Meso-macro approach for composites forming simulation

The F.E. analysis of woven composite reinforcement forming is an alternative to geometrical draping computation. It permits to account for mechanical behaviours of the fabric and static boundary conditions of the process. In this paper, macroscopic forming simulations of woven composite reinforcements are performed using finite elements composed of woven cells, the mechanical behaviour of which are computed by F.E. analyses at mesoscale i.e. on the unit cell of the fabric. The objective is to only calculate the relevant quantities in the woven finite element. The in-plane biaxiale tensile behaviour and the in-plane shear behaviour are obtained by 3D analyses of the woven cell submitted respectively to tension and shear. They need to take the specificities of the mechanical behaviour of the yarn (made of thousand of fibres) into account. Especially an objective derivative based on the fibre rotation is used. These computations on the unit woven cell have proved to be consistent with experimental tests. An example of deep drawing of a square box using the proposed approach is presented. Angles between warp and weft directions are computed as well as wrinkles.     

Rate constitutive equations for computational analyses of textile composite reinforcement mechanical behaviour during forming

Textile composite reinforcements are made up of fibres. Consequently, their mechanical behaviour is a result of the possible sliding and the interactions between the fibres. When they are formed on double curved shapes, these fabrics are submitted to large strains, in particular large in-plane shear. Among the mechanical behaviour models for these textile reinforcements, continuous models are most commonly used for forming simulations because they can be used with standard finite elements. The objective of the present paper is to propose a continuous approach for textile reinforcement deformation analysis based on a rate constitutive equation specific to materials made of fibres. The objective derivative of this constitutive model is defined by the fibre rotation. This constitutive model is implemented in ABAQUS and can be used in most commercial F.E. software. The approach is extended to materials with two-fibre directions in order to perform simulations of woven fabric forming processes. A set of simulations of large deformations of textile composite reinforcements at the mesoscopic scale (deformation of a woven unit cell) and at the macroscopic scale (deep drawing) is presented to show the efficiency of the proposed approach.     

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.     

Modelling of composite sheet forming: a review

The use of composite materials in sheet forming applications is gaining popularity with the rise of consumer demands and specific mechanical properties. In addition to unidirectional (UD) fibres, the use of textile reinforcements such as woven fabric and knitted fabric has been shown to be feasible in recent years. This paper gives a survey on the modelling of composite sheet forming for both UD fibre and textile composites. Two broad approaches are reviewed here—the mapping approach and the mechanics approach. Mapping approaches for UD fibre composites, woven fabric composites and knitted fabric composites are elucidated on the basis of their fibre geometry. For the mechanics approach both the viscous fluid models and elastic solid models, as a means of describing the constitutive properties, are reviewed. Various updating methods for modelling large deformation found in sheet forming are then described. Finally, a guideline for the choice of modelling techniques for various types of fibre/fabric reinforcements and suggestions for future work are given.     

A Meso–Macro Three Node Finite Element for Draping of Textile Composite Preforms

The composite textile reinforcement draping simulations allows the conditions for a successful process to be determined and, most importantly, the positions of the fibres after forming to be known. This last point is essential for the structural computations of the composite part and for resin injection analyses in the case of LCM processes. Because the textile composite reinforcements are multiscale materials, continuous (macro) approaches and discrete (meso) approaches that model the yarns have been developed. The finite element that is proposed in this paper for textile fabric forming is composed of woven unit cells. The mechanical behaviour of these is analyzed by 3D computations at the mesoscale regarding biaxial tensions and in plane shear. The warp and weft directions of the woven fabric can be in arbitrary direction with respect to the direction of the element side. This is very important in the case of multi-ply deep drawing and when using remeshing. The element is efficient because it is close to the physic of the woven cell while avoiding the very large number of unknowns in the discrete approach. A set of validation tests and forming simulations on single ply and multi-ply are presented and show the efficiency of the approach. In particular the importance of the in-plane shear behaviour is emphasized in the case of a draping on a cube.     

