Prediction for progression of transverse cracking in CFRP cross-ply laminates using Monte Carlo method

This study predicted transverse cracking progression in laminates including 90° plies. The refined stress field (RSF) model, which takes into account thermal residual strain for plies including transverse cracks is formulated, and the energy release rate associated with transverse cracking is calculated using this model. For comparison, the energy release rate based on the continuum damage mechanics (CDM) model is formulated. Next, transverse cracking progression in CFRP cross-ply laminates including 90° plies is predicted based on both stress and energy criteria using the Monte Carlo method. The results indicated that the RSF model and the CDM model proposed in this study can predict the experiment results for the relationship between transverse crack density and ply strain in 90° ply. The models presented in this paper can be applied to an arbitrary laminate including 90° plies.     

Failure behavior of quasi-isotropic carbon fiber-reinforced polyamide composites under tension

In this paper, the microscopic failure behavior of quasi-isotropic carbon fiber-reinforced polyamide-6 (CF/PA6) laminates under tension was investigated experimentally. Laminates of two layups, namely [45°/0°/?45°/ 90°]_s and [45°/0°/?45°/ 90°]_2s, were made from CF/PA6 tapes of two different manufacturers and then subjected to tensile testing. Crack initiation and progression on the polished free edge of specimens were examined using optical microscopy, under several load levels. Crack growth behavior through the specimen width was also traced by observing the crack configurations in different sections in the specimen width direction. The effects of the spatial distribution of fiber on the microscopic damage events were elucidated. The difference in failure behavior between the present CF/PA6 laminates and conventional thermosetting CF/Epoxy laminate is discussed.     

Experimental study on delamination migration in composite laminates

The transition of delamination growth between different ply interfaces in composite tape laminates, known as migration, was investigated experimentally. The test method used promotes delamination growth initially along a 0/θ ply interface, which eventually migrates to a neighbouring θ/0 ply interface. Specimens with θ = 60° and 75° were tested. Migration occurs in two main stages: (1) the initial 0/θ interface delamination turns, transforming into intraply cracks that grow through the θ plies; this process occurs at multiple locations across the width of a specimen, (2) one or more of these cracks growing through the θ plies reaches and turns into the θ/0 ply interface, where it continues to grow as a delamination. A correlation was established between these experimental observations and the shear stress sign at the delamination front, obtained by finite element analyses.Overall, the experiments provide insight into the key mechanisms that govern delamination growth and migration.     

Influence of intralaminar cracking on the apparent interlaminar mode I fracture toughness of cross‐ply laminates

One of the major difficulties in interlaminar fracture tests of multidirectional laminates is the high tendency for intralaminar cracking and the resulting wavy crack propagation. Experimental work showed that this occurred in double cantilever beam (DCB) tests of cross‐ply laminates having a starter crack on a 0°/90° interface. Moreover, under steady‐state propagation conditions, the apparent values of the critical strain energy release rate G_Ic were two times higher than those of 0°/0° specimens. In this paper, a finite‐element‐based progressive damage model was used to simulate crack propagation in cross‐ply specimens. The results showed that transverse cracking alone cannot be responsible for the above difference of G_Ic values. Therefore, the higher propagation G_Ic values for cross‐plies must be attributed to the more extensive fibre bridging observed and to plastic deformations of the 90° interfacial ply.     

Damage characterisation of thermally shocked cross-ply ceramic composite laminates

Damage due to thermal shock in cross-ply Nicalon/calcium aluminosilicate ceramic matrix composites has been investigated. Heated specimens of two simple [(0°/90°)_s and (90°/0°)_s] and two multi-layer [(0°/90°)_3s and (90°/0°)_3s] materials were quenched into water at room temperature. Crack morphologies were assessed by reflected light microscopy and scanning electron microscopy. The use of image assembling software allowed the generation of reflected light microscopy images of all of the thermally-shocked surfaces onto which the crack patterns were then superimposed. This allowed clear identification of damage mechanisms and accurate quantification of damage accumulation with increasing severity of thermal shock. Damage was first detected in the central plies of each composite. Composites with 0° central plies exhibited slightly higher resistance to thermal shock than their counterparts with 90° central plies. Although damage extended to the outer plies as the severity of the shock increased, crack density was found to vary with position at every shock: it was highest in the central plies and gradually reduced towards the outer plies. Multiple matrix cracking perpendicular to the fibre direction was the damage mode identified in 0° plies, while 90° plies contained cracks that ran along the ply length. At more severe shocks the morphology of these crack patterns was affected in significantly different ways. In addition, the thinner, simple cross-ply composites exhibited much higher resistance to thermal shock than their multi-layer counterparts.     

