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The importance of modeling  

This article is excerpted from the paper, “The promise of ultrasonic phased arrays and the role of modeling in specifying systems” presented by authors Guillaume Neau, Ph.D. and Deborah Hopkins, Ph.D. at the ASNT Fall Conference & Quality Testing Show held in Houston on October 23 - 27th, 2006. You may download the paper here.

Modeling results obtained using CIVA (developed by the Commissariat à l'Énergie Atomique in France) are used here to illustrate some of the unique features of phased array systems, and to demonstrate how modeling can be used to determine the optimal inspection strategy, which, in turn, can be used to specify the appropriate probe and to determine hardware needs.

Understanding and visualizing the beam radiated in the test specimen

The example discussed in detail here is the use of the same linear-array probe with two different sectorial scanning strategies. In this case, simulation is used to understand and visualize the beam shape, to help the engineer find the optimal inspection procedure. The simulation image shown in Figure 5a is the acoustic beam resulting from firing 7 elements (of a 64-element linear array) with focusing at a distance of 35 mm. The images correspond to the case where the probe is used with a wedge angled at 45° on a steel specimen. The acoustic beam shown in the upper-left image of figure hereafter is from the first shot in a sectorial scan. For subsequent shots, the beam is steered in increments of one degree up to 70 degrees, while maintaining the focal point at a distance of 35 mm (the middle and final shots of the sequence are displayed in the center and lower-left images of Figure 5). What the simulation shows is that the beam is not well focused, meaning that resolution and the ability to size defects will not be optimal with this configuration. In addition, a side lobe is evident (shear wave at 45 degrees), that becomes more and more significant for angles greater than 62 degrees. The creation of side lobes results in signals that are more complicated and generally more difficult to interpret.  

beam steering and focusing using 7 elements of a 64-element probe beam steering and focusing using 16 elements of a 64-element linear array

Radiated beams (shear waves) for 7- and 16-element probe configurations (left and right, respectively). The dots on the images indicate the targeted focal points.  

To improve the inspection, simulations were run using different numbers of elements to optimize the beam in the sample. Recall that the right-hand column of the above figure  shows the ultrasonic beam obtained using 16 elements focused at a fixed distance of 35 mm for each angle in the sectorial scan. By comparing the left- and right-hand columns, it is easy to see that the beam in the second case (left-hand column) is much better focused, which allows detection of smaller defects and improved sizing. Using the -6dB sizing technique, the focal spots can be determined and compared for both cases.

Although this relatively simple case might not warrant a modeling study, the complex geometries encountered in practice, along with physical constraints that limit access, make modeling an extremely valuable tool for determining optimal inspection strategies. For example, in those cases were access to the part is limited, it is very useful to be able to determine the minimum size and number of elements necessary to perform the required measurements. For the case presented here, it is possible to compare the 7- and 32-element configurations to determine the optimal tradeoff between size and detection capability.  

Wave-defect interaction: evaluating the sensitivity of an NDT procedure  

Using CIVA simulation software, it is not only possible to characterize the acoustic field for any phased-array configuration, but it is also possible to determine the sensitivity of the proposed inspection procedure. Even with sophisticated modeling tools there is still a need for calibration experiments, but they can usually be reduced to validation experiments performed on reference specimens (for example, a block with side-drilled holes). The reference test specimens are modeled and the results are compared to experimental measurements. The CEA is continually validating CIVA with experimental data [1], and the results displayed in figure hereafter are an example of how modeling results are validated.  

Wave-defect interaction: comparing simulated and experimental results

Sectorial scans (top images) and dynamic echo curves (graphs below scans). Laboratory measurements are displayed on the left, and the results of the corresponding simulations are shown on the right. Experimental and simulation results are within 1 dB agreement.  

In this case, experimental and simulation results are shown for an aluminum block containing side drilled holes obtained from a focused, sectorial scan using 40 elements of a 64-element Imasonic probe. The sensitivity of proposed inspection protocols is determined by quantifying the defect response in terms of gain compared to the reference case (calibrated defects); i.e., if the gain required to identify the defect is within the dynamic range of the phased-array controller, then it will be possible to detect the defects in question. A series of parametric studies is often carried out, for example, to study the dependence between detectability and the size of the defect, its orientation, and/or its geometry.    

1. Mahaut S., Chatillon S., Kerbrat E., Porre J., Calmon P. and Roy O., “New features for phased array techniques inspections: simulation and experiments”, Proceedings of the WCNDT, 2004.