Transverse Matrix Cracking Research Articles

Influence of fatigue damage on the impact performance of toughened-interleave carbon fibre epoxy composite laminates

The impact performance of mechanically fatigued carbon fibre-reinforced polymer (CFRP) composite laminates with and without thermoplastic toughening particles has been investigated through a joint experimental and numerical campaign. Prismatic carbon fibre/epoxy specimens with added toughening particles at the ply interfaces were mechanically fatigued with different load amplitudes leading to a loss in apparent stiffness of 10% to 15%. Following the fatigue loading, high resolution computed tomography (CT) has been performed, revealing varying degrees of delamination starting from the free edges along the length of the specimens. In addition, transverse matrix cracks are observed in all fatigued specimens regardless of the amount of delamination. The residual ballistic impact performance of the damaged specimens has been investigated in a dynamic three-point bending configuration at three different velocities, showing a significant detrimental effect of even barely visible initial delamination. In addition, post-mortem CT scans and detailed finite element simulations are used to gain further insight into the mechanisms by which the two types of initial damage affected the impact resistance of the laminates. Finally, repeating the same experiments on a similar CFRP system without discrete toughening particles showed that their inclusion significantly increased the impact resistance both with and without prior fatigue damage.

Modeling of progressive high-cycle fatigue in composite laminates accounting for local stress ratios

A numerical framework for simulating progressive failure under high-cycle fatigue loading is validated against experiments of composite quasi-isotropic open-hole laminates. Transverse matrix cracking and delamination are modeled with a mixed-mode fatigue cohesive zone model, covering crack initiation and propagation. Furthermore, XFEM is used for simulating transverse matrix cracks and splits at arbitrary locations. An adaptive cycle jump approach is employed for efficiently simulating high-cycle fatigue while accounting for local stress ratio variations in the presence of thermal residual stresses. The cycle jump scheme is integrated in the XFEM framework, where the local stress ratio is used to determine the insertion of cracks and to propagate fatigue damage. The fatigue cohesive zone model is based on S-N curves and requires static material properties and only a few fatigue parameters, calibrated on simple fracture testing specimens. The simulations demonstrate a good correspondence with experiments in terms of fatigue life and damage evolution.

Tensile damage evolution and mechanical behaviour of SiCf/SiC mini-composites through 4D in-situ micro-CT and data-driven modelling

Damage evolution of SiCf/SiC ceramic matrix mini-composites (CMMCs) was characterised by using a 4D in-situ micro-computed tomography (CT) tensile test and digital volume correlation (DVC) technique. Additionally, a CT damage data-driven shear lag model was developed to predict its tensile stress-strain response. A 4D in-situ X-ray CT tensile test of a unidirectional SiCf/SiC mini-composite was first carried out. Then two ad-hoc deep-learning image segmentation models were developed to automatically identify its microstructure and damages induced by tension, respectively. Damage evolution was quantitively characterised by visualising the initiation and propagation of matrix cracks in three-dimensions (3D). A two-step approach was employed to evaluate its 3D internal strain distributions at various loading levels, which further revealed strain concentrations and helped establishing the tensile stress-strain response of the CMMCs. It was observed that transverse cracking is the predominant damage mode, and the average crack opening displacement increases with loading. A high-fidelity X-ray CT data-driven shear lag model was developed, incorporating inputs of transverse matrix crack spacing calculated by the 4D in-situ CT test data. The predicted stress-strain response showed a good correlation with the experimental results.

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.

Shear strength determining mechanism of a +/−45 laminate under tensile loading

The shear strength of a composite material is determined as a result of a complex damage and failure process, but the detailed progression has not been clearly elucidated. Here, the mechanism of determining the strength of a ±45 laminate under tensile loading is revealed from exquisitely designed experiments in conjunction with high-fidelity numerical simulation. Synchrotron radiation computed tomography is employed for extremely high-resolution images of damage status inside the composite just before its catastrophic failure. The ex situ observations discover the unique and consistent failure progression; one major matrix crack is initiated either in the +45 or −45 layer and delamination follows after the initial crack completely grows along both the fiber and transverse directions. After the delamination failure is triggered, remaining intact layers start to fail with multiple transverse matrix cracks. The failure of the intact layers is represented as a load drop in the global stress–strain curve. This sequential and interactive failure progression determines the shear strength of the ±45 laminate. The numerical analysis finds that the location of the initial matrix crack is dependent on the microstructure. Once the matrix crack is initiated, the numerical simulation exactly reproduces the experimentally observed failure process.

