Modelling of ductile fracture considering the effect of stress triaxiality and the energy partition theory in thin high-strength steel sheets

Abstract It is well recognized in the literature that the fracture process of thin metal sheets involves three energy dissipation mechanisms i.e., plasticity, necking and surface separation. However, the complex stress state in thin structures hinders the experimental assessment of these quantities and, consequently, the failure modelling. This work evaluates the contribution of these mechanisms to the ductile damage of a thin advanced high strength steel sheet under different stress triaxiality ranges. The essential work of fracture test was carried out on a set of different notch geometry specimens that cover a wide range of stress states. The experimental trend of these specimens was simulated in ABAQUS/Explicit using a VUSDFLD subroutine. Bai and Wierzbicki uncoupled fracture model, which is a function of fracture plastic strain to stress triaxiality ( η ) and normalized Lode angle ( $$\overline{\theta })$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mi>θ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , was selected as damage initiation criterion. A quantitative relationship of the fracture energy ( G 0 ) as a function of ( η ) was proposed in this work and implemented in the model as a damage evolution law. The model captures well the experimental response and the influence of ( η ) on the softening behavior of the material. It was found that the sensitivity of G 0 to η is significant between 0.7 and 1.5. Above this rage, it seems that ( η ) has no influence on G 0 . The model showed also the relationship between the two local damage parameters ( G 0 ) and the necking ( G n ) with respect to the stress state. G 0 represents less than 10% of the total work of fracture, while the largest contribution comes from ( G n ).