On the influence of tool contact stress on tensile instabilities in plane strain stretching and bending of sheet metals

It is well known that the widely used forming limit curve (FLC) based upon in-plane stretching fails to account for the delay in plastic instability in the presence of appreciable bending and tool contact pressure. The recently proposed General Incremental Stability Criterion (GISC) - a generalization of the Modified Maximum Force Criterion (MMFC) to triaxial loading - revealed the dependence of the boundary conditions on the formation of tensile instabilities. Nevertheless, it remains unclear how the combined effect of radial bending stresses and tool contact pressure affects the formation of an acute neck. It is shown in this study that a compressive normal stress causes a shift of the strain state from initial plane strain tension to positive minor strains for material layers within the cross-section. The convex (outer) layer remains in a state of plane strain-plane stress. Accounting for the shift in the strain state is key to capture the dependence of the contact pressure on necking. A simplified modelling approach, which enforces plane strain tension of the cross-section, was able to capture the formability gain due to bending but failed to account for the delay in plastic instability due to the contact pressure. An incremental multi-layer model was required to account for non-monotonic loading due to bending over the punch and the biaxial shift in the strain path caused by the contact pressure. The models were then applied to the experimental forming limits of a 3rd Gen 1180 advanced high strength steel to demonstrate the formability gains under triaxial loading due to the contact pressure.

Automated summary

The commonly used forming limit curve (FLC) does not consider the delay in plastic instability caused by bending and tool contact pressure. The General Incremental Stability Criterion (GISC) has revealed the influence of boundary conditions on tensile instabilities. However, the effect of radial bending stresses and tool contact pressure on necking is still unclear.