13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- , T s c T k T (1) where T – temperature, ρ – density (4550 kg/m3), c – heat capacity (600 J/(kg·K)), k – heat conductivity (6.5 W/(m·K)), s – unknown specific power of the heat source (W/m3), τ – a constant related to the losses of heat by heat exchange with the surroundings (103 J/(m3·K)). The heat power of sources close to fracture moment (at 5.06 sec after beginning of the last stage of test) is shown in Fig. 3. At the last moments before fracture, we can observe pronounced plastic deformation at crack tip and plastic zone has a “butterfly form” near the crack tip as it is presented in Fig. 3. Figure 3. Experimental data of heat power field near the crack tip at the beginning of unstable crack propagation. Taking into account assumption from [5, 6], we also suppose that some of the irreversible plastic work contributes to heat generation while the rest is stored as energy of crystal defects accompanying plastic deformation, traditionally known as the stored energy of cold work. To define the plastic work near the crack tip we used the solution for stress distribution at crack tip obtained by Hutchinson, Rice and Rosengren (HRR-solution). Specific plastic work in the direction of crack propagation can be written as [7]: 1 0 ( ) ( , ) , 1 p n e p n n J t w x t d n I x (2) where n – hardening coefficient (in our case n=4), In – function of hardening coefficient, x – distance from the crack tip, σe – tabulation function, J(t) – energy J-integral that is the function of applied cycling loading and crack length. Time dependence of J-integral is presented in Fig. 4. Figure 4. Time dependence of energy J-integral during cycling loading.
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