On the Effects of Elastic Nonlinearity in Metals

The variation in Young’s modulus and Poisson’s ratio of metals during uniaxial deformation is examined. Predictions are made on the basis of a nonlinear description of the constitutive relation between stress and strain involving both second- and third-order elastic constants. A comparison of measured and predicted variations shows good agreement, with the relative change in Young’s modulus being on the order of 10 times the elastic strain for most metals. The material nonlinearity is then examined as a possible cause for changes in the natural frequency of a beam subject to an axial residual stress. An upper bound for the frequency change involving the maximum stress, initial Young’s modulus and a nonlinearity parameter is derived.