Matrix Cracking In Composite Laminates Research Articles

A damage model for matrix cracks in composite laminates under fatigue loading based on continuum damage mechanics

A damage model for transverse matrix cracks in composite laminates under fatigue loading was presented in this paper. The model was prosed based on the theory of continuum damage mechanics (CDM) at macro level and could capture the ‘edge effect’ of matrix cracks in composite laminate under fatigue loading. To obtain the constitutive equation of UD lamina containing transverse matrix cracks, a polynomial Gibbs free energy function was derived, and a macro damage parameter was introduced to characterize the influence of matrix cracks on multidirectional stiffness properties of UD composite. To predict the initiation and evolution of matrix cracks, a previously deduced initial crack initiation life function and a Paris-like equation in terms of damage driving force were employed, respectively. Prediction results of two cross-ply laminates under fatigue loading with different stress levels were compared to the experimental results and prediction results obtained from previously proposed model. The comparison results indicate the presented model is more effective and reliable in predicting the initiation and evolution of matrix cracks and the corresponding stiffness degradation in composite laminates under fatigue loading.

Crack density estimation method for composite laminates based on discrete form stiffness degradation models

Matrix cracking of composite laminates leads to stiffness degradation and dominates the medium leakage of liner-less composite vessels. A stiffness degradation model can be established through the machine learning method, which provides only discrete form equivalent moduli data without explicit analytical results. This paper further explored the use of the discrete form data set of stiffness degradation in the crack density estimation for composite laminates by using an iterative process. Furthermore, different mixed-mode fracture criteria were discussed. The results showed that Benzeggagh-Kenane (B-K) criterion and the power law criterion are more appropriate in mixed-mode crack density analyses.

Analysis of Stochastic Matrix Crack Evolution in CFRP Cross-Ply Laminates under Fatigue Loading

The present work aims at understanding the stochastic matrix crack evolution in CFRP cross-ply laminates under tension–tension fatigue loading. An experimental campaign was carried out on twenty-three specimens at different stress levels, while two optical techniques were used for the in-situ monitoring of the accumulation of transverse matrix cracks. The results showed a significant scatter in crack evolution among specimens. This stochastic behaviour was further investigated using image analysis and numerical modelling. It was found that transverse matrix cracks can be classified into the independent and dependent cracks based on a critical crack spacing. Furthermore, the severity of interaction among cracks was quantified by introducing a dependent crack ratio. Finally, a strength-based probabilistic model was proposed to describe the scattering regime of the crack evolution. The agreement between model and test results indicates that local strength variations of 90 plies are the dominant scattering source governing the initial fatigue resistance to cracking and determining the accumulation of transverse matrix cracks among specimens. These results may provide a new insight into the stochastic nature of matrix cracking in composite laminates and aid in the design of fatigue resistance properties.

The effect of staggered matrix crack induced delamination growth on the mechanical properties of cross-ply laminates

Matrix cracking in composite laminates is a common sub-critical damage mechanism that forms under thermomechanical loading and may induce delamination, which is a prevailing critical damage mechanism. Previous studies have considered induced delamination stemming from a symmetric pattern of matrix cracks despite observations revealing matrix crack patterns are staggered. In this study, delamination cracks induced from staggered matrix cracks in [90n/0m/90n]s cross-ply laminates is investigated analytically for the first time. A new energy-based analytical model is developed within the framework of classical lamination theory, where distinct zones along the induced delamination cracks are defined in the unit cell and a crack closure technique is employed. The laminate stiffness and strain energy release rate (ERR) are predicted for increasing induced delamination crack length. The analytical results were in excellent agreement with that of a finite element analysis (FEA) of the unit cell, demonstrating the accuracy and robustness of the developed model.

Evaluation of matrix cracking in composite laminates based on anomaly indices

The paper aims to develop a Lamb waves-based automated method dealing with early detection and accurate evaluation of matrix cracking in composite laminates. An anomaly-detection method devoted to the quantification of the extent to which a laminate plate deviates from its intact state is developed. In view of the nonlinear and chaotic dynamic properties of laminate plate caused by matrix cracking, recursive quantitative analysis (RQA) of sensed Lamb waves is introduced to characterize matrix cracking in composite laminates. The problem of damage detection is then recast as one-class classification problem in the space spanned by a set of RQA features, with the aim of global differentiation between normal and anomalous observations, respectively related to intact and supposed damaged laminate. To further quantify the damage degree of matrix cracking, an anomaly indices (AI) based on support vector data description (SVDD) is formed by combining a set of RQA features correlated with matrix cracking, thus the operating condition variability is implicitly included in the model through the feature fusion. The results of simulations and experiments verified that the proposed AI is sensitive to matrix cracking and can be used to quantify its severity degree.

