Unidirectional Plies Research Articles

Numerical research on elasto-plastic behaviors of fiber-reinforced polymer based composite laminates

A new pressure-dependent elasto-plastic constitutive model for polymer based composite laminates with unidirectional plies is established and implemented into finite element software to simulate off-axis loading tests of two kinds of composites. The validity of the new plasticity model is proved by available off-axis loading test results. Additionally, accuracies and efficiencies of the backward Euler algorithm and the forward Euler algorithm respective in solving plastic deformation of fiber-reinforced composite materials are analyzed. Compared with the forward Euler algorithm based plasticity model, the backward Euler scheme shows comparative prediction accuracy of laminate plastic behavior and better computational efficiency. This paper is expected to facilitate the numerical predictions of composite laminates’ elasto-plastic behaviors for researchers and engineers.

Damage growth and strain localization in compressive loaded fiber reinforced composites

To increase the use of polymeric structural composites, a major issue is to properly account for intra-laminar failure mechanisms, such as fiber kinking which is typically induced in compression. We propose a new set of continuum damage models that are able to predict fiber kinking response under compression. A structure tensor based formulation is established at the unidirectional ply level, where the elastic material response is governed by transverse isotropy. To consider geometrical effects in conjunction with fiber kinking instability, a continuum damage formulation at finite strain is developed. The fracture area progression includes a convective and a local damage production involving a finite progression speed. In this framework, two damage evolution models are considered; one non–local model including the gradient damage effect and a local one, without the gradient enhancement. The models are implemented in a FE–code and validated for a compression loaded specimen. The models are computationally robust and can predict the localized nature of fiber kinking. A thorough sensitivity study is presented to show how the different formulations influence the predicted responses.

Material characterization of filament-wound composite pipes

In obtaining mechanical properties of filament-wound fibre reinforced plastic pipes, standardized tests are often used to obtain bulk properties. Being a laminated composite, individual layers of the lamina will behave differently and therefore pipe-level characterizations are usually unable to fully describe the localised responses in detail. Unlike flat composite layups, obtaining unidirectional ply properties in cylindrical filament-wound composites is not as straight-forward. In this work, the composite pipe stress homogenization theory was applied in reverse to obtain the corresponding ply properties in the filament-wound pipe through successive iterations towards experimentally obtained bulk properties. Initial estimates of ply properties were obtained through a combination of extensive literature search and applications of micromechanics theories. With the iterated ply properties, finite element models simulating the tests used to obtain bulk properties were performed to validate the accuracy of the material properties. In addition, additional validation was performed on a smaller pipe section to evaluate the scalability of using ply properties across pipes of different dimensions. It was found that the ply properties obtained was able to accurately predict the responses for pipes of various dimensions.

Determination of the longitudinal compressive strength of a CFRP ply through a tensile test on a laminate

In this study, an innovative test is proposed to identify the longitudinal compressive strength of a unidirectional ply. The key idea consists in designing a laminate that, when subjected to a tensile loading, fails by compressive failure in its central 90°-ply, due to the Poisson effect, without any prior damage. Six specimens have been tensile tested to failure. No intra-laminar matrix damage could be detected before the final failure. Fibre kinking in the 90°-ply is observed experimentally in the failed specimens. This damage mechanism, located in the gauge section of the specimens, leads to the final failure. A fast computational identification method is used to determine the longitudinal compressive stress and strain within the 90°-ply at failure, from this specific tensile test. The identified average failure properties are consistent with those obtained through conventional compression tests, but the associated scattering is much lower. Consequently, this innovative method leads to an increase in the design allowable, resulting in higher performance designs.

