3D Four-directional Braided Composites Research Articles

Key issues in microstructure modeling of 3D braided composites

Numerical analysis based on micromechanics is an effective method to study the mechanical properties of three-dimensional (3D) braided composites, in which the establishment of micromechanics model is the basis of mechanical analysis. The direction cosine of fiber yarns and the characterization of geometric parameters of microstructure are two key issues in the modeling of microstructure. Focusing on these two key issues, the three-cell model of 3D four-directional braided composites are studied to comprehensively analyze various spatial directions of fiber yarns in the 45° division and horizontal division of unit cell, so as to obtain the detailed fiber yarn direction cosine. Aiming at the cross sections of three types of fiber yarns, the complex relationship between the braiding process parameters and the geometric parameters of the unit cell is analyzed and deduced. The unit cell structure is quantitatively characterized by using the braiding process parameters as the initial parameters, and the calculation methods of the volume fraction of fiber yarns and yarn filling coefficient are obtained. Finally, the predicted elastic constants by stiffness-volume averaging method are compared with experimental results, demonstrating the analysis results of fiber yarns directions. This paper can provide a theoretical reference for the microstructure modeling of 3D multi-directional braided composites, and has certain practical value in engineering.

Investigation of parameterized braiding parameters and loading directions on compressive behavior and failure mechanism of 3D four-directional braided composites

Three-dimensional (3D) braided composites have been witnessed outstanding advances in structural applications in the past few decades. Herein we established parameterized finite element model to characterize, on a mesoscopic scale, the compressive behaviors of 3D braided composites where the relative displacement boundary conditions were applied, and the cross-sectional extrusion and realistic spatial architecture among braiding yarns were considered. Moreover, the associated relationships between damage evolution and strength prediction and different loading directions, braiding angles and fiber volume fraction, were then thoroughly investigated. The damage evolution was evaluated quantitatively based on continuous damage mechanics. The main damage and failure patterns of the yarn and matrix were presented. The results convincingly concluded that the compressive behaviors remarkably depended on the braiding angle, fiber volume fraction, and loading direction. The numerical stress–strain responses agreed well with the experimental, proving that stiffness degradation and failure strength could be predicted accurately using the established model.

Progressive damage simulation of 3D four-directional braided composites based on surface-interior unit-cells models

To accurately predict the longitudinal tensile mechanical properties of 3D four-directional braided composites, parameter modeling for surface and interior unit-cells mesoscopic solid models was implemented and the deviation of yarn spatial traces and squeeze deformation of yarn cross-section were considered in the surface unit-cell model. Voxel mesh was used to discrete models on which appropriate boundary conditions were imposed and damage models for each constituent of composites were added into a user-defined material subroutine (UMAT) in finite element analysis software ABAQUS. By simulation analysis of surface-interior unit-cells models for 3D four-directional carbon fiber/epoxy braided composites with 30° and 45° interior braiding angles respectively, using the volume-weighted average method, longitudinal tensile modulus and strength for braided composites specimens with different thicknesses were predicted. The progressive damage process of composites was studied by counting the number of integration points with the same damage modes. Results show that the longitudinal tensile mechanical properties predicted based on surface-interior unit-cells models for 3D four-directional braided composites agree well with experimental results, and damage analysis results reflect reasonably progressive damage process of surface and interior unit-cells.

Modeling and Two-Step Homogenization of Aperiodic Heterogenous 3D Four-Directional Braided Composites

The mechanical properties of the material are essential to identify the material behavior of the structure. Predicting four-directional braided composites’ mechanical properties based on accurate modeling is an essential issue among researchers. In this research, the principle of minimum energy loss-based mechanics of structure genome was used for the two-step homogenization of three-dimensional (3D) four-directional braided composites. In the first step homogenization, the micro-scale model’s effective mechanical properties were decided by considering fibers and matrix; in the second step homogenization, the final effective mechanical properties of the meso-scale model were obtained by considering yarns and matrix. TexGen python script was implemented for accurate modeling of 3D four-directional braided cells with jamming effects. The current process sustainability was validated for 3D four-directional braided polymer matrix composites (PMCs) material by available finite element analysis (FEA) and experimental literature. The method is further extended for 3D four-directional braided ceramic matrix composites (CMCs) to confirm its versatility for standard composites. A commercial FEA was also performed on the meso-scale braided cell to validate the two-step homogenization results. This research explored fast and more accurate modeling and analysis techniques for 3D four-directional braided composites.

A novel surrogate modeling strategy of the mechanical properties of 3D braided composites

In this paper, a surrogate-based modeling methodology is developed and presented to predict the elastic properties of three dimensional (3D) four-directional braided composites. Using this approach, the prediction process becomes feasible with only a limited number of training points. The surrogate models constructed using Finite Element (FE) method and Diffuse Approximation, reduce the computational time and cost for preparing experimental samples. In the FE model, multiscale method is applied to couple the computations of elastic properties at microscale and mesoscale. Subsequently, a parametric study is performed to analyze the effects of the three design parameters on the elastic properties. Satisfactory results are obtained via the surrogate-based modeling predictions, which are compared with the experimental measurements. Moreover, the predictions obtained from surrogate models concur well with the FE predictions. This study orients a new direction for predicting the mechanical properties based on surrogate models which can effectively reduce the sample preparation cost and computational efforts.

