This paper present a new analytical formulation 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.
The non-dependent domain is justified by numerical approach. 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 specimen under opening mode loading for wood material.
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