Publications

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The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method. Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.

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Cracks in glass-to-metal seals can be a threat to the hermeticity of isolated electronic components. Design and manufacturing of the materials and processes can be tailored to minimize the residual stresses responsible for cracking. However, this requires high fidelity material modeling accounting for the plastic strains in the metals, mismatched thermal shrinkage and property changes experienced as the glass solidifies during cooling of the assembly in manufacturing. Small plastic strains of just a few percent are typical during processing of glass-to-metal seals and yet can generate substantial tensile stresses in the glass during elastic unloading in thermal cycling. Therefore, experimental methods were developed to obtain very accurate measurements of strain near and just beyond the proportional limit. Small strain tensile characterization experiments were conducted with varying levels and rates of strain ratcheting over the temperatures range of -50 to 550 °C, with particular attention near the glass transition temperature of 500 °C. Additional experiments were designed to quantify the effects of stress relaxation and reloading. The experimental techniques developed and resulting data will be presented. Details of constitutive modeling efforts and glass material experiments and modeling can be found in Chambers et al. (Characterization & modeling of materials in glass-to-metal seals: Part I. SAND14-0192. Sandia National Laboratories, January 2014).

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A simple, mode-mixity dependent toughness cohesive zone model (MDG_c CZM) is described. This phenomenological cohesive zone model has two elements. Mode I energy dissipation is defined by a traction–separation relationship that depends only on normal separation. Mode II (III) dissipation is generated by shear yielding and slip in the cohesive surface elements that lie in front of the region where mode I separation (softening) occurs. The nature of predictions made by analyses that use the MDG_c CZM is illustrated by considering the classic problem of an elastic layer loaded by rigid grips. This geometry, which models a thin adhesive bond with a long interfacial edge crack, is similar to that which has been used to measure the dependence of interfacial toughness on crack-tip mode-mixity. The calculated effective toughness vs. applied mode-mixity relationships all display a strong dependence on applied mode-mixity with the effective toughness increasing rapidly with the magnitude of the mode-mixity. The calculated relationships also show a pronounced asymmetry with respect to the applied mode-mixity. As a result, this dependence is similar to that observed experimentally, and calculated results for a glass/epoxy interface are in good agreement with published data that was generated using a test specimen of the same type as analyzed here.

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The material characterization tests conducted on 304L VAR stainless steel and Schott 8061 glass have provided higher fidelity data for calibration of material models used in Glass - T o - Metal (GTM) seal analyses. Specifically, a Thermo - Multi - Linear Elastic Plastic ( thermo - MLEP) material model has be en defined for S S304L and the Simplified Potential Energy Clock nonlinear visc oelastic model has been calibrated for the S8061 glass. To assess the accuracy of finite element stress analyses of GTM seals, a suite of tests are proposed to provide data for comparison to mo del predictions.

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