Fatigue behavior and failure mechanism of basalt FRP composites under long-term cyclic loads

This paper studies the fatigue behavior of basalt fiber reinforced epoxy polymer (BFRP) composites and reveals the degradation mechanism of BFRP under different stress levels of cyclic loadings. The BFRP composites were tested under tension–tension fatigue load with different stress levels by an advanced fatigue loading equipment combined with in-situ scanning electron microscopy (SEM). The specimens were under long-term cyclic loads up to 1 × 10⁷ cycles. The stiffness degradation, S–N curves and the residual strength of run-out specimens were recorded during the test. The fatigue strength was predicted with the testing results using reliability methods. Meanwhile, the damage propagation and fracture surface of all specimens were observed and tracked during fatigue loading by an in-situ SEM, based on which damage mechanism under different stress levels was studied. The results show the prediction of fatigue strength by fitting S–N data up to 2 × 10⁶ cycles is lower than that of the data by 1 × 10⁷ cycles. It reveals the fatigue strength perdition is highly associated with the long-term run-out cycles and traditional two million run-out cycles cannot accurately predict fatigue behavior. The SEM images reveal that under high level of stress, the critical fiber breaking failure is the dominant damage, while the matrix cracking and interfacial debonding are main damage patterns at the low and middle fatigue stress level for BFRP. Based on the above fatigue behavior and damage pattern, a three stage fracture mechanism model under fatigue loading is developed.     

High-cycle fatigue of hybrid carbon nanotube/glass fiber/polymer composites

Glass fiber polymer composites have high strength, low cost, but suffer from poor performance in fatigue. Mechanisms for high-cycle (>10⁴ cycles) fatigue failure in glass fiber composites consist primarily of matrix-dominated damage accumulation and growth that coalesce and propagate into the fibers resulting in ultimate fatigue failure. This investigation shows that the addition of small volume fractions of multi-walled carbon nanotubes (CNTs) in the matrix results in a significant increase in the high-cycle fatigue life. Cyclic hysteresis measured over each cycle in real time during testing is used as a sensitive indicator of fatigue damage. We show that hysteresis growth with cycling is suppressed when CNTs are present with resulting longer cyclic life. Incorporating CNTs into the matrix tends to inhibit the formation of large cracks since a large density of nucleation sites are provided by the CNTs. In addition, the increase in energy absorption from the fracture of nanotubes bridging across nanoscale cracks and nanotube pull-out from the matrix is thought to contribute to the higher fatigue life of glass composites containing CNTs. High-resolution scanning electron microscopy suggests possible mechanisms for energy absorption including nanotube pull-out and fracture. The distributed nanotubes in the matrix appear to inhibit damage propagation resulting in overall improved fatigue strength and durability.     

Fatigue life assessment of nodular cast iron containing casting defects

The fatigue behaviour of a nodular cast iron containing casting defects has been investigated in the high-cycle fatigue regime. In this paper, we propose a fatigue life assessment model for flawed materials based on a fracture mechanics approach which takes into account the position and size of the defect, short crack behaviour and the notch effect introduced by the defect. The fatigue behaviour of smooth samples, and long and short crack behaviour have been experimentally determined in order to identify the relevant mechanical parameters; these being introduced into the model. An experimental study has been made both in air and in vacuum in order to account for the position of the defect, noting that internal defects are supposed to be under vacuum conditions. Experimental results, which are based on a two-crack front-marking technique specially developed for this study, show that the propagation of natural cracks is controlled by the effective stress intensity factor in air as well as in vacuum. The K calculation for a short crack in the stress field of a notch is analysed using numerical elastic–plastic results. Comparison between experimental results and the computation of fatigue life for fatigue lives less than 10⁶ cycles shows that the fatigue behaviour of nodular cast iron is controlled by a propagation process. The model proposed is thus relevant for fatigue lives less than 10⁶ cycles so that the defect can be considered as a crack and the initiation stage neglected. Closer to the fatigue limit, this study shows that the initiation stage should be considered in the assessment of fatigue life of nodular cast iron, because a single macroscopic propagation assessment is not enough to describe the whole fatigue life. The defect cannot be considered as a pre-existent crack in the high-cycle fatigue range (>10⁶ cycles), and the initiation stage that contains microcrack propagation around the defect should be evaluated when assessing the high-cycle fatigue life of nodular cast iron.     

