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Finite element analysis of three-dimensional corner stress singularities and its application in microelectronics packaging.

机译：三维角应力奇点的有限元分析及其在微电子封装中的应用。

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摘要

Plane strain and plane stress assumptions, although generally valid in the interior part of a wedge configuration, don't apply in the vicinity of corner points, at which stress and displacement fields are three-dimensional in nature. In this study a finite element procedure has been developed to compute singular eigenstates that characterize the exact solution of linear elastostatic problems in the vicinity of these threedimensional corners. The asymptotic stress field is composed of terms of the form r −λf(&thetas;,&phis;;λ), where r is the radial distance from the comer point, &thetas; and &phis; are spherical coordinates, and f(&thetas;,&phis;;λ) is the angular function defined on a spherical shell of unit radius which surrounds the corner (r → 0). The order of the singularity, λ, can be real or complex. The accuracy, completeness and efficiency of the method are fully demonstrated by taking into consideration of six rigid body motion modes.; The displacement eigenstates for the terminal point of an interfacial surface crack with and without contact consideration is fully investigated. The structure of all singular eigenstates are fully illustrated by plotting the eigen-displacements on the free surface and eigen-displacement jumps across the crack faces. It is found that in general three real eigenvalues exist without contact consideration and two otherwise. In all cases in-plane shear deformation dominates the displacement fields and it has a stronger singularity than the interior part of a perpendicular crack. Contact constraint changes little anti-symmetric mode asymptotics but it does dramatically change the behavior of the symmetric mode singularity. The study also shows that a critical intersection angle at the free surface can be determined so that the corner point has the same square root singularity as the interior part of the crack front.; For a typical Flip-Chip assembled Chip-on-Board (FCOB) package, it is shown that the stress singularities at three-dimensional comers are always more severe than those at the corresponding two-dimensional edges, which suggests that they are more likely to be the potential crack initiation or delamination sites. Based on the results obtained, several guidelines for minimizing edge stresses in IC packages are presented.
机译：平面应变和平面应力假设虽然通常在楔形结构的内部有效，但不适用于拐角点附近，在拐角点处应力和位移场本质上是三维的。在这项研究中，已经开发出了一种有限元程序来计算奇异本征态，这些奇异本征态表征了这些三维角附近线性弹性静力学问题的精确解。渐近应力场由形式为 r -λ f （＆thetas;，phis;λ）的项组成，其中 r 是距拐角的径向距离＆thetas;。和＆phis;是球形坐标，而 f （＆thetas;，phis;λ）是定义在围绕角的单位半径球壳上的角函数（ r →0） 。奇数级λ可以是实数，也可以是复数。通过考虑六个刚体运动模式，充分证明了该方法的准确性，完整性和效率。充分研究了考虑和不考虑接触的情况下界面裂纹的端点的位移本征态。通过在自由表面上绘制本征位移和在裂纹面上的本征位移跃迁，可以充分说明所有奇异本征态的结构。可以发现，通常存在三个实际特征值而不考虑接触，否则两个。在所有情况下，平面内剪切变形都主导着位移场，并且比垂直裂纹的内部具有更强的奇异性。接触约束几乎不会改变反对称模式的渐近性，但确实会极大地改变对称模式奇点的行为。研究还表明，可以确定自由表面的临界相交角，以使拐角点具有与裂纹前沿内部相同的平方根奇点。对于典型的倒装芯片组装的板上芯片（FCOB）封装，表明三维角上的应力奇异性总是比相应的二维边缘上的应力奇异性更严重，这表明它们更有可能是潜在的裂纹萌生或分层位置。根据获得的结果，提出了一些用于最小化IC封装中边缘应力的准则。

著录项

  • 作者

    Xu, Anqing.;

  • 作者单位

    Lehigh University.;

  • 授予单位 Lehigh University.;
  • 学科 Engineering Mechanical.; Engineering Packaging.
  • 学位 Ph.D.
  • 年度 2002
  • 页码 169 p.
  • 总页数 169
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 机械、仪表工业;包装工程;
  • 关键词

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