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.     

The role of microdamage in tensile failure of graphite/epoxy laminates

Damage development during quasistatic tensile loading of several laminates of graphite/epoxy material is examined and compared to damage development in laminates of a similar graphite/epoxy material subjected to tension-tension fatigue loading. Emphasis is placed upon following damage development at the microstructural level. Evidence of the important role of off-axis ply cracks in localizing and controlling fiber fracture in adjacent load-bearing plies for both loading modes is resented. The relationship between fiber fracture density and static load level is presented for tensile loading of unidirectional and cross-ply laminates by direct observation of fiber fracture in situ. The frequencies of occurrence of multiple adjacent fiber fractures are also reported. The cross-ply laminate results are compared with those from fatigue testing. Significant differences are described and discussed.     

Microscopic fatigue damage progress in CFRP cross-ply laminates

Damage progress in toughened-type carbon fibre-reinforced plastic (CFRP) cross-ply laminates under tensile fatigue loading was measured using the replica technique. The laminate configuration was [0/90_m/0], where m = 4, 8 and 12. The damage parameters, transverse crack density and delamination ratio, were determined. A power-law model was proposed, relating the cyclic strain range and the number of cycles at transverse crack initiation. Based on experimental data, a simple shear-lag analysis combined with the modified Paris law was conducted to model the transverse crack multiplication. An extension of the shearlag analysis for laminates containing delaminations initiating from the tips of the transverse cracks was used to conduct a modified Paris law analysis for delamination growth.     

The mechanical behavior of optical fiber sensor embedded within the composite laminate

Mechanical behavior, such as tensile and fatigue strength, of the optical fiber sensor embedded within the composite laminate was investigated. Tensile and fatigue tests were performed to evaluate the static and fatigue characteristics of optical fibers embedded within three types of laminated composite specimens, [0₆/OF/0₆]_T, [0₂/90₄/OF/90₄/0₂]_T and [0₃/90₃/OF/90₃/0₃]_T. The initiation of damage and fracture of the optical fiber were detected by observation of the intensity drop-off of laser signal transmitted through the optical fiber during test. Experimental results showed that the fatigue strength of optical fiber embedded within the cross-ply laminate is much lower than the fatigue strength of optical fiber within the unidirectional ply laminate. It was also found that the optical fiber embedded within unidirectional ply laminate fractured due to the fatigue damage accumulation of internal defects of optical fiber itself. However the optical fiber embedded within the cross-ply laminate fractured due to the growth of transverse matrix crack of host composite laminate.     

A comparison of as-fatigue and re-consolidation residual properties for notched quasi-isotropic [0/45/90/−45]2S and cross-ply [0/90]4S AS4/PEEK composite laminates

A comparison of the as-fatigued and re-consolidated properties have been made between notched quasi-isotropic [0/45/90/−45]_2S and cross-ply [0/90]_4S AS4/PEEK laminates. For the former, the ±45° plies tend to constrain longitudinal damage development so that damage growth primarily occurred in the transverse direction, causing more widespread damage. This led to prominent mechanical properties degradation, shorter fatigue lives and lower residual strengths. For cross-ply laminates, quick and extensive longitudinal crack tangential to the hole and the corresponding 90° fiber shear off brought about effective stress concentration alleviation. This discouraged further damage development. Hence, their fatigue lives exceeded one million cycles even at high cyclic stress levels and their residual strengths were significantly higher than their virgin strength. On the other hand, the re-consolidation process removed most of the defects that alleviated the stress concentration and thus decreased the strengths. Detailed study of the residual strength changes and damage development history revealed that the residual as-fatigued and re-consolidated strengths were governed by the competition between local structural decay and its resulting stress concentration alleviation.     

