Dynamic analysis of the response of lateral piezoresistance gauges in shocked ceramics

The ability to quantify the complete stress state in solids subjected to shock wave, uniaxial strain loading, is an important need. Toward this end, the dynamic behavior of lateral piezoresistance gauges embedded in shocked ceramics was examined using two-dimensional, numerical calculations to understand the relationship between the mechanical and piezoresistance response of manganin foils and the sample lateral stresses. The results show that the dynamic mechanical states within and near a lateral gauge deviate significantly from uniaxial strain due to perturbations caused by gauge emplacement including the presence of epoxy bonds. The dynamic response of the gauge represents a coupling of the sample material response and gauge emplacement details. In general, direct time-resolved inference of the sample lateral stress from the lateral gauge data, using simple assumptions about the gauge mechanical state, is not meaningful. A rigorous interpretation of the lateral gauge data requires the use of two- or three-dimensional computations. However, the present results show that for an assumed time-independent sample response, the equilibrium gauge response (corresponding to a constant state) is a good measure of the far-field, lateral stress in the shocked sample. Hence, lateral gauge data can be analyzed to provide sample lateral stresses with reasonable accuracy in particular situations. Given the importance of determining lateral stresses in shocked solids, various issues related to the use of lateral piezoresistance gauges including the limitations in extrapolating the present results are discussed.