Beyond plain weave fabrics – I. Geometrical model

In response to the large variety of weaving styles offered by the textile industry, a new general approach for the geometrical modeling of 2D biaxial orthogonal woven fabric reinforcements for composite materials is proposed here. New geometrical parameters are introduced in order to describe general families of twill and satin woven patterns, and a new classification of woven fabrics is proposed based on these parameters. Generation of the 3D internal geometry of the woven fabric families is achieved based on new geometrical functions that consider the actual configuration of the composite material in all its complexity. The proposed geometrical model is intended as the foundation for further analytical or numerical modeling of the mechanical properties of the composite materials reinforced with these fabrics.     

考虑双拉耦合的复合材料编织物各向异性超弹性本构模型

为了准确描述复合材料编织物的各向异性力学特性,首先,基于纤维增强复合材料连续介质力学理论提出了一种考虑纤维双拉耦合的复合材料编织物各向异性超弹性本构模型,该模型中单位体积的应变能被解耦为便于参数识别的纤维拉伸变形能、双拉耦合引起的挤压变形能和纤维间角度变化产生的剪切变形能;然后,给出了模型参数的确定方法,并通过拟合单轴拉伸、双轴拉伸和镜框剪切实验数据得到了本构模型参数;最后,利用该模型对双轴拉伸和镜框剪切实验进行了数值仿真,并将模拟结果与实验结果对比分析。结果表明:提出的本构模型适用于表征复合材料编织物在成型过程中由于大变形引起的非线性各向异性力学行为。所得结论表明提出的本构模型具有简单、实用的优点,且材料参数容易确定,可为复合材料编织物成型的数值模拟和工艺优化奠定理论基础。      

Analyses of fabric tensile behaviour: determination of the biaxial tension–strain surfaces and their use in forming simulations

The forming of fibre fabric reinforcements without a matrix is possible because of their very specific mechanical behaviour. The lack of some rigidities is due to possible motions between the fibres. For the fabrics used as reinforcement in the R.T.M. process and composed of warp and weft yarns made with untwisted fibres, the tension stiffness is very preponderant compared to the others. The tensile behaviour of such a fabric is biaxial, i.e. the tension-deformation states in warp or weft directions depend on the other direction because of the interweaving. It is given by the knowledge of two surfaces relating the warp and weft tensions to the two strains in these directions (or that of a single surface if the fabric is balanced). In the present paper, three complementary methods are investigated in order to determine these surfaces. A biaxial tensile device on a cross-shaped specimen is first used. 3D finite element simulations of the unit woven cell are then presented. This mesoscopic study permits to understand some phenomena at the elementary woven cell level. Finally a simplified model, which is consistent with the geometry of the plain weave woven mesh is presented. The agreement of the two last methods with experimental results is shown. From these tensile behaviour surfaces, a dynamic explicit approach for the simulations of a fabric sheet forming process is presented. The interests of the method are both its good numerical efficiency, particularly due to the direct use of the biaxial tension surfaces, and its proximity with fabric physics.     

碳纤维织物力学性能和冲压成形实验研究

在实际成形过程中,碳纤维复合材料往往处于复杂的应力状态,开展近于真实载荷环境下的力学试验分析,能够更准确地认识实际应用中材料的成形性能和变形机理.为获得碳纤维织物的基本力学特性,设计了平纹碳纤维织物拉伸试样及成形试样,进行了单轴拉伸、双轴拉伸、镜框剪切试验和方盒冲压成形实验研究,对比了不同双拉比及纱线取向对力学性能及成形性能的影响.研究结果表明:碳纤维织物具有高度的非线性、各向异性和双拉耦合特性,即经纬向纤维的力学性能会相互影响;剪切变形是成形过程中的主要变形模式,当剪切角达到临界锁死角时,织物发生起皱现象;同种织物不同纱线取向试样表现出不同的成形性能,因此可以根据零件几何形状选择合适纤维取向的织物,从而减少缺陷,优化成形零件的力学性能.研究结果为后续建立碳纤维织物本构模型和成形仿真奠定了基础.     

