Hyperelastic model for large deformation analyses of 3D interlock composite preforms

A hyperelastic constitutive law is proposed to describe the mechanical behaviour of 3D layer to layer angle interlock composite reinforcements. The objective of this model is to simulate shaping of thick textile preforms for RTM processes. After the identification of the independent deformation modes of initially orthotropic reinforcements, a strain energy potential is built up based on strain invariants representative to those modes assuming an additive composition of them. The parameters of the proposed constitutive model are identified using standard and specific mechanical tests performed on a 3D interlock material. Then, the model is validated on forming simulations on a single curve and double curve shapes. Three point bending tests on thick interlock reinforcements have been analysed experimentally and numerically. The specific transformation of cross sections is depicted by the proposed hyperelastic model.     

Consistent Finite Element mesh generation for meso-scale modeling of textile composites with preformed and compacted reinforcements

A new automated method to generate smooth Finite Element meshes for the meso-scale representation of textile composites unit cells with preformed and compacted reinforcements is presented. The reinforcement geometry is obtained from textile geometry preprocessors or by modeling of the preforming step. It is then transformed into a geometric model of the entire composite unit cell, taking into account the real yarn shape after preforming and compaction, the contact interactions between the yarns, as well as the resulting local variations of fiber volume fraction. A consistent mesh of the complete cell, conformal between the parts, is ensured, without the need for inserting artificial matrix layers between the yarns. The methodology is illustrated by mechanical modeling of the representative unit cell of a multi-layer composite with a compacted and nested woven reinforcement.     

Textile composite double dome stamping simulation using a non-orthogonal constitutive model

Stamping is one of the most effective ways to form textile composites in industry for providing high-strength, low-weight and cost-effective products. This paper presents a fully continuum mechanics-based approach for stamping simulation of textile fiber reinforced composites by using finite element (FE) method. A previously developed non-orthogonal constitutive model is used to represent the anisotropic mechanical behavior of textile composites under large deformation during stamping. Simulation are performed on a balanced plain weave composite with 0°/90° and ±45° as initial yarn orientation over a benchmark double dome device. Simulation results show good agreement with experimental output in terms of a number of parameters selected for comparison. The effects of meshing and shear moduli obtained from bias extension test and picture frame test on forming simulation results are also investigated.     

Dynamic micromechanical modeling of textile composite strength under impact and multi-axial loading

Micromechanical finite element modeling has been employed to define the failure behavior of S2 glass/BMI textile composite materials under impact loading. Dynamic explicit analysis of a representative volume element (RVE) has been performed to explore dynamic behavior and failure modes including strain rate effects, damage localization, and impedance mismatch effects. For accurate reflection of strain rate effects, differences between an applied nominal strain rate across a representative volume element (RVE) and the true realized local strain rates in regions of failure are investigated. To this end, contour plots of strain rate, as well as classical stress contours, are developed during progressive failure. Using a previously developed cohesive element failure model, interfacial failure between tow and matrix phases is considered, as well as classical failure modes such as fiber breakage and matrix microcracking. In-plane compressive and tensile loading have been investigated, including multi-axial loading cases. Highly refined meshes have been employed to ensure convergence and accuracy in such load cases which exhibit large stress gradients across the textile RVE. The effect of strain rate and phase interfacial strength have been included to develop macro-level material failure envelopes for a 2D plain weave and 3D orthogonal microgeometry.     

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.     

Rate dependent modelling of the forming behaviour of viscous textile composites

A predictive approach to modelling the forming of viscous textile composites has been implemented in two finite element codes; Abaqus Standard™ and Abaqus Explicit™. A multi-scale energy model is used to predict the shear force–shear angle–shear rate behaviour of viscous textile composites, at specified temperatures, using parameters supplied readily by material manufacturers, such as fibre volume fraction, weave architecture and matrix rheology. The predictions of the energy model are fed into finite element simulations to provide the in-plane shear properties of two different macro-scale constitutive models implemented in the finite element codes. The manner of coupling predictions of the multi-scale energy model with the macro-scale models is shown to affect the rate-dependent material response in the simulations. These coupling methods are evaluated using picture frame test simulations.     

A numerical investigation into the influence of fabric construction on ballistic performance

The use of high-performance fibres has made it possible to produce lightweight and strong personal body armour. Parallel to the creation and use of new fibres, fabric construction also plays an essential role for performance improvement. In this research, finite element (FE) models were built up and used to predict the response of woven fabrics with different structural parameters, including fabric structure, thread density of the fabric and yarn linear density. The research confirmed that the plain woven fabric exhibits superior energy absorption over other structures in a ballistic event by absorbing 34% more impact energy than the fabric made from 7-end satin weave. This could be explained that the maximum interlacing points in this fabric which help transmit stress to a larger fabric area, enabling more secondary yarns to be involved for energy dissipation. It was found that fabric energy absorption decreases as fabric is made denser, and this phenomenon becomes more pronounced in a multi-ply ballistic system than in a single-ply system. The research results also indicated that the level of yarn crimp in a woven fabric is an effective parameter in influencing the ballistic performance of the fabrics. A low level of yarn crimp would lead to the increase of the fabric tensile modulus and consequently influencing the propagation of the transverse wave. In addition, it was found that for fabrics with the same level of yarn crimp, low yarn linear density and high fabric tightness were desirable for ballistic performance improvement.     

Modelling microscopic flow in woven fabric reinforcements and its application in dual-scale resin infusion modelling

A physical unit cell impregnation model is proposed for the micro-scale flow in plain woven reinforcements. The modelling results show a characteristic relationship between tow impregnation speed, the surrounding local macro-scale resin pressure and the tow saturation within the unit cell. This relationship has been formulated into a mathematical algorithm which can be directly incorporated into a continuum dual-scale model to predict the ‘sink’ term. The results using the dual-scale model show a sharp resin front in inter-tow-pore spaces and a partially saturated front region in intra-tow-pore spaces. This demonstrates that the impregnation of fibre tows lags behind the resin front in the macro pore spaces. The modelling results are in agreement with two reported experimental observations. It has been shown that the unsaturated region at the flow front could increase or have a fixed length under different circumstances. These differences are due to the variation in tow impregnation speed (or the time required for the tow to become fully impregnated), the weave architecture and the nesting and packing of plies. The modelling results have also demonstrated the drooping of the inlet pressure when flow is carried out under constant injection rates. The implementation of the algorithm into a dual-scale model shows coherence with a single-scale unsaturated model, but demonstrates an advantage in flexibility, precision and convenience in application.     

Late-stage fatigue damage in a 3D orthogonal non-crimp woven composite: An experimental and numerical study

Late-stage fatigue damage of an E-glass/epoxy 3D orthogonal non-crimp textile composite loaded in the warp direction has been investigated using a combination of mechanical testing, X-ray micro computed tomography (μCT), optical microscopy and finite element modelling. Stiffness reduction and energy dissipated per cycle were found to be complementary measurements of damage accumulation, occurring in three stages: a first stage characterised by rapid changes, a more quiescent second stage, followed by a third stage where the (decreasing) stiffness and (increasing) energy dissipation change irregularly and then rapidly, to failure. Microscopy of specimens cycled into the transition between the second and third stages showed macroscopic accumulations of fibre fractures in sections of warp tows which lying adjacent to the surface weft tows which are crowned-over by the Z-tows. At these locations, the warp tow fibres are subjected to stress concentrations both from transverse weft tow matrix cracks and resin pocket cracks.     

Kinematic modelling of 3D woven fabric deformation for structural scale features

A multi-scale approach to modelling is optimal for computationally intensive problems of a hierarchical nature such as 3D woven composites. In this paper an approach capable of modelling feature/component scale fabric deformations and defects is proposed. The proposed technique starts with a meso-scale model for predicting the as-woven geometry of a single unit cell using a high fidelity digital element method. The unit cell geometry is then converted into a macro-scale fabric model by geometric reduction then tessellation. On the macro-scale, two and three dimensional approaches to yarn geometry representation are proposed, with an accompanying yarn mechanical model. Each approach is evaluated based on solution accuracy and computational efficiency. The proposed approach is then verified against experimental results on the meso- and macro-scales. The applicability of this modelling technique to larger scale compaction problems is then investigated. The proposed algorithm was found to be accurate and computationally efficient.     

