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A conservative integral for bimaterial notches subjected to thermal stresses
Author(s) -
BanksSills Leslie,
Ishbir Chaim
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.996
Subject(s) - stress intensity factor , eigenfunction , isotropy , mathematics , eigenvalues and eigenvectors , mathematical analysis , singular integral , linear elasticity , singularity , finite element method , elasticity (physics) , integral equation , geometry , materials science , structural engineering , physics , composite material , quantum mechanics , engineering
In this investigation, a conservative integral based on the Betti reciprocal principle is developed to obtain stress intensity factors for a bimaterial notch in which the body is subjected to a thermal load. The bonded materials are linear elastic, isotropic and homogeneous. According to the linear theory of elasticity, stresses in the neighbourhood of the notch tip are generally singular as a result of the mismatch of the elastic constants. Eigenvalues and eigenfunctions depend upon the mechanical properties and wedge angles. They may be real, complex or power‐logarithmic. Real and complex eigenvalues are considered in this study. The stress intensity factor represents the amplitude of the stress singularity and depends upon material properties, geometry and load or temperature. Because of the highly singular behaviour of one of the integrals that is part of the conservative integral, the former is carried out by a hybrid analytical/numerical scheme. The finite element method is employed to obtain displacements caused by the temperature distribution in the body. The conservative integral is applied to several problems appearing in the literature. Both good agreement between those results and the ones obtained here, as well as path stability for all problems is attained. A wide range of material parameters is also studied. Copyright © 2004 John Wiley & Sons, Ltd.