Studies On The Evaluation Of Thermal Stress Intensity Factors For Bi-Material Interface Cracks

Abstract

Components of turbines, combustion chambers, multi-layered electronic packaging structures and nuclear reactors are subjected to transient thermal loads during their service life. In the presence of a discontinuity like crack or dislocation, the thermal load creates high temperature gradient, which in turn causes the stress intensification at the crack tips. If proper attention is not paid in the design and maintenance of components on this high stress in the vicinity of crack tips, it may lead to instability in the system and decrease in the service life. The concepts of thermal fracture mechanics and its major parameter called transient thermal stress intensity factors can greatly help in the assessment of stability and residual life prediction of such structures. The evaluation of thermal stress intensity factors becomes computationally difficult when the body constitutes of two different materials or is non-homogenous or made of composites. Fracture at bi-material interface is different from its homogenous counterpart because of mixed mode stress condition that prevails at the crack tip even when the geometry is symmetric and loading unidirectional. Because of this, the mode 1 and mode 2 stress intensity factors can not be decoupled to represent tension and shear stress fields as can be done in the case of homogeneous materials. Mathematically, the stress intensity factors at bi-material interfaces are complex due to oscillatory singularity that exists at the crack tip. Although plenty of literature is available for bi-material systems subjected to mechanical loads, very little information is available on problems related to thermal loads. Besides, problems related to transient thermal loads need special attention, since no thermal weight functions are available and the existing methods are computationally expensive. Therefore, the present investigation has been undertaken to develop computational and analytical approaches for obtaining the Mode 1 and Mode 2 stress intensity factors for bi-material interface crack problems using conservation of energy principle in conjunction with the weight function approach for various kinds of thermal loads. In the beginning of the studies, a method to extract the Mode 1 and Mode 2 stress intensity factors for bi-material interface crack subjected to mechanical load is proposed using the concept of Jk integrals. This is extended to thermal loads using J2 line integral and J2 domain integral. Furthermore, weight functions are analytically derived for thermal bi-material stress intensity factors and a computational scheme is developed. These methods are validated for several benchmark problems with known solutions.