Modelling of fatigue damage progression and life of CFRP laminates

A progressive fatigue damage model has been developed for predicting damage accumulation and life of carbon fibre‐reinforced plastics (CFRP) laminates with arbitrary geometry and stacking sequence subjected to constant amplitude cyclic loading. The model comprises the components of stress analysis, fatigue failure analysis and fatigue material property degradation. Stress analysis of the composite laminate was performed by creating a three‐dimensional finite element model in the ANSYS FE code. Fatigue failure analysis was performed by using a set of Hashin‐type failure criteria and the Ye‐delamination criterion. Two types of material property degradations on the basis of element stiffness and strength were applied: a sudden degradation because of sudden failure detected by the fatigue failure criteria and a gradual degradation because of the nature of cyclic loading, which is driven by the increased number of cycles. The gradual degradation of the composite material was modelled by using functions relating the residual stiffness and residual strength of the laminate to the number of cycles. All model components have been programmed in the ANSYS FE code in order to create a user‐friendly macro‐routine. The model has been applied in two different quasi‐isotropic CFRP laminates subjected to tension–compression (T–C) fatigue and the predictions of fatigue life and damage accumulation as a function of the number of cycles were compared with experimental data available in the literature. A very good agreement was obtained.     

Stress Distributions around Holes in Composite Laminates Subjected to Biaxial Loading

An approximate solution has been derived for the in-plane stresses near a circular hole, in an orthotropic composite laminate under biaxial loading. The derived stresses were found to be in good agreement with the exact analytical solution, for a series of laminates investigated. However, the degree of accuracy of the approximate stress distribution is strongly influenced by the laminate lay-up and the biaxiality ratio. The resultant stresses could be employed in stress based fracture models to investigate the notch sensitivity and fracture mechanisms of composite plates with an open-hole subjected to biaxial loading.     

Experimental characterization of damage behavior in polycyanate CFRP laminates under high temperature atmospheric exposure

This study focuses on the experimental characterization of damage behavior due to thermo-oxidative-induced matrix shrinkage in carbon fiber reinforced plastics (CFRP) with polycyanate ester. To investigate the effects of laminate configuration on matrix shrinkage behavior, [90]₈ and [0]₈ unidirectional laminates, [±45]_2S angle ply laminates, and [45/0/–45/90]_3S quasi-isotropic laminates were exposed to high temperature atmospheric environment at 180 °C to analyze matrix shrinkage up to 2000 h. These samples were removed from convection oven to observe sample side surface changes. The thermo-oxidative-induced matrix shrinkage was measured on the side surface of CFRP sample by confocal laser microscopy. The results suggested thermo-oxidative-induced matrix shrinkage depended on aged hours, fiber-to-fiber distance, and fiber orientation angle. The matrix shrinkage coefficient could be calculated with a tensorial transformation and empirical formula. The model can predict matrix shrinkage tendency of the 45° intra-lamina layer in quasi-isotropic laminate using the data of 0° and 90° matrix shrinkage in the quasi-isotropic laminates.     

A probabilistic approach for transverse crack evolution in a composite laminate under variable amplitude cyclic loading

This paper presents a theoretical approach for predicting transverse cracking behavior in a cross-ply laminate with a thick transverse ply under variable amplitude loads for which the cracks grow instantaneously, or very quickly, across the specimen width. The transverse crack density was derived on the basis of the slow crack growth (SCG) concept using the Paris law in conjunction with the Weibull distribution for a brittle material subjected to multi-stage cyclic loading. A fracture criterion obtained was related with the empirical rules by Miner and Broutman & Sahu. Next, the probabilistic SCG model was applied to transverse cracking in a cross-ply laminate under multi-stage cyclic loading. The two-stage fatigue tests with various loading sequences and amplitudes were conducted for carbon fibre reinforced plastic (CFRP) cross-ply laminates in addition to single-stage fatigue tests for various maximum stresses. The experiment results were compared with the predictions to verify the validity of the model.     

