Numerical simulation of injection/compression liquid composite molding. Part 2: preform compression

In the injection/compression liquid composite molding process (I/C-LCM), a liquid polymer resin is injected into a partially open mold, which contains a preform of reinforcing fibers. After some or all of the resin has been injected, the mold is closed, compressing the preform and causing additional resin flow. This paper addresses compression of the preform, with particular emphasis on modeling three-dimensional mold geometries and multi-layer preforms in which the layers have different mechanical responses. First, a new constitutive relation is developed to model the mechanical response of fiber mats during compression. We introduce a new form of nonlinear elasticity for transversely isotropic materials. A special case of this form is chosen that includes the compressive stress generated by changes in mat thickness, but suppresses all other responses. This avoids the need to model slip of the preform along the mold surface. Second, a finite element method, based on the principle of virtual displacement, is developed to solve for the deformation of the preform at any stage of mold closing. The formulation includes both geometric and material nonlinearities, and uses a full Newton–Raphson iteration in the solution. An open gap above the preform can be incorporated by treating the gap as a distinct material layer with a very small stiffness. Examples show that this approach successfully predicts compression in dry preforms for three-dimensional I/C-LCM molds.     

Isothermal flow simulation of liquid composite molding

This paper proposes a finite element/nodal volume procedure for the isothermal flow simulation of liquid composite molding processes. The formulation and the numerical implementation of the procedure are described. A scheme is introduced to prevent the procedure from possible locking in the flow calculation. The capability and the numerical accuracy of the procedure are investigated through a number of numerical examples.     

Modeling forces generated within rigid liquid composite molding tools. Part B: Numerical analysis

Liquid composite molding (LCM) processes generate forces on tooling due to internal resin pressure fields and the resistance to compaction offered by fiber reinforcements. In Part A of this work the authors have presented a detailed study on the evolution of total clamping force during resin transfer molding (RTM) and injection/compression molding (I/CM) cycles. The influence of the complex compaction response of two different reinforcements was demonstrated, important effects including stress relaxation, an apparent lubrication by the injected fluid, and permanent deformation. In the current paper attempts are made to model clamping force evolution utilizing elastic reinforcement compaction models. The predictions are shown to have significant qualitative errors if a single elastic model is applied, particularly if forces due to reinforcement compaction dominate those due to fluid pressure. By using a combination of elastic models significant qualitative and quantitative improvements were made to the predictions. It is concluded that careful characterization of both reinforcement permeability and compaction response are required for an accurate LCM tooling force analysis.     

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。     

Influence of meshing on the numerical simulation of liquid composite molding processes

Computer simulation has been an efficient and cost-effective tool for the Liquid Composite Molding (LCM) processes, including the RTM, VARTM, and resin infusion, compared to trial-and-error. The Control Volume Finite Element Method (CVFEM) has been the predominant method for simulation. Two critical issues of CVFEM are simulation accuracy and computational efficiency, and they are strongly dependent on meshing. In this paper, the influence of meshing on the simulation accuracy is investigated. Both uniform and non-uniform meshes are studied. The results show that for a radial flow, simulation accuracy can be significantly improved by using non-uniform meshes. A case study is conducted and it is shown that for a point injection, the computation time for mold filling simulation can be reduced by more than 99% while maintaining the same simulation accuracy.     

Modeling forces generated within rigid liquid composite molding tools. Part A: Experimental study

The term liquid composite molding (LCM) encompasses a growing list of processes, including resin transfer molding (RTM), injection/compression molding (I/CM), and resin infusion (a.k.a. VARTM). All LCM techniques involve compressive deformation of the fiber reinforcement prior to, and in many cases during mold filling. Forces acting on molds are primarily due to the requirement to compact the reinforcement, and pressure generated due to resin flow through these fibrous structures. An experimental study of the forces exerted on a mold during the RTM and I/CM processes is presented here. Two reinforcing materials have been considered, exhibiting significantly different resistance to compaction. The evolution of mold clamping force has been shown to be strongly influenced by the complex, non-elastic compaction behaviour of fiber reinforcements. The important effects include stress relaxation, an apparent lubrication by the injected fluid, and permanent deformation. Efforts to simulate the experiments will be presented in Part B of this study.     

