Plastic and fracture analyses for applications to sheet metal forming and metal cutting

An approximate macroscopic yield criterion for anisotropic porous sheet metals is adopted to develop a failure prediction methodology that can be used to investigate the sheet metal failure under forming operations. The Marciniak-Kuczynski approach is employed to predict failure by assuming a slightly higher void volume fraction inside randomly oriented imperfection bands in a material element. A non-proportional deformation history including relative rotation of principal stretch directions is identified in a critical element of a mild steel sheet from a fender forming simulation. The results based on the failure prediction methodology show that the gradual rotation of principal stretch directions lowers the failure strains of the critical element under the given deformation history.; Failure of sheet metal due to void growth and coalescence is also investigated under pre-bending/unbending conditions. Mroz's hardening rule proposed based on the cyclic plastic behavior of metals observed in experiments is generalized to characterize the material anisotropic hardening behavior due to loading/unloading with consideration of the damage evolution. Our simulation results show that pre-bending/unbending affects the failure of sheet metals due to different stress and plastic deformation histories through the thickness.; In order to understand shear dominant fracture, governing equations for asymptotic crack-tip fields in perfectly plastic Mises materials under combined in-plane and out-of-plane shear loading conditions are investigated. The solutions for singular plastic sectors and non-singular plastic sectors are obtained and used to assemble asymptotic mixed mode II and III crack-tip fields. In the assembly of the asymptotic crack-tip fields, stress discontinuities along the border between two constant stress plastic sectors are admitted based on the corresponding perturbation and finite element solutions for low strain hardening materials. The trends of the angular stress distributions of the crack-tip fields agree with those of the available computational results for low strain hardening materials. In addition, shear dominant notch-tip solutions, similar to mixed mode II and III crack-tip solutions, are investigated with traction boundary conditions on two notch surfaces. The notch-tip stress solutions are obtained in terms of the parameters from metal cutting. Finally, the implications of the notch-tip solutions to metal cutting are examined.