Characterization and modeling of stiffness reduction in SCS-6-Ti composites under low cycle fatigue loading

The stiffness reduction and evolution of microstructural damage of a unidirectional silicon carbide fiber reinforced titanium matrix composite under tension-tension fatigue were investigated. Tests were conducted under load control with maximum applied stresses ranging from 750 to 945 MPa. The crack density of the interfacial reaction layer and matrix, matrix crack length, and interfacial debonding length as a function of fatigue cycles and applied stress levels were measured. The results showed that the composites exhibited an initial regime with slow stiffness reduction, followed by a rapid stiffness drop regime and a plateau regime with minimal change in stiffness for the applied stress levels used in this study. The residual stiffness at N = 10⁶ cycles is independent of the applied stress levels, while the microstructural damage accumulation varied with the applied stresses. A partial crack shear-lag model was also developed to predict the residual stiffness as a function of fatigue damage accumulation. Analytical simulation indicated that the profile of the stiffness reduction curves was dominated by the matrix crack density, while the extent of stiffness reduction was dominated by the matrix crack length.     

Cyclic deformation of tungsten monofilament-reinforced multicrystalline copper composites

In an attempt to understand the cyclic deformation behavior of continuous fiber reinforced metal matrix composites, plastic strain controlled tests have been performed on tungsten monofilament-reinforced, multicrystalline, copper composites. The cyclic hardening response of the composites greatly depends on the fatigue dislocation structures corresponding to the strain amplitude. For example, at high strain amplitude, i.e. 1×10⁻³, secondary slip stimulated by the self-stresses of the primary dislocations becomes more active, and secondary hardening even occurs during saturation. At low strains, loop patches form and are associated with fine slip. At intermediate strains, persistent slip bands occur, but their distribution is altered by the presence of the fiber. The paper introduces a simple model to link the cyclic stress–strain response of the multicrystalline composites to those of monolithic single crystals and fibers. This model not only represents the fiber reinforcement by the rule of mixtures, but also adopts the Sachs model for the single crystal–polycrystal conversion factor. The results calculated by the model show very good agreement with the experimental data in all strain amplitudes at which the composites were fatigued. This encouraging outcome suggests that the new model could be applied to high-cycle fatigue of commercial continuous-fiber-reinforced polycrystalline metal matrix composites.     

A unified fatigue life model based on energy method

A new unified fatigue life model based on the energy method is developed for unidirectional polymer composite laminates subjected to constant amplitude, tension–tension or compression–compression fatigue loading. This new fatigue model is based on static failure criterion presented by Sandhu and substantially is normalized to static strength in fiber, matrix and shear directions. The proposed model is capable of predicting fatigue life of unidirectional composite laminates over the range of positive stress ratios in various fiber orientation angles. By using this new model all data points obtained from various stress ratios and fiber orientation angles are collapsed into a single curve.

The new fatigue model is verified by applying it to different experimental data provided by other researchers. The obtained results by the new fatigue model are in good agreements with the experimental data of carbon/epoxy and E-glass/epoxy of unidirectional plies.     

Cryogenic fatigue behavior of plain weave glass/epoxy composite laminates under tension-tension cycling

This paper focuses on understanding the tension-tension fatigue behavior of woven glass fiber reinforced polymer laminates at cryogenic temperatures. Tension-tension fatigue tests at frequencies of 4 and 10 Hz with a stress ratio of 0.1 were conducted at room temperature, 77 and 4 K. The fatigue stress versus cycles to failure (S-N) relationships and fatigue limits for 10⁶ cycles were obtained. Fractured specimens tested under fatigue tests were also examined with optical microscope.     