Establishing RVE model composed of dry fibers and matrix for 3D four-directional braided composites

Traditional representative volume element (RVE) model composed of impregnated yarns and surrounding matrix for the 3D four-directional braided composites, requires periodic mesh in order to impose periodic boundary condition, which is quite challenging and time-consuming due to complex internal mesoscopic architecture. In this regard, this study presents a novel approach to establish a parametric RVE model comprised of dry fibers and matrix through integrating Matlab with Abaqus. The technique is able to produce RVE models of arbitrary braiding angle, fiber volume fraction, etc. by simply changing the input values for the Matlab procedure. Based on this, finite element analysis is performed on the proposed model to predict tensile modulus of the 3D four-directional braided composites and examine the influence of mesoscopic geometry and material parameters. Numerical application demonstrates that this technique has good prediction accuracy for the small braiding angle case while great deviation for the big braiding angle case. In the end, the technique’s advantages and disadvantages over the traditional RVE model, and its potential applications are discussed.

A novel macro-meso finite element method for the mechanical analysis of 3D braided composites

Finite element method based on the mesoscopic scale periodic unit-cell models was often employed to analyze the mechanical properties of 3D braided composites with obvious shell-core structural feature. To obtain the accurate predicted results, the contribution of the interior and surface unit-cell models to the overall mechanical properties should be considered for the finite element modeling. However, how to apply reasonable boundary conditions to the surface unit-cell model is still an interesting issue worth studying, which has great effect on the prediction precision of surface unit-cell model. Meanwhile, it is valuable to develop a novel macro-meso finite element modeling approach combined with the shell-core structural feature of 3D braided composites, which can contribute to improving the prediction precision and saving the computational costs. In this paper, a new integrated surface unit-cell model with the true yarn microstructure at the mesoscopic scale is proposed for 3D four-directional braided composites firstly. Secondly, a novel macro‑meso scale finite element modeling strategy for predicting the elastic properties and the micromechanical responses is presented. Thirdly, the key modeling procedures based on the solid unit-cell models are given. Finally, comparison of the calculated results with the available experimental data validates the effectiveness of the macro‑meso finite element model. The effects of the braiding angle and the fiber volume fraction of specimens on the elastic properties are discussed in detail. Discussion results indicate that the present macro‑meso finite element modeling strategy can be utilized to efficiently predict the mechanical performances of 3D braided composites.

Progressive damage simulation in 3D four-directional braided composites considering the jamming-action-induced yarn deformation

Due to the jamming action in the manufacturing process, local curvature and fiber reorientation are inherent in nature to the yarn in 3D four-directional braided composites, which results in different failure modes comparing with the constant yarn cross-section. Therefore, a novel unit cell model with jamming-action-induced yarn deformation was developed in this study. Then using the developed unit cell model, the progressive damage process of 3D four-directional braided composites under unidirectional tension was examined on the basis of Murakami-Ohno damage theory. Numerical results reveal stress concentration and higher stress level induced by the jamming action. As a consequence, predicted stress-strain curve by employing the developed unit cell model agrees well with the experimental data. In addition, earlier damage initiation and lower predicted strength are observed, compared with the original unit cell model without considering the inherent yarn deformation. Furthermore, owing to the jamming-action-induced yarn deformation, the yarn longitudinal damage firstly fails at the regions where the yarn is curved, and subsequently damage fails near the damaged elements in the first stage.

Evaluation of three unit cell models in predicting the mechanical behaviour of 3D four-directional braided composites

This paper compares three types of the unit cell models in their capability to predict the mechanical behaviour involving macroscopic material properties and mesoscopic stress distribution for the 3D four-directional braided composites. The unit cell model is periodically meshed in Hypermesh 11.0 and finite element analysis is performed under six kinds of monotonic loading cases by employing ABAQUS/Standard 13.0. Then the effective material properties of the braided composites are obtained in the framework of mean field homogenization. The influences of the yarn cross-section shape and curvature on the macroscopic material property and mesoscopic stress distribution are discussed. This paper lays the ground for choosing the yarn cross-section shape and trajectory in the established unit cell model for the 3D four-directional braided composites.

Multi-size unit cells to predict effective thermal conductivities of 3D four-directional braided composites

Based on the structure of the full unit cell which is formulated by three translational symmetries, three further 180° rotational symmetries of three-dimensional (3D) four-directional braided composites are clarified in this paper. It is for the first time that each rotational symmetry is used to reduce the full unit cell to a half, quarter, and eighth size. The corresponding boundary conditions for thermal analysis are derived precisely according to each rotational transformation. The effective thermal conductivities of composites with different fiber volume fractions and interior braiding angles are calculated by the full, quarter and eighth unit cells. In order to confirm the significance of accurate boundary conditions, additional comparison calculations with adiabatic boundary conditions are conducted and the result reveals that inappropriate boundary conditions may lead to an un-neglectable error in the prediction of thermal conduction behaviours. The numerical model is validated by good agreement between the numerical results and the available experimental ones.

A model for longitudinal tensile strength prediction of low braiding angle three-dimensional and four-directional composites

Abstract Based on random crack core theory, a model for predicting the longitudinal tensile strength of three-dimensional (3D) four-directional composites with low braiding angle is established. The model carries out accurate theoretical predictions of the longitudinal tensile strength of 3D four-directional braided carbon fiber/resin composites. The average stiffness method is used to calculate elastic constants of an inner single cell of 3D four-directional braided composites. Meanwhile, the corresponding relationship between failure probability of a unidirectional composite fiber bundle and stress level is given based on the random crack core model of the longitudinal tensile strength of a unidirectional composite. Furthermore, strength algorithms of low braiding angle 3D four-directional composites under different damage modes are built on the basis of the Tsai-Hill criterion. In this paper, the dispersion of single fiber strength is also considered in the model, so the size effect of the composite strength can be reflected effectively. At last, the longitudinal tensile strength of 3D four-directional braided carbon fiber/resin composites is predicted and analyzed, and the result shows that this model has high prediction accuracy.

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.

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.

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.

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.