13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- reaches the second stationary configuration, when PZ X vanishes. A newly drawn material constitutes the new PZ. Then, the same degradation process takes over the drawn material and crack propagates through the second PZ the same way as in the first step. In CT specimen, the maximal value of PZ X increases with CL length. As a result, the equilibrium PZ size increases and the duration of steps decreases with step number leading to an accelerated CL growth and final instability and transition to rapid crack propagation. (a) (b) Figure 5. (a) Numerical simulation of discontinuous crack layer growth for a CT specimen at 80°C; (b) Numerical simulation of transition from continuous to discontinuous CL growth. The second example presents a different scenario of CL propagation: a transition from continuous to a discontinuous, stepwise CL growth shown in Figure 5 (b). In this case, at the beginning, the PZ material degradation rate is comparable with the rate of PZ growth. In such case, the crack starts to grow into PZ before PZ reaches equilibrium. This process appears as continuous CL growth and the lines of ( ) cr t and L(t) practically coincide up to 33 t hours as shown in Figure 5 (b). However, with increase of tot K the PZ growth rate increases whereas the degradation rate of PZ material is the same. Thus, PZ “runs” away from the crack and PZ size becomes larger and larger and finally reaches the equilibrium size. It triggers a transition of from continuous CL growth mechanism to the discontinuous one. After such transition, the same process of discontinuous CL growth as described above (Figure 5 (a)) takes place. For comparison with the vast literature on phenomenological crack growth studies, we introduce an average rate of crack layer growth L as a ratio between CL length increment in discontinuous growth and the duration of corresponding step. A correspondence between L and the SIF due to remote load K in double logarithmic scale represents the crack layer growth simulation in the conventional Paris-Erdogan equation form. The rate L depends on basic fracture parameters such as kinetic coefficients 1k and 2k in Eq. 3, dr , tr and as well as elastic and creep properties. It also depends on specimen shape and size, crack size as well as the magnitude and rate of applied load. The relation between the numerical simulation of L and the remote load SIF K allows one to establish a correspondence between empirical coefficients in Paris-Erdogan equation and basic material properties. Apparently, there are changes in the SCG pattern depending on load, CL size and temperature. It can be translated into different powers in Paris-Erdogan equation.
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