Off-axis fatigue behaviour and its damage mechanics modelling for unidirectional fibre–metal hybrid composite: GLARE 2

The fatigue behaviour of a unidirectional fibre–metal laminate GLARE 2 has been studied under various off-axis loading conditions. Tension–tension fatigue tests were first performed at room temperature on nine kinds of plain coupon specimen with a different off-axis angle. A non-dimensional effective stress defined on the basis of the classical static failure theory was applied as an off-axis fatigue strength parameter. A macroscopic fatigue damage mechanics model was then developed using the non-dimensional effective stress, and it was compared with the classical fatigue failure models for composites. The absolute off-axis fatigue strength decreases as the off-axis angle increases. The longitudinal fatigue strength of GLARE 2 is about two times as high as that of the high-strength aluminium alloy, while the transverse fatigue strength is almost one-half. The S–N relationships are almost linear for all off-axis angles in the intermediate range of fatigue life 10³<N_f<10⁵, and they are followed by fatigue limits. The off-axis fatigue data plotted using the strength ratio (i.e. the maximum fatigue stress normalized by the static strength) are approximately represented by a single master S–N curve. The non-dimensional effective stress succeeds in describing this characteristic of the off-axis fatigue behaviour. The damage mechanics model developed using the non-dimensional effective stress can favourably reproduce the directional nature of the constant amplitude off-axis fatigue behaviour of GLARE 2. This model has an advantage over the classical fatigue failure models for composites with respect to the numerical procedure for fatigue life analysis.     

Effect of water on the fatigue behaviour of a pa66/glass fibers composite material

The aim of this study is to evaluate the effect of the humidity on the long term behaviour of glass fiber reinforced thermoplastic in fatigue. Two sets of samples were studied, one set contained 0.2 wt% of water, the second 3.5 wt%. The fatigue tests are performed at a 10 Hz frequency, at room temperature and two various relative humidity ratios, 50% RH and 96% RH. The S–N curve of dried samples (0.2%) is above the one of humid samples (3.5%), the endurance limit at 10⁷ cycles for dried samples is equal to 40 MPa against 35 MPa for the second set. For a given strain, the fatigue life is higher for humid samples because the induced stress is much lower due to the plasticizing effect of water. Though the tests are carried out at room temperature (23 °C), the sample temperature at the surface reaches values higher than Tg and whatever the applied strain, the matrix is in a rubbery state when the fracture occurs. On the basis of S.E.M. examinations, the following scenario is proposed: crack initiation at the fiber end, crack propagation along the fiber sides going with debonding, then crack propagation in the rubbery matrix.     

Flexural fatigue of short glass fiber reinforced a blend of polyphenylene ether ketone and polyphenylene sulfide

Flexural fatigue tests were conducted on injection molded glass fiber reinforced a blend of polyphenylene ether ketone and polyphenylene sulfide composite using four-point bending with different stress ratios and different frequencies. The fatigue behavior of this material was described. The constructed S-N curves shift their trends obviously at the maximum cyclic stress being about 80% of the ultimate flexural strength. Examinations of failure surfaces for various loading conditions show that the fatigue failure mechanisms appear to be matrix yielding at high stresses and crack growth at low stresses. Analyses of the fatigue data at various stress ratios reveal that the data at low stress superimpose to form a single curve which is nearly linear when they are plotted as stress range versus number of cycles to failure in bilogarithmic axes, while the data at high stresses also converge to yield a single curve when they are plotted as (S _max S _range)^1/2 against specimen lifetimes (S _max is the maximum stress andS _range is the stress range). These results show that for the studied material the main factor influencing the lifetime is the stress range at low stresses and the parameter (S _max S _range)^1/2 at high stresses. Comparison of fatigue data in the frequency range of 0.89–7.0 Hz was made, no significant effect of frequency on the fatigue behavior is found.     

