Out-of-Plane Displacement Derivative Measurements Using Interferometric Strain/Slope Gage

Abstract

An optical method originally developed for measuring derivatives of in-plane displacements is redefined to measure derivatives of out-of-plane displacements. The technique is based on interference of laser beams reflected and diffracted from two microindentations closely depressed on a specimen surface. As in-plane and out-of-plane displacements cause the microindentations to move relatively to each other, the two interference fringe patterns change accordingly. Movement of the interference fringes is monitored with linear photodiode arrays and analyzed via a computer-controlled system that allows simultaneous measurements of the in-plane and out-of-plane displacement derivatives. The technique is referred to as the interferometric strain/slope gage (ISSG). Having short gage length (̃100 μm), the technique is unique for measurements of high deformation gradients and for applications in complex geometries. Its principle as well as an experimental validation of measuring bending strains/stresses and deflection slopes in a cantilever beam is presented. The experiment shows that both the first-order and second-order derivatives of out-of-plane displacements can be obtained. Measurement sensitivities to in-plane and out-of-plane rigid-body motions are systematically investigated. The technique can be potentially extended to measure large deflection angles. The derived governing equations indicate a coupling effect between the in-plane and out-of-plane components. The associated instrumentation for data acquisition and analysis is described in great detail.