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
　　Received: October 03, 2011 / Accepted: November 12, 2011 / Published: February 25, 2012.
　　Abstract: 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.
　　Key words: Displacement, stress, green’s functions, stress intensity factors, energy release rates.
　　Consider a Single Edge Notch (SEN) specimen as shown in Fig. 4 in which a crack propagates surrounded by a layer of damage. Experimental measurements of the crack opening displacement and the concentration of damage in the vicinity of the crack are needed for evaluating the different energy release rates.
　　The work W done by an applied force F at the grips(x2 = H) is given as follows:
　　Theoretical expressions for translation (J), isotropic expansion (M), distorsion (N) representing the active parts of crack driving forces are formulated. It is also shown in a number of cases that J has a significant statistical distribution. It is the expenditure of energy into various modes of crack propagation meaning the translational motion of the crack with the process zone unchanging on one hand and the expansion as well as the distorsion of the DZ on the other hand. These latest along with the change in concentration and interaction effects constitute an important percentage of the total energy release rate. Besides, the distribution of energy into modes varies size from one experiment
　　to the other as being a loading history dependant quantity.
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