Cross-ply Laminates Research Articles

An analytical approach to model transverse inter-fibre fracture evolution in cross-ply carbon fibre reinforced polymers laminates under a three-point bending test

The prerequisite to equip structures with in situ electrical health monitoring systems in a meaningful manner is to estimate potential damage locations. In this context, an analytical approach to model the spatial and temporal evolution of transverse inter-fibre fractures (IFF) is exemplified for [Formula: see text] cross-ply laminates under three-point bending. The model is based on the tensile load in the bottom 90°-layer. The effective stress is computed directly from the specimen displacement, whereas the strength is considered to be periodically distributed due to material inhomogeneities along the specimen. The continuous comparison between the sinusoidal strength function and the effective stress allows modelling progressive damage in form of IFF. A modified Hann window is used to consider their effect to the bottom 90°-layer. Experiments with the same configuration are performed and the observed IFF evolution is used to tune the model parameters in an optimisation procedure, e.g., the peak separation of the sinusoid and the length of the Hann window. The comparison between model and experiment shows a high level of agreement. The model is thus capable to reproduce experiments with minimal computational effort. This makes it highly suitable as input for electrical monitoring models that rely on the continuous damage evolution of the investigated structure. In its current form, the model is limited to the specified configuration. However, the simple analytical approach allows it to be easily adapted. It is furthermore shown that progressive composite damage in terms of spatial and temporal evolution can be accurately described using an analytical approach.

Equivalent elastic modulus measurement of cross-ply composite plates using Lamb waves

This paper proposes a simple and effective Lamb wave-based measurement method for the elastic moduli of cross-ply composite plates, considered equivalent to a single-layer orthotropic plate with nine independent elastic constants. The effects of theses constants on the phase velocities of the fundamental S0 and A0 modes are investigated. The phase velocity of the S0 mode depends only on the equivalent tensile elastic modulus and in-plane Poisson’s ratio in the low-dispersive frequency-thickness product regime, whereas the phase velocity of the A0 mode depends almost only on the equivalent shear elastic modulus. Moreover, the in-plane Poisson’s ratio of cross-ply laminates changes sufficiently small to neglect its effect on the phase velocities of the S0 mode. Therefore, the tensile and shear elastic moduli of the plates can be estimated using the S0 and A0 modes, and the mapping relations between the phase velocities of these modes and the elastic moduli are established. The proposed approach has been numerically and experimentally tested on cross-ply carbon fiber reinforced laminates, and validated by theoretical values and conventional tensile tests.

Study on impact resistance and parameter optimization of patch‐repaired plain woven composite based on multi‐scale analysis

AbstractPatch‐repaired plain woven composite structures were exposed to internal damage caused by impact during service, which reduced mechanical properties. A multi‐scale modeling strategy was proposed to study the impact resistance characteristics of patch‐repaired plain woven carbon‐fiber‐reinforced‐polymer (CFRP) laminates. The micro representative volume element (RVE) was extracted from the yarn; a local homogenization method was used to obtain the equivalent cross‐ply laminate (ECPL) cells corresponding to the mesoscale RVE. The finite element model (FEM) of patch‐repaired plain woven laminate was established by extending the ECPL cells. The FEM was checked by the low‐velocity impact (LVI) tests, and the impact parameter errors were within 10%. Furthermore, impact resistance of repaired specimens under different impact conditions (e.g., the impact energy was 3 ~ 20 J) was studied. Finally, patch parameters (patch thickness, patch size, off‐axis angle) of the repaired specimen were optimized by multi‐objective optimization based on the surrogate model and response surface method (RSM). After multi‐objective function optimization, the optimal patch parameter configuration (the thickness of the patch was 0.87 mm, the diameter was 66 mm, and the off‐axis angle was 44.2°) reduced the absorbed energy value of the repaired specimen from 4.9089 to 4.1640 J, and the delamination area of the repaired specimen from 605 to 280 mm2. All the results provide a reference for patch repair of plain woven composites.

