The elasto-plastic response of lateral piezoresistance gauges in shock wave studies

Abstract

One of the most important issues in shock-wave research is that of the exact determination of the lateral stresses in shock-loaded solids. This component of the stress tensor enables one to determine the shear strength of the loaded specimen (τ) by using the well-known relation 2τ = σ 1 - σ 2 where σ 1 and σ 2 are the longitudinal and lateral stresses, respectively (Bernstein, D., Godfrey, C., Klein, C. & Shimin, A., Research on manganin pressure transducers. In Behaviour of Dense Media under High Dynamic Pressures. Gordon and Breech, NY, USA, 1968, pp. 461-8). The only direct techniques to measure the lateral stress, in one-dimensional shock studies, is with piezoresistance gauges embedded in the specimen in such a way that its plane is perpendicular to the shock propagation direction. The present paper reviews some of the recent developments of this technique, with particular attention to the issue of the relation between the elasto-plastic properties of the gauge material and its response to the stress field. We derive analytical expression for the critical stresses, in the matrix, which mark the onset of yielding of the lateral gauge. These are important in analyzing the response of the lateral gauge in order to derive the exact value of the measured lateral stress.