Siryabe, Rénier, Meziane, Galy and Castaings (Ultrasonics 79, 2017) showed that ultrasonic plane-wave transmission coefficients of an aluminium–epoxy–aluminium joint can be inverted for the elastic properties of a degraded interphase — a thin compliant layer at each adherend–adhesive interface — provided the adhesive's bulk moduli are known in advance, and vice versa; the recovered interfacial normal and shear stiffnesses kLk_L and kTk_T varied monotonically with destructively measured bond strength, but no mechanics-based relation between stiffness and strength was established. This problem concerns the two coupled questions that work left open and that jointly block quantitative non-destructive evaluation (NDE) of weak adhesive bonds: (i) simultaneous recovery of the adhesive layer's effective elastic moduli and both interfacial stiffnesses from one ultrasonic dataset, which would localize weakness as adhesive or cohesive without prior assumptions; and (ii) a validated, mechanics-based relation predicting the joint's mechanical strength from the recovered interfacial parameters. Prior work has addressed these questions only partially — shear-only coupled inversion via shear-horizontal guided waves (Koodalil et al. 2021), a simulated stiffness–strength scaling model (Cantrell 2018), phase-based interfacial-stiffness measurement (Haldren et al. 2022; Takunju et al. 2023), and empirical or data-driven strength correlates — while a 2023 assessment states that no widely adopted NDE method measures interfacial bond strength. Both cores remain open.

Background

Adhesive bonding joins two solids (the adherends) through a polymer adhesive layer, and is attractive in aerospace and automotive structures for its light weight and load-spreading behaviour. Its Achilles heel is qualification: a joint can be weakened either cohesively (the adhesive bulk itself is under-cured or degraded) or adhesively (the thin region where adhesive meets adherend is contaminated or poorly bonded), and no non-destructive method can currently measure how strong a finished joint is — strength is instead ensured by process control and destructive witness coupons. The thin, chemically distinct region between adherend and bulk adhesive, whose properties differ from both, is called the interphase; its mechanical degradation is what 'weak adhesion' means physically. A kissing bond is the limiting case: two surfaces in intimate mechanical contact that transmit compression but little tension or shear because there is no true adhesion, making it nearly invisible to conventional pulse-echo ultrasound. The classical ultrasonic probe of interfacial quality is the imperfect-interface or spring model (Baik and Thompson, 1984): at wavelengths long compared with interfacial microdefects, a partially bonded interface behaves like distributed elastic springs, characterized by a normal (longitudinal) stiffness kLk_L and a transverse (shear) stiffness kTk_T, both rising toward infinity for a perfect bond; oblique-incidence measurements are especially sensitive to them (Pilarski and Rose, 1988). In immersion inspection, an ultrasonic plane-wave transmission coefficient (UPWTC) — the ratio of transmitted to incident pressure amplitude, measured or simulated as a function of frequency and incidence angle — can be computed for arbitrary multilayers by the stiffness matrix method, a standard algorithm that propagates elastic fields through stacked anisotropic layers including spring-type interfaces. Siryabe et al. (2017) modelled each interphase as a thin isotropic compliant layer, measured UPWTCs in a water tank for eight aluminium–epoxy–aluminium samples spanning two adhesive cure levels and four surface treatments, and inverted them. When interphases were degraded but (incorrectly) assumed perfect, the recovered adhesive moduli became artificially direction-dependent — 'apparent anisotropy', explained by a rule-of-mixtures argument and itself a signature of interfacial weakness. With adhesive properties known, the interfacial stiffnesses were recovered and decreased monotonically with degradation, and all ultrasonically measured parameters varied monotonically with bond strengths measured in destructive mechanical tests — but only monotonically, without theory. Two coupled obstacles remain. First, the inversion is not identifiable when both parameter sets are unknown: over accessible frequency–angle windows, a softer adhesive and a more compliant interface produce partially compensating signatures, and for well-bonded interfaces many large stiffness values are indistinguishable from perfect continuity, so the present procedures must assume either the adhesive moduli or the interfacial properties a priori. Second, kLk_L and kTk_T are linear-elastic, small-amplitude parameters, whereas joint strength is governed by defect populations, interfacial chemistry, stress concentrations, and viscoelastic or plastic dissipation at failure; no established mechanics maps one onto the other, which is what a quantitative strength prediction requires. (Guided-wave variants of these measurements use Lamb waves — elastic waves guided by the bonded plate stack — or shear-horizontal (SH) waves, whose particle motion is parallel to the layering; lap-shear strength, the standard destructive metric, is the failure load of an overlapped joint pulled in tension.)

Problem Statement

For adhesively bonded joints of the tri-layer type — two elastic adherends joined by an adhesive layer, with thin compliant interphases possible at each adherend–adhesive interface — ultrasonic plane-wave transmission coefficients measured over a range of frequencies and incidence angles encode both the adhesive layer's effective elastic moduli and the interfacial normal and shear stiffnesses kLk_L and kTk_T of the two interfaces. The problem left open by Siryabe et al. (2017) comprises two open questions: (1) Coupled inversion — construct and validate an inversion procedure that, from a single ultrasonic dataset acquired on one joint, simultaneously recovers the adhesive layer's effective elastic moduli and the interfacial stiffnesses (or equivalently interphase elastic properties) of both interfaces, without assuming either set known a priori, and that is demonstrably well-conditioned enough to distinguish imperfect from perfect interfacial bonding on realistic measurement data, thereby determining whether a given weakness is cohesive (reduced adhesive moduli) or adhesive (degraded interfaces) and quantifying each separately. (2) Stiffness–strength relation — establish a mechanics-based relation that predicts the joint's mechanical strength, i.e., the failure threshold measured in destructive tests such as lap-shear loading, from the ultrasonically recovered interfacial (and, as required, adhesive) parameters, going beyond the monotonic-only correlation reported in the source, and validate it over joints spanning controlled variations of interfacial quality and adhesive cure state. Part (1) supplies the measurable physical parameters and part (2) converts them into the strength assessment that is the ultimate objective of quantitative non-destructive evaluation of weak bonds. The natural joint class is that of the source demonstration — elastic, geometrically uniform adherends with an epoxy-type adhesive and weak interphases — but the answer may not assume nominal interphase properties or known adhesive moduli.

References

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