An anisotropic mechanical fatigue damage evolution model for Pb-free solder materials

Abstract

Evaluating state of damage in a ductile material as it experiences mechanical fatigue and cyclic loading poses much complexity, and has been the subject of many researches. This study revisits the anisotropic damage model developed by Lemaitre [Lemaitre, J. 1992. A course on damage mechanics. Springer-Verlag Publishing, Berlin] and proposes to use his model combined with two damage models, a micro-mechanics and mechanism-based damage evolution model (Energy Partitioning Damage Evolution (EPDE) [Ladani, L.J., Dasgupta, A., 2008b. A meso-scale damage evolution model for cyclic fatigue of viscoplastic materials. Int. J. Fatigue 2. doi:10.1016/j.ijfatigue.2008.03.013]), and a Unified Creep Plasticity-based (UCP-based) model [ McDowell, D.L., Miller, M.P., Brooks, D.C., 1994. A unified creep plasticity theory for solder alloys. In: Schroeder, S.A., Mitchell, M.R. (Eds.), Fatigue of Electronic Materials, ASTM STP 1153. American Society of Testing and Materials, Philadelphia, pp. 42–59] to predict the state of damage. These two models are then examined for pure shear and are applied to Pb-free solder materials. New anisotropic damage model exponents are generated using experimental data for Pb-free solder for both EPDE and UPC-based models. The exponents generated using these anisotropic models are compared with exponents generated previously under the assumption of isotropic and homogenous damage evolution. These two models were verified using a 3-D Finite Element simulation of the test specimen. Load drops produced by EPDE and UCP-based models were compared with the experiments. The same test set up was used formerly (by Zhang [Zhang, Q. 2004. Isothermal Mechanical and Thermo-Mechanical Durability Characterization of Selected Pb-free solders. Ph.D. Dissertation Defense, Department of Mechanical Engineering, University of Maryland, College Park]) to generate the creep and plastic material properties, and E-P damage model constants for Pb-free solders. Therefore, EPDE exponents that were generated in this study show a much closer correlation with the experimental results.