Transverse Cracking In Cross-ply Laminates Research Articles

Equivalent stress concept to account for the effect of local cyclic stress ratio on transverse cracking in tension–tension fatigue

Presented test results on transverse cracking in cross-ply laminates upon tension–tension cyclic loading show that the increase of crack density depends not only on the maximum transverse stress in the cycle but also on the local cyclic stress ratio RTloc in the analyzed layer. To include the effect of the RTloc in the model with statistical failure stress distribution for crack initiation (based on Weibull distribution) adapted for fatigue, an equivalent stress is introduced in a similar manner as the equivalent strain energy release rate has been used for delamination crack propagation. The equivalent stress in the layer is defined as a power function of the maximum stress and the stress ratio in the layer. It was found, testing laminates with two different fiber contents that higher the local stress ratio in 90-layer, higher the transverse cracking resistance. Transverse crack density simulation using the developed equivalent stress model has been validated against test results.

Analytical study of transverse cracking in cross-ply laminates under combined loading based on a new coupled micro-meso approach

In this study, an analytical solution based on plane strain model in classical linear elasticity theory is presented for damage analyses of general cross-ply laminates under combined thermo mechanical loading. Equally spaced transverse cracks are considered in any of the 90° plies allows to apply a unit cell based coupled micro-meso model. Thereby, a unit cell includes transverse cracking in the composite ply level is considered to predict the stress and displacement fields that satisfy the equilibrium equations and continuity conditions. Then, a set of fourth order ordinary differential equations is derived and solved by an analytical method. The exact solutions of the differential equations are presented to determine the stress distributions at any point in the laminate subjected to the thermo mechanical in-plane and out-of-plane loadings. It is shown that the predicted stress distributions in the unit-cell are in good agreement with the results of finite element method and the available analytical methods. This method explicitly provides the stress and displacement functions for any point considering transverse cracking, which is an important inquiry for the continuum damage analyses of composite laminates.

The effect of voids on matrix cracking in composite laminates as revealed by combined computations at the micro- and meso-scales

Voids are an important type of manufacturing defects in fiber-reinforced composites. Matrix cracking is sensitive to the presence of voids. Although this cracking occurs at the ply scale, its dynamics is strongly affected by ply’s microstructure, in particular, fiber distribution, fiber content, and the presence of voids. In the current study, a computational approach to simulate the influence of intra-laminar voids on cracking in composite laminates is developed. The approach combines finite element models of two scales: a micro-scale model, where the fibers and voids are modeled explicitly, and a meso-scale model, where the cracking phenomenon is captured on the ply scale. The micro-scale model, incorporating plasticity and damage in the matrix, provides input for the meso-scale model, which simulates the progressive cracking by means of the extended finite element method. The methodology is applied to investigate the effect of voids on the density of transverse cracks in cross-ply laminates in function of the quasi-static tensile load. Different sizes and contents of voids, which are chosen based on experimental micro-computed tomography data, are simulated. The numerical experiments show that the presence of voids leads to earlier start of the cracking, with the crack density evolution less sensitive to voids.

Experimental study of the size effect on transverse cracking in cross-ply laminates and comparison with the main theoretical models

Transverse cracking of off-axis plies is typically the first step of some failure mechanisms in long fiber reinforced laminated composites. It is well known that the off-axis ply thickness affects strongly the strain level which this ply is able to withstand without cracking. Experimental evidences show that this critical strain level increases strongly with decreasing ply thickness for the thinnest plies, confirming a clear size effect. This fact could be used to inhibit transverse cracking with the use of the recently developed ultra-thin plies. However the classical failure criteria for composites are not able to predict this size effect. From the first tests in the 1970s, several models with very different hypotheses were proposed to predict this size effect. Surprisingly there is still not a clear consensus in the scientific community about which is the adequate model, though their fundamentals are radically different. In this work an extensive test campaign is carried out on self-similar [0/90]s cross-ply laminates of AS4/8552 carbon/epoxy. The size effect is evaluated spanning a broader spectrum of thicknesses than in the tests presented in the literature until now, in order to explore the range of thicknesses where the differences between predictions of the main theoretical models are larger. In spite of the inherent dispersion in the experimental results, the comparison shows that the purely stress-based criteria underestimates the apparent strength of the off-axis ply. The other models predict very similar results, particularly for the thinnest laminates, with slight underestimations or overestimations, depending on the model.

