13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- original structure “coarsening” and the general trend is decrease of , this allows to assume that plasticity mechanisms and the transition to failure are the sequential structure-scaling transitions in ensembles developing substructure defects. Full strain rate can be represented as the sum of three components: elastic strain rate eε , plastic strain rate p ε and strain rate caused by defects: e p ε ε ε p. (4) Elastic strains defined by linear Hooke’s law: 0 0 e K , (5) ' ' 2 e G σ ε , (6) where K - isotropic elastic modulus, G - elastic shear modulus, 0 - spherical stress tensor, 'σ - deviator of stress, 0 - spherical elastic strain tensor, ' ε - deviator of elastic strain. According to thermodynamic laws we can write dissipation inequality: ' : : 0 p F T T σ ε p q p , (7) where F is a part of the free energy, which is responsible for the energy defect subsystem, - density, q- heat flux vector, T- temperature. Assuming a qusilinear relationship between the thermodynamic forces and flows, there were obtained constitutive equations for calculating kinetics of plastic and structural strains: ' p A ε σ , (8) p F A p p , (9) Parameters pA , A are kinetic coefficients having following form 1 exp 2 2 A G G , (10) 1 exp 2 2 p p A G G . (11) These coefficients determine material relaxation properties due to the characteristic times of orientational transitions p and relaxation transitions activated by stress respectively. This form allows us to describe the aggregate of load curves at different strain rates. Based on the received earlier the approximation of the non-equilibrium free energy ( F) derivative of the p in one-dimensional case and on the assumption of coaxiality pand σ, we can write ' ( ) m c F F f p Σ γ γ γ p ’ (12) 2 0.5192( 0.0061 2 ) ( ) 0.0054 0.5814 0.0061 f , (13) where ' ' / 2G Σ σ - dimensionless stress deviator tensor, / cp γ p - dimensionless deformation caused by defects, / cp , 2 / mF , - effective temperature factor responsible for the susceptibility of the system, 0 / G V , 3 0 0 V r - characteristic volume of the defect nucleus with radius 0r . The system of equations (4)-(12) can be considered as a closed system of equation for modeling of damage accumulation and plasticity process in metals.
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