Transverse Matrix Cracking Research Articles

Damage accumulation analysis of cfrp cross-ply laminates under different tensile loading rates

This paper investigates the loading rate effect on both mechanical properties and damage accumulation process of [0°2/90°4]S carbon fiber-polymer laminates under tensile loading. In-situ edge observations, Acoustic Emission and Digital Image Correlation techniques were utilized simultaneously to monitor the state of damage in real time. Results showed that the axial modulus and strength were less sensitive to loading rates than failure strain, which increased with the decrease of the loading rate. In the viewpoint of damage accumulation process, high density and uniform distribution of transverse matrix cracks, and H-shape crack patterns, incorporating inter-laminar cracks, were more likely to occur at low loading rates while variable crack spacing occurred at higher rates. When loading rates were lower than a certain level, maximum transverse matrix crack density decreased slightly due to the restriction of relatively widely generated inter-laminar cracks. Furthermore, the cumulative acoustic emission energy of low-frequency signals was linearly correlated to transverse matrix crack density, providing a promising way to quantify crack accumulation in real time. Finally, spatial consistence was observed between transverse matrix cracks at edges and stress concentrations at the exterior 0° ply, and the peaks of axial strain at local concentration regions locate either near the newest cracks or at the place with minimum crack spacing.

Unfolding the early fatigue damage process for CFRP cross-ply laminates

This study investigates the early fatigue damage of cross-ply carbon/epoxy laminates. The aim is to unfold the damage accumulation process, understand the interaction between different damage mechanisms, and quantify their contribution to stiffness degradation. Tension-tension fatigue tests were performed, while edge observation and DIC technique monitored the damage evolution. It was found that different accumulation process and interactive levels between transverse matrix cracks and delamination exist for specimens with similar stiffness degradation. A linear increase of stiffness degradation was observed with the increase of matrix crack density, while the growing trend of stiffness degradation converged with the increase of delamination.

A Real-Time NDT Method Based on FBG Sensor Spectrums to Detect the Transverse Matrix Cracks in Composite Materials

Transverse matrix cracking is probably the first and most dominant mode of damage in composite materials. In this paper, a real-time Non-Destructive Testing (NDT) method was proposed to detect the transverse cracks by Fiber Bragg Grating (FBG) sensors. The experiment of observing the crack growth and recording FBG’s reflection spectrums as well as Finite Element Method (FEM) methods were conducted to help verifying the regularities of the reflection spectrum distortions in the cracking angle-ply [0n/ ± θm/0n] laminates. The results showed that the shape of the spectrum was highly correlated to the crack density of composites. From undamaged state to high crack density conditions, the shape of the spectrum experienced an ‘original-splitting-regressive’ process. Under the assumed ideal periodic strain distribution conditions, the peak width w of the reconstructed spectrums and crack density $$\rho$$ showed very good linearity which provided the possibility for quantitative detection of the crack density of composites.

In-situ strength effects in long fibre reinforced composites: A micro-mechanical analysis using the phase field approach of fracture

Transverse intralaminar cracks in layers with perpendicular orientation referred to the main loading direction have a significant effect on the apparent ultimate strength of the corresponding composite laminate. This effect stems from the fact that such transverse cracks generally promote the occurrence of other failure mechanisms leading to the specimen collapse in subsequent stages of the loading process. With the aim of conducting a careful investigation regarding the onset and progression of transverse intralaminar cracking events, a micro-mechanical analysis of cross-ply laminates is herein proposed. Particularly, the cross-ply laminates belonging to the family [0°2/90°n/0°2] are considered via the generation of high-fidelity micro-mechanical models, which reproduce the internal fiber arrangements related to the reference results in Saito et al. 2012, Experimental evaluation of the damage growth restraining in 90° layer of thin-ply CFRP cross ply laminates, Adv. Comp Mat, 21:1,57–66. Differing from alternative approaches, current predictions are equipped with the combined used of two fracture-based modeling methods: (i) the variational phase field (PF) approach for triggering crack events into the matrix, and (ii) the bilinear cohesive zone model (CZM) for the simulation of fibre-matrix decohesion failures. Relying on this computational methodology, the focus of this work is to analyze the influence of the transverse ply thickness (n) on the onset and propagation of damage under tensile conditions, in conjunction with the transition from micro-cracking to meso-scale damage states. For this purpose, several models are generated into the FE package ABAQUS using user-defined capabilities, replicating configurations of specimens included in previous experimental investigations, i.e. through the consideration of different transverse ply thickness (n = 1, 2, 4). Present results show the potential of the proposed methodology to predict the transverse matrix cracking phenomena and the ability and reliability for capturing the delay of the crack with thinner plies, a phenomenon which is usually denominated as in-situ effect in the related literature.

