Effect of loading history in necking and fracture

Abstract

The effect of Lode angle parameter, or the third deviatoric stress invariant, on plasticity and fracture is studied using flat-grooved transverse plane strain specimens. A generalized asymmetric plasticity model for isotropic materials with both pressure and Lode angle dependence is developed. Calibration method of the plasticity model is discussed in detail. Test results on 2024-T351 aluminum alloy confirmed the proposed plasticity model. Similarly, a generalized asymmetric 3D empirical fracture locus with six free parameters is proposed. The proposed fracture locus, which depends on both stress triaxiality (or pressure) and the Lode angle parameter, is calibrated using two types of methods: classical specimens under uniaxial testing, and the newly designed butterfly specimens under biaxial testing. Experimental results on 2024-T351 aluminum alloy, 1045 steel, and A710 steel validated the proposed 3D fracture locus. A concept of forming severity is introduced to study the loading history effect on metal forming limit diagram (FLD). Given the necking locus under proportional loading conditions, and using a non-linear accumulation rule of forming severity index, the proposed model well predicts the FLDs under different pre-loading conditions. As an extension of the ductile fracture locus defined and calibrated under proportional loading conditions, a new damage accumulation rule considering the loading history effect is proposed. The new model uses the accumulated difference between directions of the back stress tensor and the current stress tensor to describe the non-proportionality of a load path. Several types of tests with complex loading histories were designed and performed to study the loading history effect on ductile fracture. Extensive experimental studies on 1045 steel confirmed the proposed ductile fracture model. The proposed model is successfully applied to predict fracture of crushed prismatic tubes undergoing strain reversal.