A new conservation integral for arbitrarily curved cracks under thermal loading, which consists of path and area integrals, is proposed. This integral is derived by modifying the G* integral for arbitrarily curved cracks under mechanical loading, which was suggested by Beom and Earmme. Comparing with the G* integral of Beom and Earmme, the proposed integral under thermal loading has one additional term in area integral which is related to the temperature. If there exists contact between crack surfaces within the integration region, another line integral is added to take care of traction. The conservation integral is shown to be a valid fracture parameter for the curved interface crack and has a physical meaning of energy release rate when the crack is assumed to grow along the curved interface.
The conservation integral can be recast into a domain integral so that the energy release rate computed by the finite element method is less sensitive to the inaccuracy in the numerical integration within the crack tip region. The finite element analysis results by the domain integral expression for energy release rate of a semi-circular crack, whose surfaces are thermally insulated, in an infinite plate under uniform heat flux is compared with the exact energy release rate which is derived by Chung et al., and the validity of the proposed conservation integral for calculating the energy release rate has been proved.
In order to illustrate the usefulness of the proposed integral as the energy release rate, the following examples with the thermally insulated crack surface are studied: - semi-circular crack in an infinite plate under uniform heat flux
- elliptical crack in an infinite plate under uniform heat flux
- crack along the cosine shaped interface of the film and substrate under uniform heat flux
In these examples, the contact of crack surfaces, which can occur in thermal problem, are taken into account by using the interface element of ABAQUS in order to avoid the interpenetration of the crack surface. The energy release rate for the case with contact between the crack surfaces is lower than that with no contact assumed. It is also shown that the conservation integral is independent of the size and shape of the integration domain. The results of sensitivity study have shown a clear property of the path independency on integration contour and insensitiveness to the mesh size in the crack tip region when comparing with the J integral approach which is used in the conventional analysis of the curved crack using the fine mesh.
In this paper, the proposed conservation integral has been proved as a useful and convenient tool for calculating the energy release rate of the curved interface crack having the property of insensitiveness to the mesh size and the independence on the integration contour. Therefore, it is concluded that the proposed conservation integral is a useful fracture parameter in obtaining the energy release rate for the arbitrarily curved cracks under thermal loading.