Prediction for progression of transverse cracking in CFRP cross-ply laminates using Monte Carlo method

This study predicted transverse cracking progression in laminates including 90° plies. The refined stress field (RSF) model, which takes into account thermal residual strain for plies including transverse cracks is formulated, and the energy release rate associated with transverse cracking is calculated using this model. For comparison, the energy release rate based on the continuum damage mechanics (CDM) model is formulated. Next, transverse cracking progression in CFRP cross-ply laminates including 90° plies is predicted based on both stress and energy criteria using the Monte Carlo method. The results indicated that the RSF model and the CDM model proposed in this study can predict the experiment results for the relationship between transverse crack density and ply strain in 90° ply. The models presented in this paper can be applied to an arbitrary laminate including 90° plies.     

Nonlinear constant fatigue life diagrams for carbon/epoxy laminates at room temperature

Exploration of a full shape of constant fatigue life (CFL) diagram and development of an efficient CFL diagram-based fatigue life prediction method are attempted for multidirectional CFRP laminates. On three kinds of CFRP laminates of [45/90/−45/0]_2s, [0/60/−60]_2s and [0/90]_3s lay-ups, tension–tension, tension–compression and compression–compression fatigue tests are performed at room temperature for two different stress ratios each. Experimental results clearly show that a stress ratio has a significant influence on the fatigue behavior of those CFRP laminates, and the CFL diagrams delineated using alternating stress and mean stress become asymmetric about the alternating stress axis. The alternating stress component of fatigue load for a given constant value of fatigue life turns maximum in the case of fatigue loading at a critical stress ratio that is nearly equal to the ratio of compressive strength to the tensile one. The shape of CFL diagrams progressively changes from a straight line to a nonlinear curve as a given constant value of fatigue life increases. A new and efficient method for accurately predicting an asymmetric nonlinear CFL diagram is then developed which is based on the static strengths in tension and compression and the reference S–N relationship fitted to the fatigue data for the critical stress ratio. The theoretical CFL diagram constructed following the proposed procedure agrees well with the experimental CFL diagram, regardless of the type of CFRP laminate. It is also demonstrated that the S–N relationships predicted using the proposed CFL diagram-based fatigue life prediction method adequately coincide with the experimental results for fatigue loading with a variety of different stress ratios in the range of fatigue life up to 10⁶ cycles.     

Tensile behavior of epoxy based FRP composites under extreme service conditions

A well established technique for strengthening reinforced concrete (RC) members is based on the use of externally bonded (EB) FRP composites. Nevertheless, limited knowledge is available on the mechanical properties of FRP composites at extreme service environments. The performance of structural members strengthened with EB-FRP laminates exposed to extreme service temperatures or freeze–thaw cycles is mainly associated to either the bond between the FRP laminate and concrete substrate, or the mechanical properties of the laminates. This paper focuses on the latter aspects and presents results on a series of tensile tests of glass and carbon FRP (GFRP and CFRP) coupon specimens exposed to temperatures ranging between ?15 and +70 °C, or after freeze–thaw cycles, including FRP specimens with different number of plies. The experimental results for GFRP specimens indicate a low influence of ply number on FRP mechanical properties, and a minor reduction of axial tensile strength and strain with increasing the temperature. Results for CFRP specimens subjected to extreme service temperatures reflect a significant reduction of mechanical properties, while freeze–thaw cycles do not significantly influence the mechanical performance.     

Piezoresistive effect of plain-weave CFRP fabric subjected to cyclic loading

The present study deals with electrical resistance changes in woven-fabric CFRP during loading. Four kinds of plain weave woven-fabric CFRP laminated specimens are prepared and subjected to cyclic tensile loading that does not cause any damages, and the electrical resistance changes of the specimens are measured experimentally by the four-probe method. As a result, the present study shows that the electrical resistance of a specimen comprised of six ±45° plies decreases remarkably with increasing number of loading cycles. The decrease is caused by shear plastic deformation of ±45° plies. The thickness shrinkage caused by shear plastic deformation increases the number of fiber contacts, and this decreases the interlaminar contact resistance between the plies. For a single ±45° ply, the same electrical resistance decrease caused by the shear plastic deformation is observed, and the magnitude of the decrease is smaller than that of the six-ply laminate tested. This is because the effect of interlaminar contact resistance decrease does not exist for a single ±45° ply. For the six 0°/90° plies, the present study shows that electrical resistance in the through-thickness direction is decreased by out-of-plane plastic deformation of carbon fiber and misalignment of the plies.     

