PSI - Issue 28

Vedernikova Alena et al. / Procedia Structural Integrity 28 (2020) 1160–1166 Author name / Structural Integrity Procedia 00 (2019) 000–000

1162

3

This fact led to the suggestion that critical distance is a parameter determined by the features of the fracture process. 3. Mathematical model of damage to fracture transition One of the possible descriptions of defect kinetics is the statistical model of the defect ensemble (Naimak et al. (2004)). The constitutive equation for structural strain tensor (induced by microcracks and microshears) has the form:

p           p F 

Г  p σ

σ

Г

(3)

,

pσ

where p Г , pσ Г are the kinetic coefficients, F is the specific Helmholtz free energy, p is the defect density tensor, σ is the stress tensor, and  is the volumetric mass. Free energy release kinetics allows the presentation of damage evolution equation in the form:     s max ap qp kp p p              , (4) where max  is the maximum value of the stress tensor component near the concentrator;  and s are the degree of polynomials that determines the character of generation and the rate of diffusion of defects; q , a , k are the material parameters;  ,  are the dimensionless stress and free energy corresponding. The self-similar solution of Eq. (3) in the one-dimensional case with approximation (4) for constant stress values and parameters s 1    can be written (Samarskii et al. (1995)):

1

 2 s 1 s s 2   

 

1  

c   x       L   

s





 





(5)

2

p x, t

s    q t t

sin

,

 

c

where c t is the critical time and c L is the fundamental length scale. The fundamental length scale

c L is defined by the following expression:

c k L 2 s 1 s q    ,

(6)

Equations (3)-(6) will be used for the explain the fundamentals of fracture mechanisms near the stress concentrators under tensile tests. 4. Numerical results in the one-dimensional case For the explanation of the fracture mechanisms near stress concentrators consider an analytical solution for tensile of infinite plate with semi-circular notch. The final stress distribution near stress concentrator can be evaluated as (Glinka et al. (1987)):

2

4



   





K 1 x   

 

n 3 x 2 r  

 

  x, 0  

(7)

,

1          1 1

t



y

3

2 r 



n