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.     

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.     

Three-dimensional reconstruction of resin flow using capacitance sensor data assimilation during a liquid composite molding process: A numerical study

Liquid composite molding (LCM) is a method to manufacture fiber-reinforced composites, where dry fabric reinforcement is impregnated with a resin in a molding apparatus. However, the inherent process variability changes resin flow patterns during mold filling, which in turn may cause void formation. We propose a method to reconstruct three-dimensional resin flow in LCM, without embedding sensors into the composite structure. Capacitance measured from pairs of electrodes on molding tools and the stochastic simulation of resin flow during an LCM process are integrated by a sequential data assimilation method based on the ensemble Kalman filter; then, three-dimensional resin flow and permeability distribution are estimated simultaneously. The applicability of this method is investigated by numerical experiments, characterized by different spatial distributions of permeability. We confirmed that changes in resin flow caused by spatial permeability variations could be captured and the spatial distribution of permeability could be estimated by the proposed method.     

Coupling filtration and flow during liquid composite molding: Experimental investigation and simulation

Molding composites constituted of fiber reinforcements, resin and fillers is of prime interest for many transportation applications. Dealing with the flow of particle-filled resin in a fibrous network raises the issue of particle retention and viscosity increase. The present study aims at simulating such molding through an efficient coupling between a filtration model, that has been previously described, and a flow model (Darcy’s law). First, filling experiments are realized so as to separate cases: cake filtration, retention and no retention for two types of single-scale porous materials (polyester felt and glass fiber mat) injected with a resin filled with micro-beads. Then results of filler content, viscosity, permeability, pressure, retention profiles are simulated from the coupling between filtration and flow. Experimental data of filler profiles in the final parts, resin flow front evolution and injection times are compared with predictions obtained from the simulation.     

In-plane permeability characterization of a unidirectional flax/paper reinforcement for liquid composite molding processes

Principal in-plane permeabilities of a unidirectional flax/paper reinforcement are characterized in terms of reinforcement material and manufacturing parameters at a constant fiber volume fraction (V_f). ANOVA result shows that surface density of the unidirectional flax layer is the most important parameter on the mean and variance of the K₁ permeability. On the other hand all four studied parameters are concluded to affect the K₂ permeability. The K₁ permeability is found close to that of a twill weave flax fiber fabric reported in the literature and only one order of magnitude lower than a plain weave glass fiber fabric. Impregnation of the reinforcement with epoxy resin shows that a large area of the molded plaques was dominated by capillary forces during resin injection. This means capillary number and subsequently the resin injection velocity should be optimized for reducing void content in the final composite.     

Simultaneous gate and vent location optimization in liquid composite molding processes

In liquid composite molding processes the resin is injected into the mold cavity, which contains pre-placed reinforcement fabrics, through openings known as gates while the displaced air leaves the mold through openings called as vents. Gate and vent locations determine process outputs such as fill time, pressure requirements and whether the fabrics will be saturated entirely, a requirement for the success of the mold filling operation. Disturbances such as racetracking, in which the resin flows faster along the edges of the mold, further complicate the gate and vent selection process. In this study, a cascaded optimization algorithm, which is created by integration of branch and bound search and map-based exhaustive search, is proposed for simultaneous gate and vent location optimization in the presence of racetracking. Three case studies are presented to demonstrate usefulness of this methodology and the results are validated in a Virtual Manufacturing Environment.     

Intelligent model-based control of preform permeation in liquid composite molding processes, with online optimization

Manufacturing of quality products via liquid molding processes such as Resin Transfer Molding (RTM), calls for a precise control of resin progression through fibrous preforms during mold fill. Lack of an effective process control leads to formation of dry spots and voids that are detrimental to product quality. This study presents the use of physics-based process simulations in real-time, towards a generalized process control. The implementation of process simulations for on-line model-predictive control requires that the simulation time scales be less than the time scales of the process. An artificial neural network trained using data from numerical process models is used to provide rapid, real-time process simulations for the model-based control. A simulated annealing algorithm, working interactively with the neural network process model, is used to derive optimal control decisions rapidly and on-the-fly. The controller performance is systematically demonstrated for several processing scenarios.     

Dynamic saturation curve measurement for resin flow in glass fibre reinforcement

A methodology is presented to determine the saturation curve of a resin/glass fabric system, during infiltration in a transparent mould under constant flow rate. Video acquisitions are transformed by image analysis into saturation level versus position and time, and coupled to inlet pressure measurements. A numerical multiphase flow model is then used to simulate the infiltration for various combinations of drainage curve parameters. The numerical parameters to describe the saturation and relative permeability are determined by response surface optimization. The drainage curve and relative permeability equations determined at one time are shown to adequately describe the entire injection process, and to be flow-rate dependent.     

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.     

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.     

