Issue 49

M. Bannikov et alii, Frattura ed Integrità Strutturale, 49 (2019) 383-395; DOI: 10.3221/IGF-ESIS.49.38 389 Averaging s over an elementary volume gives a tensor of microshears density [23]: ( , , ) W s dV   p s l b (10) where: V - volume, ( , , ) W s l b - distribution function of orientation and intensity of microshears. In its physical meaning p is a strain due to defects. The total strain rate ( ε  ) consists of three components: plastic ( p ε  ), elastic ( e ε  ) and due to defects ( p  ): e p    ε ε ε p     From the second law of thermodynamics, it follows that the energy dissipation can be represented as: : : 0 p F F TS δ δ         σ ε p p     , (11) where: T - temperature; S  - rate of change of entropy; σ - stress tensor; - no equilibrium free energy. According to the Onsager principle, еhe following relations are obtained from (11): 1 2 p l l   σ ε p   (12) 2 3 p F l l       ε p p   (13) 4 F l δ δ      (14) where: 1 l , 2 l , 3 l , 4 l - kinetic coefficients, in the general case, depending on state parameters, satisfying the constraint: 2 1 3 2 0 l l l   . Relations (12)-(14) are complemented by Hooke's law in the rate formulation and approximation for non-equilibrium free energy. Thus, the complete system of constitutive equations looks as follows: ( : ) 2 ( ) p λ G     σ D E E ε ε p     (15) 1 2 p d F       ε σ p  (16) 2 3 d F       p σ p  (17) 4 F δ δ      (18) 2 2 2 1 2 3 4 : ln( ) 2 2 2 d m p p F c p c c c p p F δ G        σ p (19) d s   σ σ σ , 1 ( : ) 3 s  σ σ E E