The Effect of Various Fiber Orientations and Boundary Conditions on Natural Frequencies of Laminated Composite Beam

This paper investigates the free vibration characteristics of laminate composite beam for various lamination schemes and under various boundary conditions. A beam model with the aspect ratio (length to thickness) of 25 to 150 made of carbon/ epoxy laminates under free vibration were constructed using a commercially available finite element software (ANSYS). The varied parameters are the lamination schemes (cross ply, angle ply and unidirectional ply) and boundary conditions (Clamp-Free (C-F), Clamp-Clamp (C-C), Clamp-Hanger (C-H), Free-Free (F-F) and Hanger-Hanger (H-H) ). For each case, finite element simulations were performed and the natural frequencies were determined. Mode shapes were also analyzed to observe the beam’s deformation behavior. Results showed that increasing aspect ratio will decrease natural frequencies for the first seven mode shapes. In terms of lamination scheme, the unidirectional ply produced the highest frequency (34.26 Hz), followed by cross ply (34.05 Hz) and angle ply (13.60 Hz) at the aspect ratio of 25. In terms of boundary conditions, the Hanger-Hanger boundary condition produced the highest natural frequency (2272.52 Hz) at the aspect ratio of 25, while Clamped-Free boundary condition produced the lowest frequency (2.28 Hz) at the aspect ratio of 150. In general, it can be concluded that the current study is useful and has contributed significant knowledge to better understand of effect of various fiber orientations and boundary conditions on the natural frequencies of laminated composite beam.

Investigation on multiaxial strength reduction for multi-directional laminates under variable amplitude loading

Due to their excellent ratio of high strength and stiffness to low density, the use of composite materials in lightweight solutions is growing in widely varying industry sectors. Most of the lightweight structures are loaded cyclically and therefore there is the need for optimized computation models concerning the fatigue of composite materials. The present study mainly focuses on the fatigue life estimation of continuous fibre reinforced plastics under variable amplitude loads. The approach is based on iterative ply-wise calculation of multiaxial stress states using classical laminate theory and a subsequent analysis of the material effort with the use of the failure criteria by Puck. A number of suitable linear and nonlinear residual strength models are examined for an in-depth approach on the multiaxial strength reduction at the ply-level. The aim of this study is to calculate fatigue life of multi-directional laminates with input data from uni-directional plies only. The model is finally validated for a multi-directional laminate under variable amplitude loads with arbitrary pulsating and alternating stress ratios using experimental data from the well documented composite fatigue data base OptiDAT.

Development and assessment of modelling strategies to predict failure in tow-based discontinuous composites

Tow-Based Discontinuous Composites (TBDCs) are a growing class of materials that combine manufacturability, light-weight, and high performance. This study proposes multi-scale modelling approaches to predict the tensile strength and failure envelopes of tow-based discontinuous composites, by representing the actual composite (with randomly-oriented tows) as an equivalent ply-by-ply laminate. Several modelling approaches are considered for the different scales, including (i) a stochastic bi-linear shear-lag formulation accounting for the random location of tow-ends and matrix cracking, (ii) a novel failure criterion for a discontinuous uni-directional ply accounting for the interaction between tow pull-out and transverse failure, and (iii) a ply-discount method or a maximum strain energy criterion for the final failure of the composite. The model computes full failure envelopes for ply-by-ply laminates equivalent to TBDCs within minutes, and the results show good agreement with experimental data.

Finite element modelling of cutting force in shearing of multidirectional carbon fibre reinforced plastic laminates

Lightweight structural components made of carbon fibre reinforced plastics are manufactured near-net-shape. However, in order to fulfil geometrical or functional requirements, carbon fibre reinforced plastic components have to be trimmed and pierced in a finish processing step. Shearing is a highly productive technology that is potentially suitable for cost-effective finishing of carbon fibre reinforced plastic components in high-volume series production. Shearing of carbon fibre reinforced plastic has not yet been sufficiently researched. Cutting force is an important characteristic of the shearing process. Up to now, there exists limited knowledge on numerical modelling of the cutting forces in carbon fibre reinforced plastic shearing. In order to address this, a finite element process model of carbon fibre reinforced plastic trimming was developed in this work. The process modelling included a formulation of continuum mechanical material model for a unidirectional ply as well as a development of a kinematic model of the trimming process. The developed finite element process model was validated by means of experimental data. The simulated and experimentally determined maximum specific cutting forces demonstrated a very good qualitative and quantitative agreement.