Inline quantification and localization of transverse matrix cracking in cross-ply CFRP during quasi-static tensile testing by a joint event-based evaluation of acoustic emission and passive IR thermography

Understanding the complex damage characteristics of fiber reinforced plastics under mechanical loading is essential for lightweight design. In this study, acoustic emission (AE)1 analysis and passive IR thermography (pIRT) are coherently combined for the quantitative characterization and localization of damage progression in cross-ply carbon fiber reinforced plastics under quasi-static tensile loading. A new evaluation methodology is presented that utilizes acoustic events as trigger for pIRT analysis. Rigourosly transferring the event-based evaluation scheme from AE to pIRT analysis allowed for the first time to extract and compare characteristic features from both: thermal and corresponding acoustic events and to correlate them to the underlying damaging event. This way, the thermal and acoustic footprint of transverse matrix cracking (TMC) in the outer 90° layers was successfully identified and used for the determination of TMC onset and density throughout the test. This highlights the potential for the inline characterization of damage progression with this new approach.

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.

A bi-phasic modelling approach for interlaminar and intralaminar damage in the matrix of composite laminates

The paper presents a new bi-phasic approach to model delamination and transverse cracking in the matrix of composite laminates by using a single constitutive law, based on a decomposition of the composite stiffness properties into idealized fibre and matrix phases. The decomposition is used in finite element models where membrane elements representing the fibre phase are embedded in a three-dimensional mesh that models the matrix phase. A single constitutive law is applied to the matrix phase by combining a Cohesive Zone Model, which models delamination between plies, with an intralaminar damage law, aimed at modelling a transverse matrix cracking within the plies. All the theoretical aspects of decomposition and constitutive law are described. Then, the numerical experimental correlations are presented considering delamination tests and the evolution of the transverse matrix cracking in cross-ply specimens, with a statistical distribution of strength properties, also in the presence of interactions between matrix cracking and delamination. The approach provides the possibility to efficiently simulate both individual delaminations and transverse cracks with a model using a single layer of elements per ply, without introducing interface elements. Moreover, it also provides new possibilities to control the interaction between intralaminar and interlaminar damage phenomena.

Discrete eigenseparation-based reduced order homogenization method for failure modeling of composite materials

This manuscript presents a new reduced order computational homogenization method for failure analysis of composite materials. The proposed approach relies on the discrete representation of the fracture process at the fine scale that consistently bridges to a continuum representation of damage at the coarse scale. In order to achieve very high computational efficiency, the proposed approach builds on the ideas of the eigendeformation-based reduced order homogenization method, but tracks microscale failure evolution over a set of discrete cohesive failure surfaces. The formulation concurrently achieves mesh size objectivity and multiscale consistency by establishing analytical relationships between the microstructure size and the macroscale element size. The performance of the proposed formulation is demonstrated in the context of three-dimensional, laminated fiber reinforced composite configurations. The numerical experiments demonstrate mesh size objectivity in the presence of multiscale failure mechanisms including fiber fracture and transverse matrix cracking.

A multidirectional damage model for fiber-reinforced plastic laminates under static load

A multidirectional damage model based on continuum damage mechanics for fiber-reinforced composite laminates is proposed in this paper. The influence of three main damage mechanisms, including transverse matrix cracking, local delamination, and fiber breakage, on the multidirectional stiffness properties of composite laminates is analyzed by introducing macro phenomenological damage variables. Then the mechanical behavior of elementary ply in laminates is modeled based on these damage variables. Besides, relations between micro-level damage variables and macro-level damage variables are established. Damage evolution laws of the three damage mechanisms are proposed to predict the degradation of multidirectional stiffness and failure strength of composite laminates under quasi-static loading. The experiment of cross-ply glass fiber-reinforced plastic laminates is carried out, and the prediction results show good agreement with the experimental results.

