Dynamic acousto-elastic testing (DAET) — a pump-probe method in which a high-frequency ultrasonic pulse probes a specimen while a low-frequency vibration dynamically strains it — was applied by La Rocca, Moysan and Payan (2012) to an epoxy-bonded aluminum alloy sample. The relative modulation of the interface reflection coefficient and of the pulse time of flight traced nonclassical hysteretic (figure-eight) loops as a function of pump strain, but the measurements remained qualitative: the multiplicative constants that would convert the relative modulation quantities into absolute changes of interface reflection coefficient, bonded-layer celerity, or stiffness were not calibrated; no constitutive description of the hysteretic loops exists that maps loop shape or area to specific interfacial mechanical states such as adhesive versus cohesive quality or defect severity; and the sensitivity and specificity of the signature for bond-state discrimination, including the confounding contributions of substrate nonlinearity, measurement noise, and spatial averaging of the probe, were never quantified. The problem is to make DAET a quantitative diagnostic for adhesive bonded joints by establishing this missing chain: absolute calibration, a hysteretic constitutive model of the bond, and validated discrimination between known interfacial states on controlled specimens.

Background

Adhesive bonding of metals and composites is attractive in aeronautic and other safety-critical industries, but its certification is blocked by a longstanding nondestructive-evaluation (NDE) gap: before fracture, no method can reliably tell an 'adhesive' failure mode (weak adhesion at the substrate–adhesive interface) from a 'cohesive' one (weak adhesive layer), nor detect 'kissing bonds' — zero-volume, low-contrast contact defects that are essentially invisible to conventional (linear) ultrasound (Nagy, 1991). Since the late 1980s, nonlinear ultrasonics has been proposed for this task, because a weak interface is mechanically nonlinear even when its linear impedance contrast is negligible.

Dynamic acousto-elastic testing (DAET) is a nonlinear, pump-probe characterization method: a continuous or pulsed high-frequency (HF) ultrasonic wave probes the specimen while a much lower-frequency (LF) stationary vibration dynamically strains it. At each phase of the LF cycle one measures the change of the HF wave's velocity or of an interface's reflection coefficient (the ratio of reflected to incident pressure amplitude, which depends on the mechanical impedance match across the interface), so the strain-dependence of the elastic properties is traced point-by-point over the vibration cycle. This is the dynamic analog of classical acoustoelasticity, in which wave speeds are measured under a quasi-static applied stress. In micro-inhomogeneous solids (rocks, concrete, cracked metals), DAET reveals 'nonclassical' nonlinearity — conditioning (a modulus change that depends on the strain history), slow dynamics (recovery of the modulus over seconds to minutes after the vibration stops), and hysteresis between the loading and unloading halves of a strain cycle, visible as closed 'loops' in the modulus-versus-strain or reflectivity-versus-strain plot; an '8-shaped' loop indicates a phase shift between the nonlinear response and the pump, as expected from a hysteretic interface. After the source paper, DAET was quantified for homogeneous bulk media: Renaud et al. (2016) measured Murnaghan third-order elastic constants (the coefficients of the cubic terms in the strain-energy expansion) of PMMA and Berea sandstone at microstrain with Monte-Carlo uncertainty budgets, and Scalerandi et al. (2015) analyzed the validity limits of DAET and the interpretation of its measured quantities; reviews (Haupert et al., 2018) cover applications to rocks, concrete, bone, cracked metals and granular media but not to adhesive bonds.

La Rocca, Moysan and Payan (2012) applied DAET to an aluminum patch bonded by epoxy to an aluminum beam: the HF pulse reflected at the bond was modulated by the LF vibration, and the extracted relative quantities tracked hysteretic 8-shaped loops of the bonded layer. Their companion work states the motivating gap explicitly: nobody can discern an adhesive from a cohesive joint before fracture. However, their results admitted only qualitative interpretation, because (i) the multiplicative constants converting the relative measured quantities into absolute changes of interface reflection coefficient, bonded-layer celerity, or stiffness were not calibrated; (ii) no quantitative constitutive description of the hysteretic loops was developed, so loop shape and area could not be tied to specific interfacial mechanical states; (iii) the specimens were not comprehensively characterized before assembly (material properties, bond-thickness distribution, defect content), so reproducibility and sensitivity bounds versus known defect types were unknown; and (iv) substrate nonlinear contributions, measurement noise, and spatial averaging of the probing beam over the interface were not quantified. Constitutive modeling of nonclassical hysteresis (e.g., Preisach–Mayergoyz-type models, in which the material is represented as a statistical ensemble of elementary hysteretic switching relays, and fast/slow-dynamics models such as Favrie, Lombard and Payan, 2015) and nonlinear NDE of weak bonds by other physics (higher-harmonic generation, nonlinear laser vibrometry: Zabbal et al., 2019; Solodov et al., 2023) have advanced since, but none of this addresses the DAET-specific calibration and inversion chain for bonded interfaces.