The effect of residual thermal stresses on transverse cracking in cross-ply laminates: an application of the coupled criterion of the finite fracture mechanics

A model to predict transverse cracking in cross-ply laminates in the presence of residual thermal stresses is developed here. This model is based on the coupled criterion of the finite fracture mechanics. This criterion has been successfully used for different materials, structures and scales to predict crack initiation. It is based on two main hypotheses: (i) crack initiation occurs as a finite-length crack onset and (ii) the crack onset requires that both stress and energy criteria are fulfilled simultaneously. The present model is developed under the generalized-plane-strain hypotheses combining the results obtained using the laminate theory and a boundary element code. The present analysis shows that the residual thermal stresses affect both the stress and the energy criteria in the form of adding a residual elastic-strain to the strain imposed by external mechanical loads. An explicit expression for this residual elastic-strain is provided. For certain composite materials as carbon/epoxy the value of this residual elastic-strain is shown to be relatively large in comparison with the nominal critical transverse strain of the material. The comparison with experiments shows that considering the residual thermal stresses using the strategy proposed here improves drastically the accuracy of the model predictions.

A numerical study of transverse cracking in cross-ply laminates by 3D finite fracture mechanics

Abstract Transverse cracking in cross-ply laminates is a key failure mechanism which needs to be understood in order to predict the failure initiation in these laminates. A new 2D model has recently been presented (Garcia et al., Int J Solids Struct 51, pp. 3844–3856, 2014) for predicting the first crack onsets in cross-ply laminates under tensile loading, which is based on the coupled criterion of the Finite Fracture Mechanics (FFM). This 2D model is able to predict a strong size effect on the critical strain leading to the first crack onsets, which agrees with some experiments found in the literature. However, some earlier studies have shown that the 3D effects can be relevant in determining the origin of the size effect found in these experiments. Therefore, a 3D application of the coupled criterion, which formulates this criterion as an optimization problem, is proposed here. The objective function to be minimized, under the stress and energy criteria described previously, is the critical strain leading to the first crack onset. The finite number of variables of the optimization define the crack geometry after its onset. Since the crack geometry is parametrized, the variables in the optimization are the parameters defining the crack geometry. The objective function is evaluated by combining FRANC3D and Abaqus. As occurs in the 2D model, the results predict the strong influence of the transverse-ply thickness on the process of transverse cracking. In particular, a slightly larger critical strain is predicted for thinner laminates. In addition, the optimal crack position also varies with the thickness: a free-edge crack onset is predicted for thick laminates, whereas for thin ones, the inside and free-edge crack positions are essentially equivalent.

FBG-based real-time evaluation of transverse cracking in cross-ply laminates

Transverse cracking is one of the most common initial failure modes of composites and has detrimental effects on the structural integrity. In this paper a novel real-time non-destructive testing method is proposed to evaluate the transverse cracking in cross-ply laminates. The FBG sensors were embedded in the cross-ply specimens [02/90n]s and [90n/02]s, n=2,3,4, at the interface along the fiber direction. The Digital Image Correlation measurement was applied in the tensile testing to determine the density of the transverse cracks. The FBG spectrum was distorted as the crack density increased and its width at a quarter of the peak w1/4 showed a high correlation with the crack density. A numerical method based on spectrum reconstruction using the Transfer Matrix Method was then introduced to investigate the relations between spectrum distortion and transverse cracking. The reconstructed spectrum has an accurate reproduction of the reflective spectrum of FBG. The results demonstrate that the spectrum distortion attributes to the non-uniform distributions of the longitudinal strain due to the transverse cracks and w1/4 can be applied as an effective indicator to evaluate the transverse crack density. The demodulation method using the FBG spectrum can be used to real-time detect the internal transverse cracks of composites.

