Swift, Hocket-Sherby, and Voce) to obtain the best fit. The flow-stress models and the material constants that were obtained from our uniaxial compression tests are given in Table 2. The flow curves that were predicted by different models are shown in Fig. 3.

Table 2 Flow-stress models and corresponding material constants
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Fig. 3
figure 3

Comparison of different flow-stress models with experimental data

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Multi-axial Forging Experiments

The samples of the AA6082 that were produced by gravity die-casting were machined into cubes with sides of 30 ± 0.5 mm (Fig. 4a). The samples were polished on SiC emery paper with up to a 1500 grit size. The multi-axial forging was done at room temperature on a 60-ton (66-ton) hydraulic press at a constant ram speed of 0.2 mm/sec. The true strain in each pass is given by Eq. (1) [21].

$$ {\upvarepsilon }_{1} = \ln \frac{{h_{f} }}{{h_{0} }}, $$
(1)
Fig. 4
figure 4

a As-cast MAF sample; b MAFed sample after first cycle; c MAFed sample after second pass of second cycle

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where hf and h0 are the final and initial dimensions, respectively, of the sample in the direction of the compression.

$$ {\upvarepsilon }_{2} = {\upvarepsilon }_{3} = {-}\frac{{{\upvarepsilon }_{1} }}{2}{\text{ (considering material to be isotropic}}). $$
(2)

The effective strain after each pass is given by Eq. (3) [21].

$$ \overline{\varepsilon }{ } = \left[ {\frac{2}{3}\left( {{\upvarepsilon }_{1}^{2} + {\upvarepsilon }_{2}^{2} + {\upvarepsilon }_{3}^{2} } \right)} \right]^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} , $$
(3)

where the total effective strain that was accumulated after one cycle (three passes) = 3 \(\overline{\varepsilon }\).

In the MAF experiment, a true strain of 0.095 ± 0.002 was given in each pass, so the total accumulated effective strain after one cycle (three passes) was 0.285 ± 0.002. Since there was a crack initiation in the second pass of the second cycle (Fig. 4b), the MAF study was done for one cycle only (Fig. 4b).

After three passes (Cycle 1) of MAF, the microhardness was measured at several points from the surface to the center of the specimen in the direction in which the last compression was done using a Vickers microhardness tester by applying a load of 0.5 kg for 10 s.

2.3 F.E. Simulation

The MAF process was simulated using QForm software. The 3-D model of the tools and MAF workpiece was prepared using CAD software separately and was imported into the software as a.step file. Triangular elements were used to mesh the tools and the block. The adaptive meshing technique was employed from a minimum mesh size of 1 to 3 mm with a multiplying factor of 0.5 mm. The Levanov model was used to define the friction between the tools and the workpiece with a friction factor (m) of 0.1 [22]. This is given by Eq. (4).

$$\tau =m\frac{{\sigma }_{T}}{\sqrt{3}}\left(1-{\text{exp}}\left(-1.25\frac{{\sigma }_{n}}{{\sigma }_{T}}\right)\right),$$
(4)

where \(\tau \) is the shear stress, \({\sigma }_{T}\) is the flow-stress, and \({\sigma }_{n}\) is the normal contact pressure.

In the material model, the von Mises yield function was used. Since the Voce hardening model fits well with the experimental flow curve, it was used in the simulation (as a subroutine) to define the flow curve. For the MAF process, the lower die was fixed, and the upper die was given the required displacement to deform the workpiece to a predetermined strain. From the simulations, the strain distribution was analyzed in the workpiece after each pass.

3 Results and Discussion

3.1 Strain Distribution

Figures 5a and d show that the strain distribution along the horizontal and diagonal axes was more homogeneous after the first pass as compared to the vertical direction due to the friction between the toll and the workpiece. In Fig. 7, it can also be seen that the inhomogeneity factor was higher in the vertical direction as compared to the other two directions. After Pass 2, there was the formation of an X-shaped zone (Fig. 5b), and the strain accumulation in this zone was greater as compared to the remaining region. This zone continued to expand in the third pass (Fig. 5c). This showed that the strain accumulated near the center as the number of passes increased. As the strain accumulated in the material, the dislocation became more piled-up to form shear bands that, in turn, formed sub-grains in the material and refined the grain sizes [23, 24]. The strain distribution after each pass is shown in Fig. 6 for comparisons among the passes.

