Issue 27

A. Kostina et alii, Frattura ed Integrità Strutturale, 27 (2014) 28-37; DOI: 10.3221/IGF-ESIS.27.04 33 e p p               (6) Elastic strains are defined by linear Hooke’s law: 0 0 e K      (7) 2 e d d G        (8) where K - isotropic elastic modulus, G - elastic shear modulus, 0  - spherical part of the stress tensor, d   - deviator part of the stress, 0 e  - spherical part of the elastic strain tensor, e d   - deviator part of the elastic strain. Dissipation function for a medium with defects can be represented in the following form [13]: : ( ) : 0 p T p q p T                    (9) where  is a free energy,  - density, q - heat flux vector, T - temperature. Dividing the thermal and mechanical problems and basing on the Onsager principle, we can obtain from (9) constitutive equations for calculating kinetics of plastic and structural strains: ( ) p p p                  (10) ( ) p p p p                (11) The kinetic coefficients   , p  and p   have the following form: 1 1 1 1 c S Exp a               2 1 1 ( , , , , ) 1 p p c c y H p p S Exp a                 1 p p      where   , p  , p   - characteristic relaxation times,  - stress intensity tensor, c S 1 a , 2 a - material constants, y S - yield stress, p - intensity of p  , , c c p  - scaling factors, ( , , , ) 2 ( 1) c c c c H p p f p p p p              - material function ( it can be considered as “degree of system nonequilibrium”). It is supposed that thermodynamic force p        can be written as: 1 1 2 c c c c c p p p p f p G p p p p                                             (12) where ( ) f p denotes a power function for modeling of nonlinear hardening process: a c c p p f k p p              (13) k is a scaling factor, a is the exponent. Eqs. (6)-(8) and (10)-(13) represent a closed system for a plastically deformed solid with nonlinear hardening. From the first thermodynamic law, we can obtain the expression for calculation the  parameter in the following form: