Numerical prediction of in-plane permeability for multilayer woven fabrics with manufacture-induced deformation

A unit cell based Computational Fluid Dynamics model is presented for predicting permeability of multilayer fabric structures. In Liquid Composites Moulding processes, fabric lay-ups undergo significant manufacture-induced deformation, combining compression, shear, and inter-layer nesting. Starting from the configuration of un-deformed fabric, the deformation is simulated geometrically by accounting for self-imposed kinematic constraints of interweaving yarns. The geometrical modelling approach is implemented in the open-source software TexGen. The permeability tensor is retrieved from flow analysis in ANSYS/CFX, based on TexGen voxel models. Using only measured geometrical data for un-deformed fabrics, deformed plain weave fabric and twill weave fabric lay-ups were modelled and their permeability tensors predicted. Comparison with experimental data demonstrates the generally good accuracy of predictions derived from the proposed numerical method.     

Simulating tape resin infiltration during thermoset pultrusion process

The thermoset tape pultrusion is a widely adopted manufacturing process to produce long, constant cross-section composite structural parts. For high volume production, low cost can be achieved by maximizing the production rate which is a function of the material and process parameters, more specifically the rate of resin infiltration and resin cure. During resin infiltration, the resin saturates the dry reinforcement either under positive pressure in the pressure chamber, or, by the action of capillary and surface forces, within the resin bath. In either case, the saturation must be completed as the tape is squeezed into the final cross-sectional form at the entrance of the heated mold where the resin will be cured to form the composite part.This paper models the resin infiltration process during pultrusion, by modifying the pre-existing simulation tool for liquid molding processes. The formulated capability can be used not only to optimize the impregnation dynamics within the pressure chamber, but can also be used to predict the required forces for the selected pulling rate. The proposed model does allow one to handle a variety of tape cross-sections, not just rectangular prisms.     

Multiscale modeling of unsaturated flow in dual-scale fiber preforms of liquid composite molding III: reactive flows

The woven, stitched or braided fabrics used in liquid composite molding (LCM) display partial saturation behind moving flow-front in an LCM mold which is caused by delayed impregnation of fiber tows. In this part 3 of the present series of three papers, a novel multiscale approach proposed in parts 1 and 2 [1] and [2] is adapted for modeling the unsaturated flow observed in the dual-scale fabrics of LCM under non-isothermal, reactive conditions. The volume-averaged species or resin cure equation, in conjunction with volume-averaged mass, momentum and energy (temperature) equations, is employed to model the reactive resin flow in the inter-tow (gap) and intra-tow (tow) regions with coupling expressed through several sink and source terms in the governing equations. A coarse global-mesh is used to solve the global (gap) flow over the entire domain, and a fine local mesh in form of the unit-cell of periodic fabrics is employed to solve the local (tow) flows. The multiscale algorithm based on the hierarchical computational grids is then extended to solve the dual-scale flow under reactive conditions. The simulation is compared with a two-color experiment and a previously published two-layer model. Significant differences between the temperatures and cures of the gap and tow regions of the dual-scale porous medium are observed. The ratio of pore volumes in the tow and gap regions, the effective thermal conductivity in the tows, and the reaction rate are identified as the important parameters for temperature and cure distributions in the gap and tow regions.     

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.     

On the effect of stacked fabric layers on the stiffness of a woven composite

Most micromechanical models for stiffness prediction of woven composites assume independence of the Q-matrix on the number of fabric layers in the composite. For example, the moduli of single and 10 layer composites are assumed to be equal in the case when all layers have the same in-plane orientation. Although this statement is likely to be true for isotropic materials or even for unidirectional laminated composites, it may not be valid in some cases of woven composites.

This paper contains experimental and theoretical investigations of plain weave carbon fiber/polyester composites. Specimens with one single and eight layers of fabrics are tested and observable differences of mechanical properties are obtained.