Hygrothermal effect on the moisture absorption in composite laminates with transverse cracks and delamination

The stiffness degradation of the cross-ply composite laminates containing a transverse cracking and delamination in 90o layer is predicted by using a modified shear-lag model by introducing the stress perturbation function. The prediction shows better agreement with the experimental results published by Ogihara and Takeda 1995, especially for laminates with thicker 90o plies in which extensive delamination occurs. A homogenised analytic model for average transient moisture uptake in composite laminates containing periodically distributed matrix cracks and delamination is presented. It is shown that the model well describes the moisture absorption in a cross-ply composite laminate containing periodically distributed transverse matrix cracks in the 90o plies. The obtained results represent well the dependence of the stiffness degradation on the crack density, thickness ratio and moisture absorption. The present study has proved to be important to the understanding of the degradation of the material properties in the failure process when the laminates in which the delamination grows extensively.

Failure mode analysis of laminated composite sandwich plate

Failure mode prediction of laminated composite sandwich plates is presented using improved higher order shear deformation theory (IHSDT) mathematical model and its C0 finite element (FE) implementation in FORTRAN. The proposed 2D IHSDT satisfies the inter-laminar shear stress continuity at each adjacent layer and nil transverse shear stress conditions at top and bottom of the plate are imposed. The parabolic shear stress variation is piecewise across thickness of each layer; hence no need of shear correction factors. The possible modes of failures are transverse matrix cracking, fiber breakage and inter-fiber shear failure of the matrix. The failure mode along with its location for laminated composite sandwich plates are obtained and are found in good agreement with the available 3D elasticity results.

Characterisation of Transverse Matrix Cracks in Composite Materials Using Fibre Bragg Grating Sensors

In this paper, we propose a novel approach to characterise barely visible transverse matrix cracks in composite structures using fibre Bragg grating (FBG) optical sensors. Matrix cracks are one of the most prevalent types of damage in composite structures, and detecting them in the internal layers of composites has remained a challenge. In this paper, we will show that the formation of cracks in the internal layers of composite structures alters the side-lobes of the reflection spectra of FBG sensors by adding new harmonics to them. We argue that the spread and the location of these harmonics depends on both the mechanical properties of the composite material and the location of the crack along the length of the FBG sensor. Via computer simulations and experimental measurements, we validate our hypotheses, and the results are in agreement with our model.

Parameter analysis of damaged region for laminates with matrix defects

Considering the influence of bridge fibers, a representative volume element (RVE) with damaged regions of vanishing thickness is developed to study for estimation of laminates with transverse matrix cracks. For the open and closed cracks, the tensile force, the compressive force and the shear force are mainly studied by the stress-based variational approach with the pending partition loads at the statically indeterminate boundary, with considering not only three cases of the ideal transverse cracks, the smooth plane-surface open crack, the smooth plane-surface closed crack and the perfect meshing open crack, but also two cases of the non-ideal transverse cracks, the open cracks and closed cracks with the resistance resisting the relative sliding of crack surfaces. The expressions of the stress components in the RVE are obtained by means of assumption of the function of inter-laminar shear stresses. The governing equations are derived from the variational analysis based on the principle of minimum complementary energy. Both the effective mechanical properties and the distributions stresses of the damaged laminates with the ideal transverse cracks and those of the laminates with the non-ideal transverse cracks are estimated on the basis of the analysis of deformation on surface of the RVE.

A continuum damage model for transverse cracking in UD composites of linear viscoelastic behaviour

A damage model for linear viscoelastic unidirectional (UD) composites undergoing transverse matrix cracking is proposed. The damage representation for the corresponding elastic UD composite with an array of dispersed matrix cracks was derived from Li’s work based on continuum damage mechanics (CDM). The elastic-viscoelastic correspondence principle (CP) was used to obtain the damage representation for corresponding linear viscoelastic UD composites in the Laplace domain, and re-expressed in the time domain by taking the inverse Laplace transformation. A damage evolution law was constructed using the Weibull distribution of defects which will develop into cracks as a result of deformation. The time-temperature superposition principle (TTSP) approach has been incorporated into this model. Applications of this damage model are described in detail, and the predictions are compared with experimental data.

Inter-relationships among elastic constants for symmetrical or unsymmetrical laminates with cracked 90-plies

The relations between the stiffness components of a symmetrical or unsymmetrical laminate having trans-verse matrix cracks only in the 90-degree laminas are explored in this work. The crack closure condition for these laminates under membrane and bending deformations is established to obtain the interrelationships. These equations also link the in-plane equivalent Young’s moduli and the Poisson’s ratios of balanced symmetric laminates. Cracks in off-axis laminas are not considered here. The present relations are validated using numerical data reported in the literature. Each inter-relationship can be used to obtain one elastic property when other property was experimentally measured or analytically calculated.

