Arlo F. Fossum

A Practical Viscoplastic Damage Model for Lead-Free Solder

This paper summarizes the results of a program to construct an internal variable viscoplastic damage model to characterize 95.5Sn-3.9Ag-0.6Cu (wt.%) lead-free solder under cyclic thermomechanical loading conditions. A unified model is enhanced to account for a deteriorating microstructure through the use of an isotropic damage evolution equation. Model predictions versus experimental data are given for constant strain-rate tests that were conducted at strain rates of 4.2 X 10 -5 s -1 and 8.3 X 10 -4 s -1 over a temperature range from -25°C to 160°C; cyclic shear tests; and elevated-temperature creep tests. A description is given of how this work supports larger ongoing efforts to develop a predictive capability in materials aging and reliability, and solder interconnect reliability.

Constitutive models for the Etchegoin Sands, Belridge Diatomite, and overburden formations at the Lost Hills oil field, California

This report documents the development of constitutive material models for the overburden formations, reservoir formations, and underlying strata at the Lost Hills oil field located about 45 miles northwest of Bakersfield in Kern County, California. Triaxial rock mechanics tests were performed on specimens prepared from cores recovered from the Lost Hills field, and included measurements of axial and radial stresses and strains under different load paths. The tested intervals comprise diatomaceous sands of the Etchegoin Formation and several diatomite types of the Belridge Diatomite Member of the Monterey Formation, including cycles both above and below the diagenetic phase boundary between opal-A and opal-CT. The laboratory data are used to drive constitutive parameters for the Extended Sandler-Rubin (ESR) cap model that is implemented in Sandias structural mechanics finite element code JAS3D. Available data in the literature are also used to derive ESR shear failure parameters for overburden formations. The material models are being used in large-scale three-dimensional geomechanical simulations of the reservoir behavior during primary and secondary recovery.

Development of the Damage State Variable for a Unified Creep Plasticity Damage Constitutive Model of the 95.5Sn–3.9Ag–0.6Cu Lead-Free Solder

A unified creep plasticity damage (UCPD) constitutive model was developed to predict the fatigue of 95.5Sn-3.9Ag-0.6Cu solder joints. Compression, stress-strain and creep properties were generated in previous studies of this solder. Crack damage was reflected in a single state variable, D ω, in the model. Isothermal fatigue tests were performed at 25°C, 100°C, and 160°C using a double-lap shear test specimen. A new approach to fitting the revised damage model is proposed based on finite element analysis (FEA) simulation of the load decay of the fatigued solder material. Accurate predictions required that those parameters be temperature dependent. The UCPD constitutive model was successfully implemented as a subroutine in the commercial finite element code ANSYS®. Consistent predictions were obtained as demonstrated by a comparison of results generated from FEA simulation of the test assembly against analogous experimental results.