Modeling material behavior during continuous bending under tension for inferring the post-necking strain hardening response of ductile sheet metals: Application to DP 780 steel

Abstract

Continuous bending under tension (CBT) testing can stretch ductile sheet metals significantly more than simple tension (ST) testing. Strength and plastic strain levels increase with the number of CBT cycles and substantially exceed those achieved in ST. Taking advantages of the improved elongation-to-fracture (ETF) achieved by CBT, samples of DP 780 steel are pre-deformed to several strain levels by interrupting their CBT testing. Sub-size specimens are machined from the CBT interrupted specimens and tested in ST. The flow curves from these secondary ST tests are then shifted according to the axial strain accumulated during pre-deformation by CBT to determine a large strain (post-necking) flow curve of the material. The identified large strain flow curve is validated with two approaches. First, the large strain flow curve is used to simulate the load versus displacement curve during CBT to large number of CBT cycles. Second, the curve is used to simulate the flow curves based on the secondary ST testing. The simulations are performed using isotropic hardening (IH) and combined isotropic-kinematic hardening (CIKH) material models. The latter model is calibrated using a set of large strain cyclic tension-compression data. An automated procedure is developed for the creation of sub-size specimens from the finite element (FE) mesh of the interrupted CBT specimen to facilitate efficient secondary ST simulations. The procedure involves cutting of the FE mesh into the sub-size specimen shape by Boolean operations in Abaqus software followed by generation of volume FE mesh and mapping of the state variables. The state variables are mapped to simulate deflection of the specimens, as the residual stress field from the prior CBT simulation evolves to reach a new equilibrium. It is found that the model reproduces the experimental load versus displacement curve, including the succession of spikes and plateaus typical of CBT, very closely. The model also predicts yielding of the interrupted sub-size specimens further verifying the identified curve. The predictions demonstrate the utility of the developed methodology for inferring the post-necking strain hardening behavior of sheets.