Nonlinear standing waves for assessing material nonlinearity in thin samples

The second harmonic generation (SHG) technique offers a quantitative damage parameter known as the acoustic nonlinearity parameter (β) capable of detecting the change in the inherent material nonlinearity. However, current SHG methods, in particular, those used for measuring β in construction materials, have an unresolved issue in their application due to limited sample sizes. The restricted sample dimensions lead to the generation of boundary-reflected waves, which hinder the selective detection of propagating waves and thus the precise evaluation of material nonlinearity through β. Furthermore, the use of large samples limits the compatibility of the SHG method with other characterization modalities, such as mechanical tests, X-ray diffraction, and computerized tomography. To address this issue, this paper introduces a new SHG method that is based on the use of nonlinear standing waves - the dominant longitudinal standing waves in a forced-free configuration. The corrections for phase delay and attenuation effect of each reflected wave are made, enabling accurate measurements of β in thin samples with no requirement in the thickness-wavelength ratio. The measured β is then employed to quantify the microstructural modification in cement paste induced by thermal damage, validating the proposed method as a promising tool for quantifying microstructural changes in materials.