Cheng, J., Potter, J.N., and Drinkwater, B.W., (2018) The Parallel-Sequential Field Subtraction Technique for Coherent Nonlinear Ultrasonic Imaging, Smart Materials and Structures, 27, 065002.
We show a new technique for imaging nonlinearities in engineering structures, e.g. aircraft wings or nuclear reactor pressure vessels. This is useful as defect-free structures are highly linear whereas defects, such as cracks, are nonlinear. So the concept is, if you can make an image the nonlinearities you will see the defects. The problem is that the nonlinearities are very small, often too small to be seen with current methods – that’s the problem this paper tries to solve. Here we form a nonlinear image from the difference between two classic imaging techniques, the so called parallel and sequential images. Parallel imaging is also known as beamforming and a array is used to produce a focus at the imaging point. In sequential imaging the array elements are fired one after the other (in a sequence) and the image formed on a computer by post-processing. The key is that if the structure is linear, these images would be identical. That is because in linear systems theory, superposition holds and so firing all the elements together is just the same as adding up the individual firings. The difference between these two images tells you where any nonlinearities are how nonlinear the structure is. An important detail is that we show how you can compensate for small instrument nonlinearities to produce even clearer nonlinear images. We then use this new technique to image small fatigue cracks. The tip of the crack is seen to be the most nonlinear part and can be tracked as the crack grows. We observe that this crack can first be seen when it reaches a length of 350 µm, corresponding to about 15% of the fatigue life of the structure. This early detection could lead to safety improvements and cost reductions in industry.
The image below shows the nonlinearity from a fatigue crack and how it, first increases in intensity, and then moves as the crack grows, following the crack tip.