Multiscale modeling of unsaturated flow of dual-scale fiber preform in liquid composite molding II: Non-isothermal flows

A novel multiscale approach is developed for modeling non-isothermal flows under unsaturated conditions in the dual-scale fabrics of liquid composite molding (LCM). The flow and temperature governing equations at the global or gap or inter-tow (∼m) level and the local or intra-tow (∼mm) levels are based on a previous dual-scale volume averaging method. To solve the coupled equations at two length-scales, a coarse global mesh is used to solve the global 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-impregnation process. (The latter is used to compute sink terms required for solving the former.) A multiscale algorithm based on the hierarchical computational grids is then proposed to solve the dual-scale flow under non-isothermal (but non-reactive) conditions. To test the proposed multiscale model, we first carry out a validation study in which the temperature histories predicted by the multiscale method are compared with experimental data available in a publication for a simple 1-D flow. Despite the lack of information about various model parameters, a reasonably good comparison with the experimental results is achieved. Then, the non-isothermal flow through a simple 1-D flow domain is carried out and the predictions of the multiscale simulation are compared with those of a previously published two-layer model. The multiscale predictions are found to be very similar to the two-layer predictions. A significant difference between the gap and tow temperatures is observed. The ratio of pore volumes in the tow and gap regions, thermal conductivity of the tows, and fiber types are identified as the important parameters for temperature distributions in the gap and tow regions. A further comparison with the single-scale flow simulation highlights significant differences between the conventional single-scale and the proposed dual-scale modeling approaches.     

Governing equations for unsaturated flow through woven fiber mats. Part 1. Isothermal flows

Correct modeling of resin flow in liquid composite molding (LCM) processes is important for accurate simulation of the mold-filling process. Recent experiments indicate that the physics of resin flow in woven (also stitched or braided) fiber mats is very different from the flow in random fiber mats. The dual length-scale porous media created by the former leads to the formation of a sink term in the equation of continuity; such an equation in combination with the Darcy's law successfully replicate the drooping inlet pressure history, and the region of partial saturation behind the flow-front, for the woven mats. In this paper, the mathematically rigorous volume averaging method is adapted to derive the averaged form of mass and momentum balance equations for unsaturated flow in LCM. The two phases used in the volume averaging method are the dense bundle of fibers called tows, and the surrounding gap present in the woven fiber mats. Averaging the mass balance equation yields a macroscopic equation of continuity which is similar to the conventional continuity equation for a single-phase flow except for a negative sink term on the right-hand side of the equation. This sink term is due to the delayed impregnation of fiber tows and is equal to the rate of liquid absorbed per unit volume. Similar averaging of the momentum balance equation is accomplished for the dual-scale porous medium. During the averaging process, the dynamic interaction of the gap flow with the tow walls is lumped together as the drag force. A representation theorem and dimensional analysis are used to replace this drag force with a linear function of an average of the relative velocity of the gap fluid with respect to the tow matrix for both the isotropic and anisotropic media. Averaging of the shear stress term of the Navier–Stokes equation gives rise to a new quantity named the interfacial kinetic effects tensor which includes the effects of liquid absorption by the tows, and the presence of slip velocity on their surface. Though the gradient of the tensor contributes a finite force in the final momentum balance equation, a scaling analysis leads to its rejection in the fibrous dual-scale porous medium if the permeability of flow through the gaps is small. For such a porous medium, the momentum equation reduces to the Darcy's law for single-phase flow.     

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

Mold-filling simulation of unsaturated flows in LCM is important for optimizing mold design quickly and cost-effectively in the virtual space. For the first time, a true multiscale approach is developed for simulating the unsaturated flow under isothermal conditions in the dual-scale fiber-mats of RTM. To solve the coupled macro-micro equation-set, a coarse global mesh is used to solve the global flow equations over the entire domain while fine local meshes in form of the periodic unit-cells of fabrics are employed to solve the local tow-impregnation process. A multiscale algorithm based on hierarchical computational grids has been proposed to simulate the unsaturated flow in the dual-scale fiber mats under isothermal conditions. The predictions are compared with measurements for a 1-D flow experiment which indicates that the proposed approach can be used to simulate the unsaturated flow accurately through dual-scale fiber mats in LCM without the use of any fitting parameters.     

