Simulating the ultrasonic scattering from complex surface-breaking defects with a three-dimensional hybrid model

Abstract

Modelling is increasingly relied upon for the design and qualification of ultrasonic inspections applied to safety-critical components. Numerical methods enable the simulation of the ultrasonic interaction with realistic defect morphologies; however, the computational requirements often limit their deployment. The hybrid simulation technique, which combines semi-analytical and numerical methods, realises the potential of high fidelity numerical modelling without the limiting computational factors. The inspection of thick section components for near-backwall surface-breaking defects results in large propagation distances across, making them a key application of hybrid modelling. This work presents a methodology for efficiently simulating the ultrasonic inspection of complex surface-breaking defects using a hybrid model. The model is initially verified against full numerical simulation; further validation is presented by comparison to an experimental scan over an artificially machined surface-breaking notch. The potential of the new hybrid method is then demonstrated by carrying out a Monte Carlo analysis on the scattered field from surfacebreaking defects with randomly rough surfaces and the results are compared to the Kirchhoff approximation.

Elastic shear wave scattering by randomly rough surfaces

“…It can be seen from equations (14), (15) that the surface slopes are approximated as constants for given incident/scattering angles, wave-types and material properties. The number of times a constant line intersects the actual slope values for a specific rough surface indicates the number of specular points, and the quality of the approximation, as illustrated in Figure 3.…”

“…The surface itself is shown by the solid curve, and for illustrative purposes, the first order approximation to its slope by the dashed curve. For a specific frequency and scattered angle, (15) determines the constant which is used by the stationary phase method to approximate the slope. We have added a straight line at this value to Figure 3 to indicate the number of points on the surface for which the stationary phase constant coincides with the real slope values.…”

“…It may seem counter-intuitive that the effect of critical angle arises only for S-S waves in the stationary phase approach, not the S-P case. Equations 14, (15) provide the explanation, since the approximation to the normal substituted into (12)-(13) depends on the ratio A αβ /C αβ , and for S-P waves, this ratio is above the threshold for all values of θ s . However, for the S-S case, for θ s > 2α crit − θ i , the ratio A αβ /C αβ becomes sufficiently negative such that the local normal approximation enforces surface wave mode-conversion of the S-P wave.…”

“…In Figure 4 From a practical point of view, the impact of the critical angle on the stationary phase approach for shear wave incidence is negligible for ultrasonic inspection of defects, since the preferred choices of incident angle, for example θ i = 45 • [15,26], are selected with the critical angle in mind. As stated by [15], it is common to operate within the range 32 • < θ i < 58 • for angled shear wave pulse-echo contact inspection set-ups [26], since it is beyond the first critical angle for steel such that only shear waves propagate within the component under inspection. Other important set-ups are designed for head-on incidence with respect to the defect surface, i.e.…”

“…The extension of the same statistical approach [8] to shear wave incidence is far from straightforward, but critical for practical NDE applications [14,15]. Firstly, the range of validity of KA is much smaller for shear, rather than longitudinal, wave incidence as explained by [16].…”