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Research Papers

# Computation of Thermal Stress Intensity Factors for Bimaterial Interface Cracks Using Domain Integral Method

[+] Author and Article Information
Ratnesh Khandelwal

Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India

J. M. Chandra Kishen1

Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, Indiachandrak@civil.iisc.ernet.in

1

Corresponding author.

J. Appl. Mech 76(4), 041010 (Apr 23, 2009) (10 pages) doi:10.1115/1.3086588 History: Received April 04, 2008; Revised August 10, 2008; Published April 23, 2009

## Abstract

The concept of domain integral used extensively for $J$ integral has been applied in this work for the formulation of $J2$ integral for linear elastic bimaterial body containing a crack at the interface and subjected to thermal loading. It is shown that, in the presence of thermal stresses, the $Jk$ domain integral over a closed path, which does not enclose singularities, is a function of temperature and body force. A method is proposed to compute the stress intensity factors for bimaterial interface crack subjected to thermal loading by combining this domain integral with the $Jk$ integral. The proposed method is validated by solving standard problems with known solutions.

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## Figures

Figure 1

Closed integration path Γ¯ in a homogenous body (Γ¯=Γc−+Γ+Γc+−Γρ)

Figure 2

Simple connected regions, A1 and A2, enclosed by integration paths Γ1=Γl++Γ1+Γc+−Γρ1 and Γ2=Γc−+Γ2+Γl−−Γρ2, respectively, in a bimaterial body

Figure 3

Plot showing the distribution of function q within the domain of Γ

Figure 4

Semi-infinite bimaterial plate subjected to constant uniform temperature load

Figure 5

Displacement boundary condition for jointed dissimilar semi-infinite plate with double edge crack under uniform temperature load

Figure 6

A typical FE mesh and shape of the contour path used for all the problems

Figure 7

Influence of mesh refinement on J2ρ for jointed dissimilar semi-infinite plate with double edge crack (ρ=8.845×10−3)

Figure 8

Semi-infinite bimaterial plate with noninsulated crack subjected to uniform thermal flow

Figure 9

Displacement and thermal boundary conditions for jointed dissimilar semi-infinite plate with noninsulated double edge crack under uniform thermal flow

Figure 10

Semi-infinite bimaterial plate with insulated central crack subjected to uniform thermal flow

Figure 11

Displacement and thermal boundary conditions for semi-infinite bimaterial plate with insulated central crack subjected to uniform thermal flow

Figure 12

Influence of mesh refinement on J2ρ for semi-infinite bimaterial plate under uniform thermal flow (ρ=7.806×10−3)

Figure 13

A bimaterial interface crack

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