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.     

The effect of fabric and fiber tow shear on dual scale flow and fiber bundle saturation during liquid molding of textile composites

In Liquid Composite Molding (LCM) processes, a fibrous reinforcement preform is placed or draped over a mold surface, the mold is closed and a resin is either injected under pressure or infused under vacuum to cover all the spaces in between the fibers of the preform to create a composite part. LCM is used in a variety of manufacturing applications, from the aerospace to the medical industries. In this manufacturing process, the properties of the fibrous reinforcement inside the closed mold is of great concern. Preform structure, volume fraction, and permeability all influence the processing characteristics and final part integrity. When preform fabrics are draped over a mold surface, the geometry and characteristics of both the bulk fabric and fiber tow bundles change as the fabric shears to conform to the mold curvature. Numerical simulations can predict resin flow in dual scale fabrics in which one can separately track the filling of the fiber tows in addition to flow of resin within the bulk fabric. The effect of the deformation of the bulk fabric due to draping over the tool surface has been previously addressed by accounting for the change in fiber volume fraction and permeability during the filling of a mold. In this work, we investigate the effect of shearing of the fiber tows in addition to bulk deformation during the dual scale filling. We model the influence of change in fiber tow characteristics due to draping and deformation on mold filling and compare it with the results when the fiber tow deformation effect is ignored. Model experiments are designed and conducted with a dual scale fabric to characterize the change in permeability of fiber tow with deformation angle. Simulations which account for dual scale shear demonstrate that the tow saturation rate is affected, requiring longer fill times, or higher pressures to completely saturate fiber tows in areas of a mold with high local shear. This should prove useful in design of components for applications in which it is imperative to ensure that there are no unfilled fiber tows in the final fabricated component.     

Simulation of void formation in liquid composite molding processes

Air entrapment within and between fiber tows during preform permeation in liquid composite molding (LCM) processes leads to undesirable quality in the resulting composite material with defects such as discontinuous material properties, failure zones, and visual flaws. Essential to designing processing conditions for void-free filling is the development of an accurate prediction of local air entrapment locations as the resin permeates the preform. To this end, the study presents a numerical simulation of the infiltrating dual-scale resin flow through the actual architecture of plain weave fibrous preforms accounting for the capillary effects within the fiber bundles. The numerical simulations consider two-dimensional cross sections and full three-dimensional representations of the preform to investigate the relative size and location of entrapped voids for a wide range of flow, preform geometry, and resin material properties. Based on the studies, a generalized paradigm is presented for predicting the void content as a function of the Capillary and Reynolds numbers governing the materials and processing. Optimum conditions for minimizing air entrapment during processing are also presented and discussed.     

Prediction of optimal flow front velocity to minimize void formation in dual scale fibrous reinforcements

Liquid Composite Molding (LCM) is an increasingly used class of processes to manufacture high performance composites. Engineering fabrics commonly used in LCM generally have a dual scale architecture in terms of porosity: microscopic pores exist between the filaments in the fiber tows, while macroscopic pores appear between the tows. Capillary flows in fiber tows play a major role on the quality of composites made by resin injection through fibrous reinforcements. This paper reports on an investigation on fabric imbibition characterization and subsequent evaluation of the optimal flow front velocity during resin injection through fibrous reinforcements. The goal is to devise more robust LCM processes and improve part quality. In order to evaluate a priori the injection conditions that minimize void formation, an impregnation model is developed based on imbibition characterization. This approach allows predicting the optimal front velocity without having to model complex dual scale flows through fibrous reinforcements and without performing expensive and time-consuming fabrication tests. After a summary of previous imbibition results obtained with a probe fluid, the optimal modified capillary numbers are computed by the new predictive model and the values are compared with results reported in the literature on void formation in LCM processes. Afterwards, capillary rise measurements are carried out with four infiltration fluids in order to evaluate the range of optimal flow front velocity that minimizes void formation. This characterization is implemented with vinyl ester resin, epoxy anhydride resin, styrene and anhydride. Finally, the optimal flow front velocity is evaluated for several fabric configurations.     