Fundamental frequency of fully clamped antisymmetric angle-ply laminated plates with structural anisotropy

An analytical solution determining the fundamental frequency of a fully clamped composite anisotropic laminated plate is presented in the paper. The plate is composed of unidirectional composite plies oriented at some angle to one of the plate sides. The plies alternating over the plate thickness differ from each other by only the sign of the angle of orientation. Such a plate is characterised by the structural anisotropy with the extension-twisting and bending-shear coupling effects which are taken into account in the appropriate constitutive equations. The governing equations model the coupled in-plane and out-of-plane plate motions. The vibration problem is solved using the Galerkin method. The beam functions corresponding to the first vibration mode of a beam with clamped ends are employed as the approximating functions. The problem is reduced to a solution of cubic algebraic equation. Based on this solution, effects of the angle of reinforcement orientation and number of plies on the fundamental frequency of the plate with structural anisotropy are investigated. The results are verified using finite element method. An assessment of the anisotropy effect on the frequency value has been performed by comparison with the results obtained based on the orthotropic model of the plate. The formula providing the number of plies for a plate with structural anisotropy is derived for the prescribed fundamental frequency.

Flax stems: from a specific architecture to an instructive model for bioinspired composite structures

The present paper proposes to carefully study and describe the reinforcement mechanisms within a flax stem, which is an exceptional natural model of composite structure. Thanks to accurate microscopic investigations, with both optical and SEM method, we finely depicted the flax stem architecture, which can be view as a composite structure with an outer protection, a unidirectional ply on the periphery and a porous core; each component has a specific function, such as mechanical reinforcement for the unidirectional ply and the porous core. The significant mechanical role of fibres was underlined, as well as their local organisation in cohesive bundles, obtained because of an intrusive growth and evidenced in this work through nanomechanical AFM measurement and 3D reconstruction. Following a biomimetic approach, these data provide a source of inspiration for the composite materials of tomorrow.

Praćenje akustične emisije tankih slojeva hibridnih kompozita pod ponovljenim kvazi-statičkim zatezanjem

This paper investigates the applicability of the acoustic emission (AE) technique for identification of the damage onset and accumulation in S-Glass/TR30-Carbon hybrid laminates under repeated quasi-static tensile loading. The samples were made of 2 layers of unidirectional thin carbon prepreg plies which were sandwiched between 2 standard thickness S-glass prepreg plies. Analysis of the AE results shows that there are two types of events regarding energy and amplitude ranges of the AE signals. The signals with low values are found to be related to the delamination of the carbon/glass interface whereas the signals with high values are linked with the carbon layer fragmentation. There are more friction related AE signals during the unloading stage than the loading stage due to collision and rubbing between existing crack faces. Increasing the strain level increases the number of fragmentations and the AE technique is able to quantify this. It is concluded that the AE technique can be used to evaluate the number of fragmentations and can identify the damage evolution of the hybrid laminate under repeated quasi-static tensile loading.

Pseudo-ductility in flexural testing of symmetric ±45° angle-ply CFRP laminates

Pseudo-ductility could be sought in composite structures to avoid their brittle behaviour and, consequently, to withstand higher levels of external loading due to an extended non-linear response. This mechanism has been deeply examined in the literature for angle-ply laminates submitted to uniaxial tests. Nonetheless, the pseudo-ductile effects could appear also under flexural loading because tension and compression are applied in different regions of the cross-sections simultaneously. In this sense, bending testing presents a higher degree of complexity introduced by the variation of the strain through the cross-section thickness. Taking this into account the main scope of this work is to understand, describe, predict and optimise the pseudo-ductile flexural response of symmetric ±45° angle-ply laminates consisting of unidirectional and continuous CFRP plies. The outcome of three-point bending tests is reviewed analytically and experimentally. The analytical study considers the different behaviour of the material under tension and compression as well as the neutral fibre deviation from the mid-height plane. During testing the full normal strain field is acquired by means of a DIC system while strain-rosettes help to complete the data. The post-process based on microscopic characterization using SEM technology allows to observe the procedure of damage initiation and its evolution. Finally, the determination of the stacking sequences that minimise the bending-twisting coupling but favour the pseudo-ductile response is developed applying optimisation techniques with design purposes.

