Crack mouth widening energy-release rate and its application

An analytical method on circumferential cracked submarine pipe-in-pipe system

“…If crack surface is parallel to axis x 1 , J 1 can be used as J-integral theory to describe crack extension energy release rate and J 2 as G * -integral theory to describe the crack mouth widening energy release rate [1]. The natures of two forms of energy release rate are identical, i.e.…”

“…The difference between the two methods is that J and G * -integral theories yield K I using different components of stress and strains for the same crack problem. Taking the cracked beam for example [1], stress and strain fields needed in J-integral method should be usually determined by numerical analysis, but the stress and strain fields needed in G * -integral method can be given by the bending theory in mechanics of materials [1,3,[8][9][10][11]. Another difference is that the crack extension energy release is realizable for J-integral theory and the crack mouth widening energy release is conceptional and unrealizable for G*-integral.…”

“…However, because pipe-in-pipe pipeline is a typical three-dimensional finite boundary composite structure, it is very difficult to get the exact solutions of stress intensity factor using the existing classical methods. In recent years, the G * -integral theory [1] was proposed, which is derived from the three-dimensional conservation law and the principle of virtual work. Present investigation will propose an analytical approach to estimate the stress intensity factors for the cracked pipe-in-pipe pipeline by using the new G * -integral theory.…”

Non-linear dynamic response to simple harmonic excitation of a thin-walled beam with a breathing crack

“…1). The condition c → 0 [40][41][42] is strictly necessary for the hole to actually represent a crack (with a finite value of c, it would be an elliptical notch, but not a crack). The crack boundary can be expressed as…”

Stress intensity factors for cracked homogeneous and composite multi-channel beams

“…However, because channel beam is a typical three-dimensional finite boundary problem, it is very difficult to get the exact solutions of stress intensity factor by using the existing classical methods. In recent years, the G * -integral theory was proposed by Xie et al (1998a), which is derived from the three-dimensional conservation law and the principle of virtual work. Because of the finite boundary crack problem, the G * -integral method greatly facilitates the analysis of stress intensity factors (Xie et al, 1998a(Xie et al, ,b, 2001(Xie et al, , 2004aXie, 1998Xie, , 2000.…”