A simple non-local modified beam model is presented to evaluate interfacial thermal stresses in bimaterial elastic beams. The model has its root in an earlier model (Suhir 1986) which assumes that the longitudinal interfacial displacement at a point depends on the interfacial shear stress at that point. Different than that earlier local model, however, the present non-local model assumes that the longitudinal interfacial displacement at a point also depends on the second gradient of the interfacial shear stress at that point. The present model satisfies both the zero-longitudinal force and the zero-shear stress boundary conditions at the free edges, and the interfacial peeling stress given by the present model is self-equilibrated. Remarkably, the present model leads to a fourth-order differential equation for the interfacial shear stress, and is considerably simpler than other known modified beam models satisfying the abovementioned conditions. This desirable feature of the present model is believed to be significant especially when the model is applied to multilayered materials. In particular, the interfacial shear stress given by the present model is found to be in reasonably good agreement with some known numerical results.
Interfacial Thermal Stresses in Bimaterial Elastic Beams: Modified Beam Models Revisited
Contributed by the Electronic and Photonic Packaging Division for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received at ASME Headquarters October 14, 2001. Associate Editor: B. Michel.
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Ru, C. Q. (July 26, 2002). "Interfacial Thermal Stresses in Bimaterial Elastic Beams: Modified Beam Models Revisited ." ASME. J. Electron. Packag. September 2002; 124(3): 141–146. https://doi.org/10.1115/1.1481037
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