13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- 3.2. Thermodynamic formalism In the thermodynamic approach, an additional behavior law consists on the relationship between energy release rate and the global damage variable. Experimentally crossing expressions (1) and (8), we can easily plot the energy release rate – damage curve as shown in Figure 1. We can clearly note a behavior difference between dry and wet samples with a higher ductility at high moisture content levels. The behavior law can be separated into two regions. The first concerns the damage growth initiation which can be described by the following criterion: 0 D and 0 D if D c Y Y (10) Where cY is a critical energy release rate value corresponding to a damage growth initiation. The second is the damage evolution function versus energy release rate. According to the global form, we propose an evolution under a Prony’s serie form such as: 1 2 1 2 1 exp 1 exp D c D c Y Y Y Y D Y Y (11) For dry and wet samples, Error! Reference source not found. and Error! Reference source not found. fixe thermodynamic parameters, respectively. Table 1. Thermodynamic parameters for dry samples cY mJ 1Y mJ 2Y mJ 1 2 k / N mm Average 207 88 794 0.94 0.06 709 Standard Variation 57 28 26 0.05 0.05 79 Table 2. Thermodynamic parameters for wet samples cY mJ 1Y mJ 2Y mJ 1 2 k / N mm Average 169 183 787 0.81 0.19 571 Standard Variation 41 67 19 0.15 0.15 50 3.3. Average global behavior The average behavior for dry and wet samples can be built by the following algorithm. Firstly, a global displacement history u t is fixed. The energy release rate DY is calculated according to expression (8). The equation (11) allows defining the damage evolution. In a last time, the global sample behavior (2) after updating the effective stiffness (1). Results can be shown in Figures 7 and 8. The model can represent the differences in terms of ductility behavior between average dry and wet tests. The main criticism that we could do on this approach and the non decoupling process of crack propagation and the process zone. If our approach allows reproducing experimental test, it cannot be generalized for other geometry and doesn’t take into account a scale effect induced by the
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