Effect of stitching on the static and fatigue properties of fibre-dominated and matrix-dominated composite laminates

The paper reports the results of an experimental investigation into the effect of stitching on the static and fatigue response of fibre-dominated and matrix-dominated laminates. The tests were conducted on Kevlar stitched carbon/epoxy laminates with quasi-isotropic ([0/±45/90]s) or angle-ply ([+302/−302]s, [+452/−452]s, [+602/−602]s) layups. The analyses show that stitching significantly reduces both the static and the fatigue strength of fibre-dominated [0/±45/90]s laminates, owing to the presence of localized fibre damage introduced during the stitching process. On the other hand, stitching does not affect the fatigue response of [+602/−602]s laminates but significantly improves the fatigue strength of [+302/–302]s and [+452/−452]s laminates. The effectiveness of stitching on the fatigue performance of the angle-ply layups was found to be directly related to the specific damage mechanisms preceding the ultimate failure, which are controlled by edge delaminations in [+302/–302]s and [+452/−452]s and transverse matrix cracking in [+602/−602]s laminates.

Modelling intralaminar damage mechanisms in fibre reinforced polymers at finite strains

An approach to predict intralaminar failure mechanisms in laminate fibre-reinforced composites, at finite strains, is proposed. Transverse matrix cracking is described by a smeared crack model, activated by an invariant-based failure criterion, where an embedded cohesive crack is considered in the continuum description. A deformation gradient decomposition based on homogenisation considerations is developed for a more objective finite strain kinematic description of transverse cracks. The local equilibrium problem is established in the reference configuration to naturally include re-orientation of the fracture plane, and the employed cohesive law is able to deal with non-monotonic loading. Moreover, a continuum damage model formulated in terms of the Green–Lagrange strain tensor is used for longitudinal failure. The simulation of an open-hole multi-directional specimen subjected to tension illustrates the ability of the proposed constitutive equations to capture experimental observations.

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.

High-fidelity simulation of low-velocity impact damage in fiber-reinforced composite laminates using integrated discrete and continuum damage models

A high-fidelity finite element (FE) model based on integrated discrete and continuum damage modeling techniques was developed to predict damage modes, locations, sizes, and damage occurrence sequence in a composite laminate during a low-velocity impact event. Fiber breakage and transverse matrix cracking were captured using the three-dimensional Hashin’s criteria, and delamination was captured by inserting a layer of cohesive elements between every adjacent composite ply. Delamination progression from one layer to another was captured by embedding cohesive elements inside each composite ply aligned with the fiber orientation and with a 45° angle to the thickness direction. The refined mesh and intralaminar cohesive elements were only used in the predicted damage region based on an analytical solution. The FE model predicted impact response was validated by drop-weight tests, and the layer-by-layer damage areas were validated and characterized by X-Ray CT inspections on 254 mm by 304.8 mm IM7/977-3 laminates with a stacking sequence of [0/45/90/-45]4s. The absorbed energy, damage areas, maximum deflection, contact time, and peak load were predicted with less than 10% error. The detailed damage occurrence sequence during the impact event was predicted through histories of energies dissipated by different damage modes. The modeling methodology developed in this work highlights the effects of modeling parameters on convergence, solution accuracy and computational efficiency, and provides an effective approach for progressive damage modeling of composite laminates.

Simulation of acoustic emission in carbon fiber-epoxy matrix composite laminates due to transverse cracking: effect of ply stacking sequence

