Analysis of piezoresistance gauges for stress in divergent flow fields

An analytical procedure is presented for interpreting resistance histories from three piezoresistance gauges in a plane at a ''point'' to uniquely determine the normal stress at that point for nonuniaxial strain loading. The response of the elements can be plastic, and the analysis is valid for unloading and reloading. The only restrictions are that the elements must be aligned with the principal directions of the flow field, and the coupling between matrix strains and gauge strains must be specified. The gauges' piezoresistance properties, constitutive properties, and the coupling relations form a set of highly nonlinear simultaneous equations that can be solved for the normal stress and in-plane strains. A computer program named PIEZOR3 performs this task. Finite-element calculations are used to generate resistance histories from which the original stresses and strains can be computed with PIEZOR3. The computational examples demonstrate the accuracy of the procedure and quantify the uncertainties in the resolved stresses arising from uncertainties in mechanical, piezoresistance, and strain-coupling parameters.