13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- All tests being filmed, the visible crack tip position can be noted versus displacements. In Figure 5, they are plotted crack length versus critical displacement corresponding to the crack tip advance. The graph highlights moisture content effect with an increase of sample compliance at a given crack length at high moisture content level (grey marks). Figure 5. Visible crack length vs critical displacement These observations prompt us to understand the cracking process by an energy approach. This one will clearly identify the effects of moisture content on the crack growth process by identifying energetic dissipation in terms of crack surface formations and process zone development. 3. Global thermodynamic approach 3.1. Thermodynamic formalism Experimental results, shown in Figure 4 and 5, enables us to describe, at a global scale, energetic balance by introducing the global Helmholtz free energy J defined by observable variables represented by the total displacement d and an internal variable inducing softening of the sample stiffness [2]. By analogy with a damage theory, we introduce a virtual damage variable D and the effective stiffness k D . Drepresents the effects of the crack growth surface and the damage evolution in the process zone. Its form can be calculated from the non damage stiffness k such as : 1 k D k or 1 k D k (1) Considering F N as the reaction force, the global sample behavior can be defined as the relationship between this force and the global displacement u such as: F k D u (2) According to the thermodynamic approaches introduced by Lemaître, let us introduce the global thermodynamic potential in the form of the Helmholtz free energy variation is defined as: u D u D (3) 50 70 90 110 130 150 170 0 1 2 3 4 5 6 7 8 9 10 Crack length (mm) Critical displacement (mm)
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