Fatigue behavior and modeling of short fiber reinforced polymer composites including anisotropy and temperature effects

Effects of anisotropy and temperature on cyclic deformation and fatigue behavior of two short glass fiber reinforced polymer composites were investigated. Fatigue tests were conducted under fully-reversed (R = −1) and positive stress ratios (R = 0.1 and 0.3) with specimens of different thicknesses, different fiber orientations, and at temperatures of −40 °C, 23 °C, and 125 °C. In samples with 90° fiber orientation angle, considerable effect of thickness on fatigue strength was observed. Effect of mold flow direction was significant at all temperatures and stress ratios and the Tsai–Hill criterion was used to predict off-axis fatigue strengths. Temperature also greatly influenced fatigue strength and a shift factor of Arrhenius type was developed to correlate fatigue data at various temperatures, independent of the mold flow direction and stress ratio. Micromechanisms of fatigue failure at different temperatures were also investigated. Good correlations between fatigue strength and tensile strength were obtained and a method for obtaining strain–life curves from load-controlled fatigue test data is presented. A fatigue life estimation model is also presented which correlates data for different temperatures, fiber orientations, and stress ratios.     

Fatigue crack propagation behavior of RC beams strengthened with CFRP under cyclic bending loads

A fatigue crack propagation equation of reinforced concrete (RC) beams strengthened with a new type carbon fiber reinforced polymer was proposed in this paper on the basis of experimental and numerical methods. Fatigue crack propagation tests were performed to obtain the crack propagation rate of the strengthened RC beams. Digital image correlation method was used to capture the fatigue crack pattern. Finite element model of RC beam strengthened with carbon fiber reinforced polymer was established to determinate J‐integral of a main crack considering material nonlinearities and degradation of material properties under cyclic loading. Paris law with a parameter of J‐integral was developed on the basis of the fatigue tests and finite element analysis. This law was preliminarily verified, which can be applied for prediction of fatigue lives of the strengthened RC beams.     

Flexural fatigue behavior of steel fibre reinforced concrete before and after cracking

This paper presents the results of a study of steel-fiber-reinforced concrete (SFRC) in flexural fatigue. An experimental technique was developed to determine the moment at which cracking is initiated, thus allowing a quantification of the survival life beyond cracking. Basically, the experimental program consisted of 8 series of flexural fatigue tests (under third-point loading) performed at three different levels of stress (70%, 75% and 85% of first-crack strength). Six SFRC mixtures (at a fiber dosage of 40 kg/m³) were prepared and tested. The variables were the water/cement ratio (0.45 and 0.35), and the fiber geometry (hooked, anchored, and crimped fibers). Two similar plain concretes (w/c=0.45 and 0.35) were used as reference mixtures. The fatigue response of the SFRC mixtures was found to be quite variable, both before and after cracking. The survival life appeared to be significant, especially at the lower level of stress investigated, but the overall variability prevented the identification of specific trends concerning the influence of the water/cement ratio and the type of fibers. The variability of the number of fibers found in the bottom half of the specimens at the critical section could not explain the variability of the survival life. It was concluded that the orientation of the fibers also had an influence in this respect, and that a fiber content higher than that utilized, or the use of larger test specimens, was probably required to limit this variability.     

Use of an energy‐based/critical plane model to assess fatigue life under low‐cycle multiaxial cycles

For engineering components subjected to multiaxial loading, fatigue life prediction is crucial for guaranteeing their structural security and economic feasibility. In this respect, energy‐based models, integrating the stress and strain components, are widely used because of their availability in fatigue prediction. Through employing the plastic strain energy concept and critical plane approach, a new energy‐based model is proposed in this paper to evaluate the low‐cycle fatigue life, in which the critical plane is defined as the maximum damage plane. In the proposed model, a newly defined NP factor κ^*  is used to quantify the nonproportional (NP) effect so that the damage parameter can be conveniently calculated. Moreover, a simple estimation method of weight coefficient is developed, which can reflect different contributions of shear and normal plastic strain energy on total fatigue damage. Experimental data of 10 kinds of materials are employed to assess the effectiveness of this model as well as three other energy‐based models.     