The theoretical part of this article consists of derivation and application of several micromechanical models on these particular composites. The use of those simplified models finally allows us to find the main mechanisms which cause the observed effects.     

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.     

Hyperelastic modelling for mesoscopic analyses of composite reinforcements

A hyperelastic constitutive law is proposed to describe the mechanical behaviour of fibre bundles of woven composite reinforcements. The objective of this model is to compute the 3D geometry of the deformed woven unit cell. This geometry is important for permeability calculations and for the mechanical behaviour of the composite into service. The finite element models of a woven unit cell can also be used as virtual mechanical tests. The highlight of four deformation modes of the fibre bundle leads to definition of a strain energy potential from four specific invariants. The parameters of the hyperelastic constitutive law are identified in the case of a glass plain weave reinforcement thanks to uniaxial and equibiaxial tensile tests on the fibre bundle and on the whole reinforcement. This constitutive law is then validated in comparison to biaxial tension and in-plane shear tests.     

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.     

Modeling of heat transfer and unsaturated flow in woven fiber reinforcements during direct injection-pultrusion process of thermoplastic composites

This paper provides a methodology for the modeling of heat transfer and polymer flow during direct thermoplastic injection pultrusion process. Pultrusion was initially developed with thermosets which have low viscosity. But the impregnation becomes a critical point with thermoplastics which exhibit higher viscosity. There are very few reported works on direct thermoplastic impregnation with injection within the die. In addition, the rare studies have not adequately addressed the issue of unsaturated flow in woven fiber reinforcements. The solution proposed here, models the polymer flow through dual-scale porous media. A heat transfer model is coupled to a flow model enriched with a sink term. Specific changes of variables are made so as to model the steady state solution of unsaturation along a continuous process. The sink term, added to the continuity equation, represents the absorption rate of polymer by the bundles. Data were measured on a pultrusion line and micrographs confirmed the modeling strategy with an unsaturated flow approach. The flow modeling coupled to heat transfer of the thermoplastic pultrusion process aims at determining the saturation evolution through the die so as to manufacture pultruded profiles with the lowest residual porosity.     

Data assimilation through integration of stochastic resin flow simulation with visual observation during vacuum-assisted resin transfer molding: A numerical study

This study investigated data assimilation through integration of visual observation with a stochastic numerical simulation of resin flow during vacuum-assisted resin transfer molding. The data assimilation was performed using the four-dimensional asynchronous ensemble square root filter and a stochastic numerical simulation by means of the Karhunen–Loève expansion of the permeability field. Through numerical experiments of linear flow, it was verified that the estimation accuracy of the resin impregnation behavior improved compared to that when using conventional data assimilation and that the permeability field could be estimated simultaneously, although it is not explicitly related to the observation. We also investigated the applicability of the proposed method to radial-injection VaRTM by varying the model thickness. The proposed method successfully estimated the resin impregnation behavior and permeability field. Additionally, the required condition for the number of ensemble members was clarified.     

Attachment mode performance of network-modeled ballistic fabric shielding

A central issue in the use of ballistic fabric shielding is the mode of attachment to the structure that it is intended to protect. In order to investigate this issue, a discrete multi-scale yarn-network model is developed for structural fabric undergoing ballistic impact, based on work found in Zohdi and Powell [Zohdi TI, Powell D. Multiscale construction and large-scale simulation of structural fabric undergoing ballistic impact. Comput Meth Appl Mech Eng 2006;195:94–109] and Zohdi [Zohdi TI. Modeling/simulation of progressive penetration of multilayered ballistic fabric shielding. Comput Mech 2002;29:61–7]. The model is comprised of a network of yarn with stochastic properties determined by smaller-scale fibrils, which are randomly misaligned. The effects of stochasticity on the overall response are explored, and the model is compared against macro-scale experiments. The key feature of the model is the fact that it does not depend on phenomenological parameters, and can be calibrated by simply measuring the properties of an individual, smallest-scale, fibril. The properties of a fibril are easily ascertained from a simple tension test. The response of the overall fabric model and ballistic experiments are in excellent agreement. The model indicates that fabric which is attached by being pinned at the corners generally absorbs more energy, relative to fabric clamped along the sides. The basis for this result is discussed at length in the body of this work. Furthermore, it is observed that a uniform-yarn model, one which ignores the stochastic nature of the yarn, over-estimates the amount of energy absorbed.     

