The Axisymmetric Problem of a Partially Insulated Mixed-Mode Crack Embedded in a Functionally Graded Pyro Magneto-Electro-Elastic Infinite Medium Subjected to Thermal Loading

Abstract

This article describes our investigation of the influence of an axisymmetric partially insulated mixed-mode crack on the coupled response of a functionally graded magneto-electro-elastic material (FGMEEM) subjected to thermal loading. The crack is embedded at the center of an infinite medium, and the material is graded in the direction orthogonal to the crack plane and is modeled as a nonhomogeneous medium with anisotropic constitutive laws. The heat conduction equation is first solved using the Hankel transform to yield the temperature field in the medium. Using the same integral transform, the magneto-electro-elasticity equations are converted analytically into a system of four singular integral equations that are solved numerically to yield the crack-tip mode I and II stress intensity factors, the electric displacement intensity factor and the magnetic induction intensity factor. The main objective of this research is to study the influence of material nonhomogeneity on the fields’ intensity factors for the purpose of gaining better understanding on the behavior of graded pyro magneto-electro-elastic materials.

Keywords:

• Embedded crack
• Functionally Graded Magneto-Electro-Elastic Material (FGMEEM)
• Magneto-electro-mechanical loads
• Mixed-mode stress intensity factors
• Singular integral equations

ACKNOWLEDGEMENTS

The first two authors are grateful for the funding provided to their laboratory by the Tunisian Ministry of Higher Education and Scientific Research. This work was performed under the framework of the International Institute for Multifunctional Materials for Energy Conversion (IIMEC) (http://iimec.tamu.edu/), which is funded by the U.S. National Science Foundation (DMR 0844082).