Experimental and numerical analyses of manufacturing process of a composite square box part: Comparison between textile reinforcement forming and surface 3D weaving

Textile reinforcement forming is frequently used in aeronautic and automobile industries as a composite manufacturing process. The double-curved shape forming may be difficult to control and can lead to defects. Numerical simulation analysis can predict the suitable forming conditions and minimize the defects. Wrinkling as one of the most common flaws can be experienced easily during textile composite forming for certain specific shapes, for example the square box. In order to product a composite square box without wrinkles, a surface 3D weaving process has been developed to weave directly the shape of final part without the step of 2D preforming. In the surface 3D weaving the three directions are completely designed. The warp and weft yarns on all the surfaces of square box are absolutely under control and the final 3D ply has a homogeneous fibre volume fraction.     

Predictive model for the detection of out-of-plane defects formed during textile-composite manufacture

A hybrid finite element model using a discrete mesoscopic approach was previously developed and has since demonstrated its ability to capture the tensile and shear behaviors of textile reinforcements for composites. The aim of the present research is to implement flexural properties into a non-homogenous beam/shell model such that the formation and shape of out-of-plane defects can be well predicted. A method for linking the measurement of bending rigidity to the determination of a compressive modulus is presented and simulations are used to demonstrate the ability of the modeling approach to predict the amplitude and curvature of out-of-plane waves. A comparison of the simulation results to experimental data shows the finite element model accurately captures this out-of-plane phenomenon.     

Homogenization of braided fabric composite for reliable large deformation analysis of reinforced rubber hose

High pressure rubber hose is in the lamination structure composed of pure rubbers and braided fabric composite layers to have the sufficient strength against the excessive radial expansion and the large deformation, in which the braided fabric layer is woven with wrap and fill tows inclined to each other with the predefined helix angle in the complex periodic pattern. The consideration of detailed geometry of braided fabric layer in the numerical analysis leads to a huge number of finite elements so that the braided fabric layer has been traditionally simplified as an isotropic cylindrical one with the homogeneous isotropic material properties of braid spun tread. However, this simple model leads to the numerical prediction and design with the questionable reliability. In this context, this paper addresses the development of an in-house module, which is able to be interfaced with commercial FEM code, for the reliable large deformation analysis of the reinforced rubber hose with the element number at the level of the traditional simple model. The in-house module is able to not only automatically generate 3-D unit cell (or RVE) model of the braided fabric layer but evaluate the homogenized orthotropic material properties by automatically performing a serious of unit cell finite element analyses based on the superposition method. The validity of the in-house module and the reliability of the homogenization method are verified through the illustrative numerical experiments.     

Finite element modeling of ballistic impact on multi-layer Kevlar 49 fabrics

This paper presents a material model suitable for simulating the behavior of dry fabrics subjected to ballistic impact. The developed material model is implemented in a commercial explicit finite element (FE) software LS-DYNA through a user defined material subroutine (UMAT). The constitutive model is developed using data from uniaxial quasi-static and high strain rate tension tests, picture frame tests and friction tests. Different finite element modeling schemes using shell finite elements are used to study efficiency and accuracy issues. First, single FE layer (SL) and multiple FE layers (ML) were used to simulate the ballistic tests conducted at NASA Glenn Research Center (NASA-GRC). Second, in the multiple layer configuration, a new modeling approach called Spiral Modeling Scheme (SMS) was tried and compared to the existing Concentric Modeling Scheme (CMS). Regression analyses were used to fill missing experimental data – the shear properties of the fabric, damping coefficient and the parameters used in Cowper-Symonds (CS) model which account for strain rate effect on material properties, in order to achieve close match between FE simulations and experimental data. The difference in absorbed energy by the fabric after impact, displacement of fabric near point of impact, and extent of damage were used as metrics for evaluating the material model. In addition, the ballistic limits of the multi-layer fabrics for various configurations were also determined.     