Transverse cracking of cross-ply laminates: A computational micromechanics perspective

Abstract Transverse cracking in cross-ply carbon/epoxy and glass/epoxy laminates in tension is analyzed by means of computational micromechanics. Longitudinal plies were modeled as homogenized, anisotropic elastic solids while the actual fiber distribution was included in the transverse plies. The mechanical response was obtained by the finite element analysis of a long representative volume element of the laminate. Damage in the transverse plies was triggered by interface decohesion and matrix cracking. The simulation strategy was applied to study the influence of ply thickness on the critical stress for the cracking of the transverse plies and on the evolution of crack density in 0 2 / 90 n / 2 s laminates, with n = 1, 2, 4 and 8. It was found that the transverse ply strength corresponding to the initiation and propagation of a through-thickness crack was independent of the ply thickness and that the transverse strength of carbon/epoxy laminates was 35% higher than that of the glass fiber counterparts. In addition, the mechanisms of crack initiation and propagation through the thickness as well as of multiple matrix cracking were ascertained and the stiffness reduction in the 90° ply as a function of crack density was computed as a function of the ply thickness.

Experimental and numerical study of oblique transverse cracking in cross-ply laminates under tension

The first damage mode in cross-ply laminates under tension is broadly accepted as transverse cracks normal to the loading direction in the 90° layers, but there is not the same agreement about the second damage mode. While most of the analytical and experimental results are based on delamination induced by transverse cracking, another type of damage, oblique cracks within the 90° layers, has also been observed as the second damage mode in [0/904]s laminates. To understand the cause of this phenomenon, FE analyses considering damage development at the interfaces were performed. The obtained results indicate that the main reason for the oblique cracking damage mode is the higher toughness of the material in mode-II compared with mode-I: when the value of shear toughness is close to the opening toughness, the second damage mode in cross-ply laminates under tensile loading is delamination induced by transverse cracks, however, if the difference between the two values is large, oblique cracks in the 90° layers are likely to appear. In the specific tested and analysed laminate, if the mode II toughness is double the mode I toughness, oblique cracking occurs but if the values of mode I and mode II toughness are close, delamination is the second damage mode.

Cohesive modeling of transverse cracking in laminates under in-plane loading with a single layer of elements per ply

This study aims to bridge the gap between classical understanding of transverse cracking in cross-ply laminates and recent computational methods for the modeling of progressive laminate failure. Specifically, the study investigates under what conditions a finite element model with cohesive X-FEM cracks can reproduce the in situ effect for the ply strength. It is shown that it is possible to do so with a single element across the thickness of the ply, provided that the interface stiffness is properly selected. The optimal value for this interface stiffness is derived with an analytical shear lag model. It is also shown that, when the appropriate statistical variation of properties has been applied, models with a single element through the thickness of a ply can predict the density of transverse matrix cracks.

A Probabilistic SCG Model for Transverse Cracking in CFRP Cross-ply Laminates under Cyclic Loading

This paper presents a probabilistic fatigue model for transverse cracking in CFRP cross-ply laminates. First, a delayed fracture model for a crack in a brittle material subjected to cyclic loading was established on the basis of the slow crack growth (SCG) concept in conjunction with the Weibull's probabilistic failure model. Second, the above probabilistic delayed fracture model was applied to transverse cracking in cross-ply laminates during cyclic loading. The stress distribution and the length of the unit element were calculated with the aid of a shear lag analysis. The transverse crack density was expressed as a function of maximum stress, stress ratio and number of cycles using the parameters associated with the Paris equation and the Weibull distribution in addition to the mechanical properties. Unknown parameters were determined from experiment data for three kinds of cross-ply laminates to reproduce the transverse crack density against the number of cycles. The parametric studies using the obtained parameters revealed the effects of the Weibull modulus, crack propagation exponent and stress ratio on evolution of transverse cracking under fatigue loading.

