Hyperelastic modelling for mesoscopic analyses of composite reinforcements

A hyperelastic constitutive law is proposed to describe the mechanical behaviour of fibre bundles of woven composite reinforcements. The objective of this model is to compute the 3D geometry of the deformed woven unit cell. This geometry is important for permeability calculations and for the mechanical behaviour of the composite into service. The finite element models of a woven unit cell can also be used as virtual mechanical tests. The highlight of four deformation modes of the fibre bundle leads to definition of a strain energy potential from four specific invariants. The parameters of the hyperelastic constitutive law are identified in the case of a glass plain weave reinforcement thanks to uniaxial and equibiaxial tensile tests on the fibre bundle and on the whole reinforcement. This constitutive law is then validated in comparison to biaxial tension and in-plane shear tests.     

Numerical modelling of forming of a non-crimp 3D orthogonal weave E-glass composite reinforcement

A hyperelastic constitutive model is implemented to study the formability on three-dimensional complex shapes of a single layer E-glass non-crimp 3D orthogonal woven reinforcement. Experimental measurements of the main deformation modes have been used to identify the strain energy density function of the constitutive model. The comparison of the finite element simulations and experimental results of tetrahedron and double-dome shaping processes demonstrated the adequacy of the adopted hyperelastic model to describe the deformation mechanisms involved during draping and the efficiency to predict the global behaviour of the non-crimp 3D woven reinforcement during complex shape forming.     

Thermomechanical analysis,modelling and simulation of the forming of pre-impregnated thermoplastics composites

In this paper, the viscoelastic behaviours of pre-impregnated (prepreg) thermoplastic composites are analysed using the bias-extension test. A new constitutive model is proposed in order to simulate the forming of thermoplastic composite prepregs at the macroscopic scale. The model is based on a continuous approach. Hyperelastic behaviours are associated with dry reinforcements. Four principal deformation modes, all considered independent, define the hyperelastic potential: the elongation in warp direction, the elongation in weft direction, the in-plane shear strain and the bending contribution. Experience shows that viscoelastic behaviour is mainly associated with the in-plane shear deformation. A non-linear visco-hyperelastic model based on the generalisation of Maxwell rheological model is considered for this type of deformation mode. The finite element simulation of a stamping case using this model is introduced. The influence of temperature on the forming stage and the performance of the model are evaluated.     

Visco-hyperelastic constitutive law for modeling of foam’s behavior

This paper proposes a new visco-hyperelastic constitutive law for modeling the finite-deformation strain rate-dependent behavior of foams as compressible elastomers. The proposed model is based on a phenomenological Zener model, which consists of a hyperelastic equilibrium spring and a Maxwell element parallel to it. The hyperelastic equilibrium spring describes the steady state response. The Maxwell element, which captures the rate-dependency behavior, consists of a nonlinear viscous damper connected in series to a hyperelastic intermediate spring. The nonlinear damper controls the rate-dependency of the Maxwell element. Some strain energy potential functions are proposed for the two hyperelastic springs. compressibility effect in strain energy is described by entering the third invariant of deformation gradient tensor into strain energy functions. A history integral method has been used to develop a constitutive equation for modeling the behavior of the foams. The applied history integral method is based on the Kaye–BKZ theory. The material constant parameters, appeared in the formulation, have been determined with the aid of available uniaxial tensile experimental tests for a specific material.     

General definition of 3D warp interlock fabric architecture

3D warp interlock fabric can be used as a fibrous reinforcement for composite material. Despite of the numerous research papers dealing with this specific woven structure, few researches were conducted to clearly define this multi-layer fabric. Moreover, in many research papers, unskilled scientists of weaving technology have some difficulty to describe the different components of the 3D warp interlock fabric and sometimes make some confusion between the different architecture. Then, with a lack of a clear definition of these 3D multi-layer fabrics, most of the research papers are conducted on a very limited number of structures such as orthogonal, angle and layer to layer interlock.Thus, based on different definitions proposed by skilled scientists, a new general definition of a 3D warp interlock fabric has been proposed to better describe the position of the several yarns located inside the 3D woven structure. Thanks to this improved definition, we hope that the scientific community will use it in order to better design new architectures and conduct finer research based on these product parameters.     