Development of an experimental bench to reproduce the tow buckling defect appearing during the complex shape forming of structural flax based woven composite reinforcements

This work investigates the tow buckling defect that may take place during the forming of complex shapes. The defect is studied independently of the process with a device specially designed. A specific instrumentation was associated to the device. Structure light interferometry was chosen to measure the elevation of the tows exhibiting the buckling defect all along its growth. The device and its instrumentation were validated in this work and a preliminary study was performed to investigate the origin of the tow buckle’s appearance and its growth kinematic. The growth kinematic of the buckle’s appearance consisting on a double simultaneous rotation of the tow exhibiting the buckle around the Z and the Y axis was established. It was shown that the in-plane bending of the tow is a key parameter that can probably be considered as a preliminary criterion that conditions the appearance and the growth of the tow buckling defect.     

Predictive modelling for optimization of textile composite forming

Wrinkling often occurs during textile composite forming and is a major problem for manufacturers. The prediction of this defect is, therefore, of major importance for the design and optimization of textile composite structures. Numerical simulations of forming for textile composites over a hemisphere have been conducted using a rate/temperature-dependent hybrid FE model. The hybrid FE model incorporates a fully predictive multi-scale energy model which determines the shear resistance of the textile composite sheet. The effects of varying the normal force distribution across the edges of the blank and blank size, together with the effect of changes in forming temperature on the final fibre pattern and wrinkling behaviour, are investigated. Predictions are evaluated against press-formed components. The results from the simulation and the experiments have good correlation and show that wrinkling can be minimized by optimizing the force distribution around the edge of the manufacturing tool and by careful choice of forming temperature.     

Simulation of the bone healing process of fractured long bones applied with a composite bone plate with consideration of the blood vessel growth

The healing process of long bones such as the tibia was simulated on the basis of a mechanoregulation theory by taking blood vessel growth into consideration. The tissue differentiation process of calluses by taking into consideration blood vessel growth was simulated by a user subroutine program based on the mechanoregulation model and a diffusion equation. Composite bone plates made of a plain weave carbon/epoxy composite (WSN3k) and a plain weave glass/polypropylene composite (Twintex) were applied to the fracture site to investigate the effect of plate modulus on the healing performance. The simulation results revealed that the flexible composite bone plate made of Twintex [0]₁₈, which had a slightly higher Young’s modulus than a cortical bone, provided the highest healing performance. Moreover, it was found that the effect of the plate modulus on the healing performance reduced when the blood vessel growth at the fracture site was considered, which reflected a more realistic bone healing process.     

Three dimensional (3D) fabrics as reinforcements for cement-based composites

This research studied the flexural behavior of cement-based elements reinforced with 3D fabrics. The effects of the through-thickness (Z direction) yarns were examined in terms of four parameters: (i) yarn properties, (ii) varying the composite content of (i.e., coverage by) high-performance aramid yarn, (iii) treatment of the fabric with epoxy, and (iv) 2D and 3D fabric composites were compared. Overall, the 3D fabric composites performed better than the 2D fabric composites, which tended to delaminate. Our results indicate that even though the Z yarns are not oriented in the direction of the applied loads, 3D fabrics still have potential applications as reinforcements for cement-based composites. Indeed, the Z yarns hold the entire fabric together, which leads to improved mechanical anchoring and mechanical properties particularly when the fabric has been treated with epoxy, i.e., to create a stiff reinforcing unit.     

Formability optimisation of fabric preforms by controlling material draw-in through in-plane constraints

A genetic algorithm is coupled with a finite element model to optimise the arrangement of constraints for a composite press-forming study. A series of springs are used to locally apply in-plane tension through clamps to the fibre preform to control material draw-in. The optimisation procedure seeks to minimise local in-plane shear angles by determining the optimum location and size of constraining clamps, and the stiffness of connected springs. Results are presented for a double-dome geometry, which are validated against data from the literature. Controlling material draw-in using in-plane constraints around the blank perimeter is an effective way of homogenising the global shear angle distribution and minimising the maximum value. The peak shear angle in the double-dome example was successfully reduced from 48.2° to 37.2° following a two-stage optimisation process.