A probabilistic static fatigue model for transverse cracking in CFRP cross-ply laminates

This paper presents a delayed-fracture model for transverse cracking in CFRP cross-ply laminates under static fatigue loading. First, a delayed-fracture model for a crack in a brittle material was established on the basis of the slow crack growth (SCG) concept in conjunction with a probabilistic fracture model using the three-parameter Weibull distribution. Second, the above probabilistic SCG model was applied to transverse cracking in cross-ply laminates under static fatigue loading. The stress and the length of the unit element in the transverse layers were calculated with the aid of a shear-lag analysis, taking the residual stress into account. The transverse crack density was expressed as a function of applied stress and time with the parameters in the Paris law and the Weibull distribution function specified, in addition to the mechanical and geometrical properties. Unknown parameters were determined from experiment data gathered in static tensile and static fatigue tests. The reproduced transverse crack density at various applied loads agreed well with the experiment results.

Effects of nonlinear viscoelastic behaviour and loading rate on transverse cracking in CFRP laminates

The progressive multiplication of matrix transverse cracks in cross-ply laminates made of long carbon fibre reinforced polymer (CFRP) is addressed in this study. Monotonic tensile tests performed on [03/903]S laminates at 120°C have shown a marked dependence of cracking development on loading rate. This paper aims to assess the impact of the material nonlinearity on the loading rate sensitivity of the damaging process. A “shear-lag” damage analysis, using the nonlinear correspondence principle and appropriate failure criteria, is carried out to numerically predict the cracking evolution. This work shows that, though important, the material nonlinearity of the undamaged material does not significantly enhance the loading rate sensitivity of the cracking process and it cannot explain alone the phenomenon. On the other hand, taking into account the loading rate dependence of the critical strength, together with the R-curve effect, which gives good predicted cracking curves, suggests that the observed rate effect pertains to the viscoelastic character of the damaged material in the process zone close to crack fronts.

Probabilistic energy based model for prediction of transverse cracking in cross-ply laminates

In the present paper an attempt is made to describe transverse cracking of cross-ply ( [ 0 ° n / 90 ° m ] s ) laminates subjected to an external applied load and a temperature change. For this purpose a new method is suggested which was developed on the basis of the energy balance based finite fracture criterion suggested by Hashin (1996) [Hashin, Z., 1996. J. Mech. Phys. Solids 44, 1129]. In this approach the value of the specific surface energy (the critical energy release rate) is assumed to be dependent on a random microdamage distribution in the material. Hence, it is assumed to be a random function of location. A new probabilistic technique is developed to take this randomness into consideration. It is shown that only one unknown probabilistic function is required, namely the probability density function of the specific surface energy. This is determined by fitting the external stress and the corresponding crack density to experimental data for any specific laminated system. The cracking process for any other laminate made of the same material may be predicted by the suggested method. Numerical simulation of progressive cracking process is described, which provides the probability density function for inter-crack distances as well as the crack density growth with increasing external loading. A simple probabilistic progressive cracking criterion is developed as well. The predicted crack density growth calculated for various laminates is in good agreement with published experimental results.

Lamb wave evaluation and localization of transverse cracks in cross-ply laminates

This paper investigates the effect of transverse cracks on the S0 mode velocity in GFRP and CFRP cross-ply laminates, and proposes a new AE source location method that considers the change in the S0 mode velocity due to the transverse cracks. We found experimentally that the stiffness and the velocity decreased as the transverse crack density increased. Analytical predictions deduced from the combination of the complete parabolic shear-lag analysis, the classical plate theory and the laminated plate theory are in good agreement with the experimental results. Utilizing this relationship between the velocity and the mechanical damage, we located AE sources of transverse cracks in cross-ply laminates with the calculated in situ velocity. We were able to show that highly accurate source location requires the reduction of the in situ value of the velocity. The present method is simple but quantitative and useful in health-monitoring for detecting and localizing the damage in composite structures.

