An accurate scheme for mixed-mode fracture analysis of functionally graded materials using the interaction integral and micromechanics models

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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Hygrothermal Fracture Analysis of Orthotropic Functionally Graded Materials UsingJk-Integral-Based Methods

Mathematical Problems in Engineering ◽

10.1155/2013/315176 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Serra Topal ◽

Serkan Dag

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Functionally Graded Materials ◽

Fracture Analysis ◽

Functionally Graded ◽

Mixed Mode Fracture ◽

Inclined Crack ◽

Element Analysis ◽

Moisture Concentration ◽

Graded Materials

This paper puts forward two differentJk-integral-based methods, which can be used to perform mixed-mode fracture analysis of orthotropic functionally graded materials subjected to hygrothermal stresses. The first method requires the evaluation of both components ofJk-integral, whereas the second method employs the first componentJ1and the asymptotic crack tip displacement fields. Plane orthotropic hygrothermoelasticity is the basic theory behind theJk-integral formulation, which is carried out by assuming that all material properties are functions of the spatial coordinates. Developed procedures are implemented by means of the finite element method and integrated into a general purpose finite element analysis software. Temperature and specific moisture concentration fields needed in the fracture analyses are also computed through finite element analysis. Each of the developed methods is utilized in conjunction with the superposition technique to calculate the hygrothermal fracture parameters. An inclined crack located in a hygrothermally loaded orthotropic functionally graded layer is examined in parametric analyses. Comparisons of the results generated by the proposed methods do indicate that both methods lead to numerical results of high accuracy and that the developed form of theJk-integral is domain independent. Further results are presented so as to illustrate the influences of crack inclination angle, crack length, and crack location upon the modes I and II stress intensity factors.

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