A fracture evolution procedure for cohesive materials

The present paper deals with the problem of the evaluation of the softening mechanical response of cohesive materials under tensile loading. A nonlinear fracture mechanics approach is adopted. A new numerical procedure is developed to study the evolution of the crack processes for 2D solids. The proposed algorithm is based on the derivation and use of the fracture resistance curve, i.e., the R-curve, and it takes into account the presence of the process zone at the crack tip. In fact, assuming a nonlinear constitutive law for the cohesive interface, the procedure is able to determine the R-curve, the process zone length and hence the mechanical response of any material and structure. Numerical applications are developed for studying the damage behavior of a infinite solid with a periodic crack distribution. Size effects are investigated and the ductile-brittle transition behavior for materials characterized by the same crack density is studied. The results obtained adopting the proposed procedure are in good accordance with the results recovered through nonlinear step by step finite element analyses, Moreover, the developed computations demonstrate that the procedure is simple and efficient.