Statistical damage analysis of transverse cracking in high temperature composite laminates

High temperature polymer composites are receiving special attention because of their potential applications to high speed transport airframe structures and aircraft engine components exposed to elevated temperatures. In this study, a statistical analysis was used to study the progressive transverse cracking in a typical high temperature composite. The mechanical properties of this unidirectional laminate were first characterized both at room and high temperatures. Damage mechanisms of transverse cracking in cross-ply laminates were studied by X-ray radiography at room temperature and in-test photography technique at high temperature. Since the tensile strength of unidirectional laminate along transverse direction was found to follow Weibull distribution, Monte Carlo simulation technique based on experimentally obtained parameters was applied to predict transverse cracking at different temperatures. Experiments and simulation showed that they agree well both at room temperature and 149 °C (stress free temperature) in terms of applied stress versus crack density. The probability density function (PDF) of transverse crack spacing considering statistical strength distribution was also developed, and good agreements with simulation and experimental results are reached. Finally, a generalized master curve that predicts the normalized applied stress versus normalized crack density for various lay-ups and various temperatures was established.

Influence of thermal history on transverse cracking in a carbon fiber reinforced epoxy composite

This paper presents the influence of thermal history on transverse cracking in carbon fiber reinforced epoxy (carbon/epoxy) composites. At first, measurement of micro-Vickers hardness and Fourier transform-infrared spectrum (FT-IR) analysis of resin are conducted to investigate the effect of thermal history on resin. Secondly, shrinkage strain and transverse strength are measured for carbon/epoxy unidirectional laminates. Thirdly, the effect of temperature and duration of thermal history on transverse cracking in cross-ply laminates is experimentally investigated. The change in the residual stress due to post-cure is also estimated for the cross-ply laminates. Transverse cracking in the cross-ply specimens after thermal history initiates at lower stresses than the critical stresses in virgin specimens. It is found that thermal history increases the hardness of resin; however, it does not change the chemical structures in resin. The decrease in the strength is mainly caused by degradation of the fiber/matrix interface.

Strength or toughness? A criterion for crack onset at a notch

Both energy and stress criteria are necessary conditions for fracture but neither one nor the other are sufficient. Experiments by Parvizi et al. on transverse cracking in cross-ply laminates corroborate this assumption. Thanks to the singularity at the tip of the notch, the incremental form of the energy criterion gives a lower bound of admissible crack lengths. On the contrary, the stress criterion leads to an upper bound. The consistency between these two conditions provides a general form of a criterion for crack nucleation. It enjoys the desirable property of coinciding with the usual Griffith criterion to study the crack growth and with the stress criterion for the uniform traction along a straight edge. Comparisons with experiments carried out on homogeneous notched materials and on bimaterial structures show a good agreement.

Development of transverse cracking in cross-ply laminates during fatigue tests

The purpose of this paper is to analyse the progressive development of transverse cracking in cross-ply laminates subjected to uniaxial fatigue tests. First, a finite-element analysis shows how an analytical model which considers a progressive shear through the thickness of the 0° layers can be used for evaluating the stress field in the case of progressive cracking across the specimen width. The paper then presents a simulation of the progression of the transverse cracking, based on statistical distributions along the specimen length for crack initiation and across the specimen width for crack growth across the specimen width. The simulation process is applied to glass-fibre/epoxy cross-ply laminates and the results obtained are compared with experimental results.

Modeling of time-dependent behavior of deformation and transverse cracking in cross-ply laminates

A model is developed to predict the transverse crack density and strain response in a cross-ply laminate under monotonic, bilinear and constant loading. First, the strain response of the cross-ply laminate due to transverse cracking is presented based on the viscoelasticity theory and shear lag analysis. The transverse crack density is given as a function of both time and stress using a probabilistic failure concept. Secondly, monotonic tensile tests, bilinear tensile tests and constant load tests of cross-ply laminates are carried out to measure the strains and transverse crack density. A few parameters necessary for the probabilistic function are determined from the monotonic tensile tests at various stress rates. Finally, good agreement of strains and crack density in bilinear and constant load cases between experimental results and predictions verifies the validity of the present model.