Modeling Ultrasonic Array Response of Real Cracks


Stress corrosion cracks can be a serious problem in many engineering industries, and especially so for critical parts. While an ultrasonic transducer can be used for the non-destructive evaluation of cracks with simple shapes, complex branching cracks, such as stress corrosion cracks, require ultrasonic arrays that consist of multiple transducers and are able to inspect at multiple angles. This project involved optimising an ultrasonic array design using real stress corrosion crack shapes obtained with X-ray CT scans and a hybrid model for simulating complex ultrasonic array responses. The model combined a finite element (FE) method with simple ray tracing. Simpleware software was used to obtain the crack geometry from X-ray CT data, contributing towards an overall methodology for improving future ultrasonic NDE of cracks.


  • Material sample scanned using X-Ray CT (X-Tek BladeRunner, Nikon Metrology)
  • Crack geometry extracted and processed in Simpleware ScanIP
  • Hybrid model, which includes efficient FE method, used to simulate ultrasonic array response
  • Hybrid model implemented in MATLAB®


Felice, M.V., Velichko, A., Wilcox, P.D., Barden, T., Dunhill, T., 2014. Obtaining geometries of real cracks and using an efficient finite element method to simulate their ultrasonic array responseInsight - Non-Destructive Testing and Condition Monitoring, (56)9, 492-498.

Thanks to


Illustrations first appeared in the paper referenced on the left, and are published here with the kind permission of The British Institute of Non-Destructive Testing and the authors.

Image Acquisition and Segmentation

Fluorescent dye penetrant inspection was used to locate a selection of cracks in a set of samples. The material around each crack was then cut away and the sample was imaged using an X-Tek BladeRunner system (Nikon Metrology).

The crack geometry was extracted from the X-Ray CT images using Simpleware ScanIP, with filtering and thresholding tools, primarily the 'Paint with Threshold' tool, used to obtain regions of interest.

Ultrasonic Scattering Simulation

The Kirchhoff Approximation and an efficient frequency-domain FE method were compared to determine the best solution for simulating ultrasonic scattering. The FE method was found to be more accurate for working with complex shapes. A hybrid model was implemented in MATLAB® combining the FE method with simple ray tracing to simulate the ultrasonic array response.

Full matrix capture (FMC) data was simulated and the hybrid model was validated against experimental results, with good agreement found between the two. The hybrid model was then used to simulate array data from the real crack geometries.


Simulation of the ultrasonic array response from real corrosion crack geometries was successfully performed. The project demonstrates the potential for optimising array designs with different parameters by using an efficient simulation-assisted approach. While simulations were carried out in 2D, the same methodology works for 3D modelling, and has applications to varied types of stress corrosion cracks and any straight or branched cracking issues.

This method therefore has the potential to reduce costs and improve accuracy in scenarios where a reliable and bespoke ultrasonic array is needed for non-destructive evaluation of cracks.