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Relations between J-, M- and N-integrals and Those with Interactions Energy in a Brittle Material



Author(s)

Mokhtar Touati¹, Mohamed Chabaat¹ and Abdelkrim Chelghoum²

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DOI:10.17265/2161-6221/2012.02.014

1. Built Env. Research Lab., Department of Structures and Materials, Civil Eng. Faculty, University of Sciences and Technology Houari Boumediene, B.P. 32 El Alia Bab Ezzouar, 16111 Algiers, Algeria
2. Department of Structures and Materials, Civil Eng. Faculty, University of Sciences and Technology Houari Boumediene, B.P. 32 El Alia Bab Ezzouar, 16111Algiers, Algeria

In this study, kinematics of the Damage Zone (DZ) or the so-called Fracture Process Zone (FPZ) which often precedes the crack during its propagation and characterized by few degrees of freedom (elementary movements) such as translation, rotation, isotropic expansion and distortion are considered. On the basis of a stress field distribution obtained by the use of a Semi-Empirical Approach (SEA), which relies on the Green’s functions, these driving forces corresponding to the mentioned degrees of freedom are formulated within the framework of the plane problem of elastostatics. Thus, expressions for translation (J), isotropic expansion (M), distorsion (N) and interactions effects representing the active parts of crack driving forces known as energy release rates are formulated in a purely theoretical context.

Displacement, stress, green’s functions, stress intensity factors, energy release rates.