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In this paper, an analytical path-dependent plastic instability model is proposed for the thin metallic sheets through considering a linear pre-straining path for the both diffuse and localized necking. The model is introduced by extending a modified maximum force (MMFC) that the MMFC considers the strain hardening on the diffuse necking as well as the loading conditions. Also, the vertex criterion will be used to prediction of localized necking. The vertex criterion presented by Sto ̈ren and Rice are usually based on the J_2 deformation theory of classical plasticity, which explores the localized necking through the rate discontinuity assumption at the necking band. Both models will be combined with the strain path effect through a linear adoption of an equivalent strain. It will be investigated by applying a pre-strain in the major and minor directions for prediction of the formability in the non-proportional loading. Moreover, a dependent to yield criterion (DYC) - angle is used for prediction of the necking band angle in the vertex theory. Finally, the quadratic Hill criterion is used to investigate the anisotropy effect. The model is verified by experimental results presented by other authors.

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Cold work hardening and nonlinear strain path, cause the failure strain change. Therefore, it is necessary to consider the created cold-work hardening and its distribution for predicting and simulating the behavior of products. The composite rupture disc cold-work hardened during manufacturing and burst and release pressure in a pressure commensurate with this hardening. In this case, the sheet metal undergoes a nonlinear strain path during forming and after slotting during the burst test. In this paper, the burst pressure of a composite Rupture disc estimated by using finite element simulation in Abaqus-implicit and explicit and by considering the strain hardening during bulge forming before the slotting process. The burst pressure is estimated according to the maximum plastic failure strain that changed due to nonlinear strain path and work hardening. The burst pressure predictions were compared and validated by experimental tests. In this paper, the effect slotting pattern, investigated by using FEM simulations and experiments. In the prepared samples for this paper, by slotting after bulge forming, the burst pressure reduces more than 80%. The simulation with this method predicts this pressure reduction with an error of about 3%.

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In the current research, the effect of strain path by two processes of conventional asymmetric rolling and asymmetric cross rolling, as well as natural aging on the microstructure and hardness of AA7075 aluminum alloy was investigated. The microstructure was examined by light microscopy and the hardness by macro-Vickers hardness tester. The results showed that the rolled sample (initial sample) had elongated grains due to rolling and the average width of the grains in this sample was 13.4 μm. By applying conventional asymmetric rolling up to 60%, the grains became more elongated and the average grain width reached 2.6 μm. By performing asymmetric cross rolling up to 40%, the average grain width reached 3.7 μm. The distribution of particles did not change significantly with rolling deformation. Shear bands were also formed in the sample after 40% and 60% conventional asymmetric rolling, as well as after 40% asymmetric cross rolling. At zero aging time, the hardness of the 60% conventionally rolled sample was higher than the 40% cross rolled sample. With increasing the aging time, the hardness of all samples increased due to natural aging. As the thickness reduction percentage increased (increasing the strain), the hardness increase percentage due to natural aging decreased. The increase in hardness due to natural aging was more noticeable in the cross-rolling process than in the conventional rolling process. After 7 days of natural aging, the hardness of the material reached its saturation limit.