User:Calnew/sandbox

Ductile fracture is the main mechanism leading to the formation and propagation of cracks in metallic structures. It is a physical process that involves the large deformation and progressive damage of materials under extreme loading conditions. A first approach to predicting ductile fracture is constitutes of using porous plasticity models in conjunction with coalescence criteria. A second approach is based on non-porous plasticity models that can be used in conjunction with damage indicator models to predict the initiation of ductile fracture.

The Hosford-Coulomb ductile fracture initiation model belongs to the second type of models. Its application thus implies the validity of the assumption that possible ductile damage does not change the stress-strain response prior to crack formation. It accounts for the effects of both the stress triaxiality $$\eta$$ and the Lode angle parameter on ductile failure.

The damage indicator D is a scalar variable that increases monotonically with the equivalent plastic strain.

$$D=\int \frac{d\bar{\epsilon_p}}{\epsilon_f}$$

Assuming a starting value of D=0 before applying any plastic deformation, the instant of fracture initiation is assumed to be attained when D=1. The denominator is a