Youn Young Earmme

Application of conservation integrals to interfacial crack problems

Abstract Properties of the J , L and M integrals, proposed by Knowles and Sternberg for homogeneous materials are explored here for bi-material interfaces. The integrals are shown to satisfy the conservation law under certain conditions on the interfaces. Relations between the stress intensity factors and the conservation integrals for interfacial cracks in isotropic, linear-elastic materials are derived. The conservation integrals for some interfacial cracks are applied to get the stress intensity factors in a very simple way without solving the complicated boundary value problems. For interfacial cracks in finite-sized medium some numerical computations are carried out to verify the usefulness of the conservation integrals.

A fracture mechanics analysis of the effects of material properties and geometries of components on various types of package cracks

Various package cracks observed in service, with different locations and propagation directions, in plastic packages of surface mount technology (SMT) are analyzed in terms of the energy release rate in fracture mechanics. It has been reported that the types of the cracks observed in the package depend on the chip size, relative thickness of the epoxy resin on the chip and under the chip pad, properties of the materials and the adhesion strength of the interfaces in the package. The stress derived from the thermal expansion mismatch of the materials during the temperature cycling and the pressure induced by the expansion of moisture absorbed in the package at soldering temperature are considered separately in estimating the effects of various parameters on the package cracks. As a result of the analysis, we find that the propagation direction of the package crack is dependent on the location of the delaminated interface from which the package crack originates and the loading type imposed on the package, and that the influence of the various parameters on the package cracks are largely dependent on the loading type. Some results of the analysis are compared with the experimental results.

An interfacial edge crack in anisotropic bimaterial under anti-plane singularity

An interfacial edge crack of a length a in two bonded dissimilar anisotropic quarter planes having an anti-plane singularity such as a screw dislocation or anti-plane line force is analyzed. The energy release rate and stress intensity factor are explicitly expressed in terms of complex potentials. The interaction problems in two bonded orthotropic quarter planes are exemplified. It is confirmed that the present solution reduces to the known solutions dealing with particular cases of the present problem.

Interactions of Spherical Precipitates in an Anisotropic Matrix

Abstract Elastic interactions between two anisotropic spherical precipitates embedded in an anisotropic elastic medium and their asymptotic behavior are investigated on the basis of an elastic field for two spheres. It is confirmed that an interaction energy between two spherical anisotropic precipitates (not necessarily identical to each other) separated by a large distance | d | is of order (| d | −3 ) or higher. Numerical computations are performed for the cases of two identical misfitting anisotropic precipitates in an anisotropic matrix of cubic symmetry. It is observed that far-field interactions (| d | ⪢ a ) depend on the anisotropic factor H = C 12 + 2 C 44 − C 11 , of the matrix. When the factor H is positive as in fcc elements, the far-field interactions are attractive between the two precipitates aligned along 〈100〉 directions of the matrix while repulsive along 〈100〉 directions. In contrast, the far-field interactions are attractive along 〈111〉 directions and repulsive along 〈100〉 directions whrn the factor H of the matrix is negative as in bcc elements. It also appears that the near-field (| d | ≈ 2 a ) interactions are strongly dependent on the direction of the alignment of the precipitates, and the differences between the elastic moduli of the precipitates and those of the matrix.

A screw dislocation interacting with an interfacial crack in two anisotropic thin films with finite thickness

Two bonded dissimilar anisotropic thin films of equal thickness h with an interfacial crack under an anti-plane singularity such as a screw dislocation or an anti-plane line force is analyzed by conformal mapping technique. The image forces on the screw dislocation, the energy release rate, and stress intensity factor are explicitly derived in terms of complex potentials. The interaction problems in two bonded orthotropic films are exemplified and the results for various particular cases of the present study are compared with the known solutions, demonstrating the versatility of this study.

Analysis of a flat annular crack under shear loading

An annular crack in an infinite isotropic elastic solid under shear loading is analyzed. General solution to the Naviers equilibrium equation is expressed in terms of three harmonic functions. Employing the Hankel transform the harmonic functions are represented by the solution of a pair of triple integral equations. The triple integral equations are reduced to a pair of mixed Volterra-Fredholm integral equations, which are numerically solved. The stress intensity factors of the annular crack under various shear loadings such as uniform radial shear, linearly varying radial shear, uniform shear and linearly varying shear are calculated as the Poissons ratio ν anda/b (a; inner radius,b; outer radius) vary.

A partially debonded circular inclusion interacting with a point singularity: A classical problem revisited

The classical problem for a partially debonded circular inhomogeneity is revisited. The interaction of the interfacial crack and a point singularity such as a point force and/or a dislocation is dealt with. Also the circular arc-shaped interfacial crack under remote stress is solved. This problem has been solved by many researchers for the cases of various loading types. However, lack of generality in the solution technique together with too complicated form of the solution makes it hard to grasp the structure of the solution. Based on the recently published technique for a perfectly bonded circular inhomogeneity, this problem is revisited. The resulting form of the solution is very simple, therefore, its structure is easily understood. Due to the merit of the present method, the image force on the edge dislocation near the tip of the interfacial crack is easily obtained.

Analysis of temperature distribution and slip in rapid thermal processing

A numerical solution of temperature and thermally induced stress in a wafer during rapid thermal processing(R. T. P) is obtained and an analysis of onset of slip is performed. Some results are compared with experiment. In this R. T. P system one side of threeinch silicon wafer is irradiated steadily for 1015 sec in the temperature rangefrom 1100 to 1150 OC by using tungsten halogen lamp as the heat source. In order to obtain the temperature distribution of a wafer in R. T. P system twodimensional heat conduction equation that incorporates radiative and convective heat transfer is proposed and the equation is solved numerically using alternating direction implicit(A. D. I) method. In dealing with the. radiative heat transfer a partially transparent body that absorbs the radiation energy is assumed and this partially transparent body undergoes multiple internal reflections and absorptions. Twodimensional (assuming plane stress and anisotropy) thermoelastic constitutive equation is used to calculate the thermal stress induced in a wafer and a finite element method is employed to solve the equation numerically. In order to predict the slip the stress resolved on the slip planes in the slip directions of silicon is compared with the yield stress of silicon which is the function of strain rate temperature and initial dislocation density. The numerical result shows that the wafer temperature at which slip occurs is affected by the heating rate of the