Forming limit prediction of anisotropic material subjected to normal and through thickness shear stresses using a modified M-K model

In some recent sheet metal forming processes such as hydroforming and incremental forming processes, normal and through thickness stresses are induced over the metal sheet, and therefore, prediction of forming limits requires considering effect of these stresses. In this investigation, a modified M-K model has been utilized to consider general stress state including normal and through thickness shear stresses on anisotropic metal sheet. This is achieved by assuming additional force equilibrium and geometrical compatibility between groove and matrix, and the numerical model has been solved by Newton-Raphson method to calculate the limiting strains. Forming limit diagrams resulting from this model have been evaluated with some published experimental data, and a good accordance between the results has been observed. It has also been concluded that exertion of normal and through thickness stresses enhances forming limits significantly.