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

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In classical one-parameter fracture mechanics, higher order terms are not taken into account, except for the term containing . The constant at , depending on the loading conditions, is called the stress intensity factor. Since the stress singularity appears at , this term is called the singular component. With the development of fracture mechanics, for a more complete characterization of the stress field at the crack tip, considerable interest is shown in the nonsingular members of the stress distribution, which is associated with their significant influence on the conditions at the crack tip. Taking into account nonsingular T-stresses at the crack tip of the normal separation, the field of the volumetric stress state in an elastic isotropic body is described by the following equations:

(4)

– nonsingular components of a three-dimensional stress field,

– stress intensity factor, –

Where and

Poisson's ratio, and – polar coordinates. T-stresses have a significant influence in determining the direction of crack propagation along with the stress intensity factor. By Matviyenko (2011) it is known that numerical finite element analysis allows determining T stresses by the stresses on the crack faces by the formula:

(5)

When finding T-stresses determine the distribution for a number of points located on the crack faces, then extrapolated to the top of the crack r = 0. It is important to note that, despite some difference in values T-stresses at θ= - π and at θ=+π (fig.1), T-stresses, according to mathematical definition, are assumed to be constant.

Fig. 1. Coordinate axes at the crack tip.

In this article, a criterion for the direction of crack growth is formulated taking into account the angular distribution T-stresses based on the maximum tangential stress criterion proposed in Matviyenko (2011) using the principle of stress averaging in the fracture process zone. The angular distribution is taken in the form of an Archimedes spiral, corresponding to the formula: