PSI - Issue 20

Prokopyev Leonid Aleksandrovich et al. / Procedia Structural Integrity 20 (2019) 93–97 Prokopyev Leonid Aleksandrovich et al. / Structural Integrity Procedia 00 (2019) 000 – 000

94 2

the direction of crack growth in structures under given operational loads. The problems of the survivability of structures at low temperatures are devoted by Andreev and Bolshakov (2016), Bolshakov and Zakharova, (2016), Ivanov et. al. (2010), Matvienko and Bolshakov (2012), Makhutov et. al. (2016) .

Nomenclature ,

polar coordinates

,

radial and tangential stresses shear stress

, ,

constants of Williams stress field expansion that depend on loading conditions nonsingular components of a three-dimensional stress field

,

stress intensity factor Poisson's ratio

,

2. The dependence of the crack growth trajectory on the parameters of the crack tip stress field In classical fracture mechanics, the stress intensity factor is considered to be the main parameter determining the stress state at the crack tip. However, in recent years, non-singular members of stress distribution (T-stresses) become relevant in fracture mechanics due to their significant effect on the stress-strain state, as well as on the trajectory of crack propagation for samples of various geometries and their loading. Crack trajectory was studied by Matviyenko Y (2011), the determination of which is based primarily on the stress distribution at the crack tip. The effect of T-stresses on the dimensions of the plasticity zone was investigated by Matviyenko and Pochinki (2012). Despite the fact that, by definition, T-stresses are constant values, in some works they are interpreted as stresses that change their value depending on the distance from the crack tip. This approach is due to the fact that it is impossible to take into account all the components of the stress-strain state at the crack tip. As a rule, only those components that have the greatest value in the crack propagation processes are taken into account. The plastic zone arising at the crack tip plays an important role in the fracture process. With viscous or viscous brittle fracture, the total energy supplied by external forces can be divided into components: the energy of the field of elastic stresses, the energy spent on breaking the interatomic bonds, as well as the energy of residual plastic deformations. The larger the fraction of the energy of residual plastic deformations, the less is the energy attributable to the direct growth of the crack with a constant amount of total energy input. Therefore, the size of the plasticity zone has the effect of resistance to crack growth. In addition, the size of the plasticity zone along the line of extension of the crack can determine the nature of the fracture. The smaller this size, the closer to the viscous brittle transition the fracture conditions will be. In view of the foregoing, the determination of the size of the plasticity zone is one of the most important tasks of fracture mechanics. Under conditions of small-scale yield strength, the size of the plasticity zone can be determined from the condition that the von Mises yield stresses are reached. The stress field near the vicinity of the crack is described by a Williams solution in the form of numerical series with the following equations:

(1)

(2)

(3)

where

– the terms of higher orders that become negligible when

.