A new energetic failure criterion and constitutive models of porous materials into the fracture process zone, in the framework of elastic-plastic fracture mechanics

In the last fifty years many efforts have been made to extend the issues of Fracture Mechanics from linear elastic to elastic - plastic behaviour of material. In this sense, one of the most pursued approach was to adopt the Griffith-like energy balance for elastic - plastic materials as energy input rate for crack growth. However, for ductile materials, during crack growth the energy release rate, so evaluated, tends to zero and, consequently, crack propagation is not possible. This conclusion is known as the paradox of Rice. Hence, a Griffith-like energy balance can be no longer identified as a generalized crack driving force. In addition, it is known that the paradox reflects the inedaquacy of the continuum mechanics to describe the ductile fracture process in a small region close to the crack tip, called Fracture Process Zone; there, material undergoes nucleation, growth and coalescence of micro-defects, which strongly affect the overall macroscopic fracture process. In order to find a criterion to predict the fracture toughness and crack propagation, it is reasonable to define an energy input rate based on microstructural behaviour of crack, rather than using a continuum approach. The aim of this work is to find a different approach to predict the residual static strength of cracked structures, which includes the continuum mechanics problem of microstructural damage phenomena. For this, an in-depth study of the damage evolution in the fracture process zone is required to determine the highly non-linear coupling between the FPZ and the plastic dissipation in the background material. In the process of damage evolution, work-hardening behaviour of material, stress triaxiality, large strain conditions and the microstructural aspects, such as void-size and void-shape, play an important role. The microscale effect of plastic flow localization is the macroscale softening of the material. We start by revisiting the inadequacy of the Griffith-like energy balance as crack driving force; meanwhile, we suggest how it is possible to find, from the point of view of continuum mechanics, a different criterion able to predict the crack growth resistance curve. In the second part of this work we define a constitutive model which take the damage evolution in the FPZ into account. Hence, the effects of stress triaxiality, void-size and void-shape on the plastic flow localization are envisaged.