Modelling the compression strength of polymer laminates in fire

A theoretical and experimental study is presented into the thermal decomposition, softening and failure of polymer matrix laminates under combined compressive loading and one-sided heating to high temperature. A thermo-mechanical model is presented for predicting the time-to-failure of laminates supporting a static compressive stress during one-sided heating. The thermal component of the model predicts the mass loss due to polymer decomposition and through-thickness temperature profile of the hot laminate. The mass loss and temperature predictions are validated against measured data, and the agreement is good. The thermal analysis is coupled to a mechanics-based model that calculates the loss in compressive strength with increasing temperature. The model can also predict the time-to-failure of the hot laminate supporting a static compressive load. The accuracy of the model is evaluated using failure times measured in fire-under-compression load tests on a woven E-glass/vinyl ester laminate. The experimental time-to-failure values decreased with increasing heat flux (temperature) and applied compressive stress, and the model can accurately predict these failure times. The paper also examines the dimensional expansion, out-of-plane distortion and failure mechanism of laminates under combined compressive loading and heating. It is envisaged that the thermo-mechanical model is a useful tool to estimate the failure time of compressively loaded composite structures exposed to high temperature or fire.     

Quantification of flexural fatigue life and 3D damage in carbon fibre reinforced polymer laminates

Carbon fibre reinforced polymer (CFRP) laminated composites have become attractive in the application of wind turbine blade structures. The cyclic load in the blades necessitates the investigation on the flexural fatigue behaviour of CFRP laminates. In this study, the flexural fatigue life of the [+45/−45/0]_2s CFRP laminates was determined and then analysed statistically. X-ray microtomography was conducted to quantitatively characterise the 3D fatigue damage. It was found that the fatigue life data can be well represented by the two-parameter Weibull distribution; the life can be reliably predicted as a function of applied deflections by the combined Weibull and Sigmodal models. The delamination at the interfaces in the 1st ply group is the major failure mode for the flexural fatigue damage in the CFRP laminate. The calculated delamination area is larger at the interfaces adjacent to the 0 ply. The delamination propagation mechanism is primarily matrix/fibre debonding and secondarily matrix cracking.     

ISOTHERMAL FATIGUE BEHAVIOR OF SIGMA/T1METAL 21S LAMINATES,PART I: EXPERIMENTAL RESULTS

Experimental results are reported on the effect of static and cyclic loading (at 0.1 and 0.001 Hz) on the inelastic response of and damage development in (0)4, (0190), and (0/ ±45/90), SiC/Ti (Sigma/Timetal 21S) laminates, and the Timetal 21S matrix, at 650^°C and 21^°C. At the elevated temperature, viscoplastic deformation of the matrix can be observed even at relatively low applied stresses. At both temperatures, reduction of unloading elastic moduli of the laminates, which indicates onset of damage by interface decohesion, also starts after hailing to relatively low stresses. The cyclic loading rate has a significant effect on the number of cycles to failure, but not on the endurance limit of the (0/90), and (0/ ±45/90), laminates loaded by constant-amplitude tension at 650^°C. In the (0)₄ laminate, higher endurance limits were detected at 0.1 Hz than at 0.001 Hz However, regardless of loading rate and layup, the total strain at failure under both static and cyclic loading at 650^°C was measured at 1 ±0.1%. The experimental results are interpreted by micromecha-nical models in Part II [1].     

Fatigue behavior of RC T-beams strengthened in shear with EB CFRP L-shaped laminates

