Matrix Cracking In Composites Research Articles

A fibre direction informed continuum damage model with enriched kinematics for modelling matrix cracking in composites

Continuum Damage Mechanics models are widely used for simulation of ply-level damage such as matrix cracking in composites. Although their ease of implementation within the finite element framework is appealing, several limitations exist such as a smeared representation of sharp cracks, mesh orientation bias of crack growth, inaccurate energy dissipation due to approximate definition of characteristic length etc. In this work, a new ‘semi-discrete’ continuum damage model is proposed for matrix cracking, that includes sharp crack kinematics. The mesh orientation bias is eliminated by a fibre-directed growth driving criterion. The crack characteristic length is exactly computed due to an accurate geometric representation of the crack surface. The model also addresses a well-known problem of spurious stress transfer across crack faces when deformation becomes large. Through several challenging benchmark problems, the model is shown to perform nearly as good as discrete crack models while being simpler and more robust.

Numerical and Experimental Study of the Effect of the Evolution of Matrix Cracks in Composites on the Nonlinear Ultrasound Response

ABSTRACT Early-onset damage in composite materials consists matrix cracking with certain regularity in distribution. However, the effect of the spatial arrangement of matrix cracks and the relationship between the direction of expansion of the cracks and the incident direction of ultrasound waves on the nonlinear parameter in nonlinear ultrasound detection is poorly understood. This study analyzes the nonlinear variation of matrix millimeter-scale and micron-scale cracks by experiment and finite-element-based numerical calculation to improve the damage evaluation of composite materials by nonlinear ultrasound and provide a reference for crack expansion prediction and imaging. The results show that millimeter and micron cracks follow the same trend, with more cracks and “dislocated” spatial arrangement, both providing positive contributions to the relative nonlinear parameter. However, when the incident direction of the ultrasound waves is orthogonal to the crack expansion direction, the evolution of the relative nonlinear parameter will follow an opposite trend with respect to the expansion size compared to when the incident direction and crack expansion direction are the same. We also propose a new nonlinear index (DI), the evolution of which can be used to identify the type of spatial distribution of the cracks in the matrix.

Detection and classification of matrix cracking in laminated composites using guided wave propagation and artificial neural networks

The guided wave propagation and artificial intelligence (AI) approaches were used to propose an intelligent model for automatic detection and classification of the matrix cracking in composites. Glass/epoxy cross-ply laminated composites were fabricated and the matrix cracking with several densities was induced in 90° layers. A non-destructive testing procedure using the fundamental antisymmetric Lamb wave propagation was performed on the intact specimens and those with 0.05, 0.15, and 0.25 matrix cracking density. The velocity of propagated Lamb wave, wave amplitudes in four different distances from the actuator, and the ratio of these amplitudes to the first received wave amplitude, in three frequencies of 100, 200, and 330 kHz were extracted from the acquired signals. The extracted sensory features were used to train three types of supervised machine learning models for the crack density classification. The linear discriminant analysis (LDA) was performed for dimensional reduction to find a linear combination of features that can better discriminate the classes. Support vector machines (SVM), linear vector quantization (LVQ) neural network (NN), and multilayer perceptron (MLP) NN were used for the classification. It was shown that SVM accounted for the highest classification accuracy (91.7%) followed by LVQ NN (88.9%) and MLP NN (77.8%), respectively.

The analysis of periodic composites with randomly damaged constituents

A new method is offered for the modeling of periodic composites in which some damaged constituents are randomly distributed. The representative volume element for such composites consists of many repetitive cells, and its direct analysis by standard methods is an expensive computational task. The proposed approach allows to diminish significantly the volume of calculations. It is based on the representative cell method and the higher-order theory. In the former, the problem of the periodic composite with randomly located damages is reduced, in conjunction with the discrete Fourier transform, to a single cell problem, formulated in the transform domain. The solution of this boundary value problem is obtained by the latter one. The inversion of the transform, in conjunction with an iterative procedure, establishes the elastic field at any point of the damaged composite. The method is employed for the evaluation of the effective properties and field distribution for a specified loading of unidirectional fiber-reinforced composites with numerous randomly located defective fibers such as lost, missing, and damaged fibers. In addition, porous materials with random distributions of pores and unidirectional composites with fibers that are randomly located within the matrix can be considered. Furthermore, random distributions of matrix cracks in composites can be simulated, and the resulting behavior can be predicted. Finally, broken layers and interfacial cracks in periodically layered composites in which the cracks are randomly located can be similarly analyzed.

Effect of Thermo-Mechanical Gradient on the Damage Mechanisms of Composite Laminates

The main purpose of this work is to characterize and discriminate the respective roles of the thermo-mechanical gradient in the damage mechanisms of composite laminates used in aeronautics in order to understand the initiation and evolution of damage modes. For this purpose, a finite element model of compact tension specimen with a series of virtual crack closure techniques is achieved in order to evaluate the energy release rate of transverse matrix cracking in composites. The continuum mechanics approach in combination with Hashin’s damage criterion is adopted to describe initiation and evolution for each damage mode proposed for carbon/epoxy laminates. The good agreement between the numerical results and experiments in other available literature shows the validation of the analysis and developed model in this paper.

