Four-directional Braided Composites Research Articles

A new geometric modelling approach for 3D braided tubular composites base on Free Form Deformation

The micro-geometry of three-dimensional (3D) braided tubular preform is more complex than that of rectangular one, especially for the interfaces between yarns. The yarn interfaces are difficult to analyze theoretically, and if two sides of the interfaces do not fit perfectly in the model, the final result will contain overlapped yarns, which is bad for finite element calculation. This paper focuses on the microstructure of 3D four-directional braided tubular composites and presents a modelling approach based on Free Form Deformation (FFD) theory. First, the planar and spatial yarn paths are analyzed and three geometrical mapping equations from rectangular unit-cell to tubular sub unit-cell are derived. The modelling approach was then developed to establish the sub unit-cell model. Finally, the established models are compared with micro computed tomography (μ-CT) scans of a dry specimen of the circular braided preform. The model not only solves the yarn-overlapping problem, but also accurately describes the key characteristics of the preform.

Analytical prediction of the elastic properties of 3D braided composites based on a new multiunit cell model with consideration of yarn distortion

A new analytical model based on a multiunit cell model (MCM) is developed to study the effects of the yarn distortion and the shell–core structure feature on the elastic properties of 3D four-directional braided composites. An idealized yarn model with consideration of the yarn distortion is proposed to calculate its elastic properties by introducing an average twist angle. Combined with the MCM, the stiffness-volume averaging theory is applied to consider the contribution of all unit cells to the elastic properties of the overall specimen. The variation of the average twist angle for the interior and surface-corner yarns has been accounted for appraising the elastic properties. The predicted elastic properties are in good agreement with the available experimental data, demonstrating the applicability of the analytical model. In addition, the effect of the average twist angle on the elastic properties is discussed and the comparison between the predicted values and the experimental results are conducted. Then the elastic properties of unit cells with their unique microstructure are analyzed. Finally, the effects of the braiding angle, the fiber volume fraction, and the number of the yarn carriers on the elastic properties are discussed in detail. Discussion results have proved that the present analytical model can be utilized to predict the elastic properties of 3D braided composites.

Predictions of effective thermal conductivities for three-dimensional four-directional braided composites using the lattice Boltzmann method

A multiple-relaxation-time lattice Boltzmann model with an off-diagonal collision matrix is adopted to predict the effective thermal conductivities of anisotropic heterogeneous materials with anisotropic components. The half lattice division scheme is used to handle the internal boundaries to guarantee the heat flux continuity at the component interfaces. Accuracy of the model is confirmed by comparing with benchmark results and existing simulation data. The present method is then employed to predict the transverse and longitudinal effective thermal conductivities of three-dimensional four-directional (3D4D) braided composites. Experiments based on the Hot Disk method are also conducted to obtain the transverse and longitudinal effective thermal conductivities of the materials. The numerically predicted results fit the experiment data well. Then, influences of fiber volume fractions, interior braiding angles and interface thermal contact resistance on the effective thermal conductivities of 3D4D braided composites are studied. The results show that the effective thermal conductivity along the transverse direction increases with the fiber volume fraction and interior braiding angle; while the longitudinal one increases with the fiber volume fraction but decreases with the increasing interior braiding angle. A larger interface thermal contact resistance leads to a smaller effective thermal conductivity. Besides, for anisotropic materials, the effective thermal conductivity obtained by the periodic boundary condition is different from that obtained by the adiabatic boundary condition.

Numerical prediction of effective thermal conductivities of 3D four-directional braided composites

The temperature distribution in a representative volume element of three-dimensional and four-directional braided composites is studied with appropriate boundary conditions by the finite element method (FEM) to predict the effective thermal conductivity of the composite. Models with elliptical, circular and hexagonal cross-section of braiding yarns are considered. The model is validated by experiments based on hot disk thermal constant analyzer. The influences of fiber volume fraction Vf, and interior braiding angle γ, on heat transfer of the composite are studied with Vf equal to 0.40, 0.50 and 0.58, and γ from 15° to 50°. The results show that for the composite studied increasing fiber volume fraction results in higher thermal conductivity in both axial and transverse direction, while a larger interior braiding angle leads to higher transverse thermal conductivities but lower axial ones.

