Quantitative, mechanism-based characterization of fatigue stiffness degradation in curved textile composites from circumferential plate acoustic wave damping

Fatigue of glass-fibre non-crimp-fabric (NCF) composite tubes causes progressive stiffness loss through matrix cracking, interfacial damage, delamination, and finally fibre fracture, and monitoring this degradation on curved load-bearing components is difficult for conventional bulk ultrasonic testing. Adden, Pfleiderer, Solodov, Horst and Busse (Composites Science and Technology 68, 2008) showed that a single standard longitudinal-wave probe on the curved surface of a tube can generate and receive guided circumferential plate acoustic waves (PAWs), and that a normalized amplitude-damping parameter $D = 1 - u/u^{0}$ correlates empirically with the mechanically measured tensile and shear stiffness degradation parameters $D_{11}$ and $D_{12}$ in three specimens under tension, torsion, and combined loading. The open problem is to turn this empirical correlation into a quantitative, mechanism-grounded non-destructive indicator: establishing the physics by which crack orientation, crack density, interfacial damage, and delamination produce PAW attenuation and scattering; validating statistically robust $D$-versus-$D_{11}$/$D_{12}$ relations on specimen sets large enough to separate loading-mode and laminate-architecture effects from NCF manufacturing variability; calibrating the measurement (frequency, probe aperture, couplant and contact pressure) and extending it to other lay-ups, fibre/resin systems, carbon-fibre-reinforced polymer (CFRP), and fatigue regimes; and determining the applicability limits, including the minimal detectable crack size, the quantitative mapping from PAW damping to absolute crack density, and robustness under industrial conditions. Later literature has advanced quantitative guided-wave damage characterization mainly for flat laminates and for observables other than PAW amplitude damping, while monitoring of composite tubes or pipes has remained largely empirical, so this core remains open.

Background

Textile composites used in curved, load-bearing structures (aerospace fuselage parts, drive shafts, wind-energy and pressure-vessel components) are frequently made from non-crimp fabrics (NCFs) — textile reinforcements in which straight fibre bundles are knitted together by stitching threads rather than interlaced as in woven fabrics, which improves fibre-direction stiffness but introduces stitching-induced defects and specimen-to-specimen variability. Under cyclic (fatigue) loading these laminates accumulate damage in a well-documented sequence: first intralaminar matrix cracks whose density grows rapidly, then crack interaction, interfacial (fibre/matrix) debonding and delamination, and finally fibre fracture; each stage reduces the effective engineering moduli. A standard way to quantify this is through relative stiffness degradation parameters, e.g. $D_{11} = 1 - E_{11}/E_{11,0}$ and $D_{12} = 1 - G_{12}/G_{12,0}$, where $E_{11}$ and $G_{12}$ are the current axial Young's modulus and in-plane shear modulus (evaluated as secant moduli from hysteresis loops) and the subscript 0 denotes the intact state.

Non-destructive tracking of this damage on curved parts is difficult. Bulk longitudinal/transverse ultrasonic probes require flat or mildly curved contact surfaces; micromechanical models that predict stiffness from crack density need fibre- and resin-level inputs that are unavailable in production; and absolute acoustic-velocity measurements demand accuracy that is impractical industrially. Guided elastic waves offer an alternative: in a plate-like wall, boundary-trapped Lamb-type modes (so-called plate acoustic waves, PAWs) propagate over large distances and interact with through-thickness microcracks. When the wall is a tube, a circumferential PAW runs around the circumference along the wall thickness, and theory predicts strong sensitivity of such modes to small cracks because the crack faces lie in the propagation path. Lamb-wave monitoring of fatigue stiffness degradation had been demonstrated on flat composite specimens (e.g. Seale, AIP Conference Proceedings 509, 2000), but not on curved textile-composite tubes.