A hybrid embedded cohesive element method for predicting matrix cracking in composites

The complex architecture of many fibre-reinforced composites makes the generation of finite element meshes a labour-intensive process. The embedded element method, which allows the matrix and fibre reinforcement to be meshed separately, offers a computationally efficient approach to reduce the time and cost of meshing. In this paper we present a new approach of introducing cohesive elements into the matrix domain to enable the prediction of matrix cracking using the embedded element method. To validate this approach, experiments were carried out using a modified Double Cantilever Beam with ply drops, with the results being compared with model predictions. Crack deflection was observed at the ply drop region, due to the differences in stiffness, strength and toughness at the bi-material interface. The new modelling technique yields accurate predictions of the failure process in composites, including fracture loads and crack deflection path.

Nonlinear wave structural health monitoring method using an active nonlinear piezoceramic sensor for matrix cracking detection in composites

A structural health monitoring methodology, based on nonlinear wave modulation spectroscopy, is presented and aims to detect matrix cracks in composites. Experiments were conducted on cross-ply carbon/epoxy strips containing matrix cracks, induced via three-point bending. Damage in all tested specimens was categorized according to the acoustic emission hits recorded during loading. The nonlinear ultrasonics methodology is applied via an active nonlinear acousto-ultrasonic piezoelectric sensor, enabling low-cost and wide-frequency operational bandwidth. This active sensor configuration involves two piezoceramic wafer actuators, one excited with a low- and the other with a high-frequency signal, and a piezoceramic sensor, all permanently bonded on the tested structure. The sensitivity of the nonlinear active sensor response at specific high carrier frequencies is depicted and damage indices are proposed. The experimental results illustrate the effectiveness of the nonlinear ultrasonic wave mixing method in matrix crack detection, as well as the potential of the new active sensor for permanent structural health monitoring.

Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear

A criterion for matrix failure of laminated composite plies in transverse tension and in-plane shear is developed by examining the mechanics of transverse matrix crack growth. Matrix cracks are assumed to initiate from manufacturing defects and can propagate within planes parallel to the fiber direction and normal to the ply mid-plane. Fracture mechanics models of cracks in unidirectional laminates, embedded plies and outer plies are used to determine the onset and direction of propagation of crack growth. The models for each ply configuration relate ply thickness and ply toughness to the corresponding in situ ply strength. Calculated results for several materials are shown to correlate well with experimental results.

A Continuum Interface Debonding Model and Application to Matrix Cracking of Composites

Based on the internal variable theory of thermodynamics, a continuum interface constitutive model relating interface traction with interface separation was developed. An interface damage variable was introduced, and an evaluation equation was derived to characterize the degradation of interfacial rigidity with interface debonding. The present constitutive model was applied to fiber pullout from the matrix, and bridging matrix cracking of composites. Relatively simple closed form formulas were obtained for shear stress distribution along the interface, pulling stress of fiber from the matrix, and stress intensity factor of the small matrix crack tip with fiber bridging. The effects of interface parameters involved in the evaluation equation on interface shear stress distribution, and pulling stress of fiber were also discussed.

Borosilicate glass reinforced with continuous silicon carbide fibres: a new engineering ceramic

Silicon carbide fibre-reinforced glass and glass-ceramic composites are under development at Harwell where current research is concerned with the whole spectrum of activities from optimization of fabrication processes, through detailed properties assessment to fabrication of components. For the case if SiC fibre-reinforced borosilicate glass, a detailed account of a powder-infiltration-hot-pressing route to composite fabrication is given, and the effects of the variation of key fabrication parameters on composite properties are discussed. A comparison of energy balance and fracture mechanics approaches to the problem of matrix cracking in composites under tension is shown to yield equivalent expressions for the matrix failure strain and the stress to propagate a crack. It is then inferred that for this composite system the stress at the tip of a crack is independent of crack length once the crack is longer than a certain equilibrium length. For aligned fibre composites the tensile strengths of material with fibres at various angles to the stressing direction are shown to fit Tsai's theoretical model for the strength of resin matrix composites. The tensile and flexural strengths of the various composite structures considered differ by approximately a factor 2. Attempts are made to reconcile these differences by discussion of classical theories of fibre bundle failure, stressed volume effects and theories of the influence of matrix cracking on bending moment. Examples of components fabricated to nett shape are shown.

Mechanics of matrix cracking in brittle-matrix fibre-reinforced composites

Energy-balance calculations for a continuum model of cracking in a uniaxially fibre-reinforced composite having a brittle matrix are presen­ted. It is assumed that the fibres are strong enough to remain intact when the matrix cracks across the entire cross section of the composite. By equating the energy availability for the cracking of continuum and discrete fibre models it is shown how the crack boundary condition relating fibre stress to crack opening must be selected. It is confirmed that the Griffith fracture criterion is valid for matrix cracking in composites. By considering the energy balance of long cracks it is shown that the limiting value of the stress intensity factor is independent of crack length and that it predicts a matrix-cracking strain that is consistent with the known result. An improved numerical method is described for solving a crack problem arising from the study of the cracking of brittle-matrix composites. Numerical results of high accuracy are obtained, which show how the cracking stress is related to the size of a pre-existing defect. Of special significance is the prediction of the correct threshold stress (i.e. matrix­-cracking stress) below which matrix cracking is impossible no matter how large the pre-existing defect.