This work focuses on the numerical simulation of the AE due to transverse cracking in laminate composites. The objective of the work is the experimental characterization and numerical simulation of the influence of the ply thickness and stacking sequence on transverse matrix cracking induced acoustic emission. AE signals induced by transverse matrix cracking are simulated numerically using finite elements (FE) for composite laminates exhibiting different number of plies and stacking sequences. 3D FE models of the specimens are set-up using Abaqus™ Standard. Either [0n/90n/0n] or [90n/0n/90n] (n=1 or 3) composite laminates are modeled, one ply thickness is 0.3 mm. Matrix transverse cracking in 90 deg. inner or outer ply is simulated. The influence of the ply thickness on acoustic emission signals recorded at the crack epicenter is significative only for inner ply transverse cracking, whereas similar signals are obtained for outer ply cracking. The frequency content of signals induced by outer ply transverse cracking does not depend on the ply thickness. Contrary to outer ply cracking, the influence of the ply thickness on inner ply transverse cracking induced signals is significative, especially on the frequency content, and on the frequency centroid only close to the crack (Fig. 1). Outer ply cracking rather exhibits signals with a low frequency content, not depending much on the ply thickness, contrary to inner ply cracking, for which the frequency content is higher and more dependent on the ply thickness. Fig.1: Frequency centroid as a function of distance between the source and the sensor obtained numerically for [0n/90 n/0n] and [90n/0n/90n] stacking sequences (n=1 or 3). Results obtained without sensor effect, with a virtual perfect sensor. EWGAE 35, Ljubljana, Slovenia, 13th – 16th Sep. www.ewg

In-situ CT characterization of 2D woven SiCf/SiC composite loading under compression

Abstract SiC fiber-reinforced SiC matrix composites (SiCf/SiC) with 2D woven fabric as preform were tested under compression with in-situ X-ray computed tomography. The microstructure and damage evolution of the material under continuous loading levels were accurately revealed by image reconstruction of CT data. There were inhomogeneous pores in SiCf/SiC composite because of the un-uniform fiber distribution in the preform. The result also showed that 2D woven SiCf/SiC composite had obvious non-linear characteristics by its compressive load–displacement curve, and the damage modes included transverse matrix cracking, interlayer cracking, longitudinal matrix cracking, and fiber bundle fracture. Matrix cracking tended to occur near the pores or holes of the material, and the number of longitudinal cracks was relatively high compared to the number of transverse cracks.

Enhancing low velocity impact characteristics of glass fiber laminates by short fiber reinforcement—Failure evolution and damage mechanisms

AbstractFor enhancing impact characteristics, woven glass fiber epoxy laminates are reinforced with short fibers. The 6‐mm‐long slender fillers, when added up to 4% in the matrix, exhibit no influence on the flexural modulus, but at 2% they maximize the laminate's flexural strength. While the dissipation energy continues to increase up to 30 J of impact, the laminates' post‐impact load bearing capacity gets significantly affected beyond 20 J. The reinforced laminates exhibit better elastic response and enhanced damage resistance with as high as 50% reduction in the visible damage area as well as up to 35% increase in the damage initiation force. The degree of damage shows excellent correlation with the visible damage area. The distinct through thickness conical region, diverging from the impact site, is attributed to the presence of microcracks oriented along the fiber directions. The cone boundary, from where the interlaminar failure initiates, is largely the manifestation of transverse matrix cracks. While the damage cone with greater divergence indicates reduced impact resistance of the laminate, the orientation of transverse matrix cracks remains unaffected by the impact energy or the filler content. At low impact energies, the failure initiated from the fiber/matrix interfaces, coalesce to form the matrix cracks, which act as a precursor to the interlaminar failure. However, at high energy levels, several failure mechanisms simultaneously develop with no clear indication of the order of damage evolution. The short fibers enhance the laminate's impact resistance either by arresting the cracks or by developing tortuous crack path with high energy dissipation.

The anti‐oxidation mechanism of SiCf/SiC–B4C modified with Al2O3 in wet atmosphere based on machine learning

AbstractTo study the anti‐oxidation mechanism of SiCf/SiC–B4C modified with Al2O3 in wet atmosphere, the damage evolution of composites after oxidation was explored by unsupervised machine learning technology (k‐means). Results display that the mean feature values of cluster‐1 (some small cracks in oxidation layer and matrix as well as fiber debonding) in composites modified with Al2O3 are larger than that in virgin after oxidation. Meanwhile, as the oxidation time increases, the concentrated area of cluster‐2 (fiber breakage, cracks in axial and transverse yarns) in both composites gradually shifts toward the direction of high mean feature values. Because Al2O3 can protect the BN from oxidation, the increase of peak frequency and risetime of composites modified with Al2O3 is less than that of virgin. Moreover, the proportion of cluster‐3 (big transverse matrix cracks) in composites modified with Al2O3 is always more than that of virgin. Based on the research results, the corresponding relationship between each damage behavior and each cluster is thoroughly built.

