Nonlinear resonance spectroscopy and slow-dynamics diagnostics can track fatigue damage in CFRP laminates, but their measured indicators evolve non-monotonically over fatigue life and their connection to specific damage mechanisms remains conjectural. The open problem is to convert these indicators into mechanism-resolved, predictive diagnostics: explain the relative roles of matrix microcracking, interfacial debonding, micro- and macro-delamination, and fiber breakage in producing the observed non-monotonic nonlinear response, and predict the evolution of the measured indicators, including the slow-dynamics recovery observables (recovery rate and recovery time), from specific damage mechanisms. Related open issues noted in the source study include which defect types act as hardening versus softening nonlinearities in composite resonance (including the effect of acoustic stress on closed cracks and crack-opening displacement) and how baseline variability, fabrication defects, and pre-imposed impact damage shape early-fatigue signatures. No study is known to resolve any of these components for cyclic-flexural-fatigued CFRP with slow-dynamics measurements.

Background

Carbon fiber reinforced polymer (CFRP) laminates accumulate fatigue damage through a sequence of coexisting mechanisms - matrix microcracking, fiber/matrix interfacial debonding, micro- and macro-delamination, and eventually fiber breakage - each of which degrades stiffness and damping in overlapping ways. In nonlinear resonance (ultrasound) spectroscopy (NRUS), a specimen is driven at one of its flexural resonance modes at a series of excitation amplitudes, and the resonance frequency and modal damping ratio are extracted at each amplitude; in damaged solids the resonance frequency typically shifts downward with increasing drive amplitude, and the slope of this shift quantifies the acoustic nonlinearity parameter β\beta. Microdamaged solids also exhibit slow dynamics: after a strong excitation is removed, the effective modulus recovers approximately logarithmically in time over seconds to minutes, a hallmark of nonlinear mesoscopic elasticity (Johnson and Sutin 2005). The amplitude-dependent shift and the recovery rate and recovery time after conditioning together provide nondestructive observables that are far more sensitive to microdamage than linear ultrasonic measures. The physical origin of this sensitivity in cracked solids is usually attributed to contact acoustic nonlinearity (CAN), the clapping and frictional rubbing of crack faces that opens and closes with the acoustic strain (Solodov, Krohn, and Busse 2002). The sensitivity of nonlinear ultrasonic indicators to fatigue damage has been demonstrated in metals (Nagy 1998), in pultruded glass-fiber composites via dynamic nonlinear resonance (Van Den Abeele, Carmeliet, and Van De Velde 2001), in impact-damaged composite laminates using nonlinear acoustics (Aymerich and Staszewski 2010), and in cyclically fatigued composite laminates using linear and nonlinear resonant techniques (Idriss and El Mahi 2018). Chakrapani and Barnard established the theoretical extraction of β\beta from NRUS measurements (2017) and then applied the full NRUS plus slow-dynamics toolkit to quasi-isotropic CFRP laminates under four-point bending in interrupted mid-to-high cycle fatigue (more than 10710^7 cycles), tracking the nonlinear frequency shift, modal damping ratio, and slow-dynamics recovery observables on a pristine specimen and two specimens with pre-imposed impact damage (Chakrapani and Barnard 2020). They observed a non-monotonic increase in nonlinearity over fatigue life and could interpret it only through conjectures about the acoustic response of microdamage at different fatigue stages, because no destructive microscopy was performed at intermediate fatigue stages; in their conclusions they additionally note that the classification of defects as hardening or softening in composite resonance is not established, that the effect of acoustic stress on closed cracks and crack-opening displacement was not directly tested, that slow-dynamics behavior remains poorly understood and material dependent, and that modeling is needed for how baseline variability, fabrication defects, and pre-imposed impact damage influence early fatigue signatures.

Problem Statement

The problem, as left open by Chakrapani and Barnard (2020), is to turn the nonlinear-resonance and slow-dynamics fatigue indicators of CFRP laminates into mechanism-resolved, predictive diagnostics. In the source study, the non-monotonic increase in nonlinearity over the fatigue life of quasi-isotropic CFRP laminates under cyclic flexural (four-point bending) loading could be interpreted only through conjectures about the acoustic response of microdamage at different fatigue stages. The open problem is to replace that conjectural interpretation with a mechanistic account of the relative contributions of matrix microcracking, interfacial debonding, micro-delamination, macro-delamination, and fiber breakage to the evolution of the measured indicators - the amplitude-dependent nonlinear frequency shift, the modal damping ratio, and the slow-dynamics recovery rate and recovery time - and to develop a model that predicts this evolution from the damage state and stated initial conditions of a specimen. Related open issues noted in the paper's conclusions include which defect types in composite resonance act as hardening nonlinearities (resonance frequency increasing with drive amplitude) and which act as softening nonlinearities (frequency decreasing), including the effect of changing acoustic stress on closed cracks and crack-opening displacement, and how baseline variability, fabrication defects, and pre-imposed impact damage shape early-fatigue signatures. The mechanistic attribution and the predictive model are the required deliverable; the hardening/softening classification and the effects of baseline variability, fabrication defects, and pre-imposed impact damage are ancillary issues that may be addressed as part of the account but are not separately required.

