Four-directional Braided Composites Research Articles

Improved unit cells to predict anisotropic thermal conductivity of three-dimensional four-directional braided composites by Monte-Carlo method

The analysis of 3D4d braided composites is challenging due to its complicated mesostructure. A parameterized modified three-dimensional four-directional (3D4d) braided composites unit cell model is developed in this work, along with a high-precision computation approach for it. A parametric representative volume element (RVE) method for three-dimensional braided composites is established, which is based on the coupling braiding parameters and discrete anisotropic characteristics. Additionally, a Monte-Carlo cycle framework for performing random effect verification of defects is established. To accomplish high-precision computation of effective thermal conductivity (ETC), the methodologies described in this paper include RVE unit modeling, yarns' anisotropy treatment and probability statistics on porosity can be applied to any multidirectional braided and heterogeneous materials. The ETCs of 3D4d braided composites with various fiber volume fractions, braiding angles and porosities are evaluated by the methodologies. The results demonstrate that the relative errors between the simulation results and the available experimental data are all limited within 2.8%, the thermophysical properties of 3D4d braided composites are obviously anisotropic and that the variation of ETCs with parameters exhibit quasi linear and divergent distribution characteristics. This work proposes and verifies two influence mechanisms of porosity on composites, which also provide a possibility to realize composites properties' interval estimate.

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.

Mechanical properties and macro–meso coupled damage behavior of three-dimensional four-directional braided composites under bending loading

A hierarchical coupled multiscale method is developed to capture the onset and propagation of damage within the three-dimensional four-directional (3D4D) braided composites subjected to bending loading. Using a directly two-scale coupled scheme, the macroscopic nonlinear behavior at the structural dangerous region could be iteratively solved, combined with the progressive damage response of the realistic mesoscale architecture. The continuum damage model is merely defined at the mesoscale and considers failure in each of constituents with the well-established Hashin failure criteria and the Bažant crack band damage model. To accelerate finite element computation in two scales, a parallel numerical implementation is presented alongside the commercial software ABAQUS/Standard. Besides the good agreement between the experimental and the predicted values, the results also show a significant effect of the braiding angle on the bending performance of 3D4D braided composites. With the increase of braiding angle, the bending stiffness and strength of 3D4D braided composites decreases, but the fracture toughness increases. This phenomenon was numerically investigated by identifying the different fundamental failure mechanism and damage development process at both the scales.

Analysis of multiple impact tests’ damage to three-dimensional four-directional braided composites

Abstract This article was designed with a plurality of impact tests of three-dimensional four-directional braided composites, and the impact response of specimen impacted by a circular punch was studied. Ultrasonic C-scanning was used to detect the internal damage area to study the damage propagation process under multiple impact loads. The finite-element software ABAQUS was used to model the meso-structure of three-dimensional four-directional braided composites. Based on material characteristics, the three-dimensional Hashin damage criterion was used for the fiber bundle, and the maximum stress criterion was used for the matrix to judge the material damage. Combined with test and simulation results, the failure mode and damage evolution process of the specimen under multiple impact loads were studied. The results showed that the impact resistance of the three-dimensional woven composite material is affected by the braided angle. The larger the braided angle of the specimen, the better the impact resistance. The damaged area of the large braided angle material expanded to the periphery, and the damaged area of the small braided angle material was primarily developed in the longitudinal direction. The failure modes of the specimen during the impact process were primarily a longitudinal tensile failure of fiber bundles, transverse tensile failure and transverse compression failure of fiber bundles and matrix.

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.

Efficient multiscale analysis method for the compressive progressive damage of 3D braided composites based on FFT

A new efficient multiscale simulation method based on fast Fourier transform (FFT) is developed to analyze the nonlinear behaviors of three-dimensional four-directional braided composites under compressive loading which is the key concern for design in the engineering application. The braid yarns within the composites are represented by the microscale unidirectional representative volume element. Both in microscale and mesoscale, FFT method combined with damage theory is used to simulate the progressive damage and failure of the composites under external loadings, in which the interface between the fiber and matrix and fiber compression instability on the microscale and the shear nonlinearity of the braid yarns under compressive loading on the mesoscale are taken into account comprehensively in the computation model. It is verified that the compressive mechanical properties of the braided composites obtained by the efficient multiscale method are in better agreement with the experimental results.