Statistical model of the transverse ply cracking in cross-ply laminates by strength and fracture toughness based failure criteria

Cross-ply laminate subjected to tensile loading provides a relatively well understood and widely used model system for studying progressive cracking of the transverse ply. This test allows to identify material strength and/or toughness characteristics as well as to establish relation between damage level and the composite stiffness reduction. The transverse ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. The variability affects both crack initiation (governed by the local strength) and propagation (governed by the local fracture toughness). The primary aim of the present study is elucidation of the relative importance of these phenomena in the fragmentation process at different transverse and longitudinal ply thickness ratios. The effect of the random crack distribution on the mechanical properties reduction of the laminate is also considered. Transverse ply cracking in glass fiber/epoxy cross-ply laminates of the lay-ups [0₂/90₂]_s, [0/90₂]_s, and [0/90₄]_s is studied. Several specimens of each lay-up were subjected to uniaxial quasistatic tension to obtain crack density as a function of applied strain. Crack spacing distributions at the edge of the specimen also were determined at a predefined applied strain. Statistical model of the cracking process is derived, calibrated using crack density vs. strain data, and verified against the measured crack spacing distributions.     

Interlaminar and intralaminar fracture modes in 0/90 cross-ply glass/epoxy laminate

Delamination of a cross-ply 0/90 glass fibre-reinforced composite laminate with an epoxy-phenol matrix was studied using a double cantilever beam test. Fracture toughness was determined by measurement of bend angle of the cantilever beams. Results obtained with this method were in agreement with those from conventional compliance and area methods. Two different fracture modes were observed: interlaminar and intralaminar. In the interlaminar fracture mode, crack jumps in the space between two neighbouring 0° and 90° plies were observed. With the interlaminar fracture mode, during crack initiation G_Ic decreased with crack length. Intralaminar fracture mode consisted of the gradual growth of a crack through a 0° ply. Fibres bridging the opposite sides of the crack were observed in this case, and fracture toughness G_Ic did not change with crack length. G_Ic (420 J m⁻²) at intralaminar fracture mode was approximately twice that at interlaminar fracture mode (220 J m⁻²). The difference in fracture toughness was explained by the dissipation of energy by fibres bridging the opposite sides of the crack at intralaminar fracture mode.     

Damage Assessment of CFRP [90/±45/0] Composite Laminates over Fatigue Cycles

The present paper develops a stiffness-based model to characterize the progressive fatigue damage in quasi-isotropic carbon fiber reinforced polymer (CFRP) [90/±45/0] composite laminates with various stacking sequences. The damage model is constructed based on (i) cracking mechanism and damage progress in matrix (Region I), matrix-fiber interface (Region II) and fiber (Region III) and (ii) corresponding stiffness reduction of unidirectional plies of 90°, 0° and angle-ply laminates of ±45° as the number of cycles progresses. The proposed model accumulates damages of constituent plies constructing [90/±45/0] laminates by means of weighting factor η ₉₀, η ₀ and η ₄₅. These weighting factors were defined based on the damage progress over fatigue cycles within the plies 90°, 0° and ±45° of the composite laminates. Damage model has been verified using CFRP [90/±45/0] laminates samples made of graphite/epoxy 3501-6/AS4. Experimental fatigue damage data of [90/±45/0] composite laminates have fell between the predicted damage curves of 0°, 90° plies and ±45°, 0/±45° laminates over life cycles at various stress levels. Predicted damage results for CFRP [90/±45/0] laminates showed good agreement with experimental data. Effect of stacking sequence on the model of stiffness reduction has been assessed and it showed that proposed fatigue damage model successfully recognizes the changes in mechanism of fatigue damage development in quasi-isotropic composite laminates.     

Some aspects of crack growth and failure in fibre reinforced composites

A theoretical analysis, previously developed to deal with the machanics of matrix cracking in unidirectional composites and with transverse ply cracking in cross ply laminates, has been developed further to deal with the tensile failure of unidirectional fibrous composites in with the fibres have a known distribution of strengths. It is proposed that, under the application of a tensile load, stable transverse cracks are formed which originate from regions of initial damage and which become unstable at some critical strain value. The model takes account of various parameters including the interfacial fibre/matrix debonding energy, the residual frictional shear strength of the debonded interface and the elastic properties of fibres and matrix. Comparisons are made between the predictions of the model and the observed failing strains of the 0° plies in carbon fibre polymer matrix laminates. The relevance of the model to the study of delayed fracture in fibrous composites is discussed. The modification of this model, previously developed to describe crack growth in the transverse plies of 0°/90° laminates, is used to predict the initial cracking strains for a wide range of CFRP laminate geometries and initial crack sizes. Some aspects of the mechanics of crack extension across interply interfaces are discussed.     

