13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- By assuming a total crack closure after unloading, the global elastic behavior (2) provides the first state equation: F u (4) Crossing expressions (2) and (4), the Helmholtz free energy can take the following form: 2 1 2 k D u (5) The energy release rate DY (associated to damage variable) can be defined as follow: DY D (6) Introducing equation (5) in (6), its definition becomes: 2 2 D u k Y D (7) Considering the damage definition in expression (1), the energy release rate (7) can be rewritten by: 2 1 2 D Y k u (8) By considering the Clausius-Duhem relationship, the dissipation, induced by the crack growth process can be defined by, Figure 6: DY D (9) Figure 6. Experimental force-displacement he curve and thermodynamic description
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