Based upon linear fracture mechanics, it is well known that the singular order of stresses near the crack tip in homogeneous materials is a constant value À1/2, which is nothing to do with the material properties. For the interface cracks between two dissimilar materials, the near tip stresses are oscillatory due to the order of singularity being À1/2 ± ie and À1/2. The oscillation index e is a constant related to the elastic properties of both materials. While for the general interface corners, their singular orders depend on the corner angle as well as the elastic properties of the materials. Owing to the difference of the singular orders of homogeneous cracks, interface cracks and interface corners, their associated stress intensity factors are usually defined separately and even not compatibly. Since homogenous cracks and interface cracks are just special cases of interface corners, in order to build a direct connection among them a unified definition for their stress intensity factors is proposed in this paper. Based upon the analytical solutions obtained previously for the multibonded anisotropic wedges, the near tip solutions for the general interface corners have been divided into five different categories depending on whether the singular order is distinct or repeated, real or complex. To provide a stable and efficient computing approach for the general mixed-mode stress intensity factors, the path-independent H-integral based on reciprocal theorem of Betti and Rayleigh is established in this paper. The complementary solutions needed for calculation of H-integral are also provided in this paper. To illustrate our results, several different kinds of examples are shown such as cracks in homogenous isotropic or anisotropic materials, central or edge notches in isotropic materials, interface cracks and interface corners between two dissimilar materials.

Usually in the study of singularity problems, only the most critical singular order is considered. For three-dimensional interface corner problems, if only the most critical singular order of stresses is considered, it is possible to lose the opportunity to compute the full modes of stress intensity factors. To fully understand the failure behavior of three-dimensional interface corners, a definition of the stress intensity factors for the lower singular orders is proposed in this paper based on that of the most critical singular order. Moreover, to compute the proposed multi-order stress intensity factors accurately and efficiently, a path-independent H-integral, which has been proven useful for the two-dimensional interface corners, is now modified into a domain-independent H-integral for the three-dimensional interface corner problems. Because the stress intensity factors characterize the fracture behavior focused on an arbitrary tip along the corner front, based on anisotropic elasticity the near tip solutions and complementary solutions of two-dimensional generalized plane strain problems are introduced and then utilized for computation of three-dimensional H-integral. To illustrate the validity of the present work, several three-dimensional numerical examples are analyzed and compared with the existing published solutions. Finally, two examples about the interface corners, which occur frequently in electric packages, are solved to show the feasibility and practicability of the proposed approach.

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It is well known that the path-independent H-integral is an appropriate tool for calculating the mixed mode stress intensity factors for the interface corners between dissimilar elastic materials. To extend the applicability of the H-integral from the mechanical loading condition to the thermal loading condition, a modified H-integral is proposed in this paper. This modified H-integral possesses an extra domain integral which needs the input of temperature field. Moreover, this domain integral contains singular functions that come from the strain components of the auxiliary system, and a special treatment should be made for the accurate computation of stress intensity factors. The near-tip solutions and auxiliary solutions of displacements, stresses, and temperature required in the calculation of H-integral are all provided in this paper. The validity and versatility of the proposed approach are then shown by carrying out several numerical examples such as cracks under mixed-mode thermal loadings, interface cracks/corners under uniform heat flow or uniform temperature change, and an electronic package, in which the chip has a heat generation rate, placed at a constant temperature ambiance.

The present work reports that highly c-axis-oriented TI-Ba-Ca-Cu-0 superconducting films with zero-resistance temperature up to 112 K were successfully prepared using the spray pyrolysis technique with a subsequent TI-diffusion treatment. The insulating Ba-Ca-Cu-0 precursor films (Ba:Ca:Cu = 2:2:3) were made by spray deposition of the related metal nitrate solution on a preheated (300"-400°C) MgO(001) single-crystal substrate. The presence of the superconducting phases of the resultant films depended strongly on the types of TI sources used. The results showed that the formation of the superconducting phases could be achieved more readily by using the bulk TI-Ba-Ca-Cu-0 rather than TI,O, as a TI source. In other words, the low TI content in the TlBaCaCuO bulk source with a resulting low TI-vapor pressure is favorable for the formation of a higher T, superconducting phase. The dominant phases in the prepared films were mainly TIBa,Ca,Cu,~O,(1223 phase) and TI,Ba,CaCu,0,(2212 phase). The critrcal current density of a film with a nearly single-phase(l223) structure was measured to be 1.2 X lo4 A/cm2 at 77 K under zero magnetic field.