Characterisation of material properties for draping of dry woven composite material

Three test methods, uniaxial bias extension, biaxial and picture frame tests are used to characterise the shear behaviour of dry woven fabric during draping. The deformation of the bias extension and biaxial specimens is measured from images of a central gauge section. The forces applied to the material are resolved into forces along and parallel to the tow directions. The deformation of the material in the bias extension and biaxial tests is found to behave in a manner which is reasonably well described by a pin-jointed net analysis. There is negligible change in the shear resistance of the material during biaxial loading, while a slight increase in shear resistance is observed in the picture frame tests. Microscopic examination of the tow architecture [Compos Sci Technol 63 (2003) 99], which shows a significantly smaller crimp amplitude for picture frame tests than for the bias extension and biaxial tests, supports the suggestion raised by Harrison et al. [Proceedings of the 10th European Conference on Composite Materials, 2002], that the increase in resistance in the picture frame tests is associated with an increase in tow cross-over force generated by large loads along the tows.     

Modeling and validation of full fabric targets under ballistic impact

The impact of three different projectiles (0.357 Magnum, 9-mm FMJ and 0.30 cal FSP) onto Kevlar® was modeled using a commercial finite-element program. The focus of the research was on simulating full-scale body armor targets, which were modeled at the yarn level, by reducing to a minimum the number of solid elements per yarn. A thorough validation of the impact physics was performed at the yarn level, single-layer level, and a full body armor system. A verification was performed by checking the numerical model against analytical predictions for yarn impact. For one-layer and multiple-layer targets validation consisted on matching experimental data of pyramid formation recorded by an ultra-high-speed camera. The full-scale targets were also instrumented with nickel–chromium wires that stretch with the yarn during the penetration event. The wires provided a second validation data set since the numerical model can reproduce the signal recorded by the wires. The third and final validation of the model is provided by a comparison of the ballistic limit predicted by the model and data obtained in tests. This is a check of the failure model used in the numerical simulations. This paper shows that the main features of the impact physics are well reproduced by the finite-element model. Prediction of ballistic limits for the 9-mm FMJ and FSP projectiles were within the scatter of the tests, while for the 0.357 projectile the difference was only 15%.     

Experimental study of damage characteristics of carbon woven fabric/epoxy laminates subjected to lightning strike

This paper experimentally investigates the damage characteristics of two stacking sequenced ([45₂/0₂/−45₂/90₂]s, [30₂/0₂/−30₂/90₂]s) carbon woven fabric/epoxy laminates subjected to simulated lightning strike. Characteristics of the damage are analyzed using visual inspection, image processing, ultrasonic scanning and scanning electron microscope. The mechanical properties of post-lightning specimens are then studied. Observations show that as the lightning strike is intensified, an enlarged resin pyrolized area appears majorly along the weft orientation while the delamination region extends equally to both of the warp and the weft direction. The resin/fiber interfacial bonding is severely damaged by a thermal–mechanical effect due to lightning strike infliction. Mechanical testing further shows that the stacking sequence can influence the failure significantly. Compared with prepreg taped material, the restrained damage area due to special designed stacking sequence, lamina thickness and the weft nylon binder make the woven fabric reinforcement a good choice for the fabrication of lightning protection structures.     