Predicting fatigue damage in composites subjected to general loading conditions

A computationally efficient fatigue analysis methodology is proposed that uses a cycle jump approach to drive the accumulation of fatigue damage and a unified local fatigue cohesive zone model that can predict the initiation and propagation of cracks using a reduced set of model parameters. A new definition of the stress ratio is proposed for general loading conditions, which include negative load ratios, unsynchronized loads, and problems where the mode mixity changes during a cycle. The cycle jump procedure was verified by performing analyses of standard double cantilever beam and mixed mode bending tests. Then, the model was validated by performing analyses of double notch shear tests and initiation of transverse matrix cracking in a [0/90] laminate using models that account for residual thermal stresses. The results indicate that the analysis methodology can reproduce experimentally measured fatigue damage initiation and evolution for a variety of different configurations and load combinations.(Keywords: C. Cohesive interface modelling, B Fatigue, B. Delamination, A. Polymer-matrix composites (PMCs))

Characterisation of damage evolution in plain weave SiC/SiC composites using in situ X-ray micro-computed tomography

The paper presents the investigation of microstructures and tensile damage evolution of plain weave SiC fibre reinforced SiC matrix (SiC/SiC) composites using X-ray computed tomography (CT). A miniature high-precision in situ X-ray CT test fixture has been developed to conduct micro X-ray CT in-situ tensile tests. Through the image reconstruction of the CT data, the actual microstructures and the damage evolution of the material under six successive loading levels have been revealed precisely. Deep-learning-based image segmentation has been employed to recognise material damages, including transverse matrix cracking, longitudinal matrix cracking, and fibre pull-outs. Three-dimensional rendering models of these damages have been created to quantify the damage initiation and evolution. Both transverse and longitudinal matrix cracking initiates and propagates gradually at the intermediate loading level, but rapidly at the high loading level. The volume fraction of longitudinal matrix cracks is much larger than that of its transverse counterpart. It indicates that the longitudinal matrix cracking is much severer damage than transverse tracking. The lengths of fibre pull-outs at the fracture surface of fibre tows are in a broad range and on average they are in the order of a hundred microns.

Automated detection and quantification of transverse cracks on woven composites

Various loading conditions—cyclic, quasi-static, and dynamic—can induce transverse matrix cracks in cross-ply and woven composite structures. Identification and quantification of this damage on a composite’s surface can provide valuable information on the overall damage state of the structure. This work seeks to develop automated methods for identifying and quantifying transverse matrix crack damage on the surface of composites. To this end, model plain weave glass–epoxy composite specimens were developed that were consistent in geometry and manufacturing process and for which the loading conditions and resulting damage quantity and damage mode could be controlled. High-resolution images (80 megapixel) were captured of the model composite specimen surfaces. These images were then subjected to a manual transverse crack identification method, which established a control with known quantity and spatial location of transverse cracks. Two automated methods were developed to identify and quantify transverse cracks. The first used 8-bit (256 shades of gray) images, an ImageJ preprocessing step, and finally used MATLAB to identify the damage. The second used 16-bit (65,536 shades of gray) images processed directly by MATLAB (no ImageJ preprocessing) to identify the damage. It was found that the 8-bit method more accurately assessed the quantity of transverse cracks because the preprocessing step reduced error-causing high-contrast artifacts (e.g., reflections, composite material inconsistencies, dirt, and ink/marks). Finally, binned scatterplot maps indicating damage quantity and spatial location were created to provide at-a-glance assessment of composite damage condition.