Fatigue life determination based on infrared thermographic data for MultiDirectional (MD) CFRP composite laminates

Infrared thermography is a useful tool for the rapid determination of fatigue properties. A previously proposed fatigue life model, which combines the stiffness degradation k(N) with thermographic data ΔTstab, has been successfully applied to UD and ±45° CFRP laminates. In view of more complex damage mechanisms in multidirectional laminates, the model is modified in this work to overcome the conservative predictions. The S-N curves determined by the modified model are compared with the experimental results of traditional fatigue tests on Quasi-Isotropic (QI) and cross-ply CFRP laminates. Very good consistency was observed. In particular, the S-N curve corresponding to fatigue life of Nfl=106 cycles is conservative compared to that from the traditional fatigue test results, but the maximum safety factors are no more than 1.15 and 1.08 for QI and cross-ply laminates, respectively. Both S-N curves corresponding to Nfl=107 cycles for two tested laminates lie within the 95% confidence interval of traditional experimental results. Therefore, based on infrared thermographic data, the modified model proposed in this study is more general. It allows to determine the S-N curves of QI and cross-ply CFRP laminates just in about ten hours of testing machine time instead of one month and a half using traditional fatigue tests, even though more experimental data (other types of MD stacking sequences, composite materials, under other fatigue modes, etc.) are necessary to demonstrate the applicability of modified model to all types of MD laminates.

Design of cost-effective hybrid soft armour panels by strategic replacement of backing layers with a non-ballistic material: A parametric study

Primary requirements of personal protective armour are light-weight, enhanced protection level, and low cost. This work explores the use of ultra-high molecular weight polyethylene (UHMWPE) cross-ply laminates and polycarbonate (PC) sheet to develop hybrid soft armour panels (SAP) for personal protection. Three SAP configurations were prepared and analysed both numerically and experimentally. These configurations were: (1) panel composed of only UHMWPE laminate, (2) panel consisting of UHMWPE laminate and two layers of PC, and (3) panel with UHMWPE laminate and three layers of PC. The ballistic performance of these SAPs was evaluated in terms of back face signature (BFS) and number of perforated layers against the 9 mm × 19 mm lead core bullet having a striking velocity 430 m s−1. Corresponding finite element models of SAPs were also developed using LS-DYNA and validated with experimental results. Further, a parametric study was performed to obtain the cost-effective hybrid solution of SAP and BFS as per IS-17051: 2018. Results revealed that SAPs retained their ballistic performance in terms of BFS for up to 52.5% substitution of the backing layers of UHMWPE laminate with PC sheets. Analyses confirmed that strategic replacement of backing layers with PC sheets is a cost-effective solution to design SAPs.

Buckling Analysis of Laminated Stiffened Plates with Material Anisotropy Using the Rayleigh–Ritz Approach

An energy-based solution for calculating the buckling loads of partially anisotropic stiffened plates is presented, such as antisymmetric cross-ply and angle-ply laminations. A discrete approach, for the mathematical modelling and formulations of the stiffened plates, is followed. The developed formulations extend the Rayleigh–Ritz method and explore the available anisotropic unstiffened plate buckling solutions to the interesting cases of stiffened plates with some degree of material anisotropy. The examined cases consider simply supported unstiffened and stiffened plates under uniform and linearly varying compressive loading. Additionally, a reference finite element (FE) model is developed to compare the calculated buckling loads and validate the modelling approach for its accuracy. The results of the developed method are also compared with the respective experimental results for the cases where they were available in the literature. Finally, an extended discussion regarding the assumptions and restrictions of the applied Rayleigh–Ritz method is made, so that the limitations of the developed method are identified and documented.

Refined Semi-Analytical Framework to Predict the Natural Vibration Characteristics of Bistable Laminates