A numerical framework to analyze fracture in composite materials: From R-curves to homogenized softening laws

A numerical framework to obtain the crack resistance curve (R-curve) and its corresponding softening law for fracture analysis in composite materials under small scale bridging has been developed. The use case addresses the intralaminar transverse tensile fracture of a unidirectional ply of carbon fiber-reinforced polymer AS4/8552. The R-curve is computed for this material using a micromechanical embedded model corresponding to the intralaminar transverse tensile fracture toughness characteristic. The model combines an embedded cell approach with the Linear Elastic Fracture Mechanics (LEFM) displacement field to analyze the local crack growth problem including fiber/matrix interface debonding and matrix ligaments bridging as the main energy dissipation mechanisms. Other large scale toughening effects as, for instance, fiber bridging were not included in the model. Parametric analysis were carried out to assess the influence of the properties of the material constituents on the R-curve behavior and on the corresponding homogenized cohesive laws.

Influence of spatial tool inclination on delamination when milling CFRP

When end milling long carbon-fibre-reinforced plastic (CFRP), delamination, mainly fibre protrusions can occur at the top layers of the machined edges. It was observed that the spatial inclination of the tool axis significantly influences delamination and has not yet been investigated in detail. The fibre cutting angle used so far for the description of the separation process only refers to the cutting velocity in the laminate plane.The spatial position of the cutting edge and the effective velocity with respect to the fibre axis of a unidirectional ply depend on the tool engagement angle and the inclination of the tool axis. Hence, a three-dimensional description of the geometrical and kinematic relationships has been established in this work for the first time. To determine the effect on delamination the model is compared to milling experiments with various tool axis inclinations towards and perpendicular to the feed direction, denoted by lead and tilt angle.The results show that fibre protrusions can be avoided if the cutting velocity is at least partially directed into the laminate plane and if the cutting edge is located partially above the fibre to be cut. The geometrical and kinematic model is applicable to any machining operation, to materials with unidirectional fibre reinforcement and to non-crimped fabrics with unidirectional top layers.

Dynamic instability of variable stiffness composite plates

Due to its tailorability intrinsic characteristics, composite materials are an effective option in structural design or on its reengineering, especially when the ratios stiffness and/or strength to weight are relevant. Dual-phase or multiphase fibre reinforced composites can thus be found in many engineering and science applications. However, in the majority of the cases these composites are made from unidirectional plies stacking. The possibility of building fibre reinforced composite structures, wherein these fibres follow curvilinear paths, may be an important enhancement to structural mechanical response and in particular to its dynamic stability, as variable fibre orientation is responsible for variable elastic stiffness within a generic layer. This work aims characterizing the dynamic instability response of variable stiffness composite plates, according to different material and geometrical parameters. To this purpose one considers Rayleigh-Ritz method to perform buckling, free vibrations and dynamic instability analyses, using orthogonal polynomials. The dynamic instability problem is solved considering Bolotin’s method. A set of verification and illustrative case studies is considered and discussed.

Theory and validation of the master ply concept for invariant-based stiffness of composites

The objective of this paper is to unveil the background theory behind the universal master ply assumption, based on the invariant approach, to describe ply elastic properties. It was demonstrated that using ply-based constitutive relations, trace-normalized stiffness properties can be derived for different materials. Theoretical predictions for trace-normalized parameters were plotted as functions of the unidirectional ply longitudinal modulus ( Ex), which defines the particular material system. Ply stiffness extensive empirical data were obtained from literature for four types of material systems (high modulus carbon/epoxy, standard modulus carbon/epoxy, aramid/epoxy, and glass/epoxy) and correlated quite well to theoretical predictions. Theoretical curves presented a nonlinear region for low Ex which gradually evolves to a plateau as Ex increases. It was verified that the master ply concept averaging the trace-normalized ply stiffness matrix elements can be applied for high modulus carbon/epoxy, standard modulus carbon/epoxy, and aramid/epoxy material systems. However, glass/epoxy systems can not be represented by this concept. The exposed theoretical background supports trace-based approach and enhances its effectiveness as a design tool, encompassing all the consequent advantages.