Nesting effect on the mode I fracture toughness of woven laminates

The fracture toughness of two woven laminates is evaluated for different nesting/shifting values between advanced layers. The analysed woven composites are manufactured using the same resin-reinforcement and same architecture, but have a different tow size (3K/12K). Three different nesting/shifting configurations are applied to the plies at the fracture surface: zero shifting, middle shifting and maximum shifting. Before being tested, the internal geometry of the material is evaluated and any shifting error is measured. For all these configurations mode I fracture tests are carried out. The differences obtained between 3K and 12K cases can be explained by fibre bridging, but not the differences between the nesting configurations. Depending on the nesting/shifting value the delaminated surface waviness is different, and consequently the fracture toughness is also influenced.     

Experimental validation of post-filling flow in vacuum assisted resin transfer molding processes

In Liquid Composite Molding (LCM) processes with compliant tool, such as Vacuum Assisted Resin Transfer Molding Process (VARTM), resin flow continues even after the inlet is closed due to the preform deformation and pressure gradient developed during infusion. The resin flow and thickness changes continue until the resin pressure becomes uniform or the resin gels. This post-filling behavior is important as it will determine the final thickness and fiber volume fraction distribution in the cured composite. In this paper, a previously proposed one dimensional coupled flow and deformation process model has been compared with the experimental data in which the resin pressure and part thickness at various locations during the post-filling stage is recorded. Two different post-infusion scenarios are examined in order to determine their impact on the final part fiber volume fraction and thickness. The effects of different venting arrangements are demonstrated. The model predictions compare favorably with the experimental data, with the minor discrepancies arising due to the variability of material properties.     

An optically-based inverse method to measure in-plane permeability fields of fibrous reinforcements

Structural composite manufacturing relying on Liquid Composite Molding technologies is strongly affected by local variability of the fibrous reinforcement. Optical techniques using light transmission are used and allow field measurements of areal weight (and fibre volume fraction) of glass fibre reinforcement. The coupling of obtained areal weight mappings along with injection flow fronts is used to extract in-plane permeability fields. The current work presents results with a focus on glass random mats, but the method can be adapted to any glass fibrous medium. A study of convergence and error due to discretization is performed. Also the influence of the stacking of fibrous layers on the preform variability is analyzed. The major advantage of the proposed technique is a relatively fast acquisition of statistical data on reinforcement variability, which can be later utilized in stochastic based process simulations.     

Effect of fabric compaction and yarn waviness on 3D woven composite compressive properties

3D-woven fabrics incorporate through-thickness reinforcement and can exhibit remarkable inter-laminar properties that aid damage suppression and delay crack propagation. However, distortions in the internal architecture such as yarn waviness can reduce in-plane properties, especially in compression. The degree of yarn waviness present in a 3D woven fabric can be affected by a range of factors including weave parameters and manufacturing-induced distortions such as fabric compaction. This paper presents a thorough analysis of the effect of fabric compaction and yarn waviness on the mechanical properties and failure mechanisms of an angel-interlock fabric in compression. Tests were conducted on coupons moulded to different volume fractions and data compared to previous measurements of local yarn angle. Major findings show the importance of yarn straightness on compressive strength and how this can be affected by optimising moulding thickness. Failure initiation was also found to be heavily influenced by weave style and yarn interlacing.     

Thermomechanical properties of bio-based composites made from a lactic acid thermoset resin and flax and flax/basalt fibre reinforcements

Low viscosity thermoset bio-based resin was synthesised from lactic acid, allyl alcohol and pentaerythritol. The resin was impregnated into cellulosic fibre reinforcement from flax and basalt and then compression moulded at elevated temperature to produce thermoset composites. The mechanical properties of composites were characterised by flexural, tensile and Charpy impact testing whereas the thermal properties were analysed by dynamic mechanical thermal analysis (DMTA) and thermogravimetric analysis (TGA). The results showed a decrease in mechanical properties with increase in fibre load after 40 wt.% for the neat flax composite due to insufficient fibre wetting and an increase in mechanical properties with increase fibre load up to 60 wt.% for the flax/basalt composite. The results of the ageing test showed that the mechanical properties of the composites deteriorate with ageing; however, the flax/basalt composite had better mechanical properties after ageing than the flax composite before ageing.