In cross-ply laminates under loading, multiple intralaminar (transverse) cracking in the 90-layers causes laminate stiffness reduction which can be predicted by analytical models studying average of the stress perturbation between transverse cracks. The commonly used analytical models such as shear-lag type or variational-type models assume that stress in damaged 90-layers does not depend on the laminate thickness coordinate. But with increase in crack density, the stress perturbations created by transverse cracks start to interact, generating high stress gradients in through-the-thickness direction in the 90-layers. Location of a new crack and features of its propagation in a high stress gradient region between two cracks in a cross-ply laminate are analyzed in this paper. FEM is used to calculate stress distribution between two cracks. The location of the next crack and its initial orientation is found using principal stresses and orientation of principal axes. Most often these cracks are initiated at ply interface in the middle between already existing cracks. Their propagation across the layer thickness is analyzed using energy release rate based criterion. It is shown that at very high crack density the crack propagation across the layer thickness is unstable in the beginning, but it is stopped when approaching the middle of the layer where the crack opening becomes zero. Presence of local delaminations at the tips of existing cracks changes the energy release rate for propagation of new transverse cracks.

Transverse cracks in the 90-layers in cross-ply laminates have singular stress state at the crack tips. This causes formation of fiber/matrix debonds which coalesce into a local delamination along the 0/90-layer interface. Various studies in the literature have predicted onset strains for local delaminations at transverse crack tips using energy-based criteria such as critical strain energy release rate (ERR) and critical generalized stress intensity factors. Although similar ERR-based analyses have been carried out to predict the delamination growth as well, a systematic parametric analysis is lacking. Such systematic analysis of parameters that can affect the growth of local delaminations including geometrical parameters, elastic constants and transverse crack density is necessary to predict delamination growth under complex thermo-mechanical loading conditions. In the present work, FEM is used to carry out ERR-based analysis of the growth of local delaminations with different shapes in carbon-fiber epoxy and glass-fiber epoxy [0m,90n]s cross-ply laminates with the help of virtual crack closure technique and J-integral method. Firstly, the ratios of elastic constants and geometrical parameters that can prominently affect the ERR values are identified by a simple analytical routine. Then, the analytical predictions are verified using FEM for local delaminations growing symmetrically (I-shaped and C-shaped) or non-symmetrically (T-shaped and S-shaped) with respect to the laminate midplane. It is shown that a non-symmetrical I-shaped crack would always transition into a symmetrical I-shaped crack before any further delamination growth, if energetically viable. Finally, a simplified strategy to calculate ERR values for local delaminations growing under combined thermo-mechanical loading is presented. 

Thermo-mechanical response of [90n/0m]s carbon/epoxy and glass/epoxy cross-ply laminates in 4-point bending is analyzed experimentally and analytically. Intralaminar cracks in surface 90°-plies and local delaminations introduced in one of the 90°-plies at large deflections reduce the laminate bending stiffness and make the laminate asymmetric due to differences in the damage state in the layers. The latter leads to residual thermal curvature that increases with intralaminar crack density and with growing local delaminations. In the present study optical microscopy was used for crack density quantification. It was also found experimentally that small local delaminations develop in the initial stage of damage evolution and under increasing load they grow rapidly from the existing and newly created crack tips. The effect of damage on residual curvature and the bending stiffness was analyzed using an analytical method, where the concept of the effective stiffness of damaged ply is used in the classical laminate theory. Analytical results were validated with a 3-D FEM simulation of the damaged laminate in a 4-point bending test. In the literature a phenomenon that the microdamage in laminate layers causes redistribution of in-plane thermal stresses is often overlooked. The present paper shows that the used analytical approach gives an accurate description of experimental results regarding two independent sets of data: the residual curvature; and the laminate bending stiffness with evolving micro-damage. The present study also renders a better insight in the mechanics of the phenomena and allows estimation of the extent of local delaminations that is difficult to measure in tests.

During the last decade new models for bending stiffness prediction of damaged composite laminates have been proposed in the literature advancing the earlier developed engineering approaches in accuracy and in complexity. However, experimental data for validation of complex analytical or engineering models are almost non-existent in the literature. In the present work a detailed experimental study was performed to investigate the bending stiffness reduction of composite cross-ply laminates with evolving micro-damage. Intralaminar cracks and local delaminations in the bottom surface 90-degree layer of carbon/epoxy and glass/epoxy cross-ply laminates were introduced in 4-point bending tests. Digital Image correlation (DIC) technique was used to experimentally determine the midplane curvature. The accuracy of beam theory for bending stiffness determination was assessed. The measured bending stiffness reduction with respect to transverse crack density was also compared with FEM predictions. The results show that the beam theory gives slightly underestimated curvature at low deflections, whereas at large deflections the beam theory overestimates the curvature and the moment-curvature relation becomes nonlinear. Nevertheless, the overall agreement between beam theory and DIC-based results is still very good, which leads to conclude that beam theory based data reduction schemes have sufficient accuracy for predicting bending stiffness even for highly damaged laminates.

