Spatial profiles as an input

PZFlex can input its excitation signals to the model in different ways; it can either be used to model piezoelectric probes with voltage inputs to piezoelectric materials as is used in probe design, or use a pressure to excite the face of an element of the mesh in order to mimic the forces produced by a transducer, known as pressure

loading. This causes the element to distort and transmit the forces onto the next element and so on, allowing the disturbance to propagate through the material as it would in the experimental case.

Here the probes used were PPM EMATs, (the structure of which was shown in Chapter 2) to generate an alternating shearing force in an orthogonal direction to that of the propagation direction of the wave. It was also shown previously that the waves are generated in the skin depth of the sample, and that in the steel samples that will be considered, this means that the forces generated by the transducer can be approximated as forces on the surface. Therefore in generating the shear horizontal forces here, the pressure loading to generate the desired guided wave will be an alternating pressure load on the surface elements of the sample. The pressure loading will be provided by a tone burst signal that is modulated by this spatial profile along a length that is matched to the size of the experimental transducer.

Getting a representative distribution of these forces on the surface of a sample is the key to generating the modes with spatial and frequency bandwidths that are similar to that seen in experiment. This works well in a plate sample where the number of elements on the flat surface for the given length of the transducer on the surface is more than adequate to provide a representation of the probe, even with a low mesh density. However, when the same forces are desired to be used on the surface of the pipe, the profile must be adjusted to account for the fact there are less element faces directly facing out from the sample, which means less faces onto which the forces can be directly applied.

The effect of this is that in order to obtain the same quality of results as the flat plate case in terms of narrowing the spatial bandwidth that is produced, the number of elements per wavelength for the pipe must be greater in order to provide a surface that is more realistic. This is an example where the propagation of the ultrasound in the sample is not limited by the size of the elements in terms of being small enough to represent a material but in the ability to apply the force profile effectively on the surface. The disadvantage of the increase in the number of elements per wavelength required is that the computational load of the model increases as well as the processing time. A new pattern of the respective amplitude of forces on the surface is then necessary in order to produce a nominal wavelength that is comparable to the experimental probe. This is separate but connected to the issue that arises from trying to generate a curved surface with cubic elements in that the number of elements representing the surface must be large enough in the first place to give a good representation of the curved surface geometrically. It must then have enough elements representing the surface for the force profile to be

generated on the surface with enough points of operation to suitably represent the forces that are seen experimentally.

Figure 4.4: Illustration of how the spatial profile of the probe is applied to the excitation signal in order to generate signals of the correct relative amplitude and the application of these signals to the relevant elements in the mesh of the finite element model with a curved surface.

The practical application of this concept is illustrated in Figure 4.4. Here the spatial profile that determines the amplitude of the forces on the surface of the sample is used to modulate the excitation signal that is input by the pulser system, this is done for every element under the active area of the transducer, so that the effect on the surface is a periodic series of excitation points with the amplitude of the excitation signal at each point different. The number of points in the profile is adjusted to match the number of elements in the mesh on which the forces can be applied in order to effectively apply the forces on the surface that approximate the transducer forces. Figure 4.4 shows a simplified version of this with only a few forces and elements selected, the full application would consider forces applied at every element on the surface.

that will be considered from these simulations is the velocity of the nodes in the direction of the shearing forces, so that an approximation of the velocities detected by the receiver can be achieved. In order to ensure that the simulation matches the experiment as much as possible, this value is taken from the surface elements of the pipe that approximate the size of the transducer used in the transmission. These outputs are then modulated by the spatial profile of the transducer in the same way as the signals were generated for the transmitter and an average over the area of the transducer taken in order to mimic the reception mechanism over the entire footprint of the transducer. This should give the best approximation of the generation and reception mechanisms that take place due to the forces in the material that are induced by the interaction of the electric and magnetic fields that the transducer generates.

In much of the work here, the model was used in two dimensions to approx- imate the wave interaction with defects. Two dimensions were used to limit the computational load and calculation time of the model. This approach is taken to be valid because the defects of interest are often of a scale that is larger than the transducer, such that the two dimensional model is representative of the propaga- tion through a defect. This means that the effect of a transducer being entirely over a defect in the axial direction will be effectively modelled by having a defect in two dimensions blocking the passage of the ultrasound around the pipe circumference. This will clearly give no axial information on sizing of defects as the scanning rig travels along the pipeline, but can be used to accurately model the interaction of the ultrasound with defects and reflection from defects in the circumferential direction around the pipeline.

From this basis of the finite element theory and its application to the situation that is presented in this study, it should be possible to model the interaction of the SH guided wave ultrasound with defects as the waves travel circumferentially around the sample. This should be comparable with the experimental situation in terms of the proportions of the different modes that are generated and should give a facility to assess the signals that are seen experimentally by knowing how they are generated and behave in the simulation.