Nonlinear non-collinear ultrasonic detection and characterisation of kissing bonds

Abstract The development of cost effective and reliable bonded structures ideally requires an NDT method to detect the presence of poor quality, weak bonds or kissing bonds. If these bonds are more compliant in tension than in compression stress-strain nonlinearities provide a possible route to detection with the use of nonlinear ultrasonic techniques. This paper focuses on the kissing bond case and the resulting contact acoustic nonlinearity of the interface. A kissing bond is created by compression loading of two aluminium blocks. Non-collinear mixing of two shear waves producing a sum frequency longitudinal wave is the method of stimulation of contact acoustic nonlinearity in this research. The parametric space of the nonlinear mixing is measured in terms of interaction angle of the input beams and the ratio of their frequencies creating a ‘fingerprint’ of the sample's bulk and interface properties in the region where the beams overlap. The scattering fingerprint of a classically nonlinear solid is modelled analytically and a kissing interface is modelled numerically; these results are compared with experimentally measured values. The experimental interface is tested with varied interfacial loading, resulting in an increase in scattering amplitude as load is increased. Secondary peaks in the parameter space also appeared as loading increased, as well as other changes in the fingerprint pattern.

the interface which together produce plane waves. Another difference be-48 tween bulk and CAN mixing is that the latter produces scattered beams in 49 both directions from the interface (12; 13). This can be thought of as being  To investigate the parameter space efficiently a computer-controlled, mo-106 torised rig was developed. The angle of each transducer is independently set, 107 their lateral separation can also be controlled, allowing a constant interac-108 tion depth to be maintained with varying interaction angle. This is shown 109 schematically in Figure 1 (a). The sample was mounted below the trans-110 ducers, with an ultrasonic phased array below it in contact with its bottom 111 surface. An array was used because as the frequency ratio is changed so is 112 the scattering angle of the produced beam. The scattering angle for bulk 113 mixing can be predicted by using the relevant equation from Table 1 of (8). 114 The 40 mm length of the array was enough to capture the signal of interest 115 in nearly all cases within the desired parameter space. The assembly was 116 placed in a water tank, submerging the input transducers, sample, and ar-117 ray to minimise the coupling variation. The temperature of the water was      that the experiment can be designed to include these ranges.

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Knowledge of the experimental geometry, apparatus, and processing tech-  . .
Where K and µ are the compression and shear moduli respectively, A, where φ is the interaction angle, c is the velocity ratio between transverse

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The most useful trends in the fingerprints appear to occur in the inter-496 action angle dimension therefore further testing was conducted at a single 497 frequency ratio, 0.9. This was selected as it was near the peak response

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The former is to allow for absolute amplitude trends to be compared and the 505 latter for comparison of fingerprint shapes. increased. This plot also shows that there was an overall trend of increased 520 28 scattering with each loading cycle. This can be explained by the fact that the interface was never fully unloaded during these cycles, each bolt was unloaded 522 from 40 Nm and re-tightened to 10 Nm in turn, keeping the faces in constant 523 contact. This method was intended to stop the faces moving relative to each 524 other between each cycle, keeping the same parts of the interface in contact.

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Due to this it is expected that the surface asperities will gradually deform 526 to match each other with each cycle, increasing the contact between the two 527 faces and thus the transmission.

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Despite the many differences in the parameter space at various loads it 529 is notable how similar the trends are when peak normalised, as shown in 530 Figure 9 (b). The shape produced is very different from the solid sample 531 response demonstrating the potential of this technique to identify the pres-532 ence of kissing bonds at a range of loads. There are also many subtle trends 533 visible in this normalised data; firstly, as torque is increased from 10 Nm 534 to 30 Nm the 100 • feature becomes more pronounced, but it is unchanged 535 when further increased to 40 Nm. Secondly, there is a notable lack of change 536 in the relative amplitudes of scattering seen at 76 • and 120 • . It might be 537 expected that these areas should respond differently to increased interface 538 load if the former is due to CAN and the latter classical bulk nonlinearities.

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If it is assumed that half the interaction volume is above the interface and where S i is the predicted classical signal amplitude from the interface 546 sample, and S s is the signal from a solid sample. As loading is increased

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The normalised data in Figure 10  of the sample were conducted, these showed even smaller variation than seen 610 above, leading to the conclusion that positioning of the sample is the primary 611 cause of the slight variation observed in '40Nm b' trends in Figure 10 (b).

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The impact of positioning is explored in the following section.   are similar to those observed as load was varied in Figure 9, such as peak 651 shifting, but others are quite different, e.g. the large peak width changes.

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This implies that the shape of the response must be related to more than just