Constitutive modeling related uncertainties: Effects on deformation prediction accuracy of sheet metallic materials

Abstract

Constitutive modeling is the most fundamental issue for nonlinearity characterization of sheet metallic materials. However, uncertainties from multiple sources inevitably involved in material characterizing make the high-order accurate constitutive modeling of sheet materials a non-trivial and challenging issue for reliable finite element (FE) simulations of forming processes. In this study, taking multi-stage cupping of aluminum and steel sheet materials as the case, from four respects of the uncertainty sources, viz., stress updating algorithms, yield criteria, flow rules and hardening laws, the epistemic uncertainties involved in constitutive modeling is articulated and the uncertainties induced errors in deformation prediction are quantitatively evaluated. Within the implicit integration framework, the differences in the updating of normal strain for plane stress and three-dimensional (3D) stress states are elaborated, and typical constitutive models are numerically implemented into explicit FE code. By combining the Hill’48-s (characterized by yield stresses), Hill’48-r (characterized by r-values), YLD2004, CPB06 or Yoon's yield model, with the associated flow rule (AFR) or the non-associated flow rule (NAFR), and Swift, Voce, Hollomon or Ludwik hardening law, the effects of the constitutive modeling related uncertainties on deformation prediction accuracy of sheet metals are investigated. The results show that the constitutive modeling related uncertainties have discrepant effects on deformation prediction of two materials for multiple forming indexes. For AA5352 alloy, the employed models cannot provide accurate prediction with the prediction errors of greater than 1%. While, for TH330 steel, the combination of the NAFR Hill’48 model and Swift hardening law can significantly reduce the uncertainties in the deformation prediction and the prediction errors are less than 1%. By introducing forming limit diagram (FLD), the above uncertainties induced errors in the deformation prediction result in different prediction of necking/fracture failure of the above alloys upon the multi-stage forming processes, viz., the failure of the AA5352 is captured with large prediction error in deformation, while the failure cannot be predicted for the TH330 with minor errors of deformation prediction.