恒压下树脂在双尺度多孔介质中的流动特性

基于复合材料液态模塑(LCM)工艺过程中存在半饱和区域的实验现象以及对预制体双尺度效应的逐步认识, 一些学者提出用沉浸模型来研究双尺度多孔介质的不饱和流动。通过体积均匀化方法描述了双尺度多孔介质复合材料液态模塑工艺模型的特征, 得到含有沉浸项的双尺度多孔介质的质量守恒方程, 并采用有限元法对方程进行数值求解, 通过具体算例计算了考虑双尺度效应时恒压树脂注射下不同时段的压力分布状态, 得到树脂在填充过程中流动前沿半饱和区域从出现到消失的过程, 采用不同注射压力进行模拟并比较。结果表明, 与单尺度多孔介质模型不同, 双尺度多孔介质模型更能反映实际树脂填充过程中出现的半饱和区域现象。     

Modelling the effect of material properties and process parameters on tow impregnation in out-of-autoclave prepregs

Out-of-autoclave prepregs based on woven fabrics initially consist of dry tows and resin-rich areas. The tows allow air evacuation in the initial stages of processing and are subsequently infiltrated by surrounding matrix. The following study analyzes the relationship between material properties, process parameters and tow impregnation for three OOA prepregs. First, a representative model for tow impregnation is developed. Then, the model parameters are determined and the model predictions are correlated to impregnation data measured by X-ray microtomography. Finally, the model is used in a parametric study to investigate the effect of fibre architecture, cure cycle temperature and resin initial degree of cure on tow impregnation rate and to predict the possible occurrence of flow-induced micro-voids.     

双尺度纤维织物二维非饱和流动的数值模拟与实验

液体模塑成型工艺(LCM)中非饱和流动的填充模拟对于在虚拟空间中快速、高效地优化工艺参数具有重要意义。采用了一种模拟双尺度纤维织物在等温条件下非饱和流动的双尺度计算模型,通过引入沉浸函数求解宏观-微观流动控制方程组,同时考虑了在微观浸渍中毛细压力的影响,在有限元/控制体积算法中实现了对非饱和流动的数值模拟。随后对三向缝合纤维织物进行了二维径向填充实验,将实验结果与数值模拟的预测值对比。结果表明,该计算模型可以较精确地模拟双尺度纤维织物中的非饱和流动。在此计算模型的基础上,讨论了流体黏度、注射流量及纤维束孔隙率对非饱和填充浸润的影响。结果表明,不同流体黏度、注射流量及纤维束孔隙率对纤维织物填充过程中非饱和区域长度、入口压力曲线及填充时间影响不同。研究结果可以对合理预测纤维织物的浸润及树脂填充过程中入口压力提供指导。     

Modeling the impact of capillary pressure and air entrapment on fiber tow saturation during resin infusion in LCM

Traditionally, capillary effects have been neglected when modeling the filling stage of Liquid Composite Molding processes. This simplification is justified because the inlet resin pressures are much higher than the capillary pressure. This simplification is also acceptable when impregnating fabrics in which their fiber tows saturate at the same rate as the bulk preform. However, this assumption is questionable for fabrics that exhibit dual scale in which the fiber tows saturate at a much slower rate than the bulk preform. In such cases, the capillary pressure can influence the time to saturate a fiber tow significantly and impact the overall impregnation dynamics. Since the flow front velocity inside the fiber tows is significantly smaller than the flow around them, it is important to include the capillary pressure that may aid the saturation of the tow. In this paper, we modify our existing simulation that can predict the filling of the bulk preform and the saturation of the fiber tows to include the capillary forces at the fiber tow level. Important parameters are identified and grouped in non-dimensional form. A parametric study is conducted to examine the role of these dimensionless parameters on the overall tow saturation levels. The modeling is extended to include the effect of entrapped air inside the tows on the overall saturation of the preform. An experimental technique using the optical properties of vinyl ester and glass fiber was used to qualitatively validate the proposed model.     

