Metallic structures are used in many applications such as aerospace, transport, and nuclear industries. Assessment of their quality before putting them into application and during their service life is important as far as safety is concerned. Identifying damages and life estimation of such structures is a common intention of such assessments; however, it is also required to check the dissolved or undissolved impurities in their material or in general to characterize the material with respect to its intact state. The information about these features of the material can be obtained using ultrasonic waves. The ultrasonic waves propagating through such material produce additional wave components with frequencies multiple of the excitation frequency called as higher harmonics. The higher harmonics generation takes place in waves because of the material nonlinearity, classified as the classical nonlinearity. The classical nonlinearity is induced in an intact state material through lattice anharmonicity, which is generally represented by the higher order elastic constants. In the case of fatigued, impacted or plastically deformed materials, the nonlinearity is further enhanced by the formation of dislocation dipole and monopole substructures.

In literature, to quantify the material nonlinearity using Lamb or Rayleigh waves, relative nonlinearity parameters (RNP) are used. These parameters are deduced from a true nonlinearity parameter (TNP) derived for longitudinal waves. Thus, the estimate of the material nonlinearity, when Lamb or Rayleigh waves are used as probing waves, with the RNP is not appropriate, as it is does not capture the physics of the waves for which it is used. Thus, two new nonlinearity parameters based on Lamb and Rayleigh wave propagation, γ_amp and δ^R respectively, are developed which can evaluate the true value of material nonlinearity embedded in the metallic planar and elongated structures, wherein the classical nonlinearity is dominant. These parameters are quite different than the conventional nonlinearity parameter β', that measures only the relative value of material nonlinearity. The parameters γ_amp and δ^R are derived in terms of the amplitudes of fundamental and second harmonics propagating within the respective waves. These harmonics are generated in the material as a result of lattice anharmonicity at the intact state and dislocations at the damaged state due to the external loading. Thus, these harmonics carry the information of the nonlinearity of the medium. In addition, a physics-based nonlinearity parameter γ_phy is also developed that can evaluate the material nonlinearity using the higher order elastic and plastic constants, and the sub-structural evolution parameters. The parameter γ_phy is independent of the wave propagation distance, and therefore it gives a global estimate of the material nonlinearity. Using the experimental and simulations results, it is found that the true value of material nonlinearity estimated using γ_amp and δ^R at its first peak match well with that of the γ_phy. This first peak is achieved at a distance called Maximum Cumulative Propagation Distance (MCPD). Thus, the material health status can be identified by comparing the value of γ_amp and δ^R at first peak with that of γ_phy.

The extensive numerical simulations are carried out in order to study the effect of various factors such as number of cycles in the tone burst, material model parameters, excitation frequency, and wave propagation distance on the evaluation of the material nonlinearity parameter γ_amp and δ^R. The study shows that the S₀ mode of Lamb wave at low frequency with approximate phase velocity matching can be used to estimate γ^s_amp with a fair accuracy. Practically, this is very helpful but a minimum 40 number of cycles are required in the tone burst in order to give a fair estimate of γ^s_amp. However, this number is 10 when the cumulative effect of S₁-S₂ mode pair is considered. It is also observed that for low excitation frequency, the MCPD is longer compared to higher excitation frequency. It is also observed that the excitation frequency should be selected such that the Cv should be minimum in order to estimate γ^s_amp accurately. The frequency selection is critical as for some frequencies multiple maxima are obtained for γ^s_amp. In this case the value of γ^s_amp corresponding to the first maximum gives the actual value of material nonlinearity. In the case of δ^R, a minimum of 20 tone burst cycles are recommended to give a fair estimate of the material nonlinearity.

The nonlinearity parameter γ^s_amp is further used to quantify the dislocation induced material nonlinearity generated in the thin metallic plate structures as a result of elasto-plastic loading and the remaining useful life of fatigued specimens. It is found that the parameter γ^s_amp increases with increase in dislocation density. In case of fatigue loading, γ_phy was used to estimate the global material nonlinearity as a function of percent fatigue life and to construct a theoretical nonlinearity curve (TNC) in terms of percent fatigue life using the higher order elastic and plastic constants of the material and sub-structural evolution parameters. The TNC plotted using γ_phy serves as a better reference for γ^s_amp obtained through experiments or simulation for a specimen to estimate its RUL in terms of percent fatigue life. The study clearly showed an advantage of using γ_amp^s over the conventional relative nonlinearity parameter β' when Lamb wave are used for estimating RUL. Next, the parameter δ^R was used to evaluate the impact induced nonlinearity in a 1018 steel I-Beam specimen and quantify the corresponding dislocation dipole density. For this purpose, the specimen was impacted with a mass having cylindrical shape from three different heights. The first peak of the nonlinearity parameter δ^R is found to be increasing beyond the intrinsic value, roughly 5%, 17%, and 35%. The trend of the results for dislocation dipole density obtained using the proposed equation are in accordance with the literature.

The parameter δ^R was further used to experimentally evaluate the intrinsic nonlinearity of a macroscopically pristine rail specimen using the non-dispersive Rayleigh waves. The estimation of a critical material property such as the intrinsic nonlinearity and its comparison with γ_phy may help in diagnosing the health status of the macroscopically pristine rail specimens in terms of the level of dissolved impurities and their microstructural consistency, before fixing them on a track. This nonlinear ultrasonic technique is generally sensitive to only lattice-anharmonicity and micro-damages such as the dislocation dipoles and monopoles. However, when these micro-damages reach a certain level of size under the action of a repetitive external loading, they are no longer sensitive to nonlinear ultrasonics. Thus, linear ultrasonics that rely on the measurement of time of arrival of defect reflected wave shall be adopted. This is because, the wave passing through such a defect, neither causes the opening and closing of the defect interfaces, nor cause the wave to change its frequency content. In view of this, a new approach using Self Adaptive and Smart Algorithm (SASA) is developed to locate the surface and sub-surface defects that occur in rail tracks using Rayleigh waves that were emitted and sensed by a fully non-contact laser transduction system. The effectiveness of the proposed approach was tested using extensive experiments conducted on a real rail track in presence of defects on its head and web.