Reconstruction of meso-structure and numerical simulations of the mechanical behavior of three-dimensional four-directional braided ceramic matrix composites

Textile-reinforced ceramic matrix composites are key structural materials for aerospace applications. In this paper, the influence of meso-structure and damage mechanisms on mechanical behavior of three-dimensional (3D) four-directional braided SiC/SiC composites is systematically investigated by using numerical simulations. First, periodic preform geometry model, also known as representative volume element (RVE), is reconstructed by using micro-computational tomography (μ-CT). Then, two damage mechanics models are employed to establish non-linear behavior of tows and matrix. Moreover, cohesive model is introduced to represent tow/tow and tow/matrix delamination behavior. It is noteworthy that homogenized tow model is derived from micromechanical model on fiber scale. Finally, macro stress-strain and failure behaviors of 3D braided SiC/SiC composites are simulated by meso-scale finite element analysis. Numerically simulated tensile modulus and strength of 3D braided SiC/SiC composites are compared with experimental results, exhibiting good consistency. Numerical simulations revealed failure mechanism and confirmed that, in addition to globally evolved damage process under tensile load, meso-scale preform caused stress concentration and subsequent local rupture behavior. Current research shows that reconstructed textile model realistically describes tensile mechanical behavior and damage evolution of 3D braided SiC/SiC 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.

Appropriate utilization of the unit cell method in thermal calculation of composites

The unit cell method is widely used in thermal calculations of composite. The formulation of a unit cell involves construction of geometric configuration and derivation of boundary conditions. The process is closely related to the structure symmetries of composites and the macro heat flux. In this work, two issues are studied to further appropriate utilization of such method. First, unit cells that formulated based on different paths with different structure symmetries could have the same configuration while different boundary conditions, and leads to some confusions; second, the uniform temperature boundary condition is frequently used without rigorous mathematical derivation and physical consideration, and leaves some uncertainty of its reliability. In this work, three typical composites, unidirectional fiber reinforced, plain woven and three-dimensional four-directional braided composites are studied. For each composite, one unit cell is formulated and two types of boundary conditions are derived. The influence of formulation path on unit cell formulation and the application scope of uniform temperature boundary conditions are then clarified based on corresponding calculations and analysis.

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.

Evaluation of Vibration Properties of Three-Dimensional, Four-Directional Braided Composites

This paper investigates the relationship between natural frequencies and different braiding parameters: the braiding angles and the fiber volume fractions for three-dimensional, four-directional (3D4d) braided composites. A systematic experiment was set up and conducted, and a corresponding finite element model was built to analyze the experimental results. Since the rate of change among the first three orders of natural frequencies for changing braiding parameters are strongly monotonous, only the first order is analyzed. Based on experimental data, the relationship between the natural frequencies of the first order and the two types of braiding parameters are compared and discussed. The findings suggest that the natural frequency of this material and its 3D4d structure can be designable.

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.

Bearing Abilities and Progressive Damage Analysis of Three Dimensional Four-Directional Braided Composites with Cut-Edge

Cut-edge is a kind of damage for the three-dimensional four-directional (3D4d) braided composites which is inevitable because of machining to meet requisite shape and working in the abominable environment. The longitudinal tensile experiment of the 3D4d braided composites with different braiding angles between cut-edge and the ones without cut-edge was conducted. Then representative volume cell (RVC) with interface zones was established to analyze the tensile properties through the fracture and damage mechanics. The periodic boundary conditions under the cut-edge and uncut-edge conditions were imposed to simulate the failure mechanism. Stress-strain distribution and the damage evolution nephogram in cut-edge condition were conducted. Numerical results were coincident with the experimental results. Finally the variation of cut-edge effect with the specimen thickness was simulated by superimposing inner cells. The consequence showed that thickness increase can effectively reduce cut-edge influence on longitudinal strength for 3D4d braided composites. Cut-edge simulation of braided composites has guiding significance on the actual engineering application.

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.