Evaluation of notch stress intensity factors by the asymptotic expansion technique coupled with the finite element method

Abstract

• The asymptotic expansion technique coupled with the FEM is proposed to evaluate notch stress intensity factors . • The singular order, stress angular function and amplitude coefficient in stress asymptotic field of a V-notch can be yielded. • There no special element is needed while the high computational accuracy is obtained. • The proposed method can be implanted into the commercial FE software to analyze V-notches in engineering structures. A characteristic analysis method coupled with the finite element method is proposed to calculate stress intensity factors for V-notches, in which the notched structure is divided into a singular stress sector and the remained part. The asymptotic expansions are introduced into the singular stress region to transform elastic governing equations into characteristic ordinary differential equations. The established equations are solved by the interpolating matrix method to provide stress singular orders and characteristic angular functions. The asymptotic solution in the singular stress region is then coupled with finite element equations built on the remained structure by interfacial continuous conditions to establish the system equations. Thus, the amplitude coefficients in the stress asymptotic expansions can be determined. The notch stress intensity factors can be evaluated after the stress angular functions and amplitude coefficients being obtained. A symmetric V-notch and an inclined V-notch are respectively investigated to verify the accuracy of calculated notch stress intensity factors by the proposed method through comparing with the reference ones. Due to only conventional finite element method is needed, the proposed method can be freely implanted into commercial finite element software to analyze the singular stress for the V-notched engineering structures. This method can be also easily generalized to analyze the singular physical field for V-notches in composite materials.