Anisotropic and asymmetrical yielding and its distorted evolution: Modeling and applications

• A unified continuum-based discontinuous (CBD) framework introducing SSM and SIM.
• Calibrating way for CBD framework related to convergence, overlapping and accuracy.
• Combination of implicit algorithm and interpolation approach for CBD implementation.
• Evaluation of SSM and SIM-based CBD models on describing distorted yield loci.
• Correlation among initial textures, distorted behaviors and non-uniform deformation.

Characterizing the anisotropy/asymmetry-induced distortional yielding and subsequent evolution is still a challenge for potential usages of hard-to-deform materials. From perspective of multiple mechanisms, two types of yield functions are classified, viz., the principal shear stress-based models (SSM) and the stress invariants-based models (SIM); then a unified continuum-based discontinuous (CBD) framework is constructed, in which SSM and SIM are introduced to capture the distorted shape of the yielding, and an interpolation approach is adopted to smoothly present the nonlinear evolution of the distorted plasticity in the full stress space. Taking the CPB06 (Cazacu et al., 2006) and Yoon's criteria (Yoon et al., 2014) as typical SSM and SIM, the CBD framework is implemented in the explicit 3D-FE platform for practical usages by combining implicit algorithm and interpolation approach, and the Nelder-Mead (N-M) method and the genetic algorithm (GA) approach are evaluated for calibrating of CBD related to convergence, overlapping and accuracy. The evaluation proves that the GA-based method is suitable for CBD, and the SIM seems to be feasible for embedding into the CBD framework because of its solid physical basis and numerical robustness. Taking high strength titanium alloy tube (HSTT) as a case, the distorted plasticity evolution of the HSTT with six typical initial textures are characterized, then the correlations among initial textures, distorted behaviors and inhomogeneous deformation are quantitatively established to improve the multi-defect constrained formability in uniaxial tension/compression and mandrel bending.