The use of externally bonded carbon fiber-reinforced polymer (EB-CFRP) to strengthen deficient reinforced concrete (RC) beams has gained in popularity and has become a viable and cost-effective method. Fatigue behavior of RC beams strengthened with FRP is a complex issue due to the multiple variables that affect it (applied load range, frequency, number of cycles). Very few research studies have been conducted in shear under cyclic loading. The use of prefabricated CFRP L-shaped laminates (plates) for strengthening RC beams under static loading has proven to be technically feasible and very efficient. This study aimed to examine the fatigue performance of RC T-beams strengthened in shear for increased service load using prefabricated CFRP L-shaped laminates. The investigation involved six laboratory tests performed on full-size 4520 mm-long T-beams. The specimens were subjected to fatigue loading up to six million load cycles at a rate of 3 Hz. Two categories of specimens (unstrengthened and strengthened) and three different transverse-steel reinforcement ratios (Series S0, S1, and S3) were considered. Test results were compared with the upper fatigue limits specified by codes and standards. The specimens that did not fail in fatigue were then subjected to static loading up to failure. The test results confirmed the feasibility of using CFRP L-shaped laminates to extend the service life of RC T-beams subjected to fatigue loading. The overall response was characterized by an accelerated rate of damage accumulation during the early cycles, followed by a stable phase in which the rate slowed significantly. In addition, the strains in the stirrups decreased after the specimens were strengthened with CFRP, despite the higher applied fatigue loading. Moreover, the addition of L-shaped laminates enhanced the shear capacity of the specimens and changed the failure mode from brittle to ductile under static loading. Finally, the presence of transverse steel in strengthened beams resulted in a substantially reduced gain in shear resistance due to CFRP, confirming the existence of an interaction between the transverse steel and the CFRP.     

Experimental characterization of microscopic damage behavior in carbon/bismaleimide composite—effects of temperature and laminate configuration

Microscopic damage behavior of high temperature CFRP, carbon/BMI (bismaleimide) under tensile loading was investigated experimentally. To clarify effects of laminate configuration and temperature on the microscopic damage behavior, 10 kinds of laminate configurations were tested at both 25 and 180 °C. Damage initiation at the free edge and progress in the width direction were observed using optical microscopy and soft X-ray radiography, respectively. Damage mechanics analysis was used to predict matrix cracking in 90° plies based on both the energy and average stress criteria. It is clarified that the critical energy release rate and critical average stress associated with matrix cracking in BMI based CFRP are larger than in epoxy-based CFRP, which certify the high crack resistance of carbon/BMI composites.     

Modelling the tension and compression strengths of polymer laminates in fire

Thermo-mechanical models are presented for predicting the time-to-failure of polymer laminates loaded in tension or compression and exposed to one-sided radiant heating by fire. Time-to-failure is defined as the time duration that a polymer laminate can support an externally applied load in a fire without failing. The models predict the temperature rise and through-thickness temperature profile in a hot decomposing laminate exposed to fire. Using this thermal data, mechanics-based models based on residual strength analysis are used to calculate the time-to-failure. A preliminary evaluation of the accuracy of the models is presented using failure times measured in fire-under-load tests on a woven glass/vinyl ester laminate. The model was evaluated at temperatures between ∼250 and 800 °C by testing the laminate at heat flux levels between 10 and 75 kW/m². It was found that the time-to-failure of the laminate decreased with increasing heat flux and increasing applied stress for both the compression and tension load conditions. The tests also revealed that the failure times were much shorter (by about one order of magnitude) when the laminate was loaded in compression. The models can predict the time-to-failure with good accuracy for both compression and tension loading for certain heat flux levels. However, because the models have only been evaluated for one type of laminate (woven glass/vinyl ester), further evaluation is necessary for other laminate systems. The paper also presents new experimental insights into the strengthening mechanisms of laminates at high temperature.     

Failure mechanisms of a notched CFRP laminate under multi-axial loading

A quasi-isotropic CFRP laminate, containing a notch or circular hole, is subjected to combined tension and shear, or compression. The measured failure strengths of the specimens are used to construct failure envelopes in stress space. Three competing failure mechanisms are observed, and for each mechanism splitting within the critical ply reduces the stress concentration from the hole or notch: (i) a tension-dominated mode, with laminate failure dictated by tensile failure of the 0° plies, (ii) a shear-dominated mode entailing microbuckling of the −45° plies, and (iii) microbuckling of the 0° plies under remote compression. The net section strength (for all stress states investigated) is greater for specimens with a notch than a circular hole, and this is associated with greater split development in the load-bearing plies. The paper contributes to the literature by reporting sub-critical damage modes and failure envelopes under multi-axial loading for two types of stress raiser.     

