Yield and damage criteria for sheet metal forming simulations

A Taylor-like polycrystal model is adopted here to investigate the plastic behavior of body centered cubic (b.c.c.) sheet metals under plane strain compression and subsequent in-plane biaxial stretching conditions. The {dollar}langle{dollar}111{dollar}rangle{dollar} pencil glide system is chosen for the slip mechanism for b.c.c. sheet metals. The {dollar}{lcub}{dollar}110{dollar}{rcub} langle{dollar}111{dollar}rangle{dollar} and {dollar}{lcub}{dollar}112{dollar}{rcub} langle{dollar}111{dollar}rangle{dollar} slip systems are also considered. For the sheet metal subjected to subsequent in-plane biaxial stretching and shear, plastic potential surfaces are determined at a given small amount plastic work. The effects of the slip system and the magnitude of plastic work on the shape and size of the yield surfaces are shown. The normal anisotropy and planar anisotropy of the sheet metal are investigated in terms of the uniaxial yield stresses in different planar orientations and the corresponding values of the anisotropy parameter R.; Three phenomenological yield criteria are adopted to describe the plastic behavior of sheet metals with normal plastic anisotropy. A rate-sensitive thin shell finite element formulation based on the virtual work principle is derived for the three yield criteria. The effects of the yield surface shapes based on the three yield criteria with the same value of the plastic anisotropy parameter R on the strain distribution and localization are investigated under a hemispherical punch stretching operation and a plane strain drawing operation. The results of the simulation show that the yield surface shape, instead of the plastic anisotropy parameter, controls the punch force, strain distribution and strain localization for the punch stretching operation. However, the yield surfaces do not affect the punch force and the strain distribution significantly.; An approximate macroscopic yield criterion for anisotropic porous sheet metals is developed under plane stress conditions. The Hill quadratic and non-quadratic anisotropic yield criteria are used to describe the matrix normal anisotropy and planar isotropy. Under axisymmetric loading, a closed-form upper bound macroscopic yield criterion is derived as a function of the anisotropy parameter R. The plane stress upper bound solutions for different in-plane strain ratios can be fitted well by the closed-form macroscopic yield criterion.