Integrated analysis for die design including brittle damage evolution

Brittle failure mechanism has been well known as growth of penny-shaped micro-cracks, referred as brittle damage, which eventually cause macro-cracks and failure. A brittle damage model is proposed, which consists of a damage function and an evolution equation for brittle damage. The damage function determines whether a micro-crack begins to grow as a yield function in plasticity, while an evolution equation gives the growth rate of a micro-crack when it grows. An integrated analysis is then proposed to model the shrink-fit, elastic deformation, fatigue, wear as well as brittle damage evolution in a die. Applications of the proposed analysis to the extrusion die with multi-layers of stress-rings are given.