Stress Intensity Factor Analysis of an Interface Crack between Anisotropic Dissimilar Materials under Thermal Stress

不同材料间界面裂纹的应力强度因子是评价电子器件、粘结结构和复合材料完整性的重要参数。在实际结构中，必须采用有限元法等数值方法来分析界面裂纹的应力强度因子。在本研究中，我们开发了一种数值方法来分析不同材料之间界面裂纹在热应力作用下的应力强度因子。本研究的最终目标是开发该方法的各向异性版本，并将其应用于电子设备的可靠性评估。我们进行了以下几项工作。(1)对热应力条件下不同材料界面裂纹的虚拟裂纹扩展法和裂纹闭合积分法进行了改进。结果表明，这两种方法都是计算界面裂纹应力强度因子最准确的方法之一。(2)利用由界面裂纹应力强度因子导出的最大环向应力准则可以预测界面裂纹的扭结方向。(3)应用界面裂纹的应力强度因子来评价半导体芯片中不同材料之间的分层。(4)开发了一种计算机程序，利用Stroll形式计算不同各向异性材料界面裂纹周围应力分布的渐近解。这是发展各向异性异质材料界面裂纹应力强度因子数值计算技术的重要一步。推导了节理半无限各向异性板在均匀拉剪作用下中心界面裂纹应力强度因子的解析解。

The stress intensity factors of an interface crack between dissimilar materials are important parameters for the evaluation of the integrity of electronic devices, adhesive structures and composite materials. We must use a numerical technique like the finite element method to analyze the stress intensity factors of an interface crack in an actual structure. In this study, we developed a numerical technique to analyze stress intensity factors of an interface crack between dissimilar materials under thermal stress. Final object of this study is to develop the anisotropic version of this method and the application to the evaluation of the reliability of electronic devices. We carried out several works as follows.(1) We modified the virtual crack extension method and the crack closure integral method for an interface crack between dissimilar materials under thermal stress condition. We demonstrated that the both methods is one of the most accurate methods to calculate the stress intensity factors of an interface crack.(2) The direction of the kinking of an interface crack can be predicted using the maximum hoop stress criterion that is derived from stress intensity factors of an interface crack.(3) We applied the stress intensity factors of an interface crack to evaluate the delamination between dissimilar materials used in semiconductor chips.(4) We developed a computer code to calculate the asymptotic solution of the stress distribution around an interface crack between dissimilar anisotropic materials using the Stroll formalism. This is the most important step to develop the numerical technique to calculate stress intensity factors of an interface crack between anisotropic dissimilar materials. We also derived the analytical solution of the stress intensity factors of a center interface crack between jointed semi-infinite anisotropic plates under uniform tension and shear.