The limits of classical beam theory for bent strip residual stress measurements in plated metals

Abstract

The bent strip method is often used for determining residual stresses in electroless nickel deposits for infrared mirror applications. In an earlier work the author derived the correct linear stress-strain relations for measuring residual stresses in plated metals using the bent strip method. However, the question of when bent strip specimen deflections become so large that the linear theory is no longer valid has never been clearly addressed. In this work, a preliminary analysis on the limits of the classical linear theory is carried out, and it is shown that the rotation angle in bending can be used as a good first order estimate of the linear limit. The relations between specimen bow out height and rotation angle for the bent strip method are derived, and numerical results are given for electroless nickel plated on brass, aluminum, and other mirror substrate materials.