复合材料液体模塑成型工艺中预成型体渗透率张量的数值预测

结合均匀化理论和计算流体动力学技术, 实现了对复合材料液体模塑工艺中预成型体渗透率张量的预测。首先, 采用均匀化理论分析了流体在多孔介质内的流动问题, 推导出广义达西定律, 证明以施加周期性边界条件的单胞为研究对象, 可以预测预成型体的渗透率张量, 并以单向纤维织物为例, 对该方法进行了验证。对于复杂结构的预成型体, 渗透率的预测分为两步, 首先分别确定预成型体中流道和纤维束的渗透率, 然后计算其整体宏观渗透率。对于二维平面织物, 该方法与其他预测方法及实验的结果吻合较好。本文还考察了单胞的微观结构对渗透率的影响, 微观结构相似的预成型体如果孔隙率相同, 但束间流道的结构不同, 其整体宏观渗透率也存在很大差别。      

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.     

Branch and bound search to optimize injection gate locations in liquid composite molding processes

In liquid composite molding (LCM) processes the resin is injected into a mold cavity containing pre-placed reinforcement fabrics through openings known as gates, and the air leaves the mold through openings called as vents. The gate and vent locations play a crucial role as to whether the resin covers all empty spaces between the fibers in the mold, which dictates the quality and the properties of the final product. Optimization methods are used to find the gate and vent locations that will create a favorable flow that will prevent dry spots. In this paper, branch and bound search is adapted to mold filling in LCM processes and is used to find the optimal injection gate location that fulfill two different objectives. First, to find the gate locations that will yield the shortest fill time. Second, to find the auxiliary gate locations that will counteract a disturbance during filling and minimize the size of the dry spot. In each case, three geometries have been studied. The results are compared with exhaustive search and genetic algorithms results to illustrate the efficiency and accuracy of branch and bound search method.     

Polyamide-6/vegetal fiber composite prepared by extrusion and injection molding

The interest for the use of vegetal fibers as polymers reinforcement has recently increased because of their unique environmental and technological advantages. This work evaluated the use of Curauá fibers in polyamide-6 composites aiming at glass fiber replacement. Fiber content of 20, 30 or 40 wt% and fiber lengths of 0.1 or 10 mm were studied. Fibers were treated with N₂ plasma or washed with NaOH solution, to improve their adhesion to PA-6. Samples with 20 wt% of short or long fibers, with or without pre-treatment, were compounded in two different co-rotating intermeshing twin-screw extruders. These samples were submitted to mechanical and thermal tests. In conclusion, non-dried raw materials improved fiber/matrix interfacial adhesion. Tensile and flexural properties of this composite are better than unfilled, but lower than glass fiber reinforced polyamide-6. However, its impact resistance and heat deflection temperature are similar to the glass fiber reinforced polyamide-6 and its lower density, enable it to replace this latter in specific non-critical applications.     

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.     

A numerical study of filling process through multilayer preforms in resin injection/compression molding

In resin injection/compression molding (RI/CM), a preform often comprises layers of different fiber reinforcements. Each fiber reinforcement has unique through thickness and in-plane permeabilities as well as compressibility, creating a heterogeneous porous medium in the mold cavity. In the present article, numerical simulation is utilized to investigate the filling process of RI/CM in such a heterogeneous porous medium. The filling stage is simulated in a full three-dimensional space by using control volume/finite element method and based upon an appropriate filling algorithm. The flow in the open gap which may be present in the mold cavity is modeled by Darcy’s law using an equivalent permeability. Numerical simulations of filling process for preforms containing two and three layers of different reinforcements in various stacking sequences are conducted with the aid of computer code developed in this study. Results show that the injection time as well as flow front progression depends on fiber types in the whole preform, fiber stacking sequence and open gap provided in the mold cavity. Simulated results also suggest that the presence of open gap at top of reinforcement can lead to both low injection time and uniform flow pattern.     

Numerical simulation and optimization of the injection blow molding of polypropylene bottles - a single stage process

Single stage injection blow molding process, without preform storage and reheat, could be run on a standard injection molding machine, with the aim of producing short series of specific hollow parts. The polypropylene bottles are blow molded right after being injected. This implies that the preform has to remain sufficiently malleable to be blown while being viscous enough to avoid being pierced during the blow molding stage. These constraints lead to a small processing window, and so the process takes place between the melting temperature and the crystallization temperature, where the polypropylene is in its molten state but cool enough to enhance its viscosity without crystallizing. This single stage process introduces temperature gradients, high stretch rate and high cooling rate. Melt rheometry tests were performed to characterize the polymer behavior in the temperature range of the process, as well as Differential Scanning Calorimetry. A viscous Cross model is used with the thermal dependence assumed by an Arrhenius law. The process is simulated through a finite element code (POLYFLOW) in the ANSYS Workbench framework. The geometry allows an axisymmetric approach. The transient simulation is run under anisothermal conditions and viscous heating is taken into account. Sensitivity studies are carried out and reveal the influence of process parameters such as the material behavior, the blowing pressure and the initial temperature field. Thickness measurements using image analysis are performed and the simulation results are compared to the experimental ones. The simulation shows broad agreements with the experimental results. An optimization loop is run to determine the optimal initial thickness repartition. Design points are defined along the preform and the optimization modifies the thickness at these locations.     

