Anisotropic hardening model based on non-associated flow rule and combined nonlinear kinematic hardening for sheet materials

 A material model for more effective analysis of plastic deformation of sheet materials is presented in this paper. The model is capable of considering the following aspects of plastic deformation behavior of sheet materials: the anisotropy in yielding stresses in different directions by using a quadratic yield function (based on Hill’s 1948 model and stress ratios), the anisotropy in work hardening by introducing non-constant flow stress hardening in different directions, the anisotropy in plastic strains in different directions by using a quadratic plastic potential function and non-associated flow rule (based on Hill’s 1948 model and plastic strain ratios, r-values), and finally some of the cyclic hardening phenomena such as Bauschinger’s effect and transient behavior for reverse loading by using a coupled nonlinear kinematic hardening (so-called Armstrong-Frederick-Chaboche model). Basic fundamentals of the plasticity of the model are presented in a general framework. Then, the model adjustment procedure is derived for the plasticity formulations. Also, a generic numerical stress integration procedure is developed based on backward-Euler method (so-called multistage return mapping algorithm). Different aspects of the model are verified for DP600 steel sheet. Results show that the new model is able to predict the sheet material behavior in both anisotropic hardening and cyclic hardening regimes more accurately. By featuring the above-mentioned facts in the presented constitutive model, it is expected that more accurate results can be obtained by implementing this model in computational simulations of sheet material forming processes. For instance, more precise results of springback prediction of the parts formed from highly anisotropic hardened materials or that of determining the forming limit diagrams is highly expected by using the developed material model.

Numerical models of plastic zones and associated deformations for elliptical inclusions in remote elastic loading-unloading with different R-ratios

Plastic zones and associated deformations ahead of a fatigue crack are well established nowadays. In-depth plane strain elasto-plastic finite element analysis is conducted in this investigation to understand the nature of cyclic plastic deformation and damage around soft and hard elliptical inclusions. Similar to fatigue crack tip, cyclic/reverse plastic zone and monotonic plastic zone are visible for soft elliptical inclusion. In the cyclic plastic zone, low cycle fatigue is the dominant cyclic deformation mode during symmetric load cycling, while ratcheting is dominant during asymmetric load cycling. The size of cyclic plastic zone depends upon the amplitude of remote stress while, the size of monotonic plastic zone depends upon the maximum remote stress. The size of monotonic plastic zone is equal to cyclic plastic zone during symmetric load cycling. The shape and size of plastic zones also depend upon the orientation of the soft inclusion. Cyclic plastic damage progression in the cyclic plastic zone for soft (MnS) inclusion is significant, while no cyclic plastic zone is visible for hard inclusion (Al2O3).