The fatigue limit of bearing steels – Part I: A pragmatic approach to predict very high cycle fatigue strength

Bearing steels and other high strength steels exhibit complex fatigue behavior in excess of 10⁷ cycles due to their sensitivity to defects like inclusions. Failure occurring in the very high cycle fatigue regime and the lack of an asymptote in the measured S–N data raise the questions as to the existence of fatigue limit and prediction of the fatigue strength of the high strength steel components. A series of two papers are written to discuss on the characteristics of the very high cycle fatigue and their implication for engineering applications. In the present paper (Part I) a deterministic defect model is developed to describe the fatigue crack growth from de-bonded hard inclusions. The model is shown to provide a unified prediction of fatigue behavior in different regimes, i.e. low cycle fatigue regime dictated by the tensile strength, high cycle fatigue regime obeying Basquin’s law and the very high cycle fatigue regime featured by the fish-eye and ODA (optically dark area) surrounding an interior fatigue-initiating inclusion on the fracture surface. The model predictions agree well with experiments. A combination of the deterministic model with a stochastic model that describes the inclusion size distribution allows prediction of fatigue strength and fatigue limit associated with certain reliability of a steel component. It is found that very high cycle fatigue, associated with interior inclusions, is attributed to the very slow crack propagation in vacuum condition, and that an asymptote for fatigue limit observed for mild steels also exists for high strength steels such as bearing steels, but extends beyond the very high cycle fatigue regime normally measured to-date. Monte Carlo simulation shows that such a fatigue limit asymptote becomes clearly visible in excess of 10¹² cycles, which is difficult to measure with today’s testing devices. Furthermore, the effects of steel cleanliness and specimen type and shape are studied by means of Monte Carlo simulations.     

Transverse crack growth behavior considering free-edge effect in quasi-isotropic CFRP laminates under high-cycle fatigue loading

The high-cycle fatigue characteristics focused on the behavior of the transverse crack growth up to 10⁸ cycles were investigated using quasi-isotropic carbon fiber reinforced plastic (CFRP) laminates whose stacking sequence was [−45/0/45/90]_s. To assess the fatigue behavior in the high-cycle region, fatigue tests were conducted at a frequency of 100 Hz in addition to 5 Hz. In this study, to evaluate quantitative characteristics of the transverse crack growth in the high-cycle region, the energy release rate considering the free-edge effect was calculated. Transverse crack growth behavior was evaluated based on a modified Paris law approach. The results revealed that transverse crack growth was delayed under the test conditions of the applied stress level of σ_max/σ_b = 0.2.     

Internal stress behavior of the short ceramic fiber reinforced aluminum alloy under tensile deformation

The in situ measurement of phase stress under tensile deformation on an A6061 alloy reinforced with SiC whiskers (Al/SiCw MMC: Metal Matrix Composite) was performed using the X-ray diffraction technique. In order to raise a preciseness of measurements, we applied a profile fitting technique to separate the nearby located diffraction peak. Tensile deformation on elastic to plastic range was applied by four points bending device and discussed internal stress behavior in the short ceramic fiber reinforced MMC. Phase stress in Al matrix was increased linearly up to 2800×10⁻⁶ in strain and then saturated immediately. On the other hand phase stress in SiC whiskers shows an unstable stress behavior. It was decreased at first because of the Poisson's effect from Al matrix but reversed over 500×10⁻⁶ applied strain. The measured phase stress behavior in elastic region agreed with the calculations using micromechanics based on Eshelby/Mori–Tanaka model except for this unstable internal stress region. The macro stress behavior in plastic region was extremely small than that of the tensile test results. It supposed that the mechanism of strength is not so much the fiber reinforcing as the dispersion strengthening like the Orowan mechanism. Regarding the fatigue property, ΔK_th of the Al/SiC MMC, this was lower than that of the A6061 alloy. On the Al/SiCw MMC specimen, many micro void formations were observed around the fatigue crack tip even under the ΔK_th of A6061. It was considered that these were caused by the high gradient of residual stress on composite process and the unstable stress behavior in low ΔK region.     

