Nonlinear Fracture Mechanics—Line Crack Idealization

The nonlinearity of fracture mechanics is most easily captured by a line crack model because all the structure volume remains elastic, which means that all the nonlinearity is moved into the boundary conditions, although at the penalty of missing the effect of crack-parallel stresses. The cohesive crack model, originated by Barenblatt, lumps all material nonlinearity into a softening relation between the cohesive stress and the opening displacement. Irwin's material length characterizing the size of the fracture process zone (FPZ) is discussed, equivalent LEFM is introduced, and the R-curves, along with their use in fracture stability analysis and size effect, are presented. The relation of cohesive law to fracture energy and strain softening behavior is described. Boundary integral analysis of the cohesive crack growth is explained. Insensitivity to the crack-parallel stresses and the non-tensorial description of the FPZ are pointed out as a limitation of the cohesive crack model. Finally, direct eigenvalue analysis of peak loads and size effect curves is presented.