A bi-directional damage model for matrix cracking evolution in composite laminates under fatigue loadings

An analytical model for prediction of transverse matrix cracks in composite laminates under fatigue loading was proposed. The micromechanics method was utilized to characterize the damaged behavior of composite laminates. The initial matrix crack initiation life was defined and deduced based on micromechanics method. Then the relation between initial matrix crack initiation life and critical energy release rate was established to obtain the distribution of initial matrix crack initiation life in cracked plies, and the evolution of matrix crack density and stiffness degradation were predicted. The prediction results were compared with experimental results and the comparison shows good agreement.

Enhanced variational approach for damage analysis of laminated composite

The main objective of this research is to introduce a new coupled analytical–numerical procedure to calculate stiffness reduction due to matrix cracks in composite laminates subjected to general loading conditions. A novel micromodel is developed for transverse cracking of general symmetric laminates based on a variational approach. The proposed method overcomes the restrictions of previous similar approaches regarding damage in laminates with general symmetric stacking sequences. A polynomial series is used for calculating the stress perturbation due to intralaminar cracks in conjunction with the principle of minimum complementary energy. The numerical part deals with well-known Newton–Raphson procedure to solve the governing equations for the unknown parameters for the stress functions. Furthermore, the analytical part can be solved just one time by a symbolic calculation for unknown geometry parameters, material properties, and loading conditions, which has the benefit to be ready for Finite Element software implementations. Comparison between the existing experimental and analytical results and the result of the present study are in good agreement.

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.

On transverse matrix cracking in composite laminates loaded in flexure under transient hygrothermal conditions

A simple predicted model using a modified Shear-lag method was used to represent the moisture absorption effect on the stiffness degradation for [0/90]2s composite laminates with transverse cracks and under flexural loading. Good agreement is obtained by comparing the prediction model and experimental data published by Smith and Ogin (2000). The material properties of the composite are affected by the variation of temperature and moisture absorption. The transient and non-uniform moisture concentration distribution give rise to the transient elastic moduli of cracked composite laminates. The hygrothermal effect is taken into account to assess the changes in the normalised axial and flexural modulus due to transverse crack. The obtained results represent well the dependence of the stiffness properties degradation on the cracks density, moisture absorption and operational temperature. The composite laminate with transverse crack loaded in axial tension is more affected by the hygrothermal condition than the one under flexural loading. Through this theoretical study, we hope to contribute to the understanding of the moisture absorption on the composite materials with matrix cracking.

Comment to the paper ‘Analysis of Progressive Matrix Cracking in Composite Laminates II. First Ply Failure’ by George J Dvorak and Norman Laws

Comment to the paper ‘Analysis of Progressive Matrix Cracking in Composite Laminates II. First Ply Failure’ by George J Dvorak and Norman Laws

Detection of matrix cracks in composite laminates by using the modal strain energy method

As the foremost mechanism of damage development, matrix cracking is the critical damage found in the early stage of structural failure of composites. This study aims to nondestructively detect matrix cracks in composite laminates by using an experimental modal analysis (EMA). An AS4/PEEK composite was used to fabricate cross-ply [02/9012/02] and quasi-isotropic [(±45/0/90)4] s laminates. The damage in the form of a matrix crack in the laminates was created by using a tensile load. The EMA was conducted on the laminates to obtain the modal displacements before and after damage. The displacements were then employed to compute the modal strain energy and to define the damage index, which is used for detecting matrix cracks. Limited by the mesh points of measurements, we used the differential quadrature method to calculate the partial differentials in the strain energy formula. The results obtained were validated by using the X-ray radiography method and three-point bending tests. The experimental results showed that the damage index well identified the location of breadthwise matrix cracks inside the laminates. However, the resolution of the damage index became poor if the spans of matrix cracks were short or the matrix cracks were scattered over the laminates.

