PSI - Issue 30

S.V. Suknev et al. / Procedia Structural Integrity 30 (2020) 179–185 S.V. Suknev / Structural Integrity Procedia 00 (2020) 000–000

181

3

e d d L    0 .

(1)

Here e L is the size of the stress concentration zone,  is the dimensionless parameter that characterizes the plasticity of the material. For brittle materials, 0   ; for ductile materials, 1   . In the case where  ~ 1, the material is characterized by moderate plastic properties. The first term in Eq. (1) characterizes the microstructure of the material itself, while the second one reflects the contribution of inelastic deformations and depends on the plastic properties of the material, geometry of the specimen, and boundary conditions. Based on the proposed approach, a set of novel (modified) nonlocal fracture criteria is developed. The applicability of the criteria developed is verified in the works by Suknev (2019a and 2019b) on the problems of the fracture of plane specimens with a circular hole in uniaxial tension and compression. Now consider the possibility of using nonlocal fracture criteria in the problem of tensile crack initiation in a plate with a circular hole subjected to biaxial loading by tension along one axis and compression along the other axis with account for the above-given ideas about the formation of the prefracture zone. 2. Quasi-Brittle Fracture Criterion The most well-known nonlocal criterion is the average stress criterion, or the line method in the TCD, which has the form 0    e d , where e d  is the equivalent stress averaged over the distance d and 0  is the uniaxial tensile strength. For brittle materials, const 0   d d . Equivalent stress is determined using the theory of the maximum tensile stress. For a plane specimen with a circular hole subjected to biaxial loading (see Fig. 1), the critical stress is calculated by the formula (Suknev 2015)        2 1 1 3 0 2 1 2 1                 c , (2) coincides with the calculation using the traditional fracture criterion. In order to describe the quasi-brittle fracture, the averaging distance 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,   5 7 1 3    L a e . Accordingly, the expression for the parameter  in Eq. (2) takes the form where d a / 1    , a is the hole radius, and  is the loading biaxiality ratio. For 1   , the calculation by Eq. (2)

5 7 1 3  

1    a d 0



,

(3)







Fig. 1. Circular hole under biaxial loading.