Fatigue damage mechanisms and residual properties of graphite/epoxy laminates

Damage mechanisms and accumulation, and associated stiffness and residual strength reductions were studied in cross-ply graphite/epoxy laminates under cyclic tensile loading. Stress-life data were fitted by a two-parameter wearout model and by a second-degree polynomial on a log-log scale. The fatigue sensitivity is highest for the unidirectional laminates and it decreases for the crossply laminates with increasing number of contiguous 90° plies. Five different damage mechanisms were observed: transverse matrix cracking, dispersed longitudinal cracking, localized longitudinal cracking, delaminations along transverse cracks, and local delaminations at the intersection of longitudinal and transverse cracks. Failure patterns vary with cyclic stress level and number of cycles to failure. Under monotonie loading, failure is brittle-like and concentrated. At high stress amplitudes and short fatigue lives failure results from few localized flaws, whereas at lower stress amplitudes and longer fatigue lives failure results from more dispersed flaws. The residual modulus shows a sharp reduction initially, followed by a more gradual decrease up to failure. The residual strength showed a sharp reduction initially, followed by a plateau or even some increase in the middle part of the fatigue life, and a rapid decrease in the last part of the fatigue life. A tentative cumulative damage model is proposed based on residual strength and the concept of equal damage curves.     

Open hole fatigue characteristics and damage growth of stitched plain weave carbon/epoxy laminates

Fatigue response of stitched plain weave carbon/epoxy laminates containing circular holes is experimentally investigated. Two carbon/epoxy laminates of cross-ply [(0/90)]₂₀ and quasi-isotropic [(±45)(0/90)₂(±45)₂(0/90)₂(±45)₂(0/90)]_s are reinforced using Kevlar-29® yarns in through-thickness direction. The laminates are drilled to produce a circular hole with diameter of 5.7 mm. Stitch configuration for cross-ply laminates is round stitch and parallel stitch, while that for quasi-isotropic laminates is parallel stitch only. For round stitch configuration, the hole is surrounded by circular stitch line of 7-mm diameter. For parallel stitch, the distance between two stitch lines (spacing) is 15 mm. In all, three independent cases are presented in this paper: Case 1 (cross-ply laminates, round stitch, tension–tension fatigue); Case 2 (cross-ply laminates, parallel stitch, tension–tension fatigue); Case 3 (quasi-isotropic laminates, parallel stitch, compression–compression fatigue). In each case, comparison with unstitched laminates is made. Case 1 shows that round stitch reduces tension fatigue curve of carbon/epoxy laminates. Round stitch seems to aggravate the damage, which is emanating from the hole rim of laminates. It gradually diverts the damage towards the edge of the specimen and causes premature fatigue failure. Case 2 shows that although parallel stitch generally does not influence the fatigue life of laminates, the damage growth due to parallel stitch is apparently unstable after 8 million cycles. As a result, laminates with parallel stitch eventually fail before reaching 10 million cycles. In contrast, unstitched laminates are able to sustain fatigue load for more than 10 million cycles. Case 3 shows that under compression fatigue load, fatigue limit of stitched plain weave laminates is better than that of the unstitched ones due to damage redistribution along the stitch lines.     

Experimental and analytical characterization of transverse cracking behavior in carbon/bismaleimide cross-ply laminates under mechanical fatigue loading

Transverse cracking behavior in high temperature bismaleimide-based carbon fiber reinforced plastics (CFRP) laminates under fatigue loading was observed. Three types of cross-ply laminate, [0/90₂/0], [0₂/90₃/0₂] and [0₂/90₄/0₂], were tested to study the effect of ply thickness. Damage observation was conducted using two methods. Optical microscopy and soft X-ray radiography were used for edge and internal damage observation, respectively. Variational approach was used to derive the energy release rate associated with transverse cracking. Multiplication of transverse cracks was modeled based on modified Paris-law approach.     

An investigation of non-linear elastic behavior of CFRP laminates and strain measurement using Lamb waves

This paper investigates the non-linear elastic behavior of unidirectional and cross-ply CFRP laminates and proposes a new method to measure tensile strain using Lamb waves. Young’s modulus was measured as a function of strain in situ using Lamb wave velocity during a tensile test. The stiffening effect of the carbon fibers on [0]₈ specimens and the softening effect of the epoxy matrix on [90]₈ specimens were accurately evaluated. Young’s modulus of the 0° ply was obtained as a quadratic function of strain. Using the function and the rule of mixture, the dependence of Young’s modulus on strain was accurately predicted for cross-ply laminates. Based on the results, the tensile strain was quantitatively correlated with the corresponding arrival time of the Lamb waves. The strains obtained from the proposed method agreed well with those from the strain gauge. Finally, the effect of transverse cracks on the in situ Young’s modulus of the cross-ply laminate under a tensile load was investigated. This method clearly detected even a small decrease in the Young’s modulus due to the transverse cracks in stiffening cross-ply laminate.     

