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.     

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。     

注射条件对LCM工艺非饱和流动特性影响

双尺度多孔纤维预制体填充过程中延迟浸润的非饱和流动现象,对基于树脂流过区域为完全饱和区域的充模理论及模拟方法提出了挑战。通过控制体/有限单元（CV/FE）法结合沉浸函数实现了液体模塑成型工艺（LCM）中非饱和填充浸润的数值模拟,并对比了恒压下的实验结果,验证了其可靠性。分析讨论了注射口压力、流量和液体黏度对双尺度多孔纤维织物非饱和填充浸润特性的影响。结果表明:在允许误差内,该数值模拟结果可靠,可用于分析讨论各因素对双尺度多孔织物非饱和流动特性的影响;填充浸润过程中,纤维织物内部非饱和区域长度并非保持不变,而是随着填充浸润的进行经历了4个变化过程;不同注射条件下,压力、流量及黏度对非饱和流动特性影响不同。研究结果对合理控制注射条件及流体特性实现双尺度多孔纤维预制件的完全浸润具有指导意义。      

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。     

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。     

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 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.     

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.     

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.     

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.     

Variations in unsaturated flow with flow direction in resin transfer molding: An experimental investigation

The dual-scale nature of fiber preforms due to the presence of large continuous gaps between fiber tows gives rise to the unsaturated flow in resin transfer molding (RTM) process which is characterized by a droop in the injection pressure history due to the delayed absorption of fiber tows (the ‘sink’ effect). In this study, we experimentally investigate the effect of change in flow direction on the unsaturated flow in three anisotropic dual-scale fiber mats. A series of 1-D mold-filling experiments involving a constant flow rate were conducted for a unidirectional woven fiber-mat, a biaxial stitched mat, and a triaxial stitched fiber-mat along with a reference single-scale random mat. In the case of the unidirectional mats, the droop in the inlet-pressure history, signifying the strength of the sink effect, is found to be strongest for flow along the micro-channels aligned with fiber tows. The droop, and hence the sink effect, is observed to weaken progressively for flow-directions at 45° and 90° to this principal direction. In the case of the biaxial and triaxial mats, the situation is more complex due to the multi-layer construction of such mats: maximum droop is found when mats are oriented at a 45° angle with respect to the fiber-mat coordinate, and it weakens in the 0° and 90° directions. The unsaturated flow effect is also quantified by measuring percentage deviation in the area under the experimental curve from that of the predicted curve. A clear correlation between the droop (through the percentage deviation) and the permeability along a flow direction in the unidirectional mats is observable, though such a relationship eludes the triaxial mat. The effect of unsaturated flow on liquid-front progress during the 1-D experiment was also studied. In contrast to the reference single-scale random mat where the observed front progress closely follow the prediction based on the single-scale physics, a small difference was observed between the observed and predicted front progress for the three dual-scale mats considered. However the difference was too small to yield any significant correlation with the flow direction.     

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.     

真空压力下树脂沿织物铺层厚度渗透速率

为了考察树脂膜熔渗(RFI)工艺过程中树脂在高温条件下沿织物铺层厚度方向的不饱和渗透特性, 应用自行设计的测试系统, 考察了液体沿织物铺层厚度方向流动前锋的影响因素, 测试并分析了液体沿玻璃纤维铺层厚度方向渗透速率的主要影响因素及其变化规律。结果表明, 液体沿纤维织物厚度方向流动为宏观上的一维流动。 真空压力增大、 树脂温度升高、 纤维体积分数减小, 均可使液体的渗透速率加快。另外, 对比发现, 70℃ E-51 环氧树脂沿玻璃纤维铺层厚度方向的渗透特性与室温下硅油的渗透特性基本相当。      

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.     

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.     

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.     

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.     

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.     

Flow modeling of the VARTM process including progressive saturation effects

Modeling of vacuum based liquid composite molding methods (e.g., VARTM) relies on good understanding of closely coupled phenomena. The resin flow depends on the preform permeability, which in turn depends on the local fluid pressure; the preform compaction behavior, and the membrane stresses in the vacuum bag. It has also been shown that for many preforms there is a significant unsaturated region behind the flow front, and that the flow in this region affects the overall flow behavior of the process. Studies of preform compaction have shown that the preform stiffness, as well as being non-linear and exhibiting significant hysteresis, is dependant on the fluid saturation. For this reason most researchers model the preform compaction based on the pressure-compaction behavior of saturated preforms during unloading. This assumption leads to an effective discontinuity in preform thickness at the flow front, which is not observed in actual experiments. In this paper an improved compaction model incorporating the saturation dependence of the compaction pressure in the partially saturated region, is used in a one-dimensional model of the VARTM process. The model gives physically more realistic results for the thickness in the flow front region, and an improved model for the consolidation of the preform at the end of infusion.