Fibre-reinforced composite laminates accumulate fatigue damage as matrix cracking, delamination and fibre–matrix debonding long before stiffness measurably degrades. Linear guided-wave observables (phase velocity, amplitudes, and elastic moduli inverted from them) and nonlinear observables (second-harmonic amplitude ratios) probe damage at different scales. In-situ laser-ultrasonic measurements on a fatigued cross-ply carbon/epoxy laminate showed a sharp drop in guided-wave amplitude in early fatigue while the phase velocity and inverted axial stiffness remained nearly unchanged, but the damage mechanisms responsible for this signature were never identified. The problem is to establish the quantitative correlation between specific fatigue damage mechanisms and measured linear and nonlinear guided-wave parameters — explaining the early amplitude drop in particular — and to validate the combined methodology on laminates with different stacking sequences and fibre orientations, with material attenuation and diffraction incorporated in the analysis, so that guided waves provide realistic, mechanism-resolved characterization of damage accumulation.

Background

Fibre-reinforced polymer composite laminates, the primary structural material of modern aircraft, accumulate fatigue damage through a sequence of mechanisms: matrix cracking (brittle cracks in the polymer matrix, usually starting in off-axis plies), delamination (separation between adjacent plies), fibre–matrix debonding, and eventual fibre breakage. This microstructural evolution precedes any measurable loss of global stiffness and is invisible to visual inspection, which motivates in-situ nondestructive evaluation (NDE) for condition-based maintenance.

Guided waves are elastic waves confined to propagate in a plate; the fundamental modes are the symmetric (S0) and antisymmetric (A0) Lamb modes. Because the plate boundaries constrain the motion, Lamb waves are dispersive — their phase velocity (speed of a wavefront of constant phase) differs from their group velocity (speed of energy transport) — so reliable measurement requires extracting phase velocity directly rather than approximating it by a group velocity. Changes in phase velocity can be inverted, using a plate theory as the forward model, to recover the laminate's elastic stiffness coefficients.

Linear ultrasonic parameters (wave speed, attenuation, reflections) respond mainly to damage comparable in size to the wavelength, so they miss the early microstructural evolution. Nonlinear ultrasonics fills this gap: in a solid with weakly nonlinear elasticity, a monochromatic primary wave of frequency ff generates a component at 2f2f (the second harmonic), and the relative second-harmonic amplitude, commonly reported through a nonlinearity parameter proportional to A2/A12A_2/A_1^2, is far more sensitive to micro-damage than any linear parameter. For plates, the second harmonic accumulates with propagation distance only under internal resonance — phase matching (the secondary mode's wavenumber equals twice the primary's) together with non-zero power flux from primary to secondary mode — which restricts the admissible primary–secondary mode pairs. Extending this framework from isotropic plates to anisotropic composites requires a third-order strain-energy function written in the invariants of the Green–Lagrange strain tensor for a transversely isotropic (TI) material — the symmetry of a unidirectional fibre lamina — with third-order elastic constants that are themselves hard to measure.

Zhao, Chillara, Cho, Qiu and Lissenden (AIP Conf. Proc. 1706, 120007, 2016) combined both approaches. A laser-generation based imaging (LGBI) system — a scanning laser source that visualizes wave propagation, from whose position–time diagrams phase velocities are read directly — tracked the S0 phase velocity, wave amplitude, and (via genetic-algorithm inversion against a third-order shear deformation plate theory) the axial stiffness coefficient C11C_{11} of a T700/3001 carbon/epoxy [0/90]4S[0/90]_4^S laminate during tension–tension fatigue, without removing the specimen from the load frame. The striking observation was that the wave amplitude dropped sharply in early fatigue while phase velocity and C11C_{11} stayed nearly constant. In parallel, they derived the internal-resonance mode-pair selection rules for cumulative second-harmonic generation in TI plates and laminates (published in full as Zhao et al., J. Appl. Phys. 119, 064902, 2016) and verified by finite-element simulation with a hyperelastic user material that the selected mode pairs produce linearly growing second harmonics — but those simulations deliberately omitted material attenuation and wave diffraction.

What the source study could not do is connect the two halves: the amplitude drop indicates that early fatigue changes the material's wave-carrying properties in a way that phase velocity and stiffness inversion do not see, but whether matrix cracking, early delamination, fibre–matrix debonding, or evolving viscoelastic damping causes it was left open. Nor was the methodology exercised beyond one cross-ply architecture, and the nonlinear modelling lacked the attenuation and diffraction physics of a real laminate. Damped-plate modelling of cumulative second harmonics is now largely established.

Problem Statement

Establish the quantitative correlation between specific fatigue damage mechanisms in fibre-reinforced composite laminates and the changes measured by linear and nonlinear guided-wave methods, and thereby convert those measurements into realistic, mechanism-resolved characterization of fatigue damage accumulation. Concretely, for laminates subjected to cyclic loading, the problem comprises three linked parts: (a) identify which damage mechanisms — matrix cracking, delamination, fibre–matrix debonding, and associated changes in viscoelastic damping — produce the observed acoustic parameter changes, in particular the sharp drop in guided-wave amplitude during early fatigue while S0 phase velocity and the inverted stiffness coefficients remain nearly unaffected, with the attribution made quantitative by relating each identified mechanism to the magnitude of the measured changes rather than resting on a qualitative mechanism suggestion alone, and supported where possible by independent damage observation (e.g. microscopy, X-ray computed tomography, or C-scan, a scanned ultrasonic image of internal damage); (b) quantify the resulting correlation between those damage mechanisms and the linear and nonlinear guided-wave parameters for the original cross-ply laminate; and (c) carry the same combined linear (phase velocity, amplitude, moduli inversion) and nonlinear (second-harmonic) characterization to at least one architecture beyond the original cross-ply one — that is, an architecture differing in stacking sequence or fibre orientation (the original study tested only one cross-ply architecture) — with material attenuation and diffraction incorporated into the interpretation and modelling, including the cumulative second-harmonic analysis. The objective is a guided-wave measurement whose changes can be read as a quantitative, mechanism-specific account of fatigue damage state in realistic composite laminates.

References

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