铺层取向误差对CFRP可折叠管件半片变形影响的数值分析与试验研究

以单层厚度为0.04mm的碳纤维/树脂(T300/5228,CFRP)超薄单向预浸料,采用真空袋-固化炉成型方法制备了一系列不同铺层复合材料"Ω"型可折叠管件半片,并采用ANSYS软件进行了有限元分析,通过实验和数值模拟方法研究了铺层方式及取向误差对变形的影响,制备的四种铺层方式制件实验测量其变形趋势与相应模拟分析结果一致,得到了铺层取向误差对变形影响较小的铺层方式。研究发现:±45°铺层比0°铺层的铺层取向误差对变形影响更大,增加90°铺层可以在一定程度上控制因铺层取向误差导致的可折叠管件半片的变形。研究结果表明通过铺层设计可以在一定程度上实现对CFRP可折叠管件半片变形的控制。     

Fatigue crack growth in thin notched woven glass composites under tensile loading. Part I: Experimental

Helicopter blades are made of composite materials mainly loaded in fatigue and have normally relatively thin skins. A through-the-thickness crack could appear in these skins. The aim of this study is to characterize the through-the-thickness crack propagation due to fatigue in thin woven glass fabric laminates. A technological test specimen is developed to get closer to the real loading conditions acting on these structures. An experimental campaign is undertaken which allows evaluating crack growth rates in several laminates. The crack path is linked through microscopic investigations to specify damage in woven plies. Crack initiation duration influence on experimental results is also underlined.     

Influence of embedded gap and overlap fiber placement defects on the microstructure and shear and compression properties of carbon–epoxy laminates

This paper presents results from an experimental study of the influence of embedded defects created during automated fiber tape placement, on the mechanical properties of carbon/epoxy composites. Two stacking sequences have been examined, [(−45°/+45°)₃/−45°] and [90°₄/0°₃/90°₄], in which gaps and overlaps have been introduced during fiber placement. These materials have been cured in an autoclave either with or without a caul plate, then analyzed by ultrasonic C-scan. The microstructures were characterized by scanning electron microscopy. In-plane shear tests were performed on the ±45° laminates and showed that the use of a caul plate does not affect mechanical behavior of plies in the embedded defect region. Compression tests were performed on 0°/90° laminates and in this case the presence of a caul plate is critical during polymerization as it prevents thickness variations and allows defects to heal.     

Macroscale assessment of low-velocity impact on hybrid composite laminates

Composites are usually brittle materials and have low impact properties. Structural dimensions, stacking sequence, ply materials, ply thicknesses and ply angles are standard variables that influence composite‘s performance against impact loads. Stacking sequence in hybrid laminates affects the failure and impact resistance. Failure mechanisms at the low-velocity impact of a rigid object in hybrid laminates are complex, and the subsurface damage in a composite laminate cannot be detected directly. However, various simulation platforms make it easy to see the impact damage between the plies of laminate. This paper numerically investigated the effect of stack sequence and hybridization of two fiber types against low-velocity impact. The current study adopted four-layer composite laminates of carbon and glass fiber layers with a stacking plan [C/C/C/C], [C/G/C/G] and [G/C/G/C], having lay-up angles as [0°/45°/−45°/90°]. Keeping the impactor mass and the incident velocity constant, the laminates were subjected to low-velocity impact. The damage contours for a failure mode were recorded and compared at the ply level. The numerical study resulted in impact imitations showing comparisons of the damage contours using Hashin failure criteria. Hybrid laminates display better performance in absorbing impact energies; however, hybrid laminates experienced more subsurface damage due to more impact energy absorption.     

Micro-mechanical analysis of the effect of ply thickness on the transverse compressive strength of polymer composites

A micro-mechanical model is used to study the effect of ply thickness on constrained 90° plies subjected to transverse compressive loading (in situ effect). For cross-ply sublaminates with conventional, standard-thickness 90° plies, failure is dominated by fibre–matrix interface cracking and large localised plastic deformation of the matrix, forming a localised band in a plane that is not aligned with the loading direction. Ultra-thin plies show a dispersed damage mechanism, combining wedge cracking with ply fragmentation/separation. Moreover, a transverse crack suppression effect is clearly observed. To the authors’ knowledge, it is the first time an in situ effect in transverse compression has been identified. When comparing the results of the micro-mechanical model with the predictions from analytical models for the in situ effect, the same trends are obtained. These results also show that, for realistic ply thicknesses, these analytical models can be considered fairly accurate.     

Monitoring local strains in cracked cross-ply composites using an embedded aramid fibre strain sensor

Single aramid fibre strain sensors have been embedded in transparent glass-fibre reinforced epoxy resin cross-ply laminates. The sensors, located at the 0°/90°/0° ply interfaces, were interrogated by a remote laser Raman microprobe which enabled the changes in the longitudinal strain in the 0° plies caused by transverse cracking in the 90° ply to be monitored. Strain magnifications of up to about 6 were measured in the crack plane, 10 m from the 0°/90° ply interface, and it is estimated that the region of enhanced strain extends to a distance of about 40 m from the interface. Crack interactions were seen to occur for crack spacings of less than two transverse ply thicknesses.     

