13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- nucleuses. Following [5] we propose that the applied stress activates the defects and this process can be described as a stochastic Poisson point process with intensity function n . Figure 1. Equilibrium defect induced strain versus applied stress for different values of initial defect concentration (curves 1,2) and the mean values of defect induced strain during deformation process (curves 3,4). Intensity function describes both the growth of active defects (which contribute to the defect induced strain) and growth defect nucleuses. Following the experimental data [5] about evolution of microcrack concentration we can assume the following approximation for intensity function 1 0 1 0 0 n 1 Erf 2 n , (3) where 0 1 0 1 , , , - material constants. The probability of find N active defects in representative material volume is N! n Exp n P N N . The stochastic consideration of defect evolution process change the self-consistency equation for defect induced deformation. The solution of equation (2,3) is presented in figure 1 (curves 3,4). For small stress values we observe a pure elasticity which passes to the plastic deformation with different intensity. The intensity of plastic deformation and damage accumulation depends on the initial concentration of defect nucleuses. 3. Thermodynamics of metals with defects A thermomechanical process of plastic deformation obeys the momentum balance equation and the first and second laws of thermodynamics. In the case of small deformation, these equations involve the following thermodynamic quantities: volumetric mass , specific internal energy e, strain and stress tensors ik and ik , heat supply r , heat flux vector q , specific Helmholtz free
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