Fig. 5
figure 5

Plastic strain distribution at mid-plane after a Pass 1, b Pass 2, and c Pass 3 and along the line from center to surface in vertical, horizontal, and diagonal directions after d Pass 1, e Pass 2, and f Pass 3

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Fig. 6
figure 6

Plastic strain distribution at mid-plane along the line from center to surface in vertical, horizontal, and diagonal directions after each pass

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Fig. 7
figure 7

Inhomogeneity factor after each pass along line from top to center in vertical, horizontal, and diagonal directions

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There was a non-uniformity of the strain distribution due to the friction between the tools and the workpiece. So, an inhomogeneity factor (IF) was used to quantify the non-uniformity in the material [25]; this is defined in Eq. (5):

$$ {\text{IF :}} = \frac{{\sqrt {\sum\nolimits_{i = 1}^{n} {{{\left( {S_{i} - S_{av} } \right)^{2} } \mathord{\left/ {\vphantom {{\left( {S_{i} - S_{av} } \right)^{2} } {\left( {n - 1} \right)}}} \right. \kern-0pt} {\left( {n - 1} \right)}}} } }}{{S_{av} }} \times 100, $$
(5)

where Si is the value at the i-th point, Sav is the average value, and n is the number of measurements in a sample.

Since the IF in the horizontal direction was mainly influenced by friction, it was almost at its maximum in all passes (Fig. 7). The IF in the horizontal direction was the lowest after the first pass, but it increased after the second pass (because of the pre-strain from the first pass) and then decreased (due to the formation of the X-shaped zone).

The microhardness values and the plastic strain simulation results were correlated after the third pass along the last compression axis from the surface to the center (Fig. 8). There was an increasing trend in both cases due to the strain hardening of the material, as the strain accumulation near the center was greater as compared to the top surface.

Fig. 8
figure 8

Strain and hardness distribution along the line from surface to center in compression direction after Pass 3

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3.2 Variation of Load in MAF

The load–displacement curve for the different passes of MAF was experimentally obtained from the N.I. data-acquisition system that was attached to the load cell and rotary displacement encoder in the hydraulic press. Figure 9b shows the jump in the required load in the initial portion of the load–displacement curve during the second pass due to the generated dislocation after the first pass. Also, the slope of the curve (after the initial load) decreased in the second and third passes; due to this, the variation in the peak load in these two passes was lower. The load–displacement curve that was obtained from the QForm simulation is also presented in Fig. 9a.

Fig. 9
figure 9

Load–displacement curves in different passes of MAF that were obtained from a simulation and b experiments

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In the experiments, the load that was predicted for the first pass was slightly greater than the experimental values, but the second and third passes correlated well with the experimental values (Table 3). The variation in the predicted and experimental loads was due to the isotropic hardening and structural change inside the material (such as dislocation interaction, texture evolution, and the possibility of sub-grain formation).

Table 3 Peak load after each pass of MAF that was obtained from simulation and experiment
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4 Conclusions

To study the behavior of AA6082 during multi-axial forging, a numerical simulation was successfully performed using QForm software. It was observed that there was a formation of an X-shaped zone after the second pass and that this zone expanded after the third pass. Although the accumulated strain was greater in this zone, there was more strain homogeneity here than could be found in the rest of the region. As there was a strain accumulation near the center of the workpiece, an increasing trend of the hardness and strain distributions could be observed after the third pass along the last compression axis from the surface to the center due to strain hardening.

The material models that were used for the FE simulation were the von Mises yield function and the Voce hardening law. Since the material model was defined for monotonic loading when a real experiment is cyclic in nature, the maximum predicted load by the model was slightly greater when compared to the experimental load values. Overall, this method can be an excellent resource for learning more about multi-axial forging; however, the material models must be re-examined in order to do this if we are to obtain a suitable response for the multidirectional load.