Numerical simulation of molding-defect formation during resin transfer molding

The present study investigated a numerical simulation of molding-defect formation during resin transfer molding using boundary element method and line dynamics. The proposed method enables to simulate small molding defects by increasing the node for required position during time evolution; thereby, the method computes high-resolution flow front without being affected by the initial mesh geometry. The method was applied to the radial injection RTM with single inlet, and it was confirmed by comparison with theoretical value based on Darcy’s law that the flow advancement was computed with high accuracy. In addition, the method was also applied to the flow advancement for inclusion problem with cylinder, and four-point injection problem. The simulated flow behavior, void formation, and shrinkage agreed with the results in references. Finally, the method was compared with experiments using two-point injection problem. The computed configuration of the flow front and weld line agreed well with the experimental results.     

A hybrid global–local approach for optimization of injection gate locations in liquid composite molding process simulations

The optimization of injection gate locations in liquid composite molding processes by trial and error based methods is time consuming and requires an elevated level of intuition, even when high fidelity physics-based numerical models are available. Optimization based on continuous sensitivity equations (CSE) and gradient search algorithms focused towards minimizing the mold infusion time gives a robust approach that will converge to local optima based on the initial solution. Optimization via genetic algorithms (GA) utilizes natural selection as a means of finding the optimal solution in the global domain; the computed solution is at best, close to the global optimum with further refinement still possible. In this paper, we present a hybrid global–local search approach that combines evolutionary GAs with gradient-based searches via the CSE. The hybrid approach provides a global search with the GA for a predetermined amount of time and is subsequently further refined with a gradient-based search via the CSE. In our hybrid method, we utilize the efficiency of gradient searches combined with the robustness of the GA. The resulting combination has been demonstrated to provide better and more physically correct results than either method alone. The hybrid method provides optimal solutions more quickly than GA alone and more robustly than CSE based searches alone. A resin infusion quality parameter that measures the deviation from a near uniform mold volume infusion rate is defined. The effectiveness of the hybrid method with a modified objective function that includes both the infusion time and the defined mold infusion quality parameter is demonstrated.     

基于化学流变学的复合材料液态模塑成型过程的灵敏度分析

为了探讨复合材料液态模塑成型（LCM）过程中充填时间和树脂流动前锋形状对材料参数及工艺参数的敏感程度,考虑树脂非稳态浸润过程中的边缘效应以及固化反应现象,引入灵敏度分析方法,推导了模腔内流体压力灵敏度和流体速度灵敏度等关键物理量参数之间所满足的数学关系,构建了充填时间灵敏度方程以及表征材料浸润缺陷形成可能性的树脂流动前锋形状函数及其灵敏度方程,并设计了各物理量的耦合求解方法及灵敏度分析的技术路线。在此基础上,自主开发了数值模拟软件,数值分析了关键材料和工艺参数对树脂流场发展的影响规律和程度。模拟结果表明,在恒压注射边界条件下,提高流体注射温度是提高生产效率最有效的方法,减少边缘区域渗透率则是最能改善树脂流动前锋形状以及充填浸润效果的途径。     

Permeability of natural fiber reinforcement for liquid composite molding processes

We investigate the influence of liquid type on the saturated permeability of natural fabrics in liquid composite molding processes. The permeability of flax woven fabric was characterized with two different liquids which have different viscosity, wettability, and sorption characteristics with flax fiber. From the experimental data, it was observed that the saturated permeability values were different for the liquid type. The fiber swell during the mold filling process and the corresponding change of fabric microstructure were assumed to be the main reason for this dependency of saturated permeability on the liquid type. The fiber swell due to the liquid sorption was characterized as a function of time, and the corresponding change of fiber diameter was investigated. The effective fiber volume fraction of wet natural fabric was defined in terms of fiber swelling ratio. The predictions by the classical Kozeny–Carman model and by the modified Kozeny–Carman model with two model constants were compared with the experimental data. It was shown that the modified Kozeny–Carman equation considering fiber swell could predict very well the saturated permeability of natural fabrics regardless of liquid type.     

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.