Guided wave-based detection of delamination and matrix cracking in composite laminates

The aim of this article was a numerical and experimental study of the active damage detection methods based on piezoelectric elements attached to a composite laminate. In considered case, guided waves were excited and received in a structure using pulse-echo method. It means that after exciting a structure with a pulse, an array of sensors located on a structure was used to ‘listen' for reflected waves coming from discontinuities. The main part of structural health monitoring system is signal-processing algorithms, which allow to detect and localize damage. Algorithm applied in this research results in special maps that indicate damage location. In this article, a damage localization algorithm was described and experimentally tested. The proposed method was successfully tested on a carbon—epoxy part of a helicopter.

Stiffness reduction and fracture evolution of oblique matrix cracks in composite laminates

A constitutive model to predict the onset and evolution of matrix cracking and the subsequent stiffness reduction is derived analytically. The formulation is valid for symmetric laminates with otherwise arbitrary stacking sequence and matrix cracks in one or two directions. The proposed model calculates the reduction of the mechanical properties of the damaged laminate as function of crack densities. The onset and evolution of matrix cracks are predicted by the model in terms of undamaged lamina properties and the critical strain energy release rates for modes I and II (GIC and GIIC). Therefore, there is not need for postulating damage evolution functions and no need for empirically adjusting the associated material parameters. The model formulation was specialized for the particular case of unidirectional loading. Comparison with experimental data showed an excellent prediction of crack initiation and evolution for a variety of laminate stacking sequences. The combination of constitutive and damage evolution equations formed an integrated, mechanistic damage model with no adjustable parameters.

The sensitivity of a polarimetric sensor embedded in unidirectional and cross-ply compositelaminates

Matrix cracking in composite laminates is the first macroscopic damage mode to be readilydetected. Polarimetric sensors embedded in composite laminates can detect thedevelopment of this damage and they have an advantage over other sensors in beingable to sense damage over long gauge lengths (potentially, many metres). In thispaper, the sensitivity of a polarimetric sensor manufactured from Hi-Bi PANDAfibre has been measured experimentally and a phase-strain model available inthe literature has been used to determine the characteristic parameters of thesensor. The sensitivity of such sensors embedded in unidirectional composites isshown to be in good agreement with theoretical predictions, allowing for materialnon-uniformity. In the case of cross-ply laminates, which are transversely anisotropic, itis shown that sensor sensitivity is dependent on the relationship of the sensoraxes to the composite axes, as well as on the degree of sensor twist. Maximumsensitivity is obtained for a combination of low twist angle and congruence betweenthe sensor optical axes and the composite axes. Twist angles of greater than90° give rise to sensitivities, which, although lower, are reasonably constant and approximatelythe same as the sensitivity of the sensor in a unidirectional composite.

Semi‐Empirical Modeling of Gas Permeability Induced by Multilayer Matrix Cracks in Composite Laminates

Gas permeability through damage networks in composite laminates is the key issue for the applicability of high‐performance composites to the cryogenic propellant tanks of space launch vehicles. A simple model for the gas permeability induced by multilayer matrix cracks in composite laminates is proposed based on the leak conductance at crack intersections, which is an extension of the model by Kumazawa et al (AIAA J. 41, 2037‐ ‐2044, 2003). Experimental evidence on the gas permeability mechanisms is summarized and reflected in the present model. In order to include the effects of applied loadings and damage sizes on the gas permeability, the leak conductance is assumed to be a function of the average crack opening displacements of the matrix cracks and the crack intersection angles. The leak conductance factor was empirically obtained as a function of the crack intersection angle, and the comparison of the gas permeability between the predictions based on the developed model and the experimental results is presented for the validity of this model.

Intra-laminar cracking in CFRP laminates: observations and modelling

Matrix cracks in composite laminates are almost invariably the first damage mechanisms in composite laminates and are the precursor to more serious forms of damage. The results presented in this paper include experimental investigations into the occurrence of these cracks in a wide range of laminates containing various angle-plies. Ultrasonic detection of these cracks using polar backscattering is found to be successful and shows promise as a method which could be applied outside the laboratory. Further work includes finite element simulations which lead to an understanding of aspects of the accumulation of damage in composite laminates.

