Disturbed State Concept Based Constitutive Modeling for Reliability Analysis of Lead Free Solders in Electronic Packaging and for Prediction of Glacial Motion.

Abstract

The disturbed state concept (DSC) based constitutive model is the focus of this research. It is applied for characterizing two problems; thermomechanical reliability analysis of electronic packages, and prediction of glacial motion. A new procedure for construction of static yield surface for materials is proposed. Further, a modified DSC model to include effect of rate of loading on material behavior is proposed.The DSC is applied to characterize the behavior of Sn-3.9Ag-0.6Cu (SAC) lead free solder alloy used in electronic packages. Proposed procedure of construction of static curve and rate dependent DSC model is applied for prediction of creep and rate dependent behavior of the SAC alloy. Laboratory test data is adopted from the literature and material parameters are determined. The DSC model is validated using the derived material parameters. A finite element analysis of the BGA 225 package is performed under cyclic thermomechanical loading. Analysis results are compared with available test data. A failure criterion for prediction of number of cycles to failure for BGA 225 is then derived.The second application of DSC discussed in this work is prediction of glacial motion. Mechanical behavior of glacial till and its contribution to overall ice movement is characterized using DSC. Two regionally significant tills are chosen and samples are collected from field. A series of laboratory tests are conducted on samples. Tests results are used for model calibration and validation. A numerical simulation of an idealized ice - till system under gravity loading is performed. Two such analyses are performed with DSC and Mohr Coulomb models and the results are compared.The DSC predicts failure when a significant portion of the material reaches a critical disturbance whereas the Mohr Coulomb model predicts failure based on peak stress. DSC predicts a gradual progression to failure whereas the Mohr Coulomb model predicts early catastrophic failure. According to DSC, the material undergoes considerable plastic strains before it reaches failure whereas the Mohr Coulomb predicts failure at very low elastic strains. In general the DSC is considered to provide a more realistic and general constitutive model for glacial tills.