References

  1. Chakrapani, S. K.; Barnard, D. J. (2020). Fatigue damage evaluation of carbon fiber reinforced composites using nonlinear resonance spectroscopy. NDT & E International 116, 102331. DOI: 10.1016/j.ndteint.2020.102331. https://doi.org/10.1016/j.ndteint.2020.102331
  2. Nagy, P. B. (1998). Fatigue damage assessment by nonlinear ultrasonic materials characterization. Ultrasonics 36, 375-381. DOI: 10.1016/S0041-624X(97)00040-1. https://doi.org/10.1016/S0041-624X(97)00040-1
  3. Van Den Abeele, K.; Carmeliet, J.; Van De Velde, K. (2001). Inferring the degradation of pultruded composites from dynamic nonlinear resonance measurements. Polymer Composites 22, 555-567. DOI: 10.1002/pc.10559. https://doi.org/10.1002/pc.10559
  4. Solodov, I. Yu.; Krohn, N.; Busse, G. (2002). CAN: an example of nonclassical acoustic nonlinearity in solids. Ultrasonics 40, 621-625. DOI: 10.1016/S0041-624X(02)00186-5. https://doi.org/10.1016/S0041-624X(02)00186-5
  5. Johnson, P.; Sutin, A. (2005). Slow dynamics and anomalous nonlinear fast dynamics in diverse solids. The Journal of the Acoustical Society of America 117, 124-130. DOI: 10.1121/1.1823351. https://doi.org/10.1121/1.1823351
  6. Aymerich, F.; Staszewski, W. J. (2010). Impact damage detection in composite laminates using nonlinear acoustics. Composites Part A: Applied Science and Manufacturing 41, 1084-1092. DOI: 10.1016/j.compositesa.2009.09.004. https://doi.org/10.1016/j.compositesa.2009.09.004
  7. Chakrapani, S. K.; Barnard, D. J. (2017). Determination of acoustic nonlinearity parameter (β) using nonlinear resonance ultrasound spectroscopy: Theory and experiment. The Journal of the Acoustical Society of America 141(2), 919-928. DOI: 10.1121/1.4976057. https://doi.org/10.1121/1.4976057
  8. Idriss, M.; El Mahi, A. (2018). Linear and nonlinear resonant techniques for characterizing cyclic fatigue damage in composite laminate. Composites Part B: Engineering 142, 36-46. DOI: 10.1016/j.compositesb.2017.12.058. https://doi.org/10.1016/j.compositesb.2017.12.058
  9. Wei, Q.; Zhu, L.; Zhu, J.; Zhuo, L.; Hao, W.; Xie, W. (2020). Characterization of impact fatigue damage in CFRP composites using nonlinear acoustic resonance method. Composite Structures 253, 112804. DOI: 10.1016/j.compstruct.2020.112804. https://doi.org/10.1016/j.compstruct.2020.112804
  10. Quan, S.; Zhang, Y.; Lin, P. (2023). Fatigue damage quantitative evaluation of carbon fiber composites at different stress ratios based on nonlinear ultrasonic. Results in Physics 51, 106695. DOI: 10.1016/j.rinp.2023.106695. https://doi.org/10.1016/j.rinp.2023.106695
  11. Haggui, M.; Jendli, Z.; El Mahi, A.; Akrout, A.; Haddar, M. (2023). Damage Analysis in Flax/Elium Composite Using Linear and Nonlinear Resonance Techniques. Journal of Vibration Engineering & Technologies 12, 2811-2827. DOI: 10.1007/s42417-023-01015-2. https://doi.org/10.1007/s42417-023-01015-2
  12. Akbulut, M.; Teke, I. T.; Ertas, A. H. (2026). Fatigue behavior and vibration-based integrity management of advanced composite structures: A comprehensive review. Journal of Low Frequency Noise, Vibration and Active Control. DOI: 10.1177/14613484261447237. https://doi.org/10.1177/14613484261447237