Prediction of Elastic Constants on 3D Four-Directional Braided Composites

In this paper, a finite element model with a prestressed unit cell is proposed to predict the elastic constants of 3D four-directional braided composites. Firstly, a finite element unit cell model with damage constitutive for 3D four-directional braided composites is established to investigate the influence of the prestresses in the unit cell. Secondly, the elastic constants of 3D four-directional braided composites are predicted with and without the prestresses in the unit cell. Finally, the influences of the braided direction and fibre content on the elastic constants of 3D four-directional braided composites are discussed. The results will provide an important guidance for designing and evaluating the mechanical properties of 3D four-directional braided composites.

Microstructure Analysis and Multi-Unit Cell Model of Three Dimensionally Four-Directional Braided Composites

In this paper, a new multi-unit cell model of three dimensionally braided composites is presented on the basis of the microstructure analysis of 3D braided preforms produced by four-step 1 × 1 method. According to a new unit cell partition scheme, the multi-unit cell model possesses five kinds of unit cells, namely interior, exterior surface, interior surface, exterior corner and interior corner unit cells. Each type of the representative volume cell has unique microstructure and volume fraction in braided composites. On the basis of these five unit cell models, the structural geometry parameters of the preforms are analyzed and the relationship between the structural parameters and the braiding parameters in different regions are derived in detail, such as the braiding angles, fiber volume fraction, yarn packing factor, braiding pitch and so on. Finally, by using the multi-unit cell model, the main structural parameters of braided composites specimens are calculated to validate the effectiveness of the model. The results are in good agreement with the available experimental data. In addition, the effect of braiding angle on the squeezing condition of braiding yarn is analyzed. The variations of the volume proportion of five unit cells to the whole specimen with rows and columns are discussed, respectively. The presented multi-unit cell model can be adopted to design 3D braided composites and predict their mechanical properties.

Numerical Prediction of Elastic Properties Law for 3D Four-directional Braided Composites with Parametric Unit Cell Model

Numerical Prediction of Elastic Properties Law for 3D Four-directional Braided Composites with Parametric Unit Cell Model

Prediction for Strength of 3D Braided Composites Based on Helix Geometry Model

A numerical model capable of calculating the strength of 3D braided composites is developed, based on the micro-structure of 3D four-directional braided composites and the assumption of the braiding yarn with a helix configuration and ellipse cross-section. The strength of 3D braided composites have been predicted through a finite multiphase element method (FMEM). Comparison was conducted for those from the present model and experiment. The results are in good agreements with the experimental results in the previous literature. The influences of braiding angle on the strength are also studied.

Strength analysis of three-dimensional braided T-shaped composite structures

In this paper, based on the properties and strength analysis of the prestressed unit cell, the pull-off behaviors of the three-dimensional (3D) braided T-shaped composite structures are estimated by means of finite element method (FEM). First, a finite element model with Hashin’s failure criterion and maximum stress failure criterion is established to investigate the influence of the prestresses on the strength of the unit cell for the 3D four-directional braided composites. Second, the influences of the braided direction and fiber content on the strength of the unit cell for the 3D four-directional braided composites are discussed. Finally, based on the predicting results of the unit cell strength, the pull-off strength and damage characterizations of the 3D braided T-shaped composite structures is predicted using the Tsai–Hill failure criterion. The results will provide an important guidance for designing and evaluating damage and strength the 3D braided T-shaped composite structures.

A Numerical Study on the Progressive Failure of 3D Four-Directional Braided Composites

The complexity of the microstructure makes the strength prediction and failure analysis of 3D braided composites difficult. A new unit cell geometrical model, taken as the representative volume element (RVE), is proposed to describe the yarn configuration of 3D braided composites produced by the four-step 1 × 1 method. Then, based on the periodical boundary conditions, a RVE-based micromechanical model by using the nonlinear finite element method has been presented to predict the progressive damage and the strength of 3D braided composites subjected to tensile loading. The numerical model can simulate the effect of damage accumulation on the tensile stress-strain curve by combining the proposed failure criteria and the stiffness degradation model. The longitudinal shear nonlinearity of braiding yarn is considered in the model. To verify the model, two specimens with typical braiding angles were selected to conduct the simulations. The predicted stress-strain curves by the model compared favorably with the experimental data, demonstrating the applicability of the micromechanical finite element model. The effect of the nonlinear shear parameter on the tensile stress-strain curve was discussed in detail. The results indicate that the tensile mechanical behaviors of 3D braided composites are affected by both the yarn shear nonlinearity and the damage accumulation.