Axial Tensile Failure Analysis of SiCf/Ti Composite Based on Continuum Cohesive Zone Model

In this paper, the failure behavior of SiC fiber-reinforced Ti-6Al-4V matrix composite (SiCf/Ti) under longitudinal loads was studied experimentally and theoretically. Experimental results show that the interface of SiCf/Ti composite is continuous and integral. Through SEM observations, it was found that transverse matrix cracks initiated from the debonding region of the interface. A three-dimensional representative volume element was developed to simulate the failure process of SiCf/Ti-6Al-4V composite. A continuum cohesive zone model is employed to describe the debonding behavior at the interface, compared with a discrete one. More accurate simulated results were obtained by a continuum cohesive zone model, corresponding to experimental results. The transverse cracking behavior of the matrix was simulated. The stress–strain curves predicted by the continuum cohesive zone model show a good agreement with the experimental results. The fiber volume fraction, interface strength and interface toughness are investigated to exhibit their influences upon the longitudinal mechanical characteristics of SiCf/Ti-6Al-4V composite.

Inter-relationships among stiffness matrix components for general laminates with transverse cracks in oblique plies

In this paper, nine inter-relationships linking the stiffness matrix components of symmetrical or unsymmetrical laminates having transverse matrix cracks in some of the off-axis plies is presented. The crack closure condition under membrane and bending deformations is established and used to obtain the inter-relationships. The derived crack closure conditions and inter-relationships are validated using a numerical model based on previous work by the authors. These inter-relationships include the eighteen stiffness matrix components and are exact within the assumptions made in the classical lamination theory. When using a two-scale finite element-based model, six loading cases would be needed to obtain the complete stiffness matrix. With the obtained inter-relationships, only four loading cases would be needed, thus saving a third of the total amount of information and computing time.

Effect of milled glass fibers on quasi-static indentation and tensile behavior of tapered laminates under acoustic emission monitoring

The present work investigates on quasi-static indentation (QSI) behavior and post-indent tensile response of tapered glass/epoxy laminates. The tapered laminates were fabricated with a cross-ply [0°/90°] stacking sequence and subjected to quasi-static indentation (QSI) for different indentation depth. The residual loading bearing capacity of the post indented samples was evaluated by performing the tensile test. The online acoustic emission (AE) technique was employed to monitor the evolution of damages and their corresponding damage mechanisms during loading. Furthermore, the milled glass fibers were used as fillers into the epoxy matrix to improve the delamination resistance of tapered glass/epoxy laminates. The influence of milled glass fibers on the indentation resistance and residual load-bearing capacity was experimentally investigated. The results show that incorporation of milled glass fibers into the epoxy matrix have significantly improved the peak load, damage onset load and contact stiffness by an average of 20%, 66%, and 59% respectively. Also, the residual load-bearing capacity of filler loaded samples increased by an average of 20% compared to baseline samples. It was observed that the transverse matrix cracking triggered the delamination damage at the tapered region, resulting in critical failure through fiber breakage.

Damage initiation of thermally degraded carbon composites in tension

This study focuses on exploring the initial failure of thermally degraded carbon fibre-reinforced polymers. It is the aim of this study to provide deep insight into the damage development and propagation as well as to understand failure mechanisms of thermally degraded composites. Carbon fibre-reinforced polymer panels with different fibre orientations are exposed to heat above maximum operational temperature (up to 200 ℃) for various durations (up to ca. 200 days). Thermal degradation of the material is characterized by scanning electron microscopy and infrared spectroscopy. The onset of the failure in tension is determined by acoustic emission analysis. The results show that the development and propagation of cracks depend on the level of thermal degradation and the fibre orientation relative to the applied load. With increasing thermal degradation, transverse matrix cracking, as the prevailing initiating failure mode, is replaced by crack initiation and propagation in the damaged outermost ply independent of its fibre orientation. Severe thermal matrix degradation is limited to this area, as characterized by infrared spectroscopy. With increasing thermal degradation of the polymer matrix, the onset of crack initiation and propagation is shifted to lower strains. The effects of damage initiation on fracture behaviour are discussed.

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.