Finite element modeling simulation of in-plane forming limit diagrams of sheets containing finite defects

Abstract

Finite element modeling (FEM) has been used to predict forming limit diagrams (FLDs) of thin sheets based on two-dimensional (2-D) finite thickness defects. The local growth of these defects is simulated until an arbitrary failure criterion is reached. Many aspects of this simulation re-produce the standard Marciniak-Kuczynski (M-K) results. For example, the plane strain intercept, FLD₀, is sensitive to the material work hardening,n, and the strain rate sensitivity,m, but is not affected by the normal anisotropy,r. The positive side of the FLD was characterized by a line of logarithmic slopeP. The value ofP decreases sharply asn andm increase. The effect ofr depends on the choice of yield function. The absolute location of the FLD, as given by the FLD₀, depends not only on the material properties, but also on the choice of failure criterion, defect geometry, and details of the simulative model (mesh size, number of defect dimensions,etc.). This is true of any measurement or simulation of the FLDs. Therefore, we propose that the FLD₀ be used as the single “fitting parameter” between modeling and experimental results: a more realistic approach based on what is actually measured in the FLD experiments. This method allows clarification of the role of material plasticity properties(e.g.,n, m, andr) vs fracture properties (contained in the FLD₀) in determining the shape of the FLDs.