RTM工艺中单向纤维排列中的缺陷迁移的数值模拟EI

Decreasing the amount of residual voids during the resin infiltration into fibrous porous media is an important aspect in manufacturing high performance composite materials.In order to better understand void transports and flow behaviors in filling process,which affects immediately the final void content,a finite-element scheme for transient simulations of the void migration in a transverse flow through the uniaxial micro-structured fibrous media is developed in this work.A volume-of-fluid (VOF) method has been incorporated in the Eulerian frame to capture the free surface of the resin flow.The implementation of periodic boundary condition to the vertical direction avoids unwanted wall effect.The void migration in a dual-scale fiber tow model was investigated.The voids are observed to be transported through the inter-tow region as well as entrapped into fiber tow.It is that the motion of void lagged behind macro flow front which implies that the adequate resin bleeding after mold filling is crucial to remove the entrapped air.     

RTM工艺中单向纤维排列中的缺陷迁移的数值模拟

Decreasing the amount of residual voids during the resin infiltration into fibrous porous media is an important aspect in manufacturing high performance composite materials.In order to better understand void transports and flow behaviors in filling process,which affects immediately the final void content,a finite-element scheme for transient simulations of the void migration in a transverse flow through the uniaxial micro-structured fibrous media is developed in this work.A volume-of-fluid (VOF) method has been incorporated in the Eulerian frame to capture the free surface of the resin flow.The implementation of periodic boundary condition to the vertical direction avoids unwanted wall effect.The void migration in a dual-scale fiber tow model was investigated.The voids are observed to be transported through the inter-tow region as well as entrapped into fiber tow.It is that the motion of void lagged behind macro flow front which implies that the adequate resin bleeding after mold filling is crucial to remove the entrapped air.     

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.     

Numerical prediction and experimental characterisation of meso-scale-voids in liquid composite moulding

Pressure gradients that drive the resin flow during liquid composite moulding (LCM) processes can be very low while manufacturing large composite parts. Capillary pressure becomes the predominant force for tow impregnation and thus meso-scale-voids can be generated, reducing the part quality. In contrast, micro-voids are created at high resin pressure gradients. In this work, a numerical method is presented to predict the creation of meso-scale-voids and their evolution. Experimental validation is conducted by measuring void content of produced composite parts with micro-computed tomography (μ-CT). Additionally, the void content as a function of the modified capillary number Ca^* is determined and the influence of the fibre volume content in the bundles on the meso-scale- and micro-void content is studied.     

Manufacturing characteristics of the continuous tow shearing method for manufacturing of variable angle tow composites

Automated fibre placement (AFP) is well-known as a cutting-edge technology for manufacturing variable angle tow (VAT) composites with tailored fibre paths. However, its process-induced defects prevent the wide application of VAT composite structures. As an alternative manufacturing method, the continuous tow shearing (CTS) technique, utilising the ability to shear dry tows, has been developed. It was shown that CTS could significantly reduce process-induced defects such as fibre wrinkling, resin rich areas and fibre discontinuities. In this paper, its manufacturing characteristics such as material characteristics, layup accuracy, and thickness variation are investigated experimentally.     