Characterization of the tool/fabric and fabric/fabric friction for woven-fabric composites during the thermostamping process

The dynamic coefficients of friction for Twintex® commingled glass-polypropylene balanced plain-weave and unbalanced twill-weave fabrics at the tool/fabric and fabric/fabric interfaces during the composite thermostamping process are characterized. The effects of fabric velocity and pressure on the coefficients of friction under conditions similar to those during the thermostamping process are studied. A phenomenological friction model accounting for pressure and velocity dependence is developed based on the experimental results and implemented into the commercial finite element codes ABAQUS/Explicit and LS-DYNA via user-defined subroutines. The mechanical behavior of the fabric is modeled using a mesoscopic approach. The friction subroutines are validated with a finite element model of the experimental friction test. The forming of a hemispherical dome is simulated using ABAQUS and LS-DYNA. Punch forces and yarn stresses are compared between variable friction and constant friction models, and the simulation results justify the necessity for a variable friction model to accurately predict part quality.     

碳纤维机织物增强热塑性树脂复合材料热冲压叠层模型

针对碳纤维增强热塑性树脂复合材料(CFRTP)在热冲压成型过程中涉及到大变形、各向异性和多场耦合的现象,为了表征CFRTP在成型中的力学特征,基于有限元方法与连续介质力学理论提出了一种热塑性树脂基体与碳纤维机织物的叠层模型。与单独采用碳纤维机织物超弹性本构模型预测CFRTP成型性能的方法相比,提出的叠层模型能够表征成型温度、压边力和纤维取向对CFRTP成型缺陷的影响,并能优化热冲压成型工艺参数。这一叠层模型具有简单实用和材料参数容易确定的优点,为碳纤维机织物增强热塑性树脂复合材料成型的数值模拟和成型工艺优化奠定了理论基础。     

Experimental and computational composite textile reinforcement forming: A review

Preforming is an important step in the manufacturing of textile-reinforced composites with resin infusion processes. It is important to control the fiber orientation to avoid fiber misalignments and wrinkles, which would reduce the mechanical properties of the composite part. The objective of the present paper is to give an overview of the literature dedicated to the textile reinforcement forming process. Therefore, experimental tests for the determination of the basic fabric properties, the experimental characterization of the forming and the numerical approaches for the modeling of the textile forming are reviewed. A great part of the literature has been devoted to the characterization of the shear behavior since it is the most important property for textile reinforcement forming processes. The bending behavior was initially neglected in mechanical models but was found to be important for the simulation of wrinkles.     

On accuracy improvement of microscopic stress/stress sensitivity analysis with the mesh superposition method for heterogeneous materials considering geometrical variation of inclusions

In this paper, a new method is proposed for improving accuracy of microscopic stress analysis/stress sensitivity analysis of heterogeneous materials considering a geometrical variation of inclusions using the mesh superposition method-based approach. In particular, the analysis, which considers a location variation of inclusions in heterogeneous materials with location change of a local mesh, is a target problem. This problem must be accurately solved for, eg, reliability evaluation with the multiscale stochastic stress analysis considering a microscopic geometrical variation of composites. The influence of a geometrical random variation of inclusions on the stress field is not negligible; further, a finite element mesh must be substantially updated for the evaluation of stress field for a significant realization. Therefore, the mesh superposition method based approach is adopted. In this paper, a problem point in the stress/stress sensitivity analysis considering the geometrical variation of inclusions when using the mesh superposition method is discussed, and improved approaches based on an improved formulation and a relocalization analysis are proposed. The proposed approaches are applied to a stress/stress sensitivity analysis of a heterogeneous material associated with a microstructure of composites. With the numerical results, effectiveness of the proposed approach is discussed.     

Mechanics of textile composites: Micro-geometry

Textile fabric geometry determines textile composite properties. Textile process mechanics determines fabric geometry. In previous papers, the authors proposed a digital element model to generate textile composite geometry by simulating the textile process. The greatest difficulty encountered with its employment in engineering practice is efficiency. A full scale fiber-based digital element analysis would consume huge computational resources. Two advances are developed in this paper to overcome the problem of efficiency. An improved contact-element formulation is developed first. The new formulation improves accuracy. As such, it permits a coarse digital element mesh. Then, a static relaxation algorithm to determine fabric micro-geometry is established to replace step-by-step textile process simulation. Employing the modified contact element formulation in the static relaxation approach, the required computer resource is only 1–2% of the resource required by the original process. Two critical issues with regards to the digital element mesh are also examined: yarn discretization and initial yarn cross-section shape. Fabric geometries derived from digital element analysis are compared to experimental results.     

