Effects of boundary conditions and anisotropy on elastically bent silicon

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. In this study, x-ray microdiffraction is used to map both the principal and anticlastic curvatures of elastically bent, rectangular (100)-type Si strips possessing width:thickness ratios of 40:1. 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 depends on crystallographic orientation and is more pronounced when the principal bending axis lies along the <100> direction as compared with the <100> direction.