A numerical study of the influence from architecture on the permeability of 3D-woven fibre reinforcement

Various modelling aspects of the permeability of three-dimensional (3D) woven textile preforms are studied using computational fluid dynamics (CFD). The models are built using a recently developed technique able to generate close to authentic representations of 3D textile arrangements. One objective of the study is to investigate how parameters such as the tow architecture and the level of detail in the CFD models influence the results. A second objective is to investigate how the inter and intra-tow porosity affect the permeability. They are varied in a way that somewhat resembles how they would change during compaction, although compaction as such is not modelled. It is concluded that the intra-tow porosity has little effect on the overall permeability of a 3D-woven preform. Detailed modelling of local variation of the intra-tow porosity is thus redundant, which is also demonstrated. The inter-tow porosity, on the other hand, has a prominent influence on the overall permeability. The overall permeability is inherently anisotropic but when the inter-tow porosity is increased the permeability does not increase uniformly but becomes more isotropic. Good agreement is obtained between the numerical simulations and experiments performed in a parallel study.     

A methodology to reduce variability during vacuum infusion with optimized design of distribution media

Seemann Composites Resin Infusion Molding Process (SCRIMP) is a widely used version of Vacuum Assisted Resin Transfer Molding (VARTM) in which a highly permeable layer (distribution media) is placed on top of the dry preform to distribute the resin with very low flow resistance to reduce the filling and hence the manufacturing time. The flow patterns during filling may vary from part to part due to the variability associated with the material, part geometry, and layup of the assembly, which may result in race-tracking channels. The process is considered as reliable and robust only if the resin completely saturates the preform despite changing filling patterns caused by flow disturbances.The resin flow pattern can be manipulated with a tailored distribution media layout as it does impact the flow patterns significantly. The continuous distribution media layout over the entire part surface works well for very simple geometries with no to little potential for race-tracking along the edges. In this study we address complex cases, which require placement of an insert within the assembly, which will introduce race-tracking along its edges, and hence uniform placement of distribution media over the entire top surface will fail to yield a void free part. We introduce a methodology using a predictive tool to design an optimal shape of distribution media, which accounts for the flow variability introduced due to race-tracking along the edges of the inserts. This iterative approach quickly converges to provide the placement of distribution media on selective areas of the preform surface that ensures complete filling of the preform despite the variability. This approach has been validated with an experimental example and will help mitigate risk involved in manufacturing complex composites components with Liquid Molding.     

Modelling flow and filtration in liquid composite moulding of nanoparticle loaded thermosets

This paper presents analytical and numerical models of liquid moulding of hybrid composites. An 1-D analytical solution of Darcy’s problem, accompanied by nanoparticle filtration kinetics and conservation, has been developed. A non-linear finite difference model incorporating variations in permeability, porosity and viscosity as a function of local nanoparticle loading was formulated. Comparison of the two models allowed verification of their validity, whilst a mesh sensitivity study demonstrated the convergence of the numerical scheme. The limits of validity of the analytical solution were established over a range of infiltration lengths and filtration rates for different nanoparticle loadings. The analytical model provides an accurate and efficient approximation of through thickness infusion of hybrid composites, whereas use of the numerical scheme is necessary for accurate simulation of in-plane filling processes. The models developed here can serve as the basis of process design/optimisation for the production of hybrid composites with controlled distribution of nano-reinforcement.     

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。     

The impact of air evacuation on the impregnation time of Out-of-Autoclave prepregs

Most Out-of-Autoclave prepregs (OoA) are only partially impregnated with resin. Their impregnation completes during the cure cycle, solely driven by the difference between atmospheric and vacuum pressure. Increased part length leads to an impregnation time gradient caused by the transient air flow inside the fibrous medium. In this work, a novel numerical approach capable of predicting the local impregnation time of a fibrous domain with resin, at isothermal conditions, under the influence of transient air flow, is proposed (delayed air evacuation). Sensitivity studies prove the robustness of the numerical scheme, for a large range of flow time-scales. The same approach is used to predict the local impregnation time of a commercial OoA prepreg tow, for a wide range of part lengths. It is demonstrated that for manufacturing long parts OoA, accurately capturing the influence of the air pressure on the local impregnation state of the tow, is important for quantifying the risk for residual tow porosity.     

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.     

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.     

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.     

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.     

Dynamic saturation curve measurement in liquid composite molding by heat transfer analysis

In Liquid Composite Molding (LCM) processes the saturation of the reinforcement by the resin may induce the creation of porosity in the preform affecting the final properties of the composite. The purpose of this work concerns the development of an experimental protocol and the associated modeling to identify the dynamic saturation curve during filling by taking advantage of sharp contrasts of thermal properties existing between dry and fully-saturated reinforcement. To identify saturation, several injections were performed with a laboratory RTM mold for which thermal design allows accurate control of heat transfer. Several heat flux sensors were used to identify the saturation curve. Sensitivity analysis proves the feasibility of the method. The results are compared with a conductometric method with good agreement. Evolution of residual voids identified for several flow rates are also consistent with those expected according to the capillary number.