| Summary: | 博士 === 國立成功大學 === 機械工程學系碩博士班 === 90 === This dissertation presents the general solutions with application of wedge and junction problems bonded by isotropic, anisotropic, or piezoelectric materials. Three topics are addressed separately: (1) The effect of stiffness and thickness ratios on popcorn cracking in IC packages; (2) A general solution on stress singularities in two-anisotropic material junction; and (3) Stress singularities at the vertex of a piezoelectric wedge with cylindrical anisotropy.
The first topic discusses the popcorn crack problem in IC package under vapor pressure and thermal load during solder reflow process. Based on the elasticity theory, the singular stress field around the apex of the delaminated interface between die-pad and resin is obtained numerically. The stress intensity factors are computed to evaluate the residual strength of the structure. Also, the structural stability is discussed by using the strain energy density theory. Two factors that are concerned include the relative stiffness ratio Edie-pad/Eresin and the relative thickness . The results show that lower stiffness ratio gives stronger stress singularity. In addition, larger will increase stress intensity factors and structural stability. As a conclusion for our case, moderate value of (say =0) is recommended for design.
The second topic presents the general solution on stress singularities of a junction composed of two dissimilar anisotropic materials. Based on the Lekhnitskii’s approach, the characteristic equation of the generalized plane deformation problem is developed. The concerned influencing parameters on the stress singularity are material constants, fiber orientations, and the bonding angle. The results of the stress singularity order are contour plotted in a circular region. With these figures, the conditions for minimum or even vanishing singularity order can be determined. The accuracy of this approach is guaranteed as the results are compared with several degenerated cases.
The objective of final topic is to derive the characteristic equations for a piezoelectric wedge with cylindrical anisotropy by using the extended Lekhnitskii formulation. The piezoelectric material (PZT-4) is poled in radial, circular and axial directions, respectively. The results show that the behavior of stress singularity orders is different from that of a wedge or even for a crack with rectilinear anisotropy.
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