Crack front position and crack back position techniques for evaluating theT-stress at crack tip using functions of a complex variable

Abstract

In this paper, the crack front position and the crack back position techniques for evaluating the T-stress using complex variables are suggested. In the crack front technique, an expression for stress components in the crack front position is expressed through a complex variable. The limit value of the expression from the crack front position will give the T-stress. In the crack back technique, the other expression of stress components in the crack back position is expressed through the complex variable. The limit value of the expression from the crack back position will give the T-stress. The suggested techniques are used to evaluate T-stress in the arc crack and the curved crack problems. It is found from a detailed derivation that both techniques give the same result in the crack problem. Numerical examples are carried out for two problems: an elliptic crack with a central crack and a curved crack with parabolic configuration.

Evaluation of the T-Stress for Multiple Cracks in an Infinite Plate Using Singular Integral Equation

“…From the crack back position technique for evaluating T-stress [Chen et al (2008a)], the explicit expression for T-stress (see Eq. (29)) is derived.…”

“…From the crack back position method [Chen et al (2008a)], we can define the T-stress at the left crack tip A j of jth crack (or at point t Aj ), (j = 1, 2, . .…”

“…Finite element method was used to obtain the T-stress. Based on the complex variable function, crack front position and crack back position techniques were suggested for evaluating the Tstress at crack tip [Chen et al (2008a)]. This technique provides a flexible way for the evaluation of T-stress in more complicated loading and shape conditions.…”

“…The SIFs can be evaluated from the solution of singular integral equation. From a definition for T-stress in the crack back position method [Chen et al (2008a) equation, the T-stresses at crack tips can be evaluated accordingly. An explicit formula for the T-stress (Eq.…”

Evaluation of T-stress for a hypocycloid hole in an infinite plate

“…From stress distribution along the crack face, a method was suggested to evaluate the T-stress (Ayatollahi et al, 1998). Crack front position and crack back position techniques for evaluating the T-stress at crack tip using functions of a complex variable were suggested (Chen et al, 2008).…”