Model for prediction of simultaneous time-dependent damage evolution in multiple plies of multidirectional polymer composite laminates and its influence on creep

A model to predict time-dependent evolution of simultaneous transverse cracking developed in multiple plies during creep loading and its effects on creep of multidirectional polymer matrix composite laminates is presented. The stress states in the intact regions of the plies are determined using the lamination theory during an incremental change in time. The stored elastic energy, determined using this stress state, is compared with a critical stored elastic energy value for damage to determine if a ply would fracture after the increment. If fracture is predicted, variational analysis is used to determine the perturbation in ply stresses due to cracking. This procedure is repeated to determine the crack evolution and creep strain. Model predictions compared well with experimental results for a [±θ_m/90_n]_s laminate.     

Experimental and numerical studies of initial cracking in CFRP cross-ply laminates

This work is concerned with the conditions for formation of the first (initial) cracks in composite laminates with cutouts or ply drop-offs subjected to in-plane loading. We study here the crack formation on the free edge of CFRP cross-ply laminates experimentally and by numerical stress and failure analysis. The free-edge surface strains are measured by the digital image correlation (DIC) technique. The numerical analysis consists of a two-scale approach, where the macro-level analysis is performed with a three-dimensional finite-element method (3D FEM) and the micro-level analysis uses a periodic unit-cell (PUC) in the transverse plies. The constitutive assumption made for the macro-level analysis is an orthotropic linear thermo-elastic solid for the unidirectional plies with a thin isotropic viscoplastic layer between the longitudinal and transverse plies. In the PUC, the fibers are assumed linear elastic, while the matrix is modeled as an elastic–viscoplastic solid. Crack formation is assumed to occur in the matrix by the dilatation induced brittle failure mechanism for which the dilatation energy density criterion is used.     

Bio-inspired hierarchical design of composite T-joints with improved structural properties

The biological principle of hierarchical (multi-scale level) design was used at the structural and laminate levels to design a novel carbon/epoxy T-joint with improved structural properties for potential use in light-weight aircraft structures. The bio-inspired structural modification mimics tree branch–trunk joints by embedding the stiffener flange into skin plies. This design concept results in increased fracture toughness due to crack branching and deflection. Simultaneously, bio-inspired ply angle optimisation was used to mimic the tailored arrangement of cellulose micro-fibrils observed in the wood cells contained within tree branch joints. The optimisation procedure minimises the interlaminar stress concentration in the T-joint radius bend and increases strength while maintaining similar global laminate stiffness properties. The hierarchical joint resulted in a significantly improved tensile strength compared to a conventionally designed T-joint. The new design additionally exhibited higher absorbed strain energy to failure load for bending and tension loading. Additionally, the hierarchical T-joint had a significantly reduced critical joint cross-sectional area (weight) due to the embedded design.     

Failure mechanisms of a notched CFRP laminate under multi-axial loading

A quasi-isotropic CFRP laminate, containing a notch or circular hole, is subjected to combined tension and shear, or compression. The measured failure strengths of the specimens are used to construct failure envelopes in stress space. Three competing failure mechanisms are observed, and for each mechanism splitting within the critical ply reduces the stress concentration from the hole or notch: (i) a tension-dominated mode, with laminate failure dictated by tensile failure of the 0° plies, (ii) a shear-dominated mode entailing microbuckling of the −45° plies, and (iii) microbuckling of the 0° plies under remote compression. The net section strength (for all stress states investigated) is greater for specimens with a notch than a circular hole, and this is associated with greater split development in the load-bearing plies. The paper contributes to the literature by reporting sub-critical damage modes and failure envelopes under multi-axial loading for two types of stress raiser.     

Fatigue life prediction of carbon fibre reinforced laminates by using cycle-dependent classical laminate theory

In this work a study about the adaption of the classical laminate theory for fatigue loads is presented. Cycle dependent stiffnesses of single UD 0°, UD 45° and UD 90° plies are implemented in order to calculate the fatigue-induced stiffness decrease of a multidirectional lay-up with the stacking sequence [0°/+45°/−45°/90°/90°/−45°/+45°/0°]. As second input alternative, UD 0°, UD 90° and ±45° plies are used. The calculated cycle-dependent stiffness parameters are compared to experimentally measured fatigue data of the multidirectional lay-up. The experimental test procedure used for the measurement of cycle-dependent stiffness parameters has been published previously. Results show that the experimentally measured stiffness decreases of the multidirectional lay-up can be estimated accurately based on the cyclic unidirectional input parameters.