Bistable unsymmetrical laminates have received significant attention in morphing applications due to their ability to attain multiple shapes when subjected to thermal loads. Morphing structures in general are subjected to dynamic operating conditions. Also, the highly nonlinear snap-through transition between stable configurations possesses rich dynamic characteristics. Therefore, understanding the dynamic characteristics of bistable laminates is essential for designing morphing structures constituting bistable elements. Thus, the present study aims to explore the dynamics of bistable unsymmetrical laminates by evaluating their natural vibration characteristics associated with small-amplitude dynamic excitation around the static equilibrium configurations. A refined semi-analytical framework is proposed to analyze the natural vibration characteristics of the bistable laminate, where the potential energy is expressed only in terms of the unknown coefficients of the assumed out-of-plane displacement function. The in-plane components are separately evaluated using the in-plane equilibrium equations and compatibility conditions. In the dynamic analysis, perturbations are imposed on the static equilibrium configurations to capture the modal characteristics. A full geometrically nonlinear finite element (FE) model of the bistable laminate has been created in a commercially available FE package to compare semi-analytical solutions. To validate the proposed frameworks, an experimental strategy to capture the natural frequencies of a bistable laminate is presented in this paper. Unsymmetric laminates mounted at its center have been used for the experimental testing, where the vibrations are measured using miniature integrated electronics piezoelectric accelerometer sensors attached at the corners. The semi-analytical and FE results are validated against the experimental observations for the selected unsymmetrical cross-ply laminates. The proposed frameworks are further extended to a family of unsymmetrical variable-stiffness (VS) laminates generated using curvilinear fiber alignments. The selected VS family can generate bistable shapes without any twisting curvature similar to that of an unsymmetrical cross-ply laminate, where the designer can expand the design space with a plethora of multiple configurations. A parametric study is performed by tailoring the VS parameters to investigate the influence of curvilinear fiber alignments on the natural vibration characteristics of bistable VS laminates.

Digital image correlation of cross-ply laminates in tension to reveal microcracking

The use of Digital Image Correlation (DIC) to reveal microstructural damage in cross-ply laminates was investigated. Matrix toughness plays a key role in governing microcracking at the tow level in near-surface plies. Experiments revealed that using a tough epoxy polymer as the matrix of the laminate resulted in increased laminate moduli in the principal directions. DIC provides insights into cross-ply laminate failure; the increase in modulus is attributed to microcrack formation in transverse plies. Early onset of matrix cracking around the tows is revealed by variations in the strain along the gauge length. The use of a tough epoxy polymer delays the load at which this cracking occurs. When an untoughened epoxy polymer is used as the matrix, microcracking can be observed at the beginning of the test, suggesting processing induced damage. The use of toughened polymers as the matrix of composite laminates is recommended to mitigate against this.

Bistable characteristics of unsymmetric cross-ply composite laminates considering different boundary shapes

The aim of this paper is to study the bistable characteristics of unsymmetric cross-ply composite laminates induced by thermal stress during the curing process when considering different boundary shapes. The changes in geometry for five types of planform shapes, have been focused, which are named rectangular planform (RP), elliptical planform (EP), trapezoidal planform (TP), diamond planform (DP) and cruciform planform (CP) respectively. The parameters that characterize the bistable performance of the laminates, including the principal curvature and snap load, were measured. The principal curvatures in different stable configurations were determined with analytical, numerical, and experimental methods, and the load-displacement curves in the snapping process were successfully obtained. Moreover, the boundary effect caused by the difference in planform shapes, which cause the local curvature of the bistable composite laminate to change, were also discussed. Predictions from an analytical shell model are verified through comparisons with nonlinear finite element simulations and experimental test results.

A multiscale homogenization iterative algorithm of 2D orthogonal prepreg carbon/aramid/epoxy woven-ply

An orthogonal mixture woven composites with aramid yarns and carbon yarns are investigated in this work. A dual-scale computational homogenization algorithm is also proposed to address the cross-scale numerical problems. Models and methods for mesoscale and macroscale are illustrated separately. Two types of meso-structures are selected for comparison, which are termed as representative unit cell (RUC) and equivalent cross-ply laminate (ECPL), and the corresponding macro-structures are referred to as RUCs and equivalent cross-ply laminate plain-woven composites (ECPL-PWC). The key finds clarified that the ECPL-PWC takes more computational expenses compared with the RUCs, but the RUCs is in acceptable agreement with testing results, as well as the evaluation results of the ECPL-PWC would obtain very satisfactory accuracy through minor numerical adjustments. The final finite element damage results reveals that the RUCs is more accurate for local damage assessment, while the ECPL-PWC is better for global damage analysis.