Crack initiation and propagation characteristics of a dual-phase Mg–Li alloy under high-cycle and very-high-cycle fatigue regimes

Ultralight Mg–Li alloys are promising aerospace materials as they are the lightest structural alloys at present; however, their fatigue behaviors remain to be explored. This work focuses on the fatigue strength and crack initiation behavior of an extruded dual-phase Mg–Li alloy (LZ91) under high-cycle and very-high-cycle fatigue regimes. The fatigue limit of LZ91 alloy at 10⁹ cycles was determined to be 78 MPa, and the fatigue ratio is 0.46. Microstructural characterization demonstrates that fatigue cracks tend to initiate at β-Li phase-enriched regions. The α-Mg phase presents a < > fiber texture with a basal plane that has low deformation in the extrusion direction and acts as an enhanced phase in relation to the β-Li phase. Deformation discrepancies cause localized cyclic plasticity at the Li phase that leads to fatigue crack initiation.     

Fatigue crack initiation and growth on a steel in the very high cycle regime with sea water corrosion

This paper is devoted to the effect of corrosion on the gigacycle fatigue strength of a martensitic-bainitic hot rolled steel used for manufacturing offshore mooring chains for petroleum platforms. Smooth specimens were tested under fully reversed tension between 10⁶ and 10¹⁰ cycles in three testing conditions and environments: (i) in air, (ii) in air after pre-corrosion and (iii) in air under real time artificial sea water flow. The fatigue strength at greater than 10⁸ cycles is reduced by a factor more than five compared with non-corroded specimens. Fatigue cracks initiate at corrosion pits due to pre-corrosion, if any, or pits resulting from corrosion in real time during the cyclic loading. It is shown that under sea water flow, the fatigue life in the gigacycle regime is mainly governed by the corrosion process. Furthermore, the calculation of the mode I stress intensity factor at hemispherical surface defects (pits) combined with the Paris-Hertzberg-Mc Clintock crack growth rate model shows that fatigue crack initiation regime represents most of the fatigue life.     

A comparative study of the fatigue and post-fatigue behavior of carbon–glass/epoxy hybrid RTM and hand lay-up composites

The paper presents a study of the fatigue and post-fatigue behavior of a hybrid carbon–glass biaxial fabric reinforced epoxy composite manufactured by the resin transfer molding (RTM) and the hand lay-up (HL) processes, with the main objective of assessing whether a material characterization run at the prototype level of a handicraft technology could be significant for a mass production technology and whether a comparison on static properties (a viable task at an industrial level) could ensure the same level of agreement for the fatigue life and residual properties. Tensile and flexural static tests as well as displacement-controlled bending fatigue tests (R ratio of 0.10) were conducted on two sets of standard specimens, having fiber orientation parallel to the loading direction (on-axis specimens) and at 45° to the loading direction (off-axis specimens). Specimens were subjected to different fatigue loading, with the maximum load level up to 60% of the average ultimate flexural strength, and damage in the laminate was continuously monitored through the loss of bending moment during cycling. After 10⁶ cycles, the fatigue test was stopped and residual properties were measured. Micrographs of sample sections revealed some voidage for HL specimens while resin rich areas were observed for RTM specimens. Results of the static tensile and flexural tests pointed out lower mechanical properties for the RTM specimens when tested on-axis and slightly higher properties when tested off-axis. Regardless of specimen fiber orientation, the fatigue and post-fatigue performance of RTM samples was inferior to that of HL specimens with the gap increasing for increasing fatigue load levels. The result was ascribed to the presence in RTM samples of resin-rich areas, which are reported to have limited influence on the laminate static properties but which may act as initiation sites for fatigue cracks.