Adden, Pfleiderer, Solodov, Horst and Busse (Composites Science and Technology 68(7-8):1616-1623, 2008) filled this gap experimentally. On hollow cylindrical glass-fibre-reinforced-polymer (GFRP) NCF specimens (47 mm diameter, ~2.3 mm wall, $[0°/45°/90°/-45°]_S$-type lay-ups) fatigued under pure tension, pure torsion, and combined tension-torsion at loading angles $\alpha$ defined by $\tan\alpha = \tau/\sigma$ (the ratio of applied shear stress $\tau$ to normal stress $\sigma$), they showed that one conventional 5-MHz longitudinal-wave probe, pressed onto the curved surface with a thin high-viscosity couplant, both generates and receives a circumferential PAW (measured speed $1200 \pm 50$ m/s; at the narrow-band 0.5 MHz detection frequency this gives a wavelength of ~2.4 mm, comparable to the wall thickness). They defined the ultrasonic damping parameter $D = 1 - u/u^{0}$, where $u$ is the mean PAW amplitude after a given number of fatigue cycles and $u^{0}$ the intact-specimen amplitude, and showed in three specimens that $D$ rises with cycle count in the same three-stage pattern as $D_{11}$ and $D_{12}$, and that $D$ correlates positively and monotonically with both $D_{11}$ and $D_{12}$, with a fit slope that depends on the loading angle $\alpha$ — interpreted, without corroborating fractography, as an effect of crack orientation (axial microcracks from torque-dominated loading versus circumferential cracks under tension). The correlations were linear fits to only 3-5 points per specimen from three specimens; no confidence intervals, absolute crack-density calibration, or detectability thresholds were established.

The study's documented limitations — three specimens with only 3-5 fit points each, no fractographic corroboration of the crack-orientation interpretation, no confidence intervals, an uncalibrated contact-amplitude measurement chain, and no absolute crack-density calibration or detectability thresholds — together with the subsequent literature, define what is needed to make the method a quantitative non-destructive testing (NDT) tool: more specimens to separate real loading-mode and architecture effects from NCF manufacturing scatter (stitching, fibre misalignment, process variations); mechanism-level understanding of how crack orientation, crack density, interfacial damage, and delamination quantitatively drive PAW amplitude attenuation and scattering, replacing empirical fits; calibration of ultrasonic sensitivity (frequency dependence, probe aperture relative to wavelength, couplant and contact-pressure effects) and extension to other NCF lay-ups, fibre types, resin systems, carbon-fibre-reinforced plastics (CFRP), and to high-cycle as well as low-cycle fatigue; and establishment of applicability limits — the minimal detectable crack size, the quantitative mapping from PAW damping to absolute crack density, and the operational limits under industrial conditions such as variable temperature and surface roughness.

Problem Statement

Can circumferential plate acoustic wave (PAW) amplitude damping be established as a quantitative, mechanism-grounded non-destructive indicator of fatigue stiffness degradation and crack density in curved textile composites, going beyond the three-specimen empirical correlation of Adden et al. (2008)? This single objective rests on the conjunction of four sub-claims, each tied to a documented limitation of the 2008 study and each independently refutable, so that a rigorous refutation of any single sub-claim settles the top-level question in the negative; the four sub-claims require a mechanism-based model and explicit quantitative design and limit estimates, quantitatively grounded in data (new experiments and specimen generation are in scope): (i) the mechanism-level physics of how crack orientation, crack density, interfacial damage, and delamination quantitatively produce PAW amplitude attenuation and scattering in curved anisotropic non-crimp-fabric (NCF) laminates, so that sensitivity can be predicted rather than fitted (the 2008 crack-orientation interpretation lacked fractographic corroboration); (ii) statistically robust relations between the ultrasonic damping parameter $D = 1 - u/u^{0}$ and the stiffness degradation parameters $D_{11} = 1 - E_{11}/E_{11,0}$ and $D_{12} = 1 - G_{12}/G_{12,0}$ (the relative losses of the axial Young's modulus $E_{11}$ and the in-plane shear modulus $G_{12}$ from their intact-state values, denoted by the subscript 0), obtained on specimen sets large enough to separate intrinsic loading-mode and laminate-architecture effects from NCF manufacturing variability (stitching, fibre misalignment, process variations) and reported with confidence intervals (the 2008 correlations were linear fits to 3-5 points per specimen from three specimens, without confidence intervals); (iii) calibration of the measurement itself — frequency dependence, probe aperture relative to PAW wavelength, couplant thickness and contact-pressure effects — and validation of the calibrated relations across other NCF lay-ups, fibre types, resin systems, CFRP, and both low-cycle and high-cycle fatigue regimes (validation must cover at least one representative member of each listed class, including both a low-cycle and a high-cycle regime; the 2008 contact-amplitude measurement chain was uncalibrated); and (iv) the applicability limits of the method, all three of which must be determined: the minimal detectable crack size, the quantitative mapping from PAW damping to absolute crack density, and the operational limits under industrial conditions such as variable temperature and surface roughness (no absolute crack-density calibration or detectability thresholds were established in 2008).

References

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