Analysis of plastic flow localization under strain paths changes and its coupling with finite element simulation in sheet metal forming

Formability of sheet metal is usually assessed by the useful concept of forming limit diagrams (FLD) and forming limit curves (FLC) represent a first safety criterion for deep drawing operations. The level of FLC is strongly strain path dependent as observed by experimental and numerical results and therefore non-proportional strain paths need to be incorporated when analyzing formability of sheet metal components. Simulations using finite element method allow accurate predictions of stress and strain distributions in complex stamped parts. However, the prediction of localized necking is a difficult task and the combination of forming limit diagram analysis with finite element simulations often fail to give the right answer, if complex strain paths are not included in these predictions.In this work a code is presented aimed at formability prediction in sheet metal forming, with a concept and structure which allows the implementation of any hardening law, yield function or constitutive equation without major difficulty. The model incorporates both approaches of the theory of plasticity, namely the phenomenological one and the physical one. Several phenomenological constitutive equations, such as, Swift hardening power law and Voce saturation hardening law, the isotropic von Mises yield criterion, the quadratic Hill yield criterion (Hill’48), the non-quadratic Hill yield criterion (Hill’79) and the Yld’96 Barlat yield criterion as well as a physics-based constitutive model accounting for the texture and strain path induced anisotropy, specifically based on the Van Houtte's anisotropic texture strain-rate plastic potential and Teodosiu and Hu microstructural hardening model, are implemented in the new model. The necking phenomenon is carried out in the framework of heterogeneous materials using the Marciniak–Kuczincki (M–K) analysis coupled with the theory of plasticity. Such code may be used to obtain forming limit curves under linear and complex strain paths as well as being used to be coupled with finite element results, as a post-processing tool, to predict occurrence of necking. Studies are presented to test and validate implemented models including some sensitivity analysis to defined variables. The influence of strain path change is presented through the consideration of several non-proportional loading sequences and theoretical results are compared with experimental ones. Also a selected sheet metal component is considered to test and validate developed code as a post-processing tool for finite element analysis and such results are compared with those obtained experimentally.