Analytical elasto-creep model of interfacial thermal stresses and strains in trilayer assemblies |
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Authors: | Hamid R Ghorbani Jan K Spelt |
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Institution: | aDepartment of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ont., Canada M5S 3G8 |
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Abstract: | A two-dimensional model has been developed for thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of short and long trilayer assemblies under both plane stress and plane strain conditions. Both linear (viscous) and non-linear creep constitutive behavior under static and cyclic thermal loading can be modeled for all layers. Interfacial stresses and strains are approximated using a combination of exact elasticity solutions and elementary strength of materials theories. Partial differential equations are linearized through a simple finite difference discretization procedure. The approach is mathematically straightforward and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The model can provide input data for thermal fatigue life prediction in solder or adhesive joints. For a typical solder joint, it is demonstrated that the predicted cyclic stress–strain hysteresis shows shakedown and a rapid stabilization of the creep energy dissipation per cycle in agreement with the predictions of finite element analysis. |
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Keywords: | Trilayer Layered beam Laminated Interfacial stress Creep Viscoelastic Strain energy Thermal cycling Hysteresis Ratcheting Shakedown Thermal stress Thermal strain Adhesive bond Solder joint Stress singularity |
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