Experimental and numerical investigation of mechanical behavior of plain woven CFRP composites subjected to three-point bending

The mechanical behavior of plain woven Carbon Fiber-Reinforced Polymer (CFRP) composites under Three-Point Bending (TPB) is investigated via experimental and numerical approaches. Multiscale models, including microscale, mesoscale and macroscale models, have been developed to characterize the TPB strength and damages. Thereinto, Representative Volume Elements (RVEs) of the microscale and mesoscale structures are established to determine the effective properties of carbon-fiber yarn and CFRP composites, respectively. Aimed at accurately and efficiently predicting the TPB behavior, an Equivalent Cross-Ply Laminate (ECPL) cell is proposed to simplify the inherent woven architecture, and the effective properties of the subcell are computed using a local homogenization approach. The macroscale model of the TPB specimen is constructed by a topology structure of ECPL cells to predict the mechanical behavior. The TPB experiments have been performed to validate the multiscale models. Both the experimental and numerical results reveal that delamination mainly appears in the top and bottom interfaces of the CFRP laminates. And matrix cracking and delamination are identified as the significant damage modes during the TPB process. Finally, the quasi-static and dynamic behaviors of plain woven composites are discussed by comparing the results of Low-Velocity Impact (LVI) and TPB simulations.

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.

Numerical simulation of inductive heating in thermoplastic unidirectional cross-ply laminates

Thermoplastic Composites can be re-melted allowing them to be joined via welding. This is an attractive alternative to conventional methods that are used to join thermoset composite parts such as mechanical fastening and adhesive bonding. In this work the inductive heating of uni-directional (UD) plies of thermoplastic carbon fiber reinforced polymer (CFRP) laminates is investigated. The focus is on developing a numerical electromagnetic and thermal simulation model that captures the main processes involved in eddy current generation and heat generation, in particular in the interface areas of the UD plies. A measurement technique has been developed to obtain the electric properties of the ply material. Furthermore, to support the modelling of both the induction heating equipment and work piece a field measurement of the magnetic field surrounding the coil and work piece has been developed. Inductive heating experiments were carried out on several thick composite laminate plates with different ply lay-ups to compare and validate the electro-magnetic-thermal simulation model. The measured surface temperatures were compared with the results from the simulation model. The results of this work can be used to support the design of UD-ply laminates to improve their ability to be welded via inductive heating. In addition, the results of this work can be used to assist in pre-determining induction welding equipment settings and heating times.

Lévy-type solutions for the buckling analysis of unsymmetrically laminated plates with rotational restraints for various plate theories

The stability behaviour of unsymmetrical laminated structures made of fibre-reinforced plastics is significantly influenced by bending–extension coupling and the comparatively low transverse shear stiffnesses. The aim of this work is to improve the analytical stability analysis of unsymmetrically laminated structures. With the discrete plate theory, the stability of laminated structures can be reduced to single laminated plates. The structure is divided into individual segments, and the surrounding structure is modelled by rotational elastic restraints. The governing equations for single plates under specific boundary conditions can be solved exactly with Lévy-type solutions. In this study, Lévy-type solutions for the mentioned boundary conditions under biaxial compressive load is described for the classical laminated plate theory, the first-order shear deformation theory and the third-order shear deformation theory (TSDT). In addition to transverse shear, bending–extension couplings of unsymmetrical cross-ply and antisymmetrical angle-ply laminates are considered. For the implementation of boundary conditions for the rotational restraints in the context of TSDT, a new set of conditions is formulated. The investigation shows very good agreement of the buckling load with comparative finite element analyses for different layups.

Static and Fatigue Tensile Properties of Cross-Ply Carbon-Fiber-Reinforced Epoxy-Matrix-Composite Laminates with Thin Plies

Carbon-fiber-reinforced epoxy-matrix composite (CFRP) laminates with thin plies have strong damage-resistance properties compared with standard prepregs. The static and fatigue tensile fracture behavior of cross-ply CFRP laminates with thin plies should be further studied to establish the applicability of thin-ply prepregs for industrial structures. In this study, the static and fatigue tensile properties of cross-ply, high-strength polyacrylonitrile (PAN)-based carbon-fiber (T800SC)-reinforced epoxy-matrix composites with thin plies were investigated. The fiber orientations of the CFRP specimens were set to cross-ply with [0/90]10S (subscript S means symmetry), [(0)5/(90)5]2S, and [(0)10/(90)10]S. The static and fatigue tensile characteristics of the cross-ply CFRPs with thick plies with [0/90]2S and [(0)2/(90)2]S were also investigated for comparison. Under static loading, the tensile strength and failure strain of the thinnest 90°-ply-CFRP specimens were more than 5% higher than those of the other 90°-ply-thickness specimens. However, the tensile moduli and Poisson’s ratios were comparable between the cross-ply CFRPs with thin and thick plies. Under fatigue loading, the fatigue responses of the thinnest 90°-ply-CFRP specimens were 3% higher than those of the other 90°-ply-thickness specimens during lower-fatigue-cycle testing (<105 cycles). However, during higher-fatigue-cycle testing (>105 cycles), the fatigue responses decreased, with a decrease in the 90°-ply thickness, and the fatigue characteristics of the thinnest 90°-ply-CFRP specimen were 7% lower than those of the other cross-ply thin- and thick-ply-CFRP specimens.

