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.     

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。     

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。     

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.     

Particle filtration and distribution during the liquid composite molding process for manufacturing particles containing composite materials

The effects of major process parameters on particle filtration and distribution were investigated by using newly developed microscopic methodology using an electron probe micro-analyzer and numerical simulation. The mapping results indicated that well-dispersed particles were distributed uniformly in the inter-tow and intra-tow regions. Agglomerates were likely to be filtered at the boundary or inside of the fiber bundle. The results of quantitative analyses showed particle concentrations in the inter-tow region to be uniform throughout the composite part, whereas the intra-tow concentrations varied according to particle size and fiber orientation. The poor dispersion state of the CNT-Ag particles resulted in quite irregular distributions. A high volume fraction of the fiber preform resulted in a lower particle concentration inside the fiber tow. Numerical analysis of the filtration of large clusters of particles indicated that filtration occurred in the initial stage of the injection process at the tow boundaries.     

树脂传递模塑工艺中的非饱和流动过程模拟与实验研究

针对编织类纤维增强体的纤维束之间与纤维束内孔隙的双尺度特点,建立了平纹织物的细观结构模型,并推导了汇函数的数学表达式。建立了局部细观流动特征的非饱和流动控制方程,利用有限元/控制体积方法求解,得到了局部饱和度分布。与实验进行比较,吻合较好。      

Multiscale analysis of laminated plates with integrated piezoelectric fiber composite actuators

This study is concerned with the detailed analysis of fiber-reinforced composite plates with integrated piezoceramic fiber composite actuators. A multiscale framework based on the asymptotic expansion homogenization method is used to couple the microscale and macroscale field variables. The microscale fluctuations in the mechanical displacement and electric potential are related to the macroscale deformation and electric fields through 36 distinct characteristic functions. The local mechanical and charge equilibrium equations yield a system of partial differential equations for the characteristic functions that are solved using the finite element method. The homogenized electroelastic properties of a representative material element are computed using the characteristic functions and the material properties of the fiber and matrix. The three-dimensional macroscopic equilibrium equations for a laminated piezoelectric plate are solved analytically using the Eshelby-Stroh formalism. The formulation admits different boundary conditions at the edges and is applicable to thick and thin laminated plates. The microscale stresses and electric displacement in the fibers and matrix are computed from the macroscale fields through interscale transfer operators. The multiscale analysis procedure is illustrated using two model problems. In the first model problem, a simply-supported sandwich plate consisting of a piezoceramic fiber composite shear actuator embedded between two graphite/polymer layers is studied. The second model problem concerns a cantilever graphite/polymer substrate with segmented piezoceramic fiber composite extension actuators attached to its top and bottom surfaces. Results are presented for the homogenized material properties, macroscale deformation, macroscale average stresses and microscale stress distributions.     

定型剂对经编织物液态成型复合材料工艺性及其力学性能的影响

研究了双马来酰亚胺树脂定型剂含量对0°/90°双轴向经编织物(Non-crimp fabric,NCF)定型效果、液态成型工艺性、复合材料力学性能的影响。采用厚度回弹、C型回弹的方法表征定型效果;采用厚度压缩与偏轴拉伸实验表征带定型剂织物成型工艺性;并采用弯曲实验与层间剪切实验表征复合材料力学性能。实验结果表明定型剂的添加显著提高了NCF织物的预定型效果;经定型剂处理后NCF织物的面内剪切模量有了较大提高,抗剪切变形能力增强;添加定型剂对0°/90°双轴向NCF织物复合材料的力学性能影响不大,但在改善其工艺性的同时并不会降低其复合材料的力学性能。     

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。     

A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks

A two-scale model is developed for fluid flow in a deforming, unsaturated and progressively fracturing porous medium. At the microscale, the flow in the cohesive crack is modelled using Darcy’s relation for fluid flow in a porous medium, taking into account changes in the permeability due to the progressive damage evolution inside the cohesive zone. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for an unsaturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two-scale approach and integrated over time. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach. The calculations indicate that the evolving cohesive cracks can have a significant influence on the fluid flow and vice versa.     

Effective permeabilities of multilayer fabric preforms in liquid composite moulding

A homogenisation method was developed to predict effective permeabilities of multilayer fabric preforms by considering interlayer continuity and coupling between in-layer flow and trans-layer flow. A simplified approach was addressed first, from which the common approaches of arithmetic mean formation and harmonic mean formation can be deduced to define the effective permeability by neglecting coupling between in-layer flow and trans-layer flow. For multilayer preforms in liquid composite moulding, the permeability predicted by such an approach, however, is generally different from the actual one because of neglecting effects of micro-structure between layers and synchronisation between in-layer flow and interlayer flow. A conceptual model for interlayer flow, based on the hydraulic radius theory, was then proposed to quantitatively characterise the effect of interlayer micro-structure on the effective permeability of multilayer fabric preforms. The predictions show good agreement with experimental results available in literature.     

