Fully nondestructive, uncertainty-quantified quantitative imaging of bonding strength at bonded solid–solid interfaces (contact acoustic nonlinearity microscopy)

A 2011 protocol demonstrated that a contact acoustic nonlinearity (CAN) microscope, combined with a model-based inversion and a chain of calibrations, can map the absolute local vertical bonding strength $B_0(x,y)$ at a bonded solid–solid interface. Its quantitative character, however, rests on a destructive tensile pull-off reference strength $B$ calibrated for each adhesive–substrate system, an unquantified calibration chain (the incident focal amplitude $A$ and the receiver transfer function $H(\omega)$), and a demonstration confined to glass specimens, one 5 MHz focusing geometry, and two adhesives. The open problem is to convert this demonstrated-but-qualified protocol into a validated measurement capability: recover spatially resolved absolute bonding strength nondestructively, establishing the absolute strength reference without destructive tensile pull-off calibration, with the absolute accuracy of the recovered strengths demonstrable against independent strength measurements.

Background

Adhesive and diffusion-bonded layered structures are used in safety-critical aerospace, automotive, and composite components, and their load-bearing capacity is set by the mechanical quality of the bonded solid–solid interfaces. Ultrasonic nondestructive evaluation (NDE) readily images gross defects such as voids and disbonds, but the review literature going back to Guyott, Cawley and Adams (1986) has consistently distinguished defect detection from the measurement of bond strength, and the latter has remained outside established NDE capability. Two specialist notions are needed. Contact acoustic nonlinearity (CAN) denotes the strong nonlinearity that arises when an acoustic wave crosses an imperfectly bonded interface: interfacial micro-gaps open and close ("clap") under the wave's oscillatory pressure, so an incident tone of frequency $f$ is partly converted into a second harmonic at $2f$; the relative size of this conversion, commonly summarized by the CAN parameter $A_2/A_1^2$ (second-harmonic amplitude divided by the squared fundamental amplitude), grows with the degree of interfacial imperfection. A kissing bond is an interface that is fully closed and hence nearly invisible to conventional (linear) ultrasound yet transmits little structural load; nonlinear methods are pursued precisely for such weak bonds.

Building on earlier studies of CAN at bonded interfaces, Chen, Zhang, Mao and Cheng developed a CAN microscope protocol culminating in the 2011 paper at issue here. A focusing transducer (a 5 MHz source on a glass lens, coupled through water) scans the interface and a 10 MHz piezoelectric receiver detects the transmitted wave. The interface is modeled by an unbonded area fraction $R$ within the acoustic focal spot, and the local vertical (normal-to-interface) bonding strength is defined as $B_0 = B(1-R)$, where $B$ is the vertical bonding strength of a fully bonded interface of the same adhesive–substrate system. A piecewise waveform model (separating open-crack and closed-crack intervals of the acoustic cycle) links the transmitted waveform, and hence the measurable CAN parameter $A_2/A_1^2$, to $B_0$. To evaluate the inversion, the paper calibrates three ingredients: (i) the incident vibration amplitude $A$ at the buried interface, obtained from a laser-vibrometer measurement (a laser interferometer measuring surface vibration) of the lens-surface amplitude together with a theoretically computed focusing amplification, giving $A = 1.5\times10^{-7}\,\mathrm{m}$; (ii) the receiving transducer's transfer function $H(\omega)$ — the frequency-dependent factor converting the recorded electrical spectral components at 5 and 10 MHz into physical vibration amplitudes — calibrated on a separate transducer of the same model; and (iii) the absolute reference $B$, obtained for each of the two adhesives used (neoprene+Bakelite glue, $B = 99.4$ kg/cm²; epoxy, $B = 201$ kg/cm²) from destructive tensile pull-off tests on separately prepared fully bonded samples. The output is a contour map of $B_0(x,y)$ over two bonded glass samples, validated only qualitatively, by agreement of the spatial pattern with optical photographs of the interface.

This was the first end-to-end demonstration that a locally measured nonlinear acoustic response can be converted into an absolute local strength map. But, as the protocol itself makes clear, three prerequisites keep it from being a fully nondestructive and generally applicable measurement: the destructive reference $B$ (so the method is nondestructive only after a destructive materials calibration), the absence of any uncertainty or sensitivity analysis for the calibration chain ($A$, $H(\omega)$, and the interface-model parameters), and the restriction of the demonstration to one material system, one frequency, one focusing geometry, and two adhesives. Later work has improved convenience and begun uncertainty-quantification research along a different observable, but has not removed these prerequisites.

Problem Statement

Develop and validate a measurement protocol that recovers the spatially resolved, absolute vertical bonding strength $B_0(x,y)$ at a bonded solid–solid interface from nondestructive acoustic measurements, within the interface model $B_0 = B(1-R)$, such that the absolute strength reference — the full-bond strength $B$ of the adhesive–substrate system — is established without destructive tensile pull-off calibration, and the absolute accuracy of the recovered strength map is demonstrable against independent strength measurements (destructive tests are permissible for such external verification, though not for calibration). The protocol must additionally quantify the uncertainty of the calibration chain — the incident focal amplitude $A$, the receiver transfer function $H(\omega)$, and the interface-model parameters — and report the uncertainty of the resulting $B_0(x,y)$ map, so that the recovered strength is uncertainty-quantified. The independent verification must be capable of certifying the spatial variation of the recovered map, not only its overall scale, by comparison against an independent measurement that supplies spatial ground truth at a resolution sufficient to resolve that variation.

References

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