The bending stiffness of carbon/epoxy and glass/epoxy cross-ply laminates with intralaminar cracks in the surface 90° plies and local delaminations were studied experimentally using 4-point bending tests. The bending stiffness is defined as the slope of the relation between the applied bending moment and the corresponding midplane curvature. To measure the midplane curvature of laminates with different damage states, the digital image correlation system was used. The reduction in the bending stiffness with increasing density of transverse cracks and delamination length was also analyzed using a 3-D FEM model. The analysis and optical microscopy observations showed that, in the initial stage of damage evolution, local delaminations were small, but with increasing load, the delaminations grew rapidly from the tips of existing and newly created cracks, enhancing the bending stiffness degradation. As an alternative to the 3-D FEM modelling of the test, analytical approaches in conjunction with the classical laminate theory were suggested. The analytical approach was based on the concept of the “effective stiffness of damaged ply,” where the initial stiffness of the damaged ply was replaced by the effective stiffness depending on the damage state. In the present work, two routines were used to determinate the effective stiffness of the damaged ply: a) back-calculation from the difference in the stiffnesses of damaged and undamaged laminates employing the FEM model of the representative volume element; b) simple analytical fitting functions. It is shown that the analytical approach suggested is accurate and convenient for predicting the degradation of bending stiffness of a laminate with an evolving microdamage.

An electrophoretic deposition (EPD) prototype was developed aiming at the continuous production of carbon nanotube (CNT) deposited carbon fiber fabric. Such multi-scale reinforcement was used to manufacture carbon fiber-reinforced polymer (CFRP) composites. The overall objective was to improve the mechanical performance and functionalities of CFRP composites. In the current study, the design concept and practical limit of the continuous EPD prototype, as well as the flexural strength and interlaminar shear strength, were the focus. Initial mechanical tests showed that the flexural stiffness and strength of composites with the developed reinforcement were significantly reduced with respect to the composites with pristine reinforcement. However, optical microscopy study revealed that geometrical imperfections, such as waviness and misalignment, had been introduced into the reinforcement fibers and/or bundles when being pulled through the EPD bath, collected on a roll, and dried. These defects are likely to partly or completely shadow any enhancement of the mechanical properties due to the CNT deposit. In order to eliminate the effect of the discovered defects, the pristine reinforcement was subjected to the same EPD treatment, but without the addition of CNT in the EPD bath. When compared with such water-treated reinforcement, the CNT-deposited reinforcement clearly showed a positive effect on the flexural properties and interlaminar shear strength of the composites. It was also discovered that CNTs agglomerate with time under the electric field due to the change of ionic density, which is possibly due to the electrolysis of water (for carboxylated CNT aqueous suspension without surfactant) or the deposition of ionic surfactant along with CNT deposition (for non-functionalized CNT aqueous suspension with surfactant). Currently, this sets time limits for the continuous deposition.

The energy release rate (ERR) of a fiber-matrix debond crack in a unidirectional composite subjected to transverse tension is studied numerically. The focus of the study is the effect of the proximity of the neighboring fibers on the ERR. For this, a hexagonal pattern of fibers in the composite cross-section is considered. Assuming one fiber to be debonded at certain initial debond arc-length, the effect of the closeness of the surrounding six fibers on the ERR of the crack is studied with the inter-fiber distance as a parameter. Using an embedded cell consisting of discrete fibers in a matrix surrounded by the homogenized composite, a finite element model and the virtual crack closure technique are used to calculate the ERR. Results show that the presence of the local fiber cluster accelerates the crack growth up to a certain initial crack angle, beyond which the opposite effect occurs. It is also found that the residual stress due to thermal cooldown reduces the ERR. However, the thermal cooldown is found to enhance the debond growth in plies within a cross-ply laminate.

A simple model for predicting intralaminar cracking in laminates under cyclic loads is proposed and validated. The model is limited to low stresses and low crack density and is based on the assumption that the non-uniformity of the fiber distribution is the main reason for the observed large variation of cracking resistance along the transverse direction of the layer. Hence, the resistance variation in quasi-static and in cyclic loading can be described by the same parameter. At low crack density the failure resistance variation is more significant than the variation of the stress state in the specimen, the latter becoming dominant at high crack density. At low crack density the Weibull distribution for probability of intralaminar cracking is used for crack density growth simulation during cyclic loading. Assuming the non-uniformity of the fiber distribution as the cause for variation of cracking resistance, the Weibull shape parameter in cyclic loading is the same as in quasi-static loading case while the scale parameter is assumed to degrade with the applied number of cycles and this dependence is described by a power function. Thus, the determination of parameters is partially done using quasi-static tests and partially using cyclic tests, significantly reducing the necessary testing time. The predictions of dependency of the cracking on the stress and number of cycles are validated against experimental observations of cracking in the 90-plies of quasi-isotropic non-crimp fabric (NCF) laminates as well as in tape based cross-ply laminates.