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.     

The use of a characteristic damage variable in the study of transverse cracking development under fatigue loading in cross-ply laminates

A two dimensional shear lag analysis of a cracked cross-ply composite laminate subjected to uniaxial loading, taking into account residual thermal stresses, has been developed. This analysis has led us to introduce a characteristic non-dimensional damage variable η, which is a function of the crack density, material properties, and lamina stacking sequence. This analysis has been applied to a CFRP composite material (T300/914). The use of the characteristic damage variable has led to phenomenological laws that allow accurate prediction of the number of fatigue cycles necessary for the initiation of the first matrix cracks, and the kinetics of this damage, up to the “saturation” stage, in any cross-ply laminate subjected to a uniaxial fatigue loading.     

Microscopic damage behavior in carbon fiber reinforced plastic laminates for a high accuracy antenna in a satellite under cyclic thermal loading

For a high accuracy antenna in next radio astronomy satellite, a candidate material is carbon fiber reinforced plastics (CFRP), because negative longitudinal coefficient of thermal expansion (CTE) for unidirectional CFRP enables a laminate with 0 CTE through appropriate laminate design. This enables high structural accuracy under large temperature fluctuation like space. On the other hand, when the laminate is subjected to thermal cycles, cyclic thermal stress occurs and causes microscopic damages. In this study, we characterized damage progress in CFRP laminates and resultant variation in mechanical properties under cyclic thermal loading. Three types of matrices, such as polycyanate ester, polyimide and epoxy resin were used to prepare CFRP laminates. Specimens were subjected to thermal cycles from ?197°C to 120°C. The test was periodically stopped for surface observation and flexural loading. Transverse cracks in 90° plies accumulated with thermal cycles, whereas flexural modulus remained constant. We also numerically evaluated temperature gradient and resultant thermal stress distribution during cooling by finite element analysis. The result indicates higher transverse stress appeared in the surface of the specimen and saturated to constant value which corresponded with the value calculated based on classical lamination theory.     

The behaviour of Kevlar fibre-epoxy laminates under static and fatigue loadings. Part I—experimental

Kevlar 49 fibre and unidirectional Kevlar fibre reinforced plastic (KFRP) laminates both show an increase in stiffness under monotonic tensile loading. This stiffening effect is time-dependent and is reversible once the load is removed. In contrast, the modulus of a cross-ply KFRP laminate is affected primarily by matrix cracking of the transverse (90°) ply, and is sensitive to strain-rate and temperature. In cyclic (tensile) loading, however, the modulus of the cross-ply laminate depends on a combination of the fibre stiffening effect and transverse matrix cracking.     

Residual Stiffness of Cracked Cross-Ply Composite Laminates Under Multi-Axial In-plane Loading

In this paper, the Equivalent Constraint Model (ECM) together with a 2-D shear lag stress analysis approach is applied to predict residual stiffness properties of polymer and ceramic matrix [0/90 _n /0] cross-ply laminates subjected to in-plane biaxial loading and damaged by transverse and longitudinal matrix cracks. It is found that the longitudinal Young’s modulus, shear modulus and major Poisson’s ratio undergo large degradation as the matrix crack density increases, with Poisson’s ratio appearing to be the most affected by transverse cracking. In cross-ply laminates with thick 90° layer strip-shaped delaminations begin to initiate and grow from the tips of matrix cracks at the 0°/90° interface. These delaminations contribute to further stiffness degradation of such laminates, and hence have to be taken into account in failure analysis models. The thickness of the 90° layer plays an important role; the thicker the 90° layer, the bigger stiffness reduction suggesting a size (volume) effect at ply level. In SiC/CAS cross-ply laminates reduction in the longitudinal modulus occurs mainly due to transverse cracks, while the shear modulus appears to be the most affected by the presence of longitudinal cracks. The shear modulus reduction ratio predicted previously by a semi-empirical formula is, in the most of cases, within 10% of the current ECM/2-D shear lag approach value. In some cases, though, the error of the semi-empirical finite element expression can be as big as 20% since it fails to capture damage mode interaction.     

