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Mathematical Problems in Engineering
Volume 2013, Article ID 315176, 11 pages
Research Article

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

1Department of Mechanical Engineering, Gazi University, 06570 Ankara, Turkey
2Department of Mechanical Engineering, Middle East Technical University, 06800 Ankara, Turkey

Received 21 April 2013; Accepted 1 August 2013

Academic Editor: Abdelouahed Tounsi

Copyright © 2013 Serra Topal and Serkan Dag. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper puts forward two different -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 of -integral, whereas the second method employs the first component and the asymptotic crack tip displacement fields. Plane orthotropic hygrothermoelasticity is the basic theory behind the -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 the -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.