A new analytical model for calculation of stiffness of three-dimensional four-directional braided composites

The present paper represents a new analytical method for calculation of the stiffness of three-dimensional four-directional braided composites. In most previous works, the analytical approach had been largely neglected in the favor of the finite element model. Among those who have used the analytical model, the braided preform has been considered as made of one, or three, types of representative unit cells, while microscopic evidence of the microstructure of preforms reveals different configurations of the yarns in the interior, surface and corner regions of a braided preform. This paper presents a Multi-Unit Cell Model in which four kinds of unit cells, namely interior, interior surface, exterior surface and corner unit cells have been introduced as representative cells. Each type of unit cell in a braided composite possesses unique mechanical properties and has been considered as a uni-directional composite. Using rotation matrices, the angle between yarns and longitudinal direction has been incorporated in general coordinates of the model. Finally, using a volume averaging method, the total stiffness of the braided composite is calculated. The results are in good agreement with the available experimental data. The effect of braiding angle on the stiffness of braided composites is also examined.

Finite element modeling of mechanical properties of 3D five-directional rectangular braided composites

A new parameterized finite element model (FEM) is established for 3-Dimensional (3D) five-directional rectangular braided composites. The model precisely simulates the spatial configuration of the braiding yarns and the axial yarns with consideration of the cross-section deformation as well as the surface contact in the braiding process. Moreover, this model orients in the same reference frame as the composites and the relationships among the structural parameters, particularly the braiding angle and the interior braiding angle, are investigated. A prediction of the effective elastic properties and the meso-scale mechanical response of 3D five-directional braided composites have been presented to verify the validation of the FEM. The effects of the braiding parameters on the mechanical properties are investigated in detail in this study. The results indicate that it is convenient to predict all the elastic constants of 3D five-directional braided composites with different parameters simultaneously using the FEM. Moreover, the FEM can successfully predict the meso-scale mechanical response of 3D five-directional braided composites containing periodical structures. In the mean while, the geometric characteristics and the mechanical properties of 3D five-directional and 3D four-directional braided composites have been compared.

Prediction of Tensile Modulus of 3D Four-Directional Braided Composites with Transverse Cracks

To a laminate model of 3D four-directional braided composites with periodic transverse cracks, a new normal stress function in weave direction is present. In this function, variations of stress with x and y are considered. By using the principle of minimum complementary energy, stress components in the representative unit are obtained. Tensile modulus of 3D four-directional braided composites with periodic transverse cracks is calculated by utilizing Hashin’s average theory and the principle of minimum complementary energy. To demonstrate the solution, some examples are analyzed.

Research on Tensile Properties and Size Effect of 3D Four-Directional Braided Composites

By the macroscopic tensile tests of the 3D four-directional braided composites, the failure pattern and fracture morphology of specimens with different geometric sizes have been observed. It is obtained that the different failure mechanisms and the material properties are relevant to the geometric sizes of samples under tensile states. The elastic properties of the braided composites are obtained by volume average method. The variation of shear modulus and Poisson ratio is obtained as well. It is shown that the elastic modulus increases with the increase of number of interior cells. The predicted results are in agreement with the experimental results. The results may provide experimental basis for further study on strength prediction and the establishment of strength criterion for 3D four-directional braided composites.

Effect of Interface Properties on Mechanical Behavior of 3D Four-Directional Braided Composites with Large Braid Angle Subjected to Uniaxial Tension

A Representative Volume Cell (RVC) chosen to epitomize the entire three dimensional four-directional braided composites is investigated to evaluate the mechanical behavior of the material by computational micromechanics. In addition to including several damage modes of braid yarn and matrix within the braided composites, the numerical model also takes into account interface damage mode by using a Cohesive Zone Model (CZM). A parametrical study is conducted to evaluate the influence of interface properties on the macro stress-strain curve and the interaction of different failure modes of the braided composites under uniaxial tensile loading. The interface damage evolution of the braided composites with large braid angle is also provided further. Preliminary results indicate that the interface damage, which is one of the key factors to cause the nonlinearity of the stress-strain relationship, can decrease the elastic modulus but not obviously control the ultimate strength of the braided composites with large braid angle.

Experimental Investigation on Compressive Properties for 3D Four-Directional Braided Composites

Based on changing the braid angle and geometrical sizes, the compressive experiment of 3D braided four-directional Carbon/Epoxy braided composites is researched. It is found that failure of the braided composites exhibits compressive and shear failure mode. The failure crack propagates mainly in one or two 45º shear direction. Epoxy matrix among braid yarns of the braided composites is squeezed out to form epoxy band. The stress-strain relations of the braided composites with 45º and 30º braid angles all appear nonlinear apparently. Meanwhile the correlation of failure modes and constitutive relation with geometrical sizes of the braided composites is obtained. The compressive stress-strain relations of the braided composites are not great affected by the geometrical sizes. The compressive strengths with great discrete behaviors do not have obvious rules with height of the braided composites.

Investigation on the compressive properties of the three dimensional four-directional braided composites

Abstract The compressive mechanical properties of three dimensional (3D) braided composites are of key concern for design in actual engineering application. A representative volume cell (RVC) is chosen to study the uniaxial compressive mechanical properties of the braided composites with different braid angles by combing damage theory and finite element method. The fiber misalignment and longitudinal shear nonlinearity of braid yarn are considered in the computation model. And their influences on the compressive behavior of the braided composites are also evaluated. The damage development of constituents within the braided composites are obtained and analyzed. The main damage and failure modes and their interaction of braid yarn are provided as well. The numerical results are found that the compressive mechanical behavior of the braided composites with lower braid angle is sensitive to the fiber initial imperfection of braid yarn. The strength of the braided composites with different braid angle is controlled by the different microscopic failure modes.

The effect of yarn distortion on the mechanical properties of 3D four-directional braided composites

A representative volume cell (RVC) is chosen to analyze the mechanical properties of 3D (3 dimensions) four-directional braided composites. Owing to braid yarns (an assembly of fibers) squeezing against each other in the braided composites, the braid yarns are distorted. Based on geometrical characteristics of the braided composites, cross-section of each braid yarn is supposed to be an octagon and divided into seven regions in the RVC. The distortion characteristics of yarns are considered in each region. Elastic properties of each region obtained by stochastic function theory are introduced into finite element model to calculate the mechanical properties of the RVC. The influences of yarn distortion on the stiffness and strength of the braided composites are obtained and discussed.

Progressive damage and nonlinear analysis of 3D four-directional braided composites under unidirectional tension

A representative volume cell (RVC) is chosen to analyze the progressive damage behavior of 3D four-directional braided composites with large braid angle subjected to uniaxial tension. An anisotropic damage model is established by Murakami-Ohno damage theory. A new damage evolvement model is proposed, which is controlled by material fracture energy of braided composites constituents and equivalence displacements. According to the different damage modes (yarn transverse tension, compression and shear; yarn longitudinal tension and compression; matrix cracking), the different damage states and progressive damage of the braided composite are obtained. The numerical results show that the main failure modes of the braided composites are transverse tension, shear breakage of yarns and matrix cracking, which are in good agreement with the relevant experimental results in some literatures.

Theoretical prediction of stiffness and strength of three-dimensional and four-directional braided composites

Based on unit cell model, the 3D 4-directional braided composites can be simplified as unidirectional composites with different local axial coordinate system and the compliance matrix of unidirectional composites can be defined utilizing the bridge model. The total stiffness matrix of braided composites can be obtained by the volume average stiffness of unidirectional composites with different local axial coordinate system and the engineering elastic constants of braided composites were computed further. Based on the iso-strain assumption and the bridge model, the stress distribution of fiber bundle and matrix of different unidirectional composites can be determined and the tensile strength of 3D 4-directional braided composites was predicted by means of the Hoffman's failure criterion for the fiber bundle and Mises' failure criterion for the matrix.