A study of fracture kinetics in welded components of nuclear power plant equipment in the presence of surface semi-elliptical variously oriented cracks

Abstract

Using strain-based fracture criteria, design formulas have been derived for the determination of stress-strain state along a contour of low-cycle surface semi-elliptical inclined cracks with consideration of volumetric anisotropy of physical-mechanical properties. The adjusted life time and strength of nuclear power plant equipment have been assessed.Keywords: life, survivability of nuclear power plant equipment, inclined semi-elliptical cracks, low-cycle loading, strains, anisotropy of properties, fracture surface.Safety and survivability of nuclear power plant (NPP) equipment are governed by operability of its individual units and elements that may contain some initial or operation-induced flaws such as variously oriented surface semi-elliptical cracks. A study of kinetics of the failure mechanism in the case of evolution of such flaws under the conditions of volumetric nominal fields of cyclic elastic-plastic strains with consideration of anisotropy of physical-mechanical properties and residual stresses allows a refined assessment of the limiting state of components and remaining life of structures and their survivability.The crack-tip stress-strain state in linearly elastic bodies is usually analyzed [1, 2] by one of the three main methods: (i) Kolosov-Muskhelishvili complex potentials, (ii) integral transformations, and (iii) eigenfunction expansion. The last one is perhaps a more general method of tackling the applied problems of nonlinear fracture mechanics.There are numerous approaches to and techniques for solving the subject problem. Exact analytical solutions currently available are few in number and they apply to cracks in infinite bodies (in practice this implies small cracks in finite bodies). These solutions have been constructed by methods of the complex variable theory, which were elaborated in the works by Muskhelishvili and Westergaard. Later on, Ishida and other researchers applied conformal mapping which made it possible to consider finite bodies. Nowadays, much attention is focused on using nonlinear fracture mechanics methods such as hodographs and eigenfunction expansion.It is practically impossible to obtain any analytical solutions for stress intensity factors K a (a =1, 2, 3) along the entire length of an arbitrary curved crack. Meanwhile, there are some solutions available for typical and simplest geometries.Within the linear theory of elasticity of isotropic body, the stress-strain state in the vicinity of the crack contour can be represented through linear superposition of three independent states of a cracked body under loading.In the most general case of loading a cracked body, the following asymptotic representation is valid for the strain tensor components near the crack contour (a = I, II, III; i j , , =1 2, 3) [3]: e r r K f ij e ij ( , ) ( ) ..., ( ) q p q a a a = + å 1 2(1)