DCB test simulation of stitched CFRP laminates using interlaminar tension test results

A simulation model for the delamination extension of stitched CFRP laminates and 3-D orthogonal interlocked fabric composites (3-D OIFC) has been developed using a 2-D finite element method incorporating interlaminar tension test results to simulate the experimental results of their DCB tests. The mechanical properties of through-the-thickness fiber were determined from the results of interlaminar tension tests in which the specimen included only one through-the-thickness yarn. The fracture phenomena around the through-the-thickness thread, such as debonding from the in-plane layer, slack absorption, fiber bridging, and the pull-out of broken threads from the in-plane layers, are also introduced into the FEM model. The present FEM simulation results were compared to DCB test results for certain stitched laminates and a 3-D OIFC, and the simulation results showed good agreement with the experimental results of DCB tests, including the load–displacement curve and Mode I strain energy release rate (GI). While it was difficult to estimate GI accurately when the DCB test specimen included different types of z-fiber fracture modes, the present model of FEM analysis can simulate the experimental results of DCB tests of stitched laminates and 3-D OIFC. It is suggested that the GI of CFRP with arbitrary z-fiber densities can be predicted by using this FEM analysis model together with interlaminar tension test results.     

Experimental Investigation About Stamping Behaviour of 3D Warp Interlock Composite Preforms

Forming of continuous fibre reinforcements and thermoplastic resin commingled prepregs can be performed at room temperature due to its similar textile structure. The “cool” forming stage is better controlled and more economical. The increase of temperature and the resin consolidation phases after the forming can be carried out under the isothermal condition thanks to a closed system. It can avoid the manufacturing defects easily experienced in the non-isothermal thermoforming, in particular the wrinkling [1]. Glass/Polypropylene commingled yarns have been woven inside different three-dimensional (3D) warp interlock fabrics and then formed using a double-curved shape stamping tool. The present study investigates the in-plane and through-thickness behaviour of the 3D warp interlock fibrous reinforcements during forming with a hemispherical punch. Experimental data allow analysing the forming behaviour in the warp and weft directions and on the influence of warp interlock architectures. The results point out that the layer to layer warp interlock preform has a better stamping behaviour, in particular no forming defects and good homogeneity in thickness.     

A Study of Strength Transfer from tow to Textile Composite Using Different Reinforcement Architectures

The paper proposes an experimental and analytical approach of designing composites with the predetermined ultimate strength, reinforced with warp interlock fabrics. In order to better understand the phenomena of transfer of tensile properties from a tow to the composite, intermediate phases of composite manufacturing have also been taken into account and tensile properties of tows taken from the loom and the woven reinforcements have also been tested. Process of transfer of mechanical properties of raw materials to the final product (composite) depends on various structural factors. Here the influence of weave structure, which ultimately influences crimp has been studied. A strength transfer coefficient has been proposed which helps in estimating the influence of architectural parameters on 3D woven composites. 3 woven interlock reinforcements were woven to form composites. The coefficients of strength transfer were calculated for these three variants. The structural parameters were kept the same for these three reinforcements except for the weave structure. In was found that the phenomenon of strength transfer from tow to composite is negatively influenced by the crimp. In general the strength transfer coefficients have higher values for dry reinforcements and afterwards due to resin impregnation the values drop.     

一种改进的Yeoh超弹性材料本构模型

橡胶通常被看作一种不可压缩各向同性的超弹性材料,其本构模型通常用应变能密度方程表示。针对Yeoh模型偏软的特性,该文提出了一种改进的Yeoh超弹性材料本构模型。基于连续介质力学大变形理论,给出了改进的Yeoh模型在三种特殊变形模式下的应力-应变关系,并与原有的Yeoh模型和实验数据进行了对比。结果表明:改进的Yeoh模型在保持Yeoh模型体现反“S”形应力-应变关系的前提下,有效地克服了Yeoh模型在预测等双轴拉伸曲线时“偏软”的特性。在较大的应变范围内能够同时准确地预测单轴、平面和等双轴拉伸-压缩的应力-应变关系,具有较大的工程应用价值。     

The Need to Use Generalized Continuum Mechanics to Model 3D Textile Composite Forming

3D textile composite reinforcements can generally be modelled as continuum media. It is shown that the classical continuum mechanics of Cauchy is insufficient to depict the mechanical behavior of textile materials. A Cauchy macroscopic model is not capable of exhibiting very low transverse shear stiffness, given the possibility of sliding between the fibers and simultaneously taking into account the individual stiffness of each fibre. A first solution is presented which consists in adding a bending stiffness to the tridimensional finite elements. Another solution is to supplement the potential of the hyperelastic model by second gradient terms. Another approach consists in implementing a shell approach specific to the fibrous medium. The developed Ahmad elements are based on the quasi-inextensibility of the fibers and the bending stiffness of each fiber.     