Resin flow modeling in compliant porous media: an efficient approach for liquid composite molding

In Liquid Composite Molding (LCM) processes such as Resin Transfer Molding (RTM) and Vacuum Assisted Resin Transfer Molding (VARTM), complete saturation of reinforcement with resin during the injection step is necessary. In RTM, reinforcement experiences no deformation during infusion but for other methods reinforcement thickness changes during the injection. To model resin flow in compliant media, RTM flow simulation software is routinely used. It has been successful in predicting flow patterns if appropriate “effective” permeability is used. The proper approach requires new implementation that couples the deformation and pressure field which is computationally more demanding. Our work describes a computationally efficient methodology to add corrections into RTM simulation environment to account for deformation. This approach is verified with known solutions and experimental validation. The simulation is applied to a complex geometry which demonstrates better computational performance and confirms that the “effective” permeability may be used to model flow in complex geometries.     

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.     

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.     

Numerical simulation of the variation of fiber orientation distribution during flow molding of Ultra High Performance Cementitious Composites (UHPCC)

In this paper, the variation of the fiber orientation distribution along the flow of fresh UHPCC was studied. In order to describe the rotational motion of a single fiber, Jeffery’s equation was adopted, in which the interaction among fibers is neglected. Two cases of flow patterns were considered: shear flow and radial flow. Starting with a three-dimensional random distribution of fibers, the fiber orientation distribution along the flow distance was simulated. These results reveal that fibers gradually become more parallel (in the case of shear flow) and perpendicular (in the case of radial flow) to the flow direction as the flow distance increases. This approach will be useful to predict flow-dependent tensile behavior considering the change of fiber orientation distribution.     

Mechanical properties of composite structures fabricated with the vacuum induced preform relaxation process

A new technique called vacuum induced preform relaxation (VIPR) can be used to improve the processing of composite parts manufactured using vacuum resin infusion methods. The VIPR process is a method for manipulating and guiding the resin filling pattern during a vacuum assisted resin transfer molding (VARTM) manufacturing process with a relatively small external vacuum chamber. This VIPR chamber can be sealed against the flexible molding surface of a VARTM mold and used to create vacuum above the preform. This causes the compressive forces compacting the fabric to decrease allowing the resin to flow faster in the effected region under the chamber. Thus the chamber can influence the resin flow pattern as well as avoid the formation of voids due to merging flow fronts. When the regulated vacuum in the chamber is applied it temporarily decreases the fiber volume fraction of the preform. It is important to investigate if this relaxation has a permanent adverse effect on the mechanical properties of the composite. The results of these tests strongly suggest that the use of the VIPR process does not compromise the mechanical properties of composite structures.     

Effect of microwave irradiation on carbon fiber/epoxy resin composite fabricated by vacuum assisted resin transfer molding

The effects of microwave irradiation for resin-curing of carbon fiber/epoxy resin composite (CFRTS), which was fabricated by vacuum-assisted resin transfer molding (VARTM) method, were investigated at 2.45 GHz frequency. The mechanical properties of CFRTS cured by microwave irradiation for 20 min at 120 °C were similar as compared to the conventional oven for 300 min at 120 °C. Moreover, the CFRTS irradiated by microwave had better adherence property between fiber and resin as compared to conventional oven at same resin-curing time. From the relation between resin-curing and mechanical property, it was found that the curing rate of microwave-irradiated CFRTS was 15 times faster as compared to conventional heating. Furthermore, the activation energies for resin-curing reaction on conventional- and microwave-cured CFRTS were estimated to be 2.7 and 1.3 × 10⁴ J/mol, respectively. The resin-curing reaction in CFRTS prepared by VARTM method was significantly promoted by microwave irradiation at short time.     

Effect of rapid curing process on the properties of carbon fiber/epoxy composite fabricated using vacuum assisted resin infusion molding

Long processing cycle makes vacuum assisted resin infusion molding (VARIM) only suitable for low and medium volumes of production, and shortening of curing time is critical to improving the processing efficiency of automotive composite parts. In this paper, unidirectional carbon fiber reinforced composite laminates were fabricated by VARIM. Three different processes (namely quick, quick-post and preheating) were employed, in which a kind of rapid curing epoxy resