After a concise review of the classical theory of plasticity, the main isotropic and anisotropic yield criteria proposed in the literature are succinctly reviewed. More emphasis is given to yield conditions expressed with principal stresses and their extension to plastic anisotropy based on linear tensor transformations. In this article, the yield functions are considered as effective plastic potentials for the determination of tensorial stress-strain relationships. For sheet metals, testing procedures needed to characterize anisotropy and methods suitable to extract the corresponding coefficients are described. Finally, further constitutive descriptions suitable for application to industrial sheet forming processes are discussed.

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An anisotropic plane stress yield function that is described by 3^rd-degree spline curves has been proposed. To fix the parameters for the model, three types of mechanical tests are needed. In this study, only uniaxial tensile tests at several angles from the rolling direction have been carried out, because stress states of the target for comparison are uniaxial stress in this case. The characteristic of this model is that the calculated flow stresses and r values fit the experimental values in all directions. Also it has been expanded to represent the differential work hardening model and the thickness measured experimentally is compared with the thickness simulated by the hole expanding test. The results of the experiment are almost in accord with the result of the simulation by the proposed method. There is little difference between the results of the differential hardening model and conventional hardening model in this case.

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In the present work, we combined a measuring method, the digital image grid method (DIGM), with the finite-element method (FEM) to analyze local strains, local stresses and the damage limit. We called the method displacement-measurement-based FEM (M-FEM). Transient displacement fields during a uniaxial tensile test were directly measured by DIGM. With the aid of M-FEM, detailed distributions of local strains and local stresses in large deformation zones were investigated. Then, the change in the local anisotropic parameter of high-strength steel sheets with plastic strain from uniform deformation to fracture was evaluated. Furthermore, the local fracture strain and damage limit of several advanced high strength steel sheets (980MPa with t1.2mm, 980MPa with t1.6mm, 1180MPa with t1.6mm) were identified by uniaxial tensile tests and M-FEM. The identified damage limit of materials agreed very well with that measured by a conventional press test. This verified the validity of M-FEM.

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With the increasing application of hot-stamped parts to automobile bodies and warm-drawn parts of magnesium alloys to electrical devices, simulation has become a basic approach to formability evaluation when designing parts and tools. However, the thermal-mechanical coupling phenomena induced in the hot-stamping process and warm-drawing process are complicated. To accurately simulate these complicated phenomena, a finite-element model for B-pillar hot stamping was created and transient temperature distribution was simulated. The thickness distribution and hardness distribution in a hot stamped B-pillar were predicted. Furthermore, a temperature-dependent anisotropic material model combined with the Hill48 yield function was developed for the simulation of the warm-drawing of magnesium alloys. The predicted results agreed well with experimental ones and simulation accuracy was demonstrated using the newly developed models.

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