二维机织复合材料弹性常数的有限元法预测

为了预测二维机织复合材料的弹性性能,建立了有限元力学分析模型。基于二维机织复合材料的几何特征,建立了参数化的单胞模型;考虑了织物纤维束呈现出的各向异性材料特征,将有限元中材料主方向转化到纤维屈曲方向,建立其力学分析有限元模型;分析了单胞边界面保持平面假设的不足,提出了对于二维机织复合材料通用的周期边界条件,获得了更为准确的二维机织复合材料的工程弹性常数。结果表明:织物衬垫单胞边界面,在单向拉伸载荷和纯剪切载荷下,呈凹凸翘曲变形,即为周期边界;应用给出的织物参数化几何建模方法与有限元求解方法,可以精确地获得工程弹性常数,数值计算结果与实验值吻合较好。      

A continuum shell finite element model for impact simulation of woven fabrics

A new computational approach is developed to predict the impact behaviour of fabric panels based on the detailed response of the smallest repeating unit (unit cell) in the fabric. The unit cell is constructed and calibrated using measured geometrical (weave architecture, crimp, voids, etc.) and mechanical properties of the fabric. A pre-processor is developed to create a 3D finite element mesh of the unit cell using the measured fabric cross-sectional micro-images. To render an efficient method for simulation of multi-layer packs, these unit cells are replaced with orthotropic shell elements that have similar macroscopic (smeared) mechanical properties as the unit cell. The aim is to capture the essence of the response of a unit cell in a single representative shell element, which would replace the more complicated and numerically costly 3D solid model of the yarns in a crossover. The 3D finite element analysis of the unit cell is used to provide a baseline mechanical response for calibrating the constitutive model in the equivalent shell representation. This shell element takes advantage of a simple physics-based analytical relationship to predict the behaviour of the fabric's warp and weft yarns under general applied displacements in these directions. The analytical model is implemented in the commercial explicit finite element code, LS-DYNA, as a user material routine (UMAT) for shell elements. Layers of fabric constructed from these specialized elements are stacked together to create fabric targets that are then analysed under projectile impact. This approach provides an efficient numerical model for the dynamic analysis of multi-layer fabric structures while taking into account several geometrical and material attributes of the yarns and the fabric.     

Methodology for characterization of internal structure parameters governing performance in NCF composites

Mechanical performance of non-crimp fabric composites is very dependent on their internal meso- and micro-structure which is defined by the manufacturing process of the fabric and composite processing conditions. This paper identifies the most important parameters which control mechanical properties of these materials. The identification is based on experimental observations and available theoretical findings. Characteristics of the internal structure of non-crimp fabric composites are analyzed in context of their significance for in-plane elastic and failure properties. Methodology for determination of most typical geometrical parameters of composites using optical observations of cross-sections of manufactured laminates is described. The methodology is applied to characterize cross-ply and quasi-isotropic composite laminates. These results are analyzed and a comparison between the laminates is performed.Discussion concerning advantages and disadvantages of the proposed methodology in terms of accuracy and usefulness along with practical recommendations of its application are presented.     

Importance of in-plane shear rigidity in finite element analyses of woven fabric composite preforming

A finite element made of woven unit cells under biaxial tension and in-plane shear is proposed for the simulation of fabric forming. The simulation is made within an explicit dynamic approach and is based on a simplified dynamic equation accounting for tension and in-plane shear strain energy. The biaxial tensile properties (given by two surfaces) and the in-plane shear properties (given by a curve) can be determined both by biaxial tensile tests and picture frame experiments or obtained by mesoscopic 3D finite element analyses of the woven unit cell. The interior load components of the proposed finite element are calculated explicitly and simply from the tensions and shear torque on four woven cells. The results obtained by the simulations of a hemispherical forming process on a very unbalanced fabric are compared to experiments. It is shown that the tension strain energy permits to describe the asymmetry of the response but that the computation of wrinkles and of the deformed states when the locking angle is exceeded needs to take the in-plane shear stiffness and its evolution with shear angle into account.