A criterion for ductile crack growth based on the energy momentum tensor

It is well known that in quasi-static crack propagation under growing external loads a Griffith-like energy balance predicts no energy surplus for fracture; this result is known as the paradox of Rice . The paradox is generally attributed to the assumptions of small scale yielding and perfect plasticity of material. In this paper we show that the paradox does not lie in the assumptions of infinitesimal strain conditions, neither in the work-hardening rules. Afterwards, we investigate the stress and strain fields, ahead of the crack front in the case of large scale yielding at the crack tip, and discover that the trace of the Energy-Momentum Tensor assumes a constant value during the whole process of crack extension. When this value is assumed as a critical condition for crack growth, we obtain a curve load versus crack extension in excellent agreement with available experimental data. The Rice's paradox is thus overcome, and a new criterion for ductile crack growth is introduced.