Ring fragmentation predictions using the Gurson model with material stability conditions as failure criteria

The Gurson constitutive model used in combination with failure criteria based on material stability and bifurcation has been used in a finite element model to predict fracture and fragmentation in a dynamic expanding ring experiment. Integration of the constitutive relation is through a two level iteration scheme operating only on scalar equations. It provides a robust solution for the large strain increments expected in shock problems. Numerically efficient failure criteria based on a bifurcation analysis and Drucker’s condition for material stability are evaluated at each integration point and at every time step. The models were used to predict the fracture strain and number of fragments for thin, electromagnetically loaded, expanding rings. The results show good predictions of time to failure. Predictions of the number of fragments are generally good, with the model based on Drucker’s hypothesis being better at the higher strain rates.