Evaluation of inherent and dislocation induced material nonlinearity in metallic plates using Lamb waves

Abstract

Previous studies carried out for quantifying the material nonlinearity of plate materials have used a nonlinearity parameter β which is derived for longitudinal waves. When Lamb waves are used as the probing waves, a relative nonlinearity parameter β′ is used. This relative nonlinearity parameter β′ is a non dimensionless parameter and gives the relative estimate of the material nonlinearity. In spite of these shortcomings, β′ is widely used for quantifying the material nonlinearity using Lamb waves. Therefore, in the present study, firstly a physics based equation giving the nonlinearity parameter γphy in terms of higher order elastic constants is derived considering the Lamb wave motion. The parameter γphy gives an actual estimate of the material nonlinearity. This equation has its elastic componentγe resulting from the lattice anharmonicity and plastic component γp resulting from the dislocations formed during fatigue or elastoplastic loading of the plate material. Secondly, a novel equation is derived to estimate the material nonlinearity γamp, which uses the amplitudes of the fundamental harmonic and second harmonic of Lamb waves generated because of the material nonlinearity. With the help of this equation, the actual inherent material nonlinearity can be estimated and it can also be used to quantify the density of dislocations once the amplitudes of the fundamental and second harmonics of Lamb waves in a specimen are made available from the experiments or simulation. Therefore, this equation is practically useful. In order to validate the model, a literature based experimental verification is used here. In the first part, the inherent material nonlinearities of two different materials are estimated and values of β′ and γamp are compared qualitatively and quantitatively. In the second part, the density of dislocations is quantified using γp as well as γp/γe. The agreement of results among γamp and γphy for virgin as well as plastically loaded specimens, confirms the validity of the proposed models.