Improving the resin transfer moulding process for fabric-reinforced composites by modification of the fabric architecture

The use of resin transfer moulding (RTM) as an economic and efficient means of producing high-performance fibre-reinforced composites is critically limited by the permeability of the fabrics employed. Commercial fabrics are available where the architecture of the reinforcement is designed to cluster the fibres giving higher permeabilities than conventional fabrics. This has been shown to improve processing times, but there is evidence that such clustering is detrimental to the mechanical performance of the resulting composite material.

The objective of this work was to relate variations in permeability, and in the laminate mechanical properties, to differences in microstructure. A series of experimental carbon fibre fabrics woven to incorporate a novel flow enhancement concept (use of 3K tows in a 6K fabric) were used to manufacture plates by RTM in a transparent mould. The progress of the resin front was recorded to computer disc during injection, thus allowing the permeabilities of the fabrics to be calculated.

The manufactured plates were subsequently sectioned for mechanical testing (moduli and strengths in tension and compression) and automated image analysis. Relationships were sought between measured permeabilities, mechanical properties and microstructures using a Quantimet 570 automatic image analyser to determine fractal dimensions from polished sections. It has been shown that variations in the microstructures can be related to the permeability and mechanical property values obtained. Further the deterioration of mechanical properties for the novel fabrics with reduced fibre volume fractions is less than has been reported for fabrics with clustered flow-enhancing tows at constant fibre volume fraction.     

Characterization of preform permeability in the presence of race tracking

For realistic simulation of resin flow in a stationary fibrous porous preform during Liquid Composite Molding (LCM) processes, it is necessary to input accurate material data. Of great importance in simulating the filling stage of the LCM process is the preform permeability; a measure of the resistance the preform poses to the flowing fluid. One method to measure permeability values is by conducting one-dimensional flow experiments, and matching the flow behavior to known analytical models. The difficulty is the edge effects such as race tracking disrupt the flow and violate the one-dimensional flow assumption. The new approach outlined in this paper offers a methodology to obtain accurate bulk permeability values despite any race tracking that may be present along the edges of the mold containing isotropic fabrics. Further, a method of approximate equivalent isotropic scaling is explained to extend the use of this method to determine permeability of anisotropic materials with race tracking present. Both approaches are validated with computer simulations, and then utilized in laboratory experimentation. The values calculated from this approach compare well with permeability values obtained from one-dimensional permeability experiments without the presence of race tracking.     

Influence of fabric shear and flow direction on void formation during resin transfer molding

In resin transfer molding, void type defect is one of common process problems, it degenerates the mechanical performances of the final products seriously. Void content prediction has become a research hotspot in RTM, while the void formation when the flow direction and the tow direction are not identical or the fabric is sheared has not been studied to date. In this paper, based on the analysis of the resin flow velocities inside and outside fiber tows, a mathematical model to describe the formation of micro- and meso-scale-voids has been developed. Particular attention has been paid on the influence of flow direction and fabric shear on the impregnation of the unit cell, so their effects on the generation and size of voids have been obtained. Experimental validation has been conducted by measuring the formation and size of voids, a good agreement between the model prediction and experimental results has been found.     

液体模塑成型工艺二维径向非饱和流动数值模拟

通过引入沉浸函数建立了双尺度多孔介质非饱和流动模型,并采用有限元/控制体积法实现了恒压及恒流注射条件下液体模塑成型（LCM）工艺二维径向非饱和流动的数值模拟,得到了不同注射条件下纤维织物内的压力场分布及半饱和区域长度随时间的变化规律,并将双尺度非饱和理论结果与单尺度饱和理论结果进行对比。结果表明：非饱和流动过程中,半饱和区域内的压力和压力梯度明显下降;半饱和区域长度随时间逐渐增加随后保持稳定,当流动前沿到达出口后半饱和区域长度开始逐渐减小;当两个主方向渗透率不同时,沿主方向半饱和区域长度也不同,渗透率越大该方向的半饱和区域长度也越大,纤维织物完全浸润时间取决于较小的渗透率。研究结果对合理预测树脂填充过程中压力分布及纤维预制件的浸润具有指导意义。