Characterization and evolution of matrix and interface related damage in [0/90]S laminates under tension. Part I: Numerical predictions

This paper considers damage development mechanisms in cross-ply laminates using an accurate numerical method that assumes a Generalized Plane Strain (GPS) state. A 2D Boundary Element Method (BEM) model is generated to investigate the two types of damage progression in a [0/90]_S laminate: transverse cracks in the 90° lamina and delamination between both laminae. The model permits the contact between the surfaces of the cracks. The study is carried out in terms of the dependence of the Energy Release Rates (ERR) of the two types of crack on their respective lengths. A special emphasis is put on the mechanisms of the joining of the two aforementioned types of crack, including the study of the distribution of the stresses along the interface between the two plies when the transverse crack is approaching this interface.     

An investigation of the damage mechanisms and fatigue life diagrams of flax fiber-reinforced polymer laminates

In this paper we investigated the fatigue damage of a unidirectional flax-reinforced epoxy composite using infrared (IR) thermography. Two configurations of flax/epoxy composites layup were studied namely, [0]₁₆ unidirectional ply orientation and [±45]₁₆. The high cycle fatigue strength was determined using a thermographic criterion developed in a previous study. The fatigue limit obtained by the thermographic criterion was confirmed by the results obtained through conventional experimental methods (i.e., Stress level versus Number of cycles to failure). Furthermore, a model for predicting the fatigue life using the IR thermography was evaluated. The model was found to have a good predictive value for the fatigue life. In order to investigate the mechanism of damage initiation in flax/epoxy composites and the damage evolution, during each fatigue test we monitored the crack propagation for a stress level and at different damage stages, a direct correlation between the percentage of cracks and the mean strain was observed.     

Matrix cracking and stiffness reduction during the fatigue of a (0/90)s GFRP laminate

Stiffness reduction due to matrix cracking in a (0/90)_s glass fibre reinforced plastic (GFRP) laminate has been studied under both quasi-static and fatigue loading. The stiffness reduction is shown to be directly proportional to the density of cracks which accumulate in the transverse ply. A model for the transverse ply crack growth during fatigue gives good agreement with the experimentally determined stiffness reduction curves.     

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.     

Damage mechanics characterization of transverse cracking behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers

Microscopic damage behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers under tensile fatigue loading is investigated. Damage observation is conducted using an optical microscope and soft X-ray radiography. The material used is CFRP with interlaminar-toughened layers, T800H/3900-2. The laminate configurations are quasi-isotropic [45/0/−45/90]_s, [0/45/−45/90]_s and [45/−45/0/90]_s to discuss the effect of stacking sequence on microscopic fatigue damages. A damage mechanics analysis is used to obtain the energy release rate for transverse cracking which is correlated to the transverse crack density growth rate. The modified Paris-law analysis proves to be valid for characterization of transverse crack multiplication when the effect of other damage is small.     

High-cycle fatigue characteristics of quasi-isotropic CFRP laminates over 10 cycles (Initiation and propagation of delamination considering interaction with transverse cracks)

High-cycle fatigue features of over 10⁸ cycles, particularly the initiation and propagation of edge delamination considering the effects of transverse cracks, were investigated using quasi-isotropic carbon-fiber-reinforced plastic (CFRP) laminates with a stacking sequence of [45/0/−45/90]_s in this study. In the relationship between a transverse crack density and initiation and growth of edge delamination, it was found that fatigue damage growth behavior varied depending on applied stress. It was observed that edge delamination initiated and grew at parts where transverse cracks were dense at ordinary applied stress, whereas it was observed that edge delamination grew before or simultaneously with transverse crack propagation at a low applied stress and high-cycle loading. In addition, the critical transverse crack density where delamination begins growing was calculated to evaluate the interaction between transverse crack and edge delamination growth.