Fatigue testing of polymer-matrix composites (PMCs) is traditionally conducted at low frequency range (below10 Hz), resulting in long testing durations and increased expenses. A viable strategy is to accelerate fatigue testing at higher frequencies within a feasible time duration. However, at higher frequencies, the self-heating effect becomes a critical factor, affecting the structural response and potentially altering the fatigue behaviour. The entropy-based thermodynamic framework effectively captures the impact of self-heating and improves fatigue response analysis by incorporating the correlation among heat dissipation rate, applied stress, and loading frequency. Unlike the conventional S-N curve methods, which may skip the self-heating effect, entropy-based models provide a rapid and more general assessment of fatigue behaviour under arbitrary applied stresses and frequencies. This study focuses on the application of entropy-based modelling to capture the complex interplay between stress, frequency, and temperature rise. This allows for predicting the life of a fatigue-loaded PMC specimen by accounting for the interplay between mechanical loading and thermal effects. The proposed framework provides a rapid methodology for characterizing the fatigue performance of PMCs, playing a key role in refining the structural integrity assessment of PMCs.

The self-heating based vibrothermography (SHVT) is a promising non-destructive testing (NDT) technique for polymer-matrix composites, which is based on inducing resonant vibrations of a tested structure. Vibrations serve as a thermal excitation for NDT inspection due to the hysteretic heating of a polymer matrix, known as the self-heating effect. In previous studies, it was validated that the controlled self-heating temperature rise ensures proper thermal excitation of tested composite structures and has a non-destructive and non-invasive character for such structures. It was shown that the increase in temperature usually below 5°C from the ambient temperature is enough to provide appropriate thermal excitation of a tested structure for identifying structural damage. The following study focuses on methods for processing of thermographic images acquired from NDT inspections using SHVT to enable accurate quantification of damage. The results of inspections of two-dimensional glass fiber-reinforced composite specimens with introduced artificial damage were used for a case study to quantify the damage and assess the accuracy of the determination of its spatial position and characteristic dimensions. The results of the processing demonstrated significant enhancement in identification of the introduced damage and allowed its precise quantification, which creates a potential for practical applications, especially during inspection of structures with single-side access or in the cases where external thermal excitation typical for most of classical thermographic techniques cannot be applied.

This paper presents an experimental investigation of a rotating eddy current (REC) system for subsurface defect detection in CFRP composites. The proposed solution employs a compact four-coil excitation probe and a controlled excitation strategy to rotate the induced eddy currents while maintaining a constant current amplitude. Experimental measurements were performed on CFRP laminates containing circular subsurface defects with different diameters and depths. The results demonstrate that the proposed REC system is capable of detecting and distinguishing defects as a function of their geometrical characteristics. The proposed REC system has improved robustness against material anisotropy, confirming the potential of the proposed approach for reliable CFRP inspection.

The fatigue degradation of polymer-matrix composite materials, especially in the case of thermomechanical fatigue, when the self-heating effect dominates the process of the cyclically bent structure in fully reversed mode, results in complex damage patterns with a heterogeneous nature. It is therefore essential to evaluate the structural condition of tested objects in a non-destructive way to predict their fatigue lifetime. One of the most accurate non-destructive testing techniques used for such examinations is X-ray computed tomography, which enables the evaluation of the resulting fatigue damage in a three-dimensional space. However, the main challenge in the evaluation of such results is the attribution of the observed damage to specific types, the assessment of its severity, and its quantitative analysis. In this study, we have proposed a novel framework based on intensity and morphological features for the classification of damage types and a 3D U-Net-based approach for segmentation. The acquired results demonstrated the high accuracy of the performance evaluation indices, which exceeded 99% for the proposed framework, allowing effective evaluation of the resulting damage and being potentially helpful in the assessment of structural performance and residual fatigue life. Such analysis contributes to the trends of NDE 4.0 and adaptive mechanics, where composite structures are tailored to specific operational conditions to reach the target lifecycle.

Accurate assessment of fatigue strength across different lifetimes traditionally requires conventional high-cycle fatigue (HCF) testing, a reliable but time consuming method. As an alternative, thermographic techniques (TT) offer a rapid estimation of fatigue strength, particularly for polymer matrix composites (PMCs) in the HCF regime. This study evaluates the effectiveness of two common thermographic approaches, the temperature-stress ∆Ts - σ and heat dissipation rate-stress q-σ approaches for estimating fatigue strength (σTT) in neat glass fiber-reinforced polymer (GFRP), GFRP with graphene nanoparticle reinforcement (GFRP-GNPs), and GFRP with hybrid nanoparticle reinforcement (GFRP-HNPs). Classical fatigue tests were conducted at 40 Hz under fully reversed loading (R = -1) and compared against thermographic predictions across multiple estimation methods: Bilinear (BL), Angular Change (AC), Minimum Curvature Radius (MCR), and Maximum Perpendicular Distance (MPD).Thermographic estimations showed strong correlation with fatigue strength σ S-N determined using S-N curve at 107 cycles, with the q-σ approach yielding an average relative error of only 0.6%. Among estimation techniques, the MPD method demonstrated the highest accuracy, with relative errors of -5.2% for

