PSI - Issue 23

I.A. Volkov et al. / Procedia Structural Integrity 23 (2019) 281–286 Author name / StructuralIntegrity Procedia 00 (2019) 000 – 000

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mechanical properties of the material can be observed. In the first approximation, this effect can be accounted for, using the concept of a degrading continuum by introducing effective stresses by Volkov and Ко rotkikh (2008) where G , К are effective moduli of elasticity defined using McDowell:   1 ; i j i j i j G F G            2 ; К F К       (8)

 6 12 (9 8 ) K G K G 

 

 



 

    4 1 / 4 3 . K GK G K     

G G

1 1     

;

 



ij  is defined:

In a similar way, effective internal variable c

G

  1 G       c c c ij ij ij F

.

(9)

2.2. Evolutionary equations of damage accumulation Experimental and theoretical analyses of damage processes of the material make it possible to express the evolutionary equation of damage accumulation in an elementary volume of materials in the following general form Volkov and Ко rotkikh (2008):         1 2 3 4 , f f f f Z Z     (10) where function 1 ( ) f  describes the effect of the deformation trajectory curvature, 2 ( ) f  is type (voluminosity) of stressed state, 3 ( ) f  is degree of accumulated damage,   4 f Z is accumulated relative energy spent on defect nucleation. Considering the fact that currently there is no reliable enough systematized experimental data characterizing creep of materials up to failure in the required range of working loads and temperatures, as well as the considerable scatter in the experimental data, an evolutionary equation in the presence of creep must be formulated in its ‘simplest’ form Volkov and Ко rotkikh (2008):     1 1 ; 1 c r c c c c c c f Z Z r           ; a c c c f c Z W W W   ; c f c c W Z W  ; c c c ij ij W e     exp( ), c c f k    (11) where  is damage degree value in the presence of creep; a c W is value of failure energy at the end of the stage of nucleation of scattered defects in the presence of creep, and f c W is value of energy corresponding to the formation of a macroscopic crack; ( ) c f  is function of voluminosity parameter of the stressed state u   ; 0 t c c W W dt   are energies spent on nucleation of scattered defects in the presence of creep; c k , c  , c r are material parameters. 2.3. Strength criterion of damaged material The condition when damage degree reaches its critical value is taken as the criterion of the end of the phase of the development of scattered microdefects (the stage of formation of a macrocrack): 1. f     (12)