Comparison of 3D yield functions for finite element simulation of single point incremental forming (SPIF) of aluminum 7075

Abstract

The deformation in sheet metal forming processes, such as stamping, occurs under plane stress condition in which through-thickness stresses (σzz, σxz, σyz) are negligible and application of a two-dimensional (2D), plane stress yield function is sufficient. However, in incremental sheet forming processes, significant out-of-plane shears develop in the sheet metal, which necessitates the use of a three-dimensional (3D) yield function to account for normal and shear stress components. To simulate the single point incremental forming (SPIF) of 7075-O aluminum alloy sheet, three different yield functions namely; von Mises, Hill's 1948, and Barlat Yld2004-18p were used. The Yld2004-18p was implemented into the commercial FEA code ABAQUS as a user material subroutine (VUMAT), by considering the cutting-plane algorithm for the integration of the elasto-plastic constitutive model. For direct CPU time comparison, the same Yld2004-18p VUMAT was reduced to von Mises and Hill's 1948 yield functions and finite element simulations of SPIF were repeated. Anisotropy coefficients of Yld2004-18p and Hill's 1948 were calculated using uniaxial tensile test data for AA7075-O. A detailed comparison of the three yield functions’ predictions were made with respect to the effective plastic strain distribution, part thickness, tool force and moment, and development of stress and strain tensor components.