Influence of fracture process zone height on fracture energy of concrete

The implication of modelling concrete fracture with a fictitious crack of zero fracture process zone (FPZ) height is addressed because FPZ height, in reality, is not zero and is bound to vary during crack growth. The ligament effect on fracture energy G_F is explained by the nonuniform distribution of a local fracture energy g_f showing the influence of specimen boundary and variation of FPZ height. The nonuniform g_f distribution is then used to determine the size-independent G_F. The recent boundary-effect model based on a bilinear g_f function is confirmed by the essential work of fracture (EWF) model for the yielding of deeply notched polymer and metal specimens. The EWF model provides a theoretical basis for the bilinear g_f distribution. The principal rationale of the boundary-effect model, the influence of FPZ height on fracture energy, is supported by experimental observations of thickness effect on fracture toughness of thin polymeric adhesives between metals.