Biaxial flexure tests have been used extensively for the strength measurements of monolithic brittle materials. However, despite the increasing applications of multilayered structures, characterization of their strengths using biaxial flexure tests is unavailable. This is because the analytical description of the relation between the strength and the fracture load for multilayers subjected to biaxial flexure tests is nonexistent. To characterize the biaxial strength of multilayers, an analytical model is developed in the present study to derive the general closed-form solutions for the elastic stress distributions in thin multilayered disks subjected to biaxial flexure tests. To verify the analytical solutions, finite element analyses are performed on trilayered disks subjected to ring-on-ring tests. Good agreement is obtained between analytical and numerical results. The present closed-form solutions hence provide a basis for evaluating the biaxial strength of multilayered systems. Depending upon the strength of the individual layers and the stress distribution through the thickness of the multilayer during testing, cracking can initiate from any layer under tension.
Thermal stress-induced damage in multilayered films formed on substrates and cantilever beams is a major reliability issue for the fabrication and application of micro sensors and actuators. Using closed-form predictive solutions for thermal stresses in multilayered systems, specific results are calculated for the thermal stresses in PZT/Pt/Ti/SiO2/Si3N4/SiO2 film layers on Si substrates and PZT/Pt/Ti/SiO2 film layers on Si3N4 cantilever beams. When the thickness of the film layer is negligible compared to the substrate, thermal stresses in each film layer are controlled by the thermomechanical mismatch between the individual film layer and the substrate, and the modification of thermal stresses in each film layer by the presence of other film layers is insignificant. On the other hand, when the thickness of the film layer is not negligible compared to the cantilever beam, thermal stresses in each film layer can be controlled by adjusting the properties and thickness of each layer. The closed-form solutions provide guidelines for designing multilayered systems with improved reliability.
Stresses normal to interfaces, i.e., interfacial peeling stresses and interfacial shear stresses, exist locally at edges of multilayers because of both the thermal mismatch between layers and the free-edge effect. These peeling and shear stresses can result in modes I and II edge delamination, respectively. However, because of the complexity of the problem, exact closed-form solutions for these stresses are very difficult if not impossible to derive even for bilayered systems. Hence, instead of the detailed stress field at edges, both the interfacial peeling moment resulting from the localized peeling stresses and the interfacial shear force resulting from the localized shear stresses are analyzed here. Exact closed-form solutions for the peeling moment and the shear force at each interface in elastic multilayered systems are derived. To illustrate the application of present closed-form solutions, specific results are calculated for five-layered thermal barrier coating systems, and a finite-element analysis is also performed to confirm the analytical results.
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