The Effect of Restraint Non-Linearity on the Instability of Growth of a Circumferential Through-Wall Crack in a Piping System

Abstract

The paper is concerned with the criterion for the instability of growth of a circumferential through-wall crack in a piping system. A simple approach involves representing the cracked section behaviour by a moment (M)–rotation (φ) relation. The criterion for unstable crack growth is then L* > EI |dφ/dM| where E is Young’s modulus and I is the second moment of area of the piping at the cracked section. L* can be viewed as a crack-system compliance length parameter or an “effective” pipe length. If the piping system, apart from the cracked system, behaves in a linear manner, L* is dependent on the system’s characteristics but most importantly, is independent of the magnitudes of any applied loadings and the characteristics of the cracked section. This paper is concerned with the effect of system non-linearity, and in particular restraint non-linearity, on the instability criterion, the considerations being based on the analyses of a simple model which contains a restraint which behaves non-linearly. In this case, we show that L* is no longer dependent only on the system’s characteristics, as is the case when the restraint behaves linearly.