A predictive modeling tool for damage analysis and design of hydrogen storage composite pressure vessels

In this paper, a predictive modeling tool is developed for damage analysis and design of hydrogen (H2) storage composite pressure vessels. It integrates micromechanics of matrix cracking into a continuum damage mechanics (CDM) description for damage evolution, and three-dimensional (3D) finite element (FE) modeling of the vessel structural response. At the scale of the composite layer (mesoscale), the temperature-dependent stiffness reduction law in terms of the damage variable for transverse matrix cracking is computed using an Eshelby-Mori-Tanaka approach (EMTA) for the initial composite thermoelastic properties and a self-consistent model for the stiffness reduction as a function of the damage variable. While transverse matrix cracking obeying a damage evolution relation can progressively evolve from an initiation to a saturation state, fiber failure is predicted by a micromechanical fiber rupture criterion that accounts for the fiber strength and matrix stress that can be computed within EMTA. The implementation of this integrated multiscale modeling model into a 3D FE formulation enables damage analysis and design of H2 storage composite pressure vessels. The developed tool is illustrated through 3D damage analyses of a cryogenically compressed H2 storage vessel model subjected to thermomechanical loadings to investigate effects of the helical layer fiber orientation and loading scenario on damage development, vessel integrity and burst pressure.

Mesh size objective fatigue damage propagation in laminated composites using the multiscale discrete damage theory

A mesh size objective multiscale modeling is developed for fatigue failure prediction of long fiber-reinforced composites based on the multiscale discrete damage theory (MDDT). MDDT tracks the failure processes along discrete failure surfaces at the microscale and concurrently bridges it to continuum-based description of damage at the macroscale. The proposed approach achieves mesh-size objectivity by introducing a length scale operator which effectively adjusts the microstructure size as a function of macroscale element size; and when a non-additive fatigue damage evolution law is used to describe progressive cracking at the microscale. Temporal multiscaling is used to track long-term fatigue damage evolution with high computational efficiency. The performance of the proposed model is demonstrated by the analysis of unnotched and open-hole laminate configurations. The results indicate mesh-size objectivity even in the presence of multiple failure mechanisms including splitting, delamination and transverse matrix cracks. The interaction between splitting and transverse cracks is investigated by a parametric study, which reveals the effects of mode I and mode II dominated degradation on the failure behavior under fatigue loading.

An Energy-Based Analysis for Machining Novel AZ91 Magnesium Composite Foam Dispersed With Ceramic Microspheres

Abstract Metal syntactic foams are a novel grade of materials that find potential applications in the manufacture of lightweight structural components and biomedical applications. For these materials to be inducted into industrial applications, it becomes imperative to study their machining behavior. In this article, for the first time in the literature, machining characteristics of AZ91 magnesium foam reinforced with thin-walled hollow alumina ceramic microspheres being studied. Through cutting experiments, it is found that finer the size of hollow microspheres and higher their volume fraction, higher was the magnitude of cutting forces recorded. The failure mechanisms that constituted chip formation during cutting AZ91 foam has been explicated through a mechanistic cutting force model. The proposed force model takes into account key hollow alumina microsphere properties such as wall thickness-to-diameter ratio, average microsphere size, and volume fraction. The scanning electron microscopic (SEM) analysis showed two key modes of failure during cutting metallic foams. Microsphere bursts and fractures control matrix plastic deformation through an effective load transfer mechanism. The transverse matrix cracks, which are initiated as a result of induced shear stress, promote the propagation of longitudinal adhesive cracks. This rapid crack growth takes place along the direction of maximum energy release rate, thus weakening the interfacial strength and reducing effective load transfer. This leads to microsphere separation, and further matrix densification due to the collapse of microsphere cavities leads to chip separation. The developed mechanistic model was in better agreement with experimental results.

Multiscale modeling of tensile fracture in fiber reinforced composites

Intralaminar fiber-matrix fracture, also known as splitting, is encountered frequently during the tensile failure of fiber reinforced polymer matrix composites (FRPMCs). The prediction of this failure mode and its influence on a macroscopically homogenized model brings associated challenges in numerical modeling. An efficient two-scale model is presented, based on the micromechanics 2-concentric cylinder (2CYL) [1] analytical method for pre-peak nonlinearity, interfaced with the 3D orthotropic smeared crack approach (SCA) [2,3] for post-peak softening behavior. A homogenized ply is modeled using standard 3D finite elements, such that a matrix crack can be captured explicitly with respect to the orientation of the ply angle. The capability of the proposed method is demonstrated by predicting the grip-to-grip longitudinal split in a 00 ply, mixed-mode matrix cracking in 450 ply, the transverse matrix cracking in 900 ply and the failure of laminate containing these plies. The predictions of the proposed method are found to be in very good agreement with corresponding experimental data [4, 5].