| In microelectronic and microelectromechanical systems, flexural loading techniques are used both for mechanically testing brittle semiconductor materials and for actuating components fabricated from these materials. For proper component design, precise knowledge of a specimen's flexural rigidity and use of the proper constitutive equations are necessary. In general usage, beam and plate components are distinguished on dimensions alone. In mechanics, however, beams and plates are differentiated based on their flexural rigidity and stress state. Since current textbooks do not provide a quantitative technique for differentiating between these two types of structures, we suggest the extension of an analysis for isotropic materials originated by Searle [1] in 1908 and expanded on by Ashwell [2] in 1950. We report X-ray microdiffraction curvature measurements of a rectangular, constant cross section (100)-type Si single crystal loaded in four-point bending and provide experimental verification of a procedure for differentiating between anisotropic, elastically bent beams and plates. We demonstrate that, by varying the degree of bending of an anisotropic strip, a single specimen can behave as both a beam and a plate.; In four-point bending, the rollers that are used for load application impose additional constraints on the specimen that affect the anticlastic specimen curvature and cause the specimen displacement and stress profiles to deviate from the pure beam bending case. We quantify the amount of roller constraint and show that the region over which the anticlastic specimen curvature is affected away from the roller is approximately five times the roller diameter. Consequently, for bending tests used to determine Poisson's ratio, if a region on the sample that is free from roller effects is not chosen, measurement errors as high as 46% can occur. Furthermore, we show that, due to the anisotropy of single crystal Si, this roller-constraining effect is more pronounced when the principal bending axis lies along the <100> direction as compared with the <110> direction. |
