An irreversible bilinear cohesive law considering the effects of strain rate and plastic strain and enabling reciprocating load

The commonly used bilinear cohesive law doesn't consider the effects of strain rate and plastic strain, but it is well known that strain rate and plastic strain can greatly affect materials' mechanical response. In this paper a new bilinear cohesive law is proposed that can handle these two effects and enables reciprocating load. Compared with the commonly used bilinear cohesive law, one difference in the new bilinear cohesive law is that normal traction and tangential traction are always coupled even when normal traction is negative. And after combined with finite thickness modeling method of cohesive element, this new bilinear cohesive law can solve problems like penetration, force discontinuity and increase of compliance. For damage evolution model, the difference between monotonically increasing effective separation and monotonically increasing damage factor is explained. The influence of strain rate (or opening speed) on stiffness, fracture strength and critical energy release rate is referred from literature. Based on zero plastic strain damage factor model, a Generalized Damage Factor Model (GDFM) is proposed that can cover all materials from zero plastic strain to full plastic strain by changing only one parameter. A Bilinear Cohesive Law Update Method (BCLUM) is proposed to make this new bilinear cohesive law handle reciprocating load, which includes the update of local coordinate system and bilinear cohesive law parameters. A single cohesive element analysis is presented first to show some basic differences among different bilinear cohesive laws, and then Tapered Double Cantilever Beam (TDCB) and Mixed Mode Bending (MMB) analyses are used to verify the proposed law.