The residual stress distribution in bimaterial beams induced by multiple thermal loadings has been investigated. Three models for the nonlinear stress-strain material behavior were considered: bilinear elastic-plastic, power law elastic-plastic, and power law purely plastic. The equations governing equilibrium, compatibility of strain, and stress-strain for the bimaterial configuration make up a system of nonlinear algebraic equations which is solved numerically. The elastic-plastic power law model leads to stress discontinuity in the layers. The other two models have been verified with a finite element analysis. Several examples are included using materials common to the microelectronics industry.
Residual Stress Analysis of Bimaterial Strips Under Multiple Thermal Loading
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Tierney, J. W., and Eischen, J. W. (December 1, 1997). "Residual Stress Analysis of Bimaterial Strips Under Multiple Thermal Loading." ASME. J. Electron. Packag. December 1997; 119(4): 281–287. https://doi.org/10.1115/1.2792250
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