The complex mechanical loading and high climatic variations on structures implies having a better understanding of their fracture mechanical behavior. It is necessary to consider three-dimensional case in the study of reel crack growth problems. For it the most common approach is the determination of the energy release rate by energetic method. Most of the studies carried out deal with two-dimensional case. The studies of complex structures request the development of specific tools for three-dimensional configurations.

This paper present a new analytical formulation and its numerical application for three-dimensional crack growth problem. This work is based on a generalization of the Rice's integral for three-dimensional crack problem. A new integral parameter in real three-dimensional case, which computes the energy release rate combining an arbitrary crack front, is developed. A physical interpretation allows to evaluate the efficiency of the proposed integral. The new integral is compared with the local path independent integral of Bui in three-dimensional cases.

Applying the theta method a integral, generalized to a volume domain, is implemented into a finite element software. The non-path dependence is proved with the use of numerical application. The energy release rate distribution along the crack front line is obtained, and compared to Bui's integral. A numerical validation, in terms of energy release rate, is carried out on a DCB (Double Cantilever Beam) specimen under opening mode loading for wood material. Various visions are also proposed to evaluate integral parameter and the energy release rate distribution along the crack front line.