ABSTRACT This study analyzes the thermomechanical fatigue behavior of short fiber‐reinforced composites (SFRCs) under different loading frequencies, focusing on the relationship between thermomechanical coupling and fatigue damage evolution. The results showed fatigue strength below 45 MPa and a pronounced dependence on loading frequency. A bilinear thermographic approach based on the stress–self‐heating temperature relationship enabled rapid fatigue life estimation, with predictions differing by less than 13% from those obtained using conventional S–N curves. Fatigue degradation was governed by complex fracture mechanisms sensitive to thermomechanical loading conditions. As demonstrated, even a slight increase in loading frequency intensified the self‐heating effect, accelerated degradation, and altered damage evolution. X‐ray computed tomography revealed that higher frequencies promoted direct fracture of reinforcing fibers, while lower frequencies led to matrix cracking and crack coalescence prior to fiber failure. Analysis of self‐heating temperature evolution and hysteresis loops further confirmed enhanced thermomechanical coupling and accelerated structural deterioration with increasing frequency. The results demonstrate that the principal effect of thermomechanical coupling is not the increase in self‐heating temperature but its influence on the evolution of fatigue degradation mechanisms, providing important implications for fatigue testing and lifetime assessment of composite structures used in automotive and aerospace applications.

This study introduces an optimal polar wavelet transform for damage detection in laminated composite circular plates. The core concept behind the proposed method lies in strategically selecting the most informative polar detail signals to extract damage-related information from vibration mode shapes. To guide this selection process, a minimum energy ratio (MER) index is introduced as a benchmark for identifying the most effective polar wavelet function by evaluating the energy balance between the approximation signal and the various detail signals. To generate reliable vibration data for the proposed damage detection framework, the mathematical model for the circular plate has been developed based on the first-order shear deformation theory (FSDT), neglecting damping effects to simplify the analysis. By introducing central and non-central finite elements, the solution is calculated using the finite element method (FEM), and a convergence study is conducted to verify the accuracy of the numerical model. The effects of different parameters such as location of damage, level of damage, noise, number of layers, and lay-ups on detecting the damages of laminated composite circular plates are considered numerically and experimentally. Results show that the developed optimal wavelet transform can more accurately predict the location of the damage compared to the traditional polar wavelet transform.

This study presents a comparative evaluation of four infrared thermography (IRT) techniques, namely step-heating, C-CheckIR, flash, and lock-in thermography, as well as ultrasonic C-scan for the detection and quantification of low-velocity impact damage (LVID) in thin laminated composites. The assessment relied on the quantitative hit/miss metric analysis, along with the dependency of thermal response on impact energy and impactor tip geometry under 20 different scenarios. The qualitative and quantitative analyses highlighted C-CheckIR and lock-in thermography were effective partially but illustrated inconsistent performance across most LVID scenarios. Flash thermography, in contrast, was identified as the most reliable thermography technique, offering consistent detection capability across a wide range of impact scenarios. Its superior performance is attributed to higher sensitivity to energy level and impactor tip size, as well as consistently lower error magnitudes in the hit/miss quantities, including relative area error, detected and missed area fractions. Furthermore, a dual-tree complex wavelet transform (DTCWT)-based algorithm was developed to fuse flash thermography and ultrasonic C-scan results, enabling complementary visualization of surface cracks and subsurface delamination. The fusion framework improved the interpretability of damage patterns, reduced false interpretations, and provided more comprehensive assessment of impact damage compared to individual non-destructive testing techniques.

This work investigates the admissibility of associative hypercomplex algebras for the construction of Julia sets generated by iterations z↦zr+c, with emphasis on generalized quaternions Hαβ and multiquaternion tensor product algebras C⊗n⊗H. It was proved and graphically demonstrated that within the considered class of associative generalized quaternion algebras, the Hamiltonian algebra is a unique case that supports non-degenerate Julia dynamics with a consistent boundedness–escape dichotomy. The remaining generalized quaternionic algebras exhibit pathological behavior due to zero divisors or degenerate norm structures, leading to collapsed or anisotropic invariant sets. In contrast, multicomplex–quaternion tensor product algebras are shown to provide a natural admissible framework for higher-dimensional Julia sets with enriched morphology. These sets preserve the classical connectivity trichotomy while symbolic and geometric complexity increase with tensor dimension and polynomial degree. The obtained results provide a unified theoretical framework for admissibility in associative hypercomplex dynamics and clarify the role of algebraic structure in the existence and organization of Julia sets.

