Measurement of Principal Residual Stresses in a Plate When Their Directions Are Unknown

Abstract

There are several methods to measure mechanically residual stresses in simple shaped objects such as flat plates, cylinders (solid or hollow) and shells. In all these cases, directions of principal stresses are already known and coincide with those of geometrical axes of the bodies. The author has published the Deflection Method to measure the two principal residual stresses in a plate and has given an analytical formula to calculate them by solving the integral equation. In general, there are some cases where the directions of the principal residual stresses are unknown and their directions and values should be determined. In this report, the author proposes an analytical formula to find out unknown directions and values of principal residual stresses existing in plates by applying the relations of elasticity in plate bending to his Deflection Method and shows examples of measurements in rolled band saw strips.