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In this paper, the finite element method was applied to analyze the deformation behavior of Al-1%Mg alloy during constrained groove pressing (CGP). Deformation inhomogeneity was studied in term of plastic strain distribution during deformation. It was found that after first pressing and flattening steps, the plastic strain is inhomogeneous but second pressing and flattening improve deformation distribution considerably. Also the regions between flat and inclined parts of sample receive less shear strain and consequently after four passes the deformation distribution is still inhomogeneous and doesn’t improve remarkably with more deformation steps.

During last decade, severe plastic deformation has received a great attention among researchers as an effective method of producing ultrafine grain nanostructured materials [1-3]. Several methods have been proposed, developed and evaluated [4-7]. These methods include equal channel angular pressing (ECAP) [

The simulation were carried out using the commercial FEM code ABAQUS. Since the CGP process is a plain strain problem the two dimensional plain strain models were used. The Al-1%Mg alloy was chosen as a model material. To obtain correct simulation results it is necessary to use an appropriate material constitutive model. This model must consider the effects of strain, strain rateand temperature on flow stress. Thereby the Johnsoncook model was used in the simulations. In this model the flow stress is expressed as follows [

where σ is the flow stress, is the strain rate, T is a temperature, and T_{r} are reference strain rate and temperature respectively, T_{m} is melting temperature and A, B, n, m and C are material constants. These material properties for Al-1%Mg alloy are listed in

In the simulation the plate with geometry of 5 (width) × 80 (length) mm^{2} was modeled with total number of 1600 temperature coupled displacement (CPE4RT) elements. The pressing speed and coefficient of friction between the die and specimen were taken to be 1 mm/s and 0.1 respectively. Average equivalent plastic strain across the section of plate was calculated by following equation [

where an equivalent plastic is strain at node i and n is the total number of nodes in the cross section of specimen. Degree of inhomogeneity at imposed plastic strain can be calculated by coefficient of variance of ε_{p} as follows [

where, Stdev (ε_{p}) is the standard deviation of imposed

equivalent plastic strain in cross section of sample.

In the previous experimental works, it was assumed that deformation occurring in the inclined regions is a simple shear and uniform. In this regard, the plastic strain introduced by shearing was calculated simply by equation γ = tg(θ), where θ is a inclination angle as shown in

Inspection of this figure reveals that after 4n pass, the imposed plastic strain on material is not uniform. Also the material between inclined parts of grooved die is deformed by shearing during pressing (1^{st} Step) and material between flat parts of die remains almost unreformed. As can be seen in this figure, the plastic strain distribution at inclined regions (1^{st} Step) is not uniform. This inhomogeneous distribution of strain at these regions finally (after every 4n step) leads to an inhomogeneity in imposed plastic strain. The equivalent plastic strain distributions on L1 and L2 lines from Point A to B (as depicted in

It’s deduced that imposed plastic strain on sample is not a pure shear. Shearing occurs mostly at inclined regions and bending occurs mainly at near surface regions. Therefore the strain at every point is due to interaction between shearing and bending. It’s worth noting that the amount of shearing and bending varies from point to point. ^{st} step) the imposed strain is inhomogeneous because only materials at inclined regions are subjected to severe deformation but regions between flat parts of die receive low plastic deformation. After 2^{nd} step the inhomogeneity increases because the same regions are deformed during flattening. Before imposing 3^{rd} step the plate is shifted one groove length to left or right and consequently during 3^{rd} and 4^{th} step the unreformed regions (during 1^{st} and 2^{nd} steps) are subjected to severe deformation. This leads to improvement of plastic strain distribution in sample. Hence at every deformation cycle (each cycle comprises 4 steps), first pressing and flattening increase the inhomogeneity but second pressing and flattening improve the strain distribution. As shown in ^{th} and 8^{th} steps the inhomogeneity factors (0.55 and 0.54 respectively) are still high and never reach to zero (theoretical value) with more deformation. As previously mentioned, this is due to the fact that regions between C and D (shown in

plastic strain is less than strain at Node 1 and Node 3.