Determination of compressive residual stress in a doubly-clamped microbeam according to its buckled shape

In this work, an analytical relationship is derived for a doubly-clamped microbeam when it buckles after release from the substrate. In terms of the relationship, compressive residual stress in the doubly-clamped microbeam can be determined according to its buckled shape, allowing one to find the compressive residual stress directly without much experimental effort. This relationship has been used to determine compressive residual stresses in four types of doubly-clamped SiO2 microbeams. In addition, four methods have been applied to find the elongations of these SiO2 microbeams, and the corresponding results are compared. Finally, the residual stresses in doubly-clamped SiO2 microbeams predicted according to the derived relationship are compared with those found in SiO2 microcantilevers, and the results have a good match.