Characterising the loading direction sensitivity of 3D woven composites: Effect of z-binder architecture

Three different architectures of 3D carbon fibre woven composites (orthogonal, ORT; layer-to-layer, LTL; angle interlock, AI) were tested in quasi-static uniaxial tension. Mechanical tests (tensile in on-axis of warp and weft directions as well as 45° off-axis) were carried out with the aim to study the loading direction sensitivity of these 3D woven composites. The z-binder architecture (the through-thickness reinforcement) has an effect on void content, directional fibre volume fraction, mechanical properties (on-axis and off-axis), failure mechanisms, energy absorption and fibre rotation angle in off-axis tested specimens. Out of all the examined architectures, 3D orthogonal woven composites (ORT) demonstrated a superior behaviour, especially when they were tested in 45° off-axis direction, indicated by high strain to failure (∼23%) and high translaminar energy absorption (∼40 MJ/m³). The z-binder yarns in ORT architecture suppress the localised damage and allow larger fibre rotation during the fibre “scissoring motion” that enables further strain to be sustained by the in-plane fabric layers during off-axis loading.     

Analytical evaluation on uniaxial tensile deformation behavior of fiber metal laminate based on SRPP and its experimental confirmation

Uniaxial tensile tests have been carried out to accurately evaluate the in-plain mechanical properties of fiber metal laminates (FMLs). The FMLs in this paper comprised of a layer of self-reinforced polypropylene (SRPP) sandwiched between two layers of aluminum alloy 5052-H34. In this study, nonlinear tensile and fracture behavior of FMLs under in-plane loading conditions has been investigated with numerical simulations and theoretical analysis. The numerical simulation based on finite element modeling using the ABAQUS/Explicit and the theoretical constitutive model based on the volume fraction approach using the rule of mixture and the modified classical lamination theory, which incorporates the elastic–plastic behavior of the aluminum alloy and SRPP, are used to predict the in-plain mechanical properties such as stress–strain response and deformation behavior of the FMLs. In addition, the pre-stretching process is used to reduce the thermal residual stresses before the uniaxial tensile tests of the FMLs. Through comparing the numerical simulations and the theoretical analysis with the experimental results, it is concluded that the adopted numerical simulation model and the theoretical approach can describe with sufficient accuracy of the actual tensile stress–strain curve.     

Effect of fiber arrangement on mechanical properties of short fiber reinforced composites

The present paper developed a three-dimensional (3D) “tension–shear chain” theoretical model to predict the mechanical properties of unidirectional short fiber reinforced composites, and especially to investigate the distribution effect of short fibers. The accuracy of its predictions on effective modulus, strength, failure strain and energy storage capacity of composites with different distributions of fibers are validated by simulations of finite element method (FEM). It is found that besides the volume fraction, shape, and orientation of the reinforcements, the distribution of fibers also plays a significant role in the mechanical properties of unidirectional composites. Two stiffness distribution factors and two strength distribution factors are identified to completely characterize this influence. It is also noted that stairwise staggering (including regular staggering), which is adopted by the nature, could achieve overall excellent performance. The proposed 3D tension–shear chain model may provide guidance to the design of short fiber reinforced composites.     

Analysis and modeling of 3D Interlock fabric compaction behavior

During the preforming stage in Liquid Composite Molding (LCM), fibrous reinforcements are compacted to obtain the specified fiber volume fraction. Numerous studies have been carried out to understand their compression behaviors. The first objective of this investigation is to study experimentally the influence of the weaving parameters on the compaction behavior of five different 3D Interlock fabrics. In parallel, composite parts were fabricated to perform a microscopic analysis of fabric deformation after compression. The second objective is to provide a model of the experimental results. Since there is no nesting in three-dimensional woven fabrics, the compaction behavior turns out to be easier to predict than for laminates. A model based on experimental observations was devised to connect the compaction behavior with the deformation modes of five fabrics investigated. The good correlation with experiments confirms the assumptions on the main factors governing the compaction and relaxation of 3D Interlock fabrics.     

Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels

The present paper shows a comparison between classical two-dimensional (2D) and three-dimensional (3D) finite elements (FEs), classical and refined 2D generalized differential quadrature (GDQ) methods and an exact three-dimensional solution. A free vibration analysis of one-layered and multilayered isotropic, composite and sandwich cylindrical and spherical shell panels is made. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the FE and GDQ methods (numerical solutions) and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 3D and 2D finite element results are obtained by means of a well-known commercial FE code. Classical and refined 2D GDQ models are based on a generalized unified approach which considers both equivalent single layer and layer-wise theories. The differences between 2D and 3D FE solutions, classical and refined 2D GDQ models and 3D exact solutions depend on several parameters. These include the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.     