Problem Statement

Establish dynamic acousto-elastic testing (DAET) as a quantitative nondestructive diagnostic for adhesive bonded joints, completing the program whose qualitative stage was reported by La Rocca, Moysan and Payan (2012) for an epoxy-bonded aluminum alloy sample. The source stated its aim as 'studying the potentialities to discern a change in the nonlinear signature of an aluminium/epoxy interface, then ... examining if that could be associated with a particular behaviour type (adhesive/cohesive)', measured through the change of the HF pulse reflection coefficient as a function of the LF vibration amplitude; the open problem is to carry that aim to a quantitative stage. Doing so involves, as facets of one open problem:

  1. Absolute calibration: determine the constants that convert the measured relative modulation quantities (the relative changes of interface reflection coefficient and of pulse time of flight extracted over the pump cycle) into absolute changes of interface reflection coefficient, bonded-layer celerity, and interfacial stiffness, including the corrections required for substrate (aluminum) nonlinear contributions, measurement noise, and spatial averaging of the probing beam over the interface.

  2. Constitutive identification: develop a quantitative constitutive description of the bonded layer that reproduces the observed nonclassical hysteretic (8-shaped) loops, such that loop shape and area can be mapped to specific interfacial mechanical states — distinguishing adhesive-quality degradation from cohesive degradation, and grading defect severity.

  3. Discrimination performance: quantify, on controlled specimens with known interfacial states, the reproducibility of the DAET signature and the sensitivity and specificity with which it discriminates those states (including the adhesive-versus-cohesive distinction that motivated the source work).

The target is a quantitative DAET capability for bonded joints, not merely the observation of hysteretic loops or relative modulation levels as in the qualitative source stage.

References

  1. C. La Rocca, J. Moysan, C. Payan (2012). 'Characterization of an epoxy bonded aluminum alloy sample applying dynamic acousto elastic testing', AIP Conference Proceedings 1430, 1261–1267 (Review of Progress in Quantitative Nondestructive Evaluation, Vol. 31). DOI: 10.1063/1.4716363, https://doi.org/10.1063/1.4716363
  2. C. La Rocca, C. Payan, J. Moysan (2010). 'Evaluation of epoxy bonded joint quality using nonlinear acoustics', conference communication, HAL hal-01298603, https://hal.science/hal-01298603
  3. G. Renaud, J. Rivière, P.-Y. Le Bas, P. A. Johnson (2013). 'Hysteretic nonlinear elasticity of Berea sandstone at low-vibrational strain revealed by dynamic acousto-elastic testing', Geophysical Research Letters 40, 715–719. DOI: 10.1002/grl.50150, https://doi.org/10.1002/grl.50150
  4. M. Scalerandi, A. S. Gliozzi, S. Haupert, G. Renaud, M. Ait Ouarabi, F. Boubenider (2015). 'Investigation of the validity of Dynamic AcoustoElastic Testing for measuring nonlinear elasticity', Journal of Applied Physics 118, 124905. DOI: 10.1063/1.4931917, https://doi.org/10.1063/1.4931917
  5. G. Renaud, M. Talmant, G. Marrelec (2016). 'Microstrain-level measurement of third-order elastic constants applying dynamic acousto-elastic testing', Journal of Applied Physics 120, 135102. DOI: 10.1063/1.4963829, https://doi.org/10.1063/1.4963829
  6. S. Haupert, G. Renaud, J. Rivière, P. Shokouhi (2018). 'Dynamic Acousto-Elastic Testing', in 'Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation' (Springer), pp. 509–546. DOI: 10.1007/978-3-319-94476-0_13, https://doi.org/10.1007/978-3-319-94476-0_13 (HAL hal-02989512)
  7. P. Zabbal, G. Ribay, J. Jumel (2019). 'Nonlinear ultrasound for nondestructive evaluation of adhesive joints', AIP Conference Proceedings 2102, 020030 (45th Review of Progress in Quantitative Nondestructive Evaluation, Vol. 38). DOI: 10.1063/1.5099734, https://doi.org/10.1063/1.5099734
  8. I. Solodov, M. Kornely, J. Philipp, E. Stammen, K. Dilger, M. Kreutzbruck (2023). 'Linear vs nonlinear ultrasonic testing of kissing bonds in adhesive joints', Ultrasonics 132, 106967. DOI: 10.1016/j.ultras.2023.106967, https://doi.org/10.1016/j.ultras.2023.106967
  9. P. B. Nagy (1991). 'Ultrasonic detection of kissing bonds at adhesive interfaces', Journal of Adhesion Science and Technology 5, 619–630. DOI: 10.1163/156856191X00521, https://doi.org/10.1163/156856191X00521
  10. N. Favrie, B. Lombard, C. Payan (2015). 'Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations', Wave Motion 56, 221–238. DOI: 10.1016/j.wavemoti.2015.02.014, https://doi.org/10.1016/j.wavemoti.2015.02.014
  11. J. N. Eiras, Q. A. Vu, M. Lott, J. Payá, V. Garnier, C. Payan (2016). 'Dynamic acousto-elastic test using continuous probe wave and transient vibration to investigate material nonlinearity', Ultrasonics 69, 29–37. DOI: 10.1016/j.ultras.2016.03.008, https://doi.org/10.1016/j.ultras.2016.03.008