Material parameter identification of the elementary ply damage mesomodel using virtual micro-mechanical tests of a carbon fiber epoxy system

A general multiscale hierarchical framework is proposed to identify the material parameters of a mesoscale model using numerical simulations based on virtual micro-mechanical tests. The identification of the material parameters is usually done with several experiments on different laminates. These experiments are replaced by virtual tests on a microscale finite element model with the same load conditions than the real experiments. The microscale model represents the unidirectional ply geometry based on its constituents, fibers and matrix, with their corresponding properties and the damage behavior of the matrix and interface between them. Under the defined load conditions, the homogenized stress-strain behavior of the laminates is obtained and then, the constitutive model parameters of the ply damage mesomodel are identified. As an example, the proposed framework is applied to identify the material parameters of the elementary ply damage mesomodel developed at LMT-Cachan. It is shown that, when the materials, geometry and load conditions are correctly defined in the micromodel, the real experiments can be replaced by virtual tests. As a result, the amount of experiments can be reduced saving costs and time. In addition, further studies can use the proposed methodology based on virtual micro-mechanical tests to improve the current mesoscale models.

Effects of ply-orientation on microstructure and properties of super-aligned carbon nanotube reinforced copper laminar composites

Abstract The super-aligned carbon nanotube (SACNT) films reinforced copper (Cu) laminar composites with different orientations of CNT ply were fabricated by electrodeposition. The results show that the tensile strength and yield strength of cross-ply composite with 5.0% (volume fraction) of SACNT reach maximum of 336.3 MPa and 246.0 MPa respectively, increased by 74.0% and 124.5% compared with pure Cu prepared with the same method. Moreover, the electrical conductivities of all the prepared composites are over 75% IACS. The result of TEM analysis shows that the size of Cu grain and the thickness of twin lamellae can be reduced by adding SACNT, and the refining effect in cross-ply composites is more significant than that in unidirectional ply composites. The enhanced strength of the Cu/SACNT composites comes from not only the reinforcing effect of SACNT films but also the additional strengthening of the Cu grain refinement caused by CNT orientation.

Semi-continuous strategy for the modelling of damage mechanisms in unidirectional composites under low velocity impacts

Abstract This article deals with the development of a finite element model for the prediction of low velocity impact damage within unidirectional composite laminates. This model is based on analysis of the impact damage observed experimentally. The modelling scale is that of the bundle of fibers of the unidirectional ply. These bundles are represented with 1D rod elements. The matrix is modeled with 2D damageable shell elements. The laminate is the built using cohesive elements. The strategy is validated by a comparison with low velocity drop weight impact tests. Several experimental parameters are varied: the materials (T700/M21 and HTA7/913), the thickness ( 1.44 m m and 2.4 m m ), the stacking sequence and the impact velocity ( 2 m . s − 1 and 3 m . s − 1 ). The calculated load-displacement curves and the damage extent correlate well with experimental results.

A method to determine composite material residual tensile strength in the fibre direction as a function of the matrix damage state after fatigue loading

Abstract The phenomenon of residual strength in composite laminates after fatigue loading has been studied for decades but is generally expressed as a function of the number of cycles applied to the specimens. Phenomenological laws deduced from these tests are therefore loading dependent and identifying a valid model for any loading condition of a given laminate requires long fatigue testing campaigns. To overcome this difficulty, a testing procedure is proposed to express the residual tensile strength of a unidirectional ply in the fibre direction, as a function of its matrix damage. The resulting behaviour is then independent of the imposed loading and can be determined by only a few fatigue tests. Experimental results obtained on glass-epoxy non-crimp fabric laminates are presented and analysed.