Estimation of degraded composite laminate properties using acoustic wave propagation model and a reduction‐prediction network

PurposeTo develop a new method for estimation of damage configuration in composite laminate structure using acoustic wave propagation signal and a reduction‐prediction neural network to deal with high dimensional spectral data.Design/methodology/approachA reduction‐prediction network, which is a combination of an independent component analysis (ICA) and a multi‐layer perceptron (MLP) neural network, is proposed to quantify the damage state related to transverse matrix cracking in composite laminates using acoustic wave propagation model. Given the Fourier spectral response of the damaged structure under frequency band‐selective excitation, the problem is posed as a parameter estimation problem. The parameters are the stiffness degradation factors, location and approximate size of the stiffness‐degraded zone. A micro‐mechanics model based on damage evolution criteria is incorporated in a spectral finite element model (SFEM) for beam type structure to study the effect of transverse matrix crack density on the acoustic wave response. Spectral data generated by using this model is used in training and testing the network. The ICA network called as the reduction network, reduces the dimensionality of the broad‐band spectral data for training and testing and sends its output as input to the MLP network. The MLP network, in turn, predicts the damage parameters.FindingsNumerical demonstration shows that the developed network can efficiently handle high dimensional spectral data and estimate the damage state, damage location and size accurately.Research limitations/implicationsOnly numerical validation based on a damage model is reported in absence of experimental data. Uncertainties during actual online health monitoring may produce errors in the network output. Fault‐tolerance issues are not attempted. The method needs to be tested using measured spectral data using multiple sensors and wide variety of damages.Practical implicationsThe developed network and estimation methodology can be employed in practical structural monitoring system, such as for monitoring critical composite structure components in aircrafts, spacecrafts and marine vehicles.Originality/valueA new method is reported in the paper, which employs the previous works of the authors on SFEM and neural network. The paper addresses the important problem of high data dimensionality, which is of significant importance from practical engineering application viewpoint.

Through-Thickness Connection of Matrix Cracks in Laminate Composites for Propellant Tank

Matrix crack accumulation in multiple plies of composite laminates is experimentally investigated to assess the through-thickness connection of matrix cracks, which is closely related to propellant leakage problems of composite tanks. Cracking patterns in [0/θ 2 /90] s laminates reveal that layup angles have a significant effect on crack induction mechanisms in contiguous plies. Matrix crack propagation behaviors in the fiber direction of θ ply induced by 90-ply cracks are investigated in terms of energy release rates using parametric-oriented finite element analysis based on an oblique coordinate system. The effect of cryogenic conditions on crack induction in contiguous plies is also studied, and discussions on through-thickness connection of matrix cracks in composite laminates are provided.

Analysis of local delaminations in composite laminates with angle-ply matrix cracks

Abstract In this paper, local delaminations growing uniformly from the tips of angle-ply matrix cracks in composite laminates loaded in tension are modelled theoretically. A 2-D shear lag method is used to determine stresses in a laminate representative segment containing one crack and two crack tip delaminations. For the calculation of the strain-energy release rate (SERR) associated with delaminations, the damaged layer is replaced with an equivalent homogeneous one with effective elastic properties. Closed-form expressions for the total SERR and its mode I and mode II components as a linear function of the first partial derivatives of the effective elastic properties of the damaged layer with respect to delamination area are derived. Dependence of SERRs and the laminate stiffness properties on delamination area, crack density and ply orientation angle is examined for balanced [0 2 /θ 2 /− θ 2 ] s and unbalanced [0 2 /θ 2 ] s carbon/epoxy laminates. The total SERR obtained in this study is compared to a simple closed-form expression for a uniform local delamination derived in earlier work by O'Brien (Local delamination in laminates with angle-ply matrix cracks: Part II Delamination Fracture Analysis and Fatigue Characterization. NASA Technical Memorandum 104076/AVSCOM Technical Report 91-B-011). It appears that matrix crack density and delamination size influence the SERR value significantly.

Multi-directional stiffness degradation induced by matrix cracking in composite laminates

A model was developed for predicting the stiffness degradation of fiber reinforced plastics (FRP), with ply configuration [0 m /±θ n ] S , induced by matrix cracking under in-plane tension. The model assumes that the cracks in off-axis plies are uniformly distributed and a damage variable D is defined. Based on the theory of fracture mechanics, the elastic moduli of cracked matrix are obtained and indicated by the damage variable D, then the reduction of elastic moduli of laminates caused by the matrix cracks was studied. Comparison with experimental values for the glass/epoxy [90 3/0] S , [0/90] S and [0/±45] S laminates shows good agreement with the theoretical prediction given by the presented model.