Hardening cohesive/overlapping zone model for metallic materials: The size-scale independent constitutive law

A new hardening cohesive/overlapping zone model for metallic materials based on Nonlinear Fracture Mechanics concepts is proposed to capture the ductile fracture phenomena. The fracture and compression behaviors of an initially cracked specimen are described by the cohesive zone model and the overlapping zone model, respectively. Both approaches assume a stress vs. displacement (fictitious opening or interpenetration) constitutive law to describe the hardening and softening behaviors in the process zones in tension and compression. As a result, the cohesive/overlapping zones are considered to be representative of the regions where the plastic dissipation in the bulk and the crack formation and propagation take place. The proposed model is applied to study the size effects in three-point-bending and compact tension tests. Furthermore, the asymptotical post-peak performances of load vs. deflection curves are determined through the plastic limit analysis using the proposed model. In this context, the fractal approach is applied to obtain scale-independent hardening cohesive/overlapping laws. Finally, experimental confirmations to the numerical simulations and to the limit analysis are discussed.