Influence of the tufting yarns on formability of tufted 3-Dimensional composite reinforcement

In aerospace industry, thicker and more complex composite parts are needed. Multilayered reinforcement is largely used as the traditional method. Recently, three-dimensional (3D) fabrics are developed to replace the multilayered reinforcements in certain applications to increase the performance in thickness direction of part, e.g. interlock structure. Currently, the development of tufting technology can be employed to produce the 3D textile composite reinforcements. The tufting parameters, such as tufting density, tufting length and tufting yarn orientations, can be completely controlled by user. In order to improve the understanding of formability of the tufted 3D fabric during manufacturing, the present work analyzes the preforming behaviours of tufted 3D reinforcement in the hemispherical stamping process. Also the preforming behaviours are compared with the samples of the multilayered forming. The experimental data demonstrated the influence of tufting yarns on the material draw-in, interply sliding, and winkling phenomenon during forming. Furthermore, the orientations of tufting yarn affected the forming results, which leaded to misalignment defect in the zone of strong in-plane shear.     

Simulation of 3D interlock composite preforming

The ply to ply interlock fabric preform enables to manufacture, by R.T.M. process, thick composite parts that are resistant to delamination and cracking. Numerical simulation of interlock reinforcement forming allows to determine conditions for feasibility of the process and above all to know the position of fibres in the final composite part. For this forming simulation, specific hexahedral finite elements made of segment yarns are proposed. Position of each yarn segment within the element is taken into account. This avoids determination of a homogenized equivalent continuous law that would be very difficult considering the complexity of the weaving. Transverse properties of fabric are taken into account within a hypoelastic constitutive law. A set of 3D interlock fabric forming simulations shows the efficiency of the proposed approach.     

Curvature determination in the bending test of continuous fibre reinforcements

Bending deformation is one of the main deformation modes in the forming of continuous fibre reinforcements. It is very specific compared to the classical continuous materials. In most textile material forming simulation models, bending stiffness is neglected, but taking into account it would give a more accurate predication, particularly the shape of wrinkles. In the deformation, fibres constituting the reinforcement can slide to each other, resulting in the bending stiffness of reinforcement is not directly related to its in‐plane tensile modulus as the classical continuous materials. Consequently, it is necessary to determine the bending stiffness by the experimental method. A cantilever bending stiffness test approach was proposed to measure the bending stiffness of continuous fibre reinforcements. A CCD camera was used to take the bending deflection shape. To calculate the curvature of bending deflection curve, uniform quartic B‐spline curve was chosen. A detailed process of curvature calculating of deflection curve was given in this paper. A single bending test gives the bending moment as a function of curvature from zero to the maximum value. Bending tests were conducted to validate the capacity of the proposed approach. A smooth curvature plot along the bending deflection curve was obtained for different types of reinforcements, and the non‐linear bending deformation behaviour can be identified with the proposed bending test method.     

Mechanical properties of carbon nanotube reinforced polymer nanocomposites: A coarse-grained model

In this work, a coarse-grained (CG) model of carbon nanotube (CNT) reinforced polymer matrix composites is developed. A distinguishing feature of the CG model is the ability to capture interactions between polymer chains and nanotubes. The CG potentials for nanotubes and polymer chains are calibrated using the strain energy conservation between CG models and full atomistic systems. The applicability and efficiency of the CG model in predicting the elastic properties of CNT/polymer composites are evaluated through verification processes with molecular simulations. The simulation results reveal that the CG model is able to estimate the mechanical properties of the nanocomposites with high accuracy and low computational cost. The effect of the volume fraction of CNT reinforcements on the Young's modulus of the nanocomposites is investigated. The application of the method in the modeling of large unit cells with randomly distributed CNT reinforcements is examined. The established CG model will enable the simulation of reinforced polymer matrix composites across a wide range of length scales from nano to mesoscale.     

Carbon nanotube reinforced hybrid composites: Computational modeling of environmental fatigue and usability for wind blades

The potential of advanced carbon/glass hybrid reinforced composites with secondary carbon nanotube reinforcement for wind energy applications is investigated here with the use of computational experiments. Fatigue behavior of hybrid as well as glass and carbon fiber reinforced composites with and without secondary CNT reinforcement is simulated using multiscale 3D unit cells. The materials behavior under both mechanical cyclic loading and combined mechanical and environmental loading (with phase properties degraded due to the moisture effects) is studied. The multiscale unit cells are generated automatically using the Python based code. 3D computational studies of environment and fatigue analyses of multiscale composites with secondary nano-scale reinforcement in different material phases and different CNTs arrangements are carried out systematically in this paper. It was demonstrated that composites with the secondary CNT reinforcements (especially, aligned tubes) present superior fatigue performances than those without reinforcements, also under combined environmental and cyclic mechanical loading. This effect is stronger for carbon composites, than for hybrid and glass composites.