Prediction of initiation of transverse cracks in cross-ply CFRP laminates under fatigue loading by fatigue properties of unidirectional CFRP in 90° direction

A fatigue life to the initiation of transverse cracks in cross-ply carbon fiber-reinforced plastic (CFRP) laminates has been predicted using properties of the fatigue strength of unidirectional CFRP in the 90° direction. In the experiments, unidirectional [90]₁₂ laminates were used to obtain a plot of maximum stress versus number of cycles to breaking, and two types of cross-ply laminates of [0/90₄]_S and [0/90₆]_S were used to evaluate the initiation and multiplication of transverse cracks under fatigue loading. Transverse cracks were studied by optical microscopy and soft X-ray photography. Analytical and experimental results showed good agreement, and the fatigue life for transverse crack initiation in cross-ply laminates was predicted successfully from the fatigue strength properties of the unidirectional CFRP in the 90° direction. The prediction results showed a conservative fatigue life than the experimental results.     

Fatigue damage and hysteresis in wood-epoxy laminates

Wood-epoxy laminates were subjected to constant amplitude fatigue tests in tension-tension (R = 0.1), compression-compression (R = 10) and reverse loading (R = –1) in order to follow property changes and fatigue damage accumulation. Hysteresis loops were captured during these tests and the form of stress versus number of cycles to failure (S-N) curves was established. Reversed loading is the most damaging mode of cyclic stress application. In terms of static strengths, the wood laminate is weaker in compression than in tension. However at low levels of stress, following many fatigue cycles, the fatigue life is greater in compression-compression than in tension-tension. The shape of captured hysteresis loops is strongly influenced by loading mode. As subcritical damage develops, loop area increases and dynamic modulus falls. In reversed loading, loop bending and distortion is observed depending on whether the damage is tension- or compression-dominated or both. Maximum and minimum fatigue strains, the dynamic modulus and loop area have been plotted as a function of the number of fatigue cycles. The majority of damage occurs towards the end of the sample life but property changes can be detected throughout fatigue tests. Normalisation of fatigue data demonstrates that the fatigue behaviour of wood-epoxy laminates is consistent.     

Predicting fatigue crack initiation in fibre metal laminates based on metal fatigue test data

A methodology is presented to predict the cycles to crack initiation in a notched fibre metal laminate subjected to cyclic loading. The methodology contains four steps. First, the far-field metal layer stress cycle is obtained using classical laminate theory. Second, the peak stress cycle is estimated from a combination of a handbook solution for the stress concentration factor in a finite isotropic plate, and analytical solutions for the stress concentration for equal situations in infinitely large plates. The third step is to adapt the amplitude of the peak stress cycle to the characteristics of S–N data for monolithic material from the literature to allow for the cycles to initiation to be read from the S–N curve for each metal layer.In contrast to what can be found hitherto in the literature about predicting the cycles to fatigue crack initiation in fibre metal laminates, the authors of this paper leave no obscurities but rather attempt to bring understanding of the complete path from situation to prediction.Test results from the literature for Glare 4B-3/2-0.3 have been replicated using the aforementioned methodology. It is shown that it can accurately predict the number of cycles to crack initiation, although the S–N data that is used for the predictions dictates the obtained accuracy. The closer the stress cycle value of the S–N data is to the value of the case analysed, the higher the accuracy obtained. Such a trend was not observed for the stress concentration factor of the S–N curves used, although a choice for S–N data with a different stress concentration factor can cause a significant change in precision. The method is also shown to work for several other fibre metal laminates.     

Zur thermischen Ermüdung der Magnesium‐Basislegierung AZ91

Thermal fatigue of magnesium‐base alloy AZ91 Thermal fatigue tests of the magnesium‐base alloy AZ91 were carried out under total strain control and out‐of‐phase‐loading conditions in a temperature range between ‐50°C and +190°C. Specimens produced by a vacuum die casting process were loaded under constant total strain and uniaxial homogeneous stress. To simulate the influence of different mean stresses, experiments were started at different temperature levels, e.g. the lower, mean or upper temperature of the thermal cycle. The thermal fatigue behavior is described by the resulting stress amplitudes, plastic strain amplitudes and mean stresses as a function of the number of thermal loading cycles. Depending on the maximum temperature and the number of loading cycles, cyclic softening as well as cyclic hardening behavior is observed. Due to the complex interaction of deformation, recovery and recrystallization processes and as a consequence of the individual temperature and deformation history, thermal fatigue processes of the material investigated cannot be assessed using results of isothermal experiments alone. The upper temperatures or the resp. temperature amplitudes determine the total fatigue lifetime.