Tsuyoshi Munakata

Stress intensity factor analysis of interface crack using boundary element method—Application of contour-integral method

A new method is presented for stress intensity factor analyses of two-dimensional crack problems including bimaterial interface crack problems. The M1-integral method, an extended version of the J-integral method, is applied to bimaterial interface crack problems, using the results obtained from the boundary element method. The accuracy of the results of internal points is improved using adaptive automatic integration for a singular boundary integral. The value of the J-integral or the M1-integral is also obtained by this automatic integration. The J-integral method is applied to a center-cracked homogeneous plate under tension. Furthermore, a bimaterial plate with an edge interface crack and a bimaterial plate with a center slant interface crack subjected to tension are analyzed. The proposed method gives accurate stress intensity factors not only for a crack in a homogeneous material but also for an interface crack between dissimilar materials.

Thermal stress analysis of silicon bulk single crystal during Czochralski growth

Abstract The thermal stress analysis of a silicon bulk single crystal with a diameter of 6 or 8 inches is performed in the cases of the [001] and [111] pulling directions by using a three-dimensional finite element program developed for calculating thermal stress in a bulk single crystal during the Czochralski growth. Elastic anisotropy and temperature dependence of material properties are taken into account in this program. The temperature distribution and shape of a silicon bulk single crystal which are required for the thermal stress analysis are obtained from a computer program for a transient heat conduction analysis which is specialized for the Czochralski growth. The stress components obtained from the thermal stress analysis are converted into the parameters related with dislocation density. The time variations of these parameters are shown in this paper. The relation between these parameters and the shape of the crystal-melt interface is discussed.

Elastic constant matrix required for thermal stress analysis of bulk single crystals during Czochralski growth

The elastic constant matrix of cubic single crystals such as GaAs and InP which are used in electronic and optical devices is required in the thermal stress analysis of their bulk single crystals during the Czochralski growth. In this paper, the components of this matrix are expressed in terms of an arbitrary Cartesian coordinate system and a cylindrical coordinate system. They depend on the azimuthal component of the cylindrical coordinate system and the terms containing the azimuthal coordinate cannot be neglected even in approximate sense. Strictly speaking, a three-dimensional thermal stress analysis may be required for those single crystals instead of an axisymmetric analysis.

Thermal stress analysis of bulk single crystal during Czochralski growth (comparison between anisotropic analysis and isotropic analysis)

Abstract A three-dimensional finite element program is developed for calculating the thermal stress in bulk single crystals during Czochralski growth. Elastic anisotropy is taken into account in this program. Thermal stress analyses of a GaAs bulk single crystal are performed in the cases of the [001] and [111] pulling directions, using its temperature distribution obtained from a heat conduction analysis and its material properties. The stress component and the dislocation density parameter are compared between the anisotropic analysis, taking account of elastic anisotropy, and the isotropic analysis, using Youngs modulus and the Poisson ratio in the {111} plane. Significant differences are found in their values and distribution patterns between both analyses.

Stress intensity factor analyses of interacting elliptical cracks using line-spring boundary element method☆

Abstract In the present paper, the line-spring model originally proposed by Rice and Levy is combined with the boundary element method to analyze the stress intensity factors of cracks in three-dimensional structures. The line-spring boundary element method proposed here greatly reduces computer run time, since it enables one-dimensional analysis of three-dimensional crack problems. The present method is first applied to the stress intensity factor analysis of an embedded elliptical crack to study the effects of types of boundary element, i.e. the constant, linear and quadratic elements, and boundary element mesh on the accuracy of the solutions. Furthermore, it is also applied to the stress intensity factor analyses of interacting elliptical cracks, that is, closely located or partly overlapped twin cracks, to clarify the interaction effect of cracks. The calculated results are compared with those of ASME Boiler and Pressure Vessel Code, Section XI, Appendix A.

Stress intensity factor analysis by combination of boundary element and finite element methods

Abstract In the present paper, a combination of the boundary element method is proposed for calculating the stress intensity factors of two-dimensional crack problems including mixed mode ones. In this method, finite elements are only allocated around a crack tip and boundary elements are used to discretize the rest of a structure. The virtual crack extension method is applied to the finite elements to obtain the stress intensity factors, together with the method for the separation of displacement components into mode I and mode II for mixed mode crack problems. The analyses are performed not only for single mode crack problems but also for mixed mode crack problems. It is found from the analyses that we can use large-sized finite elements around the crack tip for straight crack problems and select the crack extension value from the wide range of values. We can expect the stress intensity factors with the accuracy better than 1% by using the present method.

Bifurcation creep buckling analysis of circular cylindrical shell under axial compression

Abstract In some experiments conducted by other authors, axially compressive cylindrical shells with a large ratio of radius to thickness were observed to buckle with circumferential waves. In this paper, the finite element method is used to study this buckling phenomenon. The bifurcation mode and the axisymmetric mode were considered in the analysis as the mode of creep buckling. The number of circumferential waves obtained from the present analysis agrees well with experimental results. This implies that the circumferential waves observed in the creep buckling experiments are due to bifurcation.

Damage Analysis of Semiconductor Chip during Wire Bonding Process

Wire bonding, a process for connection between a semiconductor chip and a lead frame by thin metal wire, is one of the important processes of electronic packaging. Figure 1 shows a silicon chip connected with a lead frame by gold wire. The gold wire bonding process is performed as shown in Figure 2. (1) A tip of gold wire put out from a capillary is melted by an electric torch, and takes a ball shape by its surface tension. (2) A capillary goes down and presses the gold ball on an aluminum terminal set on a semiconductor chip. (3) The capillary is vibrated by ultra sonic for connecting the gold ball with the aluminum terminal. (4) The capillary moves and mashes the gold wire on a lead finger. The quick wire bonding process shorter than 0.1 seconds is desired for high performance of a wire bonding machine. High contact pressure is useful for shortening the process cycle, but it sometimes causes the damage of the semiconductor chip. Especially, a GaAs chip is easy to be broken. This paper presents the damage estimation of a GaAs chip during the gold wire bonding process.

Finite element dynamic bifurcation buckling analysis of torispherical head of BWR containment vessel subjected to internal pressure

Abstract In this paper the bifurcation buckling pressure for the torispherical head of the Mark II type BWR containment vessel subjected to dynamically applied internal pressure is calculated, using a finite element program for a dynamic analysis. Three kinds of dynamic loadings, that is, step loading, ramp loading and pulse loading are considered in the present analysis. The minimum bifurcation buckling pressure is predicted for the respective loadings. The minimum bifurcation buckling pressure for dynamic loading is much lower than the bifurcation buckling pressure for static loading.

Two-Dimensional Finite Element Analysis of a Stably Growing Crack in Inhomogeneous Materials.

The finite element method was applied to a generation phase analysis for stable crack growth in inhomogeneous materials. Experimental data on stable crack growth in bimaterial CT specimens, which were cut from a weldment of a A 533 B Class 1 steel and a HT 80 steel plate, were numerically simulated using the node-release technique to obtain the variations of the fracture mechanics parameters such as J-integral, T*-integral, J-integral and CTOA. New evaluation schemes for the integral parameters were proposed to be valid for integral paths passing a fusion line of dissimilar materials. It was examined whether simple estimation schemes of the J-integral for a monolithic CT specimen can be applied to a bimaterial CT specimen or not. The effect of inhomogeneity on the fracture mechanics parameter was discussed in terms of the Q-factor.