Suppression of cross-well vibrations of a bistable square cross-ply laminate using an additional composite strip

Suppression of cross-well vibrations of a bistable square cross-ply laminate using an additional composite strip

Mitigating cryogenic microcracking in carbon-fibre reinforced polymer composites using negative thermal-expansion nanoparticles functionalized by a polydopamine coating

Herein, we report a new method of mitigating cryogenic microcracking in carbon-fibre reinforced-plastics (CFRPs) using a negative thermal-expansion nanomaterial, zirconium tungstate (ZrW2O8), to simultaneously reduce the thermal residual stresses and enhance the fracture energy of the epoxy matrix of CFRPs. The results show that 1 wt% of added ZrW2O8 nanoparticles functionalized by polydopamine can increase the fracture energy of the matrix material by 140%, reduce the coefficient of thermal expansion by 20% and, more importantly, enhance the interlaminar fracture energy of the resulting CFRP by about 100% at −196 °C. The ZrW2O8-modified matrix has been demonstrated to successfully prevent microcracking at −196 °C in a blocked cross-ply CFRP laminate with a [04/908/04] fibre architecture.

Implementing functionally graded fibers technique to enhance pinned-joint performance in cross-ply laminate polymeric composites

There are several techniques for improving the bearing performance of laminated composites, such as metal-bonded inserts, steered fiber, nano-reinforcements of the matrix, and molded holes. Although functionally graded materials (FGM) were successfully implemented in adhesive joints, it is still not used in bolted joints. The novelty of this work and its objective are implementing the FGM concept to improve the bearing performance of pinned joints in cross-ply glass fiber-reinforced epoxy laminated composites. The effect of the joint geometries and stacking sequences on pinned joints bearing strength and failure modes were investigated. A 3-D finite element model based on Hashin's failure criteria was performed to predict joint strength and progressive failure. It was found that the FGM pinned joint (FG-CM) had higher bearing strength than the conventional pinned joints technique (C-CM). The bearing strength of composite with stacking sequence [90°/0°/90°]s was higher than that of [0°/90°/0°]s for both FG-CM and C-CM.

Mathematical and simulation based investigation towards deformation behaviour of bombyx mori moth silk /vinyl ester reinforced laminated composite

ABSTRACT This paper focuses on the composite design with fibres loaded in the longitudinal direction as well as orientated at some certain angles. The study uses Bombyx Mori Moth Silk (BMM Silk) as fibres and vinyl ester as matrix material. The two sorts of composites having cross ply and angle ply laminate were considered for deformation study using the finite element analysis. According to the ASTM D 3039 testing standard, the tensile test was carried out to design and composite study of their occurred deformation. The rule of mixture was employed in order to evaluate the elastic constants of the prepared orthotropic composite laminate along the fibre direction and the evaluation of orthogonal stresses in transverse direction was carried out using the finite element procedure. The maximum orthogonal stress value of cross ply and angle ply was found to be 44.902 and 47.779 MPa, respectively. Also, the deformation occurred for both laminates was found to be of 0.083603 and 0.076428. This concludes that the deformation occurrence is more in case of angle ply and is less in cross ply laminates.

Experimental characterization of cracking behavior initiating from microdefects in cross-ply CFRP laminates

The effects of microdefects on cracking behavior in cross-ply carbon fiber reinforced plastic (CFRP) laminates was characterized as a function of defect size. A single artificial defect with a diameter from 2.5 to 50 μm was introduced into the 90∘ layer. The strain at transverse cracking from the defect decreased with increasing defect diameter. There was a lower threshold defect size for transverse cracking in cross-ply CFRP laminates. Fiber/matrix debonding occurred around the defect followed by transverse cracking. The micromechanisms of defect-induced transverse cracking are discussed on the basis of experimental results and fracture-mechanics-based prediction.