A New Displacement-based Approach to Calculate Stress Intensity Factors With the Boundary Element Method

Abstract

The analysis of cracked brittle mechanical components considering linear elastic fracture mechanics is usually reduced to the evaluation of stress intensity factors (SIFs). The SIF calculation can be carried out experimentally, theoretically or numerically. Each methodology has its own advantages but the use of numerical methods has become very popular. Several schemes for numerical SIF calculations have been developed, the J-integral method being one of the most widely used because of its energy-like formulation. Additionally, some variations of the J-integral method, such as displacementbased methods, are also becoming popular due to their simplicity. In this work, a simple displacement-based scheme is proposed to calculate SIFs, and its performance is compared with contour integrals. These schemes are all implemented with the Boundary Element Method (BEM) in order to exploit its advantages in crack growth modelling. Some simple examples are solved with the BEM and the calculated SIF values are compared against available solutions, showing good agreement between the different schemes.

The stress intensity factor assessment in three-dimensional problems by the displacement fitting technique and the dual Boundary Element Method

“…The present study extends the DFT proposed by Gonzalez et al (2015) for three-dimensional fracture problems. The three-dimensional DBEM formulation provides the solution for internal fields and for the boundary value problem.…”

“…These high order terms improve the DFT accuracy in comparison with the classical approach, which disregards them. As previously demonstrated by Gonzalez et al (2015), the DFT is as accurate as the J-integral approaches for SIFs assessment. However, its computational requirements are considerably lower than the J-integral ones.…”

“…The displacement fitting technique (DFT) proposed by Gonzalez et al (2015) is extended herein for threedimensional problems. Figure 2a illustrates the local Cartesian coordinates ( ′, ′, ′) and spherical coordinates ( , , ) systems both with origin at the near crack front point ′.…”

“…The displacement correlation/extrapolation techniques consist of correlating or extrapolating the numerical displacement field at the crack tip with the asymptotic local displacement analytical solution. These solution techniques have been used in its classical form to extract SIFs from the finite element method (FEM) (Chan et al, 1970;Ingraffea and Manu, 1980;Banks-Sills and Sherman, 1986;Banks-Sills et al, 2005;Nejati et al, 2015) and BEM (Cruse and Wilson, 1978;Balderrama et al, 2006;Purbolaksono et al, 2012;Gonzalez et al, 2015;Cordeiro and Leonel, 2018;Cordeiro and Leonel, 2019). Recently, SIFs values have also been obtained from the extended/generalized finite element method (X/GFEM) using such scheme (Minnebo et al, 2010;Gonzalez-Albuixech et al, 2013;Schätzer and Fries, 2016;Gupta et al, 2017;Gupta and Duarte, 2018).…”

“…Recently, SIFs values have also been obtained from the extended/generalized finite element method (X/GFEM) using such scheme (Minnebo et al, 2010;Gonzalez-Albuixech et al, 2013;Schätzer and Fries, 2016;Gupta et al, 2017;Gupta and Duarte, 2018). Gonzalez et al (2015) proposed a variation of the displacement correlation technique for two-dimensional problems, which has been named as displacement fitting technique (DFT). This technique incorporates higher-order terms of the displacement asymptotic solutions near the crack front.…”