PSI - Issue 20

S.V. Suknev / Procedia Structural Integrity 20 (2019) 30–36

33

4

S.V. Suknev / Structural Integrity Procedia 00 (2019) 000 – 000

In order to describe the quasi-brittle fracture, the averaging size is determined from Eq. (1), in which the size of the stress concentration zone e e e L   grad  is calculated at the point of maximum stress. For the problem under consideration, 3 /14 l L e  . Thus, we substitute Eq. (1) into Eq. (3) and, with account for the estimate obtained for e L , obtain

 1 /( 2 3 / 7) 2 2 l l l d      



0

.

(4)





 2

c

2

/( 2 3 / 7) l l d 

l

  

0

0

0 0   C , the fracture is represented by

In the case of compression of the plate, made of the material for which / 3 the tensile cracks propagation along the loading line. The normal stress distribution

y  along this line is described

by the formula

4 4

2 2

    x p a 3 2

   

x a

,

(5)

y 





where p is the applied compressive stress (pressure), assumed to be positive. The tensile stresses reach a maximum p  max  on the boundary of the hole and, as the distance from it becomes longer, quickly decrease, asymptotically tending to zero. Therefore, as the hole diameter reduces, the average stress tends to zero too, and the critical value of the applied pressure c p , at which tensile cracks are nucleated on the boundary of the hole, respectively, tends to an unlimited value. Indeed, this value is obviously limited by the ultimate compressive strength, meaning that there is some critical value of the hole size c l l  , below which no tensile cracks are formed on the boundary of the hole. In other words, if c l l  , the material is not affected by the stress concentration. After performing calculations similar to the above-described case of tensile fracture, we obtain the formula for the critical pressure at which tensile cracks are formed in the quasi-brittle material:      / 0,1 1 1 2 / 0,2 0 3 0 0      d l d l p C c , c l l  . (6) 3.2. Point Stress Criterion Along with the ASC, the point stress criterion (PSC), or the point method in the TCD is widely used. In this criterion, the integration is replaced by calculating the equivalent stress e  at some point that is located at the distance d from the point of maximum stress. The strength criterion takes the form 0 0 ) (     x d e . The parameter d is also considered to be a material constant that does not coincide with the identical parameter in the ASC. For the quasi-brittle fracture, we obtain the formula for the critical tensile stress

2



4 0 /( 2 3 / 7) 3 /( 2 3 / 7) l l d l l l d         2 2 l

(7)





c

4

2

0

0

and the formula for the critical compressive stress





4

 0 0 3 1 2 / 2 1 2 /    d l d l

0,2





,

c l l  .

(8)

 p C c 

 2

0,2





0