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.     

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.     

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.     

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.     

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.     

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.     

Guiding selection for reduced process development time in RTM

Liquid Composite Molding (LCM) regroups a number of manufacturing techniques of polymer composites based on the impregnation of dry fibrous reinforcements by a liquid resin. It involves several complex phenomena: fibre impregnation, resin gellification and cure, thermal and rheological variations, etc. The combination of such phenomena and the wide range of processing parameters often lead to non-optimum, sometimes inappropriate, processing setups. In this work, an approach is proposed to assist manufacturing specialists in reducing process development time and improving process robustness. A software interface was developed to enable users to define and quickly compare different processing scenarios. Using fuzzy logic inference and different levels of mathematical simplification, the proposed software is able to sketch the moldability diagram of the part and perform basic process optimizations. One original feature of the proposed approach consists of integrating into the optimization loop the feedback of process engineers which helps in correcting the numerical solution. An application example is conducted in order to demonstrate the capabilities of the approach for understanding process behaviour.     

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.     

A methodology for flow-front estimation in LCM processes based on pressure sensors

Liquid Composite Molding (LCM) processes offer nowadays considerable advantages for composite manufacturers; nevertheless, their robustness is still an open issue, since part quality is sensitive to slight material and process variations, mainly arising during preform impregnation. An accurate monitoring system is thus required for early identification of filling troubles and potentially adoption of control actions. This work proposes an approach for resin flow monitoring, based on a combination of a sensing system and numerical modeling, which can be easily implemented into a generic LCM process. Using pressure data provided by few sensors placed in strategic positions inside the mold cavity, the developed methodology enables reconstruction of flow-front patterns at any impregnation time, without simulation of cavity filling. The effectiveness of the methodology is demonstrated by two test cases, which validate the approach through comparison between real and estimated flow-front profiles. Potential and limitations of the method in presence of flow disturbances have been studied through several virtual experiments, defining the range of applicability and key issues for future development.     

A stochastic approach to model material variation determining tow impregnation in out-of-autoclave prepreg consolidation

Material variations are always present even though out-of-autoclave prepregs are machine-made. They strongly determine the consolidation and may eventually lead to voids within the final part, depending on applied process conditions. To capture any contingencies, stochastic differential equations are derived to describe various interacting phenomena in OoA consolidation. In a second step the probabilistic space is discretized using the Karhunen–Loève truncation and the Probabilistic Collocation method is applied in order to use deterministic solvers for flow and compaction problems. The initial degree of impregnation is represented by an Ornstein–Uhlenbeck process and calibrated with CT-images.     

The Sink Term to Different Kinds of Fibrous Mat During the Unsaturated Filling Process

The fibrous pre-form of resin transfer molding is a dual-scale porous medium with two distinct scales of pores, i.e., pores in intra- and inter-tow, which produce an unsaturated infiltration phenomenon during filling. A sink term representing the delayed flow rate from the inter-tow gap into the intra-tow one is introduced to establish governing equations. This study mainly analyzes the sink term by tow saturation during the microscopic flow. First, fiber-tow permeability is calculated by FLOTRAN of ANSYS, Second, periodic unit cells are built according to different structures, and the concrete expression of the sink term is indirectly obtained through the numerical simulation and date fitting of tow saturation under different pressure and viscosity conditions. Results indicate that: the FLOTRAN module can be used to calculate the permeability of fiber tow in two directions; Moreover, the filling time and infiltration process for diverse unit cells with the same volume fraction are different; under the same injection condition, different unit cells have different parameters for the sink term.     

A two-phase flow model to simulate mold filling and saturation in Resin Transfer Molding

This paper addresses the numerical simulation of void formation and transport during mold filling in Resin Transfer Molding (RTM). The saturation equation, based on a two-phase flow model resin/air, is coupled with Darcy’s law and mass conservation to simulate the unsaturated filling flow that takes place in a RTM mold when resin is injected through the fiber bed. These equations lead to a system composed of an advection–diffusion equation for saturation including capillary effects and an elliptic equation for pressure taking into account the effect of air residual saturation. The model introduces the relative permeability as a function of resin saturation. When capillary effects are omitted, the hyperbolic nature of the saturation equation and its strong coupling with Darcy equation through relative permeability represent a challenging numerical issue. The combination of the constitutive physical laws relating permeability to saturation with the coupled system of the pressure and saturation equations allows predicting the saturation profiles. The model was validated by comparison with experimental data obtained for a fiberglass reinforcement injected in a RTM mold at constant flow rate. The saturation measured as a function of time during the resin impregnation of the fiber bed compared very well with numerical predictions.     

Numerical prediction of saturation in dual scale fibrous reinforcements during Liquid Composite Molding

This paper presents a fractional flow model based on two-phase flow, resin and air, through a porous medium to simulate numerically Liquid Composites Molding (LCM) processes. It allows predicting the formation, transport and compression of voids in the modeling of LCM. The equations are derived by combining Darcy’s law and mass conservation for each phase (resin/air). In the model, the relative permeability and capillary pressure depend on saturation. The resin is incompressible and the air slightly compressible. Introducing some simplifications, the fractional flow model consists of a saturation equation coupled with a pressure/velocity equation including the effects of air solubility and compressibility. The introduction of air compressibility in the pressure equation allows for the numerical prediction of the experimental behavior at low constant resin injection flow rate. A good agreement was obtained between the numerical prediction of saturation in a glass fiber reinforcement and the experimental observations during the filling of a test mold by Resin Transfer Molding (RTM).     

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.     

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.     

Transient gas flow technique for inspection of fiber preforms in resin transfer molding

A transient gas flow method was developed to determine the quality of fibrous preforms in resin transfer molding (RTM) prior to resin injection. The method aims at detecting defects resulting from preform misplacement in the mold, accidental inclusions, preform density variations, race tracking, shearing, etc. Unlike the previously developed method based on steady-state gas flow, the new method allows for the acquisition of continuous time-varying pressure data from multiple ports during a single test. The validity of the method was confirmed by one-dimensional flow experiments.     

Effect of room-temperature out-time on tow impregnation in an out-of-autoclave prepreg

Tow impregnation as a function of material out-time was investigated for an out-of-autoclave carbon fiber–epoxy prepreg. Prepreg was aged at ambient temperature for 56 days. Every 7 days, laminates were laid up and cured using vacuum bag only processing. Void content was calculated through image analysis of polished sections. Experimental results were used to validate an analytical model for tow impregnation. Model predictions were based on flow kinetics during processing conditions, taking into account increasing degree of cure and evolution of resin viscosity as a function of ambient aging time. The study found that no significant tow porosity occurred within the material’s stated out-life, that tow porosity increased once this out-life was exceeded and eventually stabilized due to the room-temperature vitrification of the resin. The model’s predicted trends were consistent with experimental results, suggesting that an increase in resin viscosity is indeed the main cause of out-time induced tow porosity and providing a means of predicting laminate quality as a function of room temperature aging time.     

基于VOF/PLIC界面追踪方法的RTM工艺充模过程数值模拟

针对基于Darcy定律的树脂传递模塑(RTM)工艺的充模过程数值模拟的局限性,将纤维预制体内的充填流动作为两相流(树脂相和空气相)处理,在动量方程中考虑了惯性项和粘性项,采用有限体积方法(FVM)离散控制方程,并与VOF/PLIC界面追踪方法相结合,发展了求解树脂在纤维预制体内非稳态流动问题的数值模拟方法.在此基础上开发了RTM工艺的充模过程数值模拟程序,其算例的数值模拟结果与解析解或实验结果吻合良好,验证了此数值模拟方法的有效性和可靠性.