Flexural loading of rectangular Si beams and plates

We review a quantitative criterion for differentiating between anisotropic, elastically bent beams and plates and provide experimental verification of this criterion through X-ray microdiffraction curvature measurements of a (1 0 0)-type Si single crystal loaded in four-point bending. In this analysis, beams and plates are differentiated through their flexural rigidity and stress state, which depend not only on specimen shape, but also on the amount of bending. In addition, we analyze the techniques used to apply flexural loads and show that the rollers that are used for load application impose additional constraints on the specimen, which cause the displacement and stress profiles to deviate from the ideal beam bending case. We quantify the amount of roller constraint using microdiffraction and show that the region over which the anticlastic specimen curvature is affected away from the roller is approximately five times the roller diameter. Due to the anisotropy of single crystal Si, this roller-constraining effect also depends on crystallographic orientation and is more pronounced when the principal bending axis lies along the 〈1 0 0〉 direction as compared with the 〈1 1 0〉 direction.