Dynamic three-point bending tests under high loading rates

The theory of dynamic three-point bending tests under high-loading rates is developed for the first time with account for structural vibration. Analytical solutions for dynamic normal (flexural) and shear stresses are derived. To study the dynamic effect, dynamic factors for both types of stresses are defined and investigated by employing a dimensionless characteristic time and a strain rate. It is found that both dynamic factors attenuate with respect to the characteristic time and, therefore, the quasi-static time thresholds and loading conditions are obtained. In addition, the dominant failure mode is studied for potential application in brittle materials in terms of normal-to-shear stress ratio, which is oscillatory in contrast to the quasi-static case. The developed theory is verified with a split Hopkinson bar test together combined with digital image correlation as well as finite-element simulations. The findings of this study can provide a guideline for test design, such as selection of specimen geometry and loading rate. As the theory provides a modal decomposition of dynamic normal and shear stresses, it can also be used in the field of structural health monitoring.