Global/local finite element analysis for singular stress fields near the junction of dissimilar elastic and elastic-plastic materials in electronic packages

Electronic packages can experience stress singularities due to the presence of dissimilar material properties, geometric discontinuities, and plastic deformation. Lack of a length parameter associated with such geometric discontinuities does not permit assessment of the singular behavior uniquely by using conventional finite elements. In such regions, the conventional finite element prediction is not capable of capturing the effect of geometry, especially in electronic packages with very small length dimensions. This shortcoming can be over-come by combining the local (conventional) elements with a global element that provides the exact nature of the singular behavior. The use of a global element in the case of dissimilar material with elastic behavior has been demonstrated. However, junctions between solder balls and underfill with the chip or substrate require the use of an element that permits the combination of elastic and elastic-plastic material behaviors. This study presents the development of such a solution to extract the exact nature of the singularity and global element stiffness matrix, as well as its implementation into ANSYS. The coupled system stiffness matrix is constructed by using the super-element option in ANSYS. Also, the procedure to utilize ANSYS pre- and post-processing in a seamless manner is described. The graphical user interface permits presentation of the information concerning fracture parameters, such as the stress intensity factor and the energy release rate. This new technique not only provides accurate results, but also allows many users to benefit from it through the use of ANSYS.