Interface crack between different orthotropic media under uniform heat flow.

Sheng-Hu Ding,Xing Li

doi:10.1186/s40064-016-3105-5

Abstract

In this paper, plane thermo-elastic solutions are presented for the problem of a crack in two bonded homogeneous orthotropic media with a graded interfacial zone. The graded interfacial zone is treated as a nonhomogeneous interlayer having spatially varying thermo-elastic moduli between dissimilar, homogeneous orthotropic half-planes, which is assumed to vary exponentially in the direction perpendicular to the crack surface. Using singular integral equation method, the mixed boundary value conditions with respect to the temperature field and those with respect to the stress field are reduced to a system of singular integral equations and solved numerically. Numerical results are obtained to show the influence of non-homogeneity parameters of the material thermo-elastic properties, the orthotropy parameters and the dimensionless thermal resistance on the temperature distribution and the thermal stress intensity factors.

Highlights

Graded materials (FGMs) are designed as the special materials which have changed micro-structure and mechanical/thermal properties in the space to meet the required functional performance (Niino et al 1987; Suresh and Mortensen 1998)
The advantages of Functionally graded materials (FGMs) are that the magnitude of residual and thermal stresses can be reduced, and the bonding strength and fracture toughness of such materials can be improved
From both the phenomenological and mechanistic viewpoints, the tailoring capability to produce gradual changes of thermo-physical properties in the spatial domain is the key point for the impressive progress in the areas of functionally graded materials (Miyamoto et al 1999)

Summary

Background

Graded materials (FGMs) are designed as the special materials which have changed micro-structure and mechanical/thermal properties in the space to meet the required functional performance (Niino et al 1987; Suresh and Mortensen 1998). The advantages of FGMs are that the magnitude of residual and thermal stresses can be reduced, and the bonding strength and fracture toughness of such materials can be improved From both the phenomenological and mechanistic viewpoints, the tailoring capability to produce gradual changes of thermo-physical properties in the spatial domain is the key point for the impressive progress in the areas of functionally graded materials (Miyamoto et al 1999). Zhou and Lee (2011) studied the thermal fracture problem of a functionally graded coating-substrate structure of finite thickness with a partially insulated interface crack subjected to thermal–mechanical supply. Zhou et al (2010) considered the thermal response of an orthotropic functionally graded coating-substrate structure with a partially insulated interface crack. Using element free Galerkin method, Pathak et al (2014) studied quasi-static fatigue crack growth simulations of homogeneous and bimaterial interfacial cracks under mechanical as well as thermo-elastic load.

The temperature satisfies

Introducing the density functions