Quantitative flaw sizing is an active research topic in the ultrasonic nondestructive evaluation (NDE) community because of important implications in mechanical and materials engineering. In the past few decades, methods such as the -6 dB drop, distance-amplitude-correction (DAC), and time-of-flight diffraction (TOFD) method, have been used to estimate the flaw size. However, these methods always break down when the flaw size is smaller than the natural diffraction limit or half of the ultrasonic wavelength (l/2). One of the reasons is that the sizing for a flaw with sub-wavelength dimension is often affected by the ultrasonic grain noise. The adverse effect of ultrasonic grain noise leads to inherent uncertainty for sub-wavelength flaw sizing, which cannot be ignored.

In this work, a framework for estimating the size and uncertainty of sub-wavelength flaws is built with statistics- and physics-based models. On one hand, three kinds of statistical models are used here. The envelope amplitude of grain noise is governed by the Rayleigh distribution, and the envelope amplitude of the coherent response generated by the grain noise and the noise free flaw echo is represented by the Rician distribution. Since, a new distribution of the noise free flaw echo can be solved by the Rayleigh distribution and Rician distribution inversely.

On the other hand, two kinds of physical models are also used here, including the diffuse ultrasonic backscatter model and the ultrasonic measurement model. The diffuse ultrasonic backscatter model is used to quantify the ultrasonic grain noise level in polycrystalline materials. Specifically, the spatial standard deviation of the grain noise is predicted by the theory, and it is substituted into the Rayleigh distribution. Moreover, the ultrasonic measurement model is used to correlate each possible amplitude of noise free flaw echo with the equivalent flaw size, where the far-field flaw scattering amplitude is given by the method of separation of variables (SOV).

Finally, to validate this framework, a stainless steel specimen is designed and manufactured with side-drilled holes of diameter 0.2 mm and different depths, and the sizes and their uncertainties are estimated by the present method. This framework provides the mathematical basis for investigating the effects of grain noise on the sub-wavelength flaw sizing.


The Effects of Ultrasonic Grain Noise on the Sub-Wavelength Flaw Sizing

No proceedings papers in 2020. Video only.

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