A thermodynamics based damage mechanics framework for fatigue analysis of microelectronics solder joints with size effects

Experimental observations of an increase in resistance with decreasing specimen size and under the presence of non-uniform plastic deformation fields have pushed the development for small scale plasticity theories since the early 90's. The observed phenomenon has been explained in terms of an accumulation of a density of geometrically necessary dislocations, which is required in order to accommodate nonuniform plastic deformation fields. This extra density of dislocations, contributes to the additional hardening observed in small scale specimens under imposed non-uniform plastic deformations. The density of geometrically necessary dislocations has been related to the gradients of plastic strain which are imposed either by the loading conditions or the geometry of the specimen. The proposed set of theories has promoted the idea that there is an additional material parameter, namely a plastic length scale. Within these theories when the material is under the presence of a non-uniform plastic deformation field and once typical structural dimensions approaches the material length scale there is an increase in resistance. Such a class of mathematical framework is currently known as strain gradient plasticity (SGP) theory. On the other hand, the current trend towards miniaturization in the microelectronics industry has raised questions about the true behavior of small structural systems. In this dissertation we address such a problem but from the perspective of eutectic solder alloys. Eutectic solder alloys as frequently used in the microelectronics industry exhibit considerable rate dependent response even at room temperature. Moreover for this type of material, the problem of interest is the response under cyclic loadings induced by thermomechanical fatigue leading to the classical case of creep-fatigue interaction. Several experimental and theoretical studies have been developed in order to generate robust constitutive descriptions for this class of applications. For a structure whose size is close to a 100mum or larger several and relatively simple to implement constitutive models are now available in the literature, and it can be generally stated that the level of understanding has reached a mature level. However, the same problem when the size of the structure is below this characteristic dimension has not been studied before. In other words, the available constitutive models completely neglect the incidence of size effects when evaluating the true behavior of the material at small scales. (Abstract shortened by UMI.)...