Experimental Study on the Photoelastic Coefficient and Its Wavelength Dispersion for Quantitative Imaging of Residual Strain in Commercial SiC Substrates

The absolute difference between two photoelastic coefficients \(\left| {p_{11} - p_{12} } \right|\) and its wavelength dispersion have been experimentally studied in commercially available (0001) 4H silicon carbide substrates by using originally developed imaging polariscopes (xIPs) with different light-source wavelengths (\(\lambda\) = 630 nm, 940 nm, and 1200 nm). The simple three-point bending test was adopted to measure the distribution of birefringence \(\left| {\Delta {\text{n}}} \right|\) in a small beam under an external load. Additionally, numerical simulation was performed to accurately estimate the distribution of \(\left| {\sigma_{1} - \sigma_{2} } \right|\) in the beam, even with its size restriction. The value of \(\left| {p_{11} - p_{12} } \right|\) was evaluated by regression analysis on the value pairs of \(\left| {\sigma_{1} - \sigma_{2} } \right|\) and \(\left| {\Delta {\text{n}}} \right|\) examined under various external loads. In order to avoid the effect of residual strain in the sample, the regression analysis was performed at many positions over the sample rather than a few representative points as is adopted conventionally. The value of \(\left| {p_{11} - p_{12} } \right|\) was obtained as 0.040, 0.090 and 0.13 at wavelengths of 630 nm, 940 nm, and 1200 nm, respectively. The wavelength dispersion revealed inverse correlation with photon energy and suggested that \(\left| {p_{11} - p_{12} } \right|\) may become close to zero at a certain wavelength shorter than 630 nm, implying a technical trade-off between the sensitivity of the photoelastic effect and the signal-to-noise ratio in polariscopic photometry, which is useful for considering the optimal wavelength in quantitative strain imaging with photoelastic technique.