A probabilistic study on the mixed-mode fracture in functionally graded materials

This paper presents a Galerkin-based meshless method for calculating stress-intensity factors (SIFs) for a stationary crack in two-dimensional functionally graded materials of arbitrary geometry. The method involves an element-free Galerkin method (EFGM), where the material properties are smooth functions of spatial co-ordinates and two newly developed interaction integrals for mixed-mode fracture analysis. These integrals can also be implemented in conjunction with other numerical methods, such as the finite element method (FEM). Five numerical examples including both mode-I and mixed-mode problems are presented to evaluate the accuracy of SIFs calculated by the proposed EFGM. Comparisons have been made between the SIFs predicted by EFGM and available reference solutions in the literature, generated either analytically or by FEM using various other fracture integrals or analyses. A good agreement is obtained between the results of the proposed meshless method and the reference solutions.

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A New Interaction Integral Method for Analysis of Cracks in Orthotropic Functionally Graded Materials

Computer Technology and Applications ◽

10.1115/pvp2003-1906 ◽

2003 ◽

Author(s):

B. N. Rao ◽

S. Rahman

Keyword(s):

Finite Element ◽

Functionally Graded Materials ◽

Mixed Mode ◽

Functionally Graded ◽

Mixed Mode Fracture ◽

Arbitrary Geometry ◽

Smooth Functions ◽

Graded Materials ◽

Element Discretization ◽

Element Method

This paper presents two new interaction integrals for calculating stress-intensity factors (SIFs) for a stationary crack in two-dimensional orthotropic functionally graded materials of arbitrary geometry. The method involves the finite element discretization, where the material properties are smooth functions of spatial co-ordinates and two newly developed interaction integrals for mixed-mode fracture analysis. These integrals can also be implemented in conjunction with other numerical methods, such as meshless method, boundary element method, and others. Three numerical examples including both mode-I and mixed-mode problems are presented to evaluate the accuracy of SIFs calculated by the proposed interaction integrals. Comparisons have been made between the SIFs predicted by the proposed interaction integrals and available reference solutions in the literature, generated either analytically or by finite element method using various other fracture integrals or analyses. An excellent agreement is obtained between the results of the proposed interaction integrals and the reference solutions.

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Detailed Solution of a System of Singular Integral Equations for Mixed Mode Fracture in Functionally Graded Materials

Journal of Mathematics Research ◽

10.5539/jmr.v12n1p43 ◽

2020 ◽

Vol 12 (1) ◽

pp. 43

Author(s):

Youn-Sha Chan ◽

Edward Athaide ◽

Kathryn Belcher ◽

Ryan Kelly

Keyword(s):

Integral Equations ◽

Functionally Graded Materials ◽

Singular Integral ◽

Mixed Mode ◽

Crack Problem ◽

Singular Integral Equations ◽

Functionally Graded ◽

Fredholm Integral Equations ◽

Mixed Mode Fracture ◽

Graded Materials

A mixed mode crack problem in functionally graded materials is formulated to a system of Cauchy singular Fredholm integral equations, then the system is solved by the singular integral equation method (SIEM). This specific crack problem has already been solved by N. Konda and F. Erdogan (Konda & Erdogan 1994). However, many mathematical details have been left out. In this paper we provide a detailed derivation, both analytical and numerical, on the formulation as well as the solution to the system of singular Fredholm integral equations. The research results include crack displacement profiles and stress intensity factors for both mode I and mode II, and the outcomes are consistent with the paper by Konda & Erdogan (Konda & Erdogan 1994).

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