This study investigates the fatigue behavior and damage mechanisms of self-reinforced polypropylene/polycarbonate (PP/PC) composites manufactured using the shear-controlled orientation injection molding (SCORIM) technique. Microstructural characterization confirmed a layered morphology with PP as the matrix and PC dispersed as spherical inclusions, leading to anisotropic mechanical properties. Thermo-mechanical fatigue tests combined with the increasing amplitude tests established a fatigue strength of 19.4 MPa. Infrared thermography identified a critical selfheating temperature of similar to 50 degrees C as the onset of macroscopic crack front formation, while final failure was associated with localized temperatures exceeding 110 C-degrees due to frictional heating. Scanning electron microscope (SEM) revealed ductile fibrillation and crazing in the core, brittle fracture in outer layers, and interlayer delamination with pull-out mechanism. X-ray diffraction (XRD) showed preserved alpha-PP monoclinic structure with slight orientation loss after fatigue, while thermogravimetric analysis (TGA) and Fourier transform infrared spectroscopy (FTIR) analysis confirmed thermal stability without chemical degradation. The results highlight the interplay of microstructure, anisotropy, and thermomechanical effects governing fatigue performance of SCORIM-processed PP/PC composites.

In this study, an improved integrated radial basis function with nonuniform shape parameter is introduced. The proposed shape parameter varies in each support domain and is defined by theta = 1/dmax, where dmax is the maximum distance of any pair of nodes in the support domain. The proposed method is verified and shows good performance. The results are stable and accurate with any number of nodes and an arbitrary nodal distribution. Notably, the support domain should be large enough to obtain accurate results. This method is then applied for transient analysis of curved shell structures made from functionally graded materials with complex geometries. Through several numerical examples, the accuracy of the proposed approach is demonstrated and discussed. Additionally, the influence of various factors on the dynamic behavior of the structures, including the power-law index, different materials, loading conditions, and geometrical parameters of the structures, was investigated.

Recently, hybrid composites attract attention due their sustainability and specific properties. However, the advantages of biodegradability of these materials imply numerous challenges in terms of repeatability of mechanical properties and structural behavior. Due to this, it is essential to investigate their structural response under specific environmental and loading conditions. One of the crucial properties of composite materials is the resistance to fatigue, which should ensure proper and safe operation of structures and components made of these materials. Under certain loading conditions, e.g., when composites are subjected to cyclic loads, the self-heating effect may occur in a non-stationary regime, accelerating the structural degradation and leading to the failure. However, the fatigue and degradation processes can be described by specific fatigue parameters. In this study, the concept of evaluation of fatigue resistance based on critical self-heating temperature was adapted to evaluate the response of hybrid composites. The determined values of the critical self-heating temperature can be used as an indicator of the development of fatigue failure and can be used as a material property specific for a given material. The adapted approach based on the critical self-heating temperature was validated with the results acquired from the acoustic emission tests, demonstrating high consistency and accuracy in determination of this fatigue property.

This study assessed the fatigue performance of glass/epoxy composite by exploring the role of loading frequency (20-50 Hz) on fatigue strength, lifespan, and damage evolution. Implementing bilinear thermographic approaches (Delta T- 6 and q(center dot)- 6) highlighted a remarkable fatigue strength reduction as frequency increased. At higher frequencies (40 Hz and 50 Hz), the discrepancies in fatigue strength values resulting from thermographic methods were more pronounced than at lower frequencies. The determined fatigue strengths at higher frequencies were then compared to those obtained from the standard S- N curves as a reference. The analysis demonstrated the closer alignment of q(center dot)- 6 results with the reference S- N curves. The unfeasibility of bilinear models at higher frequency under high-stress levels necessitated establishing a new trilinear q(center dot)- 6 model. The developed model aimed to assess the fracture fatigue entropy (FFE), alongside the entropy-based damage index (EDI) as a normalized indicator for damage evolution across low-, intermediate-, and high-cycle-fatigue regimes, facilitating the FFE-based S- N curves validated with the experimental S- N data. The new EDI-based S- N curves were then established at different levels of damage accumulation. Damage evolution was captured via real-time acoustic emission (AE) monitoring synchronized with the registered thermal responses, enabling the identification of critical fatigue cycles, where rapid damage accumulation begins, alongside determining the boundaries that indicate abrupt failure. Correlating the AE-identified critical boundaries with the stiffness reduction enabled the establishment of S- N curves based on various controlled degradation levels, bridging the knowledge gap and establishing a refined methodology for thermomechanical fatigue analysis of polymer-matrix composites (PMCs).

Hidden corrosion, not detected timely, may significantly affect the durability and integrity of aircraft structures; therefore, improvement of non-destructive testing (NDT) techniques is of high importance for reliable and safe aircraft operation. One of the commonly used NDT techniques for the detection of such a type of corrosion is the D-Sight technique, which gained wide appreciation in the aerospace sector due to its ability to perform low-cost and fast inspections of wide areas. One of the drawbacks of the method is its qualitative character, which makes it difficult to quantify corroded spots and track corrosion growth during operation. The following study aims to present recent advances in the enhancement of this technique by using advanced image processing, numerical simulations, and validation studies using reference methods (classical metrology, and digital image correlation) to make this method suitable for quantification of areas affected by hidden corrosion and monitoring its growth between periodic NDT inspections. The studies are performed on test specimens that simulate hidden corrosion and verified on results of D-Sight inspections of the Polish Air Force military aircraft. The results demonstrated good performance in identification and quantification hidden corrosion spots on D-Sight images. The approach can be used for supporting aircraft inspectors in analysis of inspection results of aircraft under operation that require periodic non-destructive testing.

This study explored the synergistic role of graphene nanoplatelets (GNPs) and carbon nanofibers (CNFs) on the thermomechanical fatigue performance of modified glass fiber-reinforced polymer (GFRP). Three composite materials were investigated including unmodified GFRP, GFRP modified with GNPs (0.75 wt% GNPs), and GFRP modified with hybrid nano-reinforcements (0.375 + 0.375 wt% GNPs and CNFs). Their fatigue strengths were assessed using two thermography-based approaches (i.e. Delta T-6, and q(center dot)- 6), with the minimum curvature radius (MCR) and maximum perpendicular distance (MPD) procedures individually incorporated into each approach. The results extracted from thermographic approaches highlighted the negative influence of GNPs on fatigue strength, while HNPs contributed to fatigue strength improvement. The S-N curves were constructed as a reference to assess the reliability of fatigue strengths derived from thermographic approaches. Unlike the MCR, incorporating MPD analysis into Delta T-6 and q(center dot)- 6 approaches demonstrated good alignment with fatigue strength values derived from S-N curves. Nevertheless, the introduced MPD-based q(center dot)-6 approach provided a more reliable strategy for assessing the fatigue strengths of these composites. Moreover, the S-N curve analysis, supported by thermal responses and microscopic observations, illustrated that while GNPs enhanced the low-cycle fatigue performance, incorporating HNPs notably improved the life of modified GFRP composite across both low-and high-cycle regimes.

Self-heating based vibrothermography (SHVT) is a promising non-destructive technique for inspecting polymer-matrix composites (PMCs) in circumstances with limited external heating feasibility, functioning under the resonant frequency excitation. This study broadened the applicability of SHVT technique for two-dimensional (2D) PMCs by examining its sensitivity and effectiveness in detecting and quantifying damage within 2D laminated composites across nine different scenarios. Atwo-step algorithm based on the concepts of the boundary of effective thermograms, and the maximal temperature ratio was proposed to methodically choose the optimal raw thermogram from a large set of registered thermograms for each scenario. The issues linked to blurred damage signatures in the raw infrared (IR) images adversely affected the overall sensitivity and accuracy of SHVT. Implementing the algorithm based on central moments improved the overall damage detectability using this technique. Additionally, the introduced hit/miss metric enabled the damage identification and quantification for all scenarios.

The self-heating effect in polymer matrix composites (PMCs) can be dangerous due to dominance of the fatigue process and its significant acceleration. Therefore, investigation of its influence on structural behavior and thermomechanical response is crucial for safe and reliable operation of PMCs. Due to lack of standardization of criteria of determination of fatigue properties, such as fatigue limit, during various modes of fatigue loading, the investigation of fatigue response attracts special attention. In some loading scenarios when the process is dominated either by mechanical fatigue degradation or self-heating effect, the classical approaches to determine fatigue limit may fail. This implies the need to establish new criteria for fatigue limit determination, also considering stress relaxation. In this study, the authors demonstrated that fatigue behavior is represented by bilinear S-N curve, which reveals different thermomechanical responses and damage mechanisms under specific loading conditions. Moreover, it was demonstrated the existence of a transition point on the intersection of these S-N curves, where dominance of self-heating effect and mechanical degradation was clearly noticeable. The fatigue process for both mentioned regimes was characterized in terms of self-heating temperature evolution and acoustic emission, which was validated by microscopic analysis and X-ray computed tomography after fatigue failure.

The study presents the vibration-based SHM system for the Dębica railway bridge located in Poland. The railway bridge owner was concerned about the excessive and self-excited vibrations of the hangers, the vibration measurement of 8 hangers per span in a total of two spans being monitored. The dynamic responses in both the transverse and longitudinal directions for each hanger under different load events over a nine-month period were recorded and introduced in this paper. The tension force and stress on each hanger are estimated through the natural frequency of the experimental vibration analysis. The proposed approaches could be used to develop a smart alarm system integrated into a vibration-based data-driven SHM system for heavy railway bridges.