Metal ductility at low stress triaxiality application to sheet trimming

The growth and coalescence of voids nucleated by decohesion or cracking of second phase particles is a common damage process for many metallic alloys. Classical damage models, based on void growth and coalescence, predict a ductility increase if the stress triaxiality is decreased. But experiments show that the material ductility decreases at very low stress triaxialities typical of sheet metal forming operations. At very low stress triaxiality no void growth is observed in metals containing second phase particles. In the present work, a new damage model for metals containing second phase particles submitted to low stress triaxiality loading is proposed.The new model is based on the observed physical damage mechanism, i.e. strain localization by reducing the inter-particle spacing during large material rotations. A two step modelling strategy has been followed to determine the ductility at low stress triaxiality. In the first step Thomason's void coalescence model is extended to large material rotations and shearing. In the second step the principles of applying this model to damage nucleated at second phase particles are described. The large material rotations observed under low stress triaxiality loading lead to large changes in the microstructure. Thus, in the second step, first appropriate representative volume and material elements are determined and then the critical damage parameters. Finally, as an example, the trimming behaviour of two aluminium sheet alloys is analyzed by the new model and the model predictions shown to be in good agreement with the experimental data, in particular for the blade displacement to crack initiation. The main outcomes of this work are: (1) a void coalescence model valid at low stress triaxiality, (2) a damage criterion valid at small stress triaxiality and large material rotations, (3) a damage variable expressed in a simple closed form for materials containing second phase particles. The damage analysis in a small fixed volume with a representative microstructure (Eulerian approach) and the damage analysis in all the material elements of the considered structure are compared in detail. In trimming (or similar processes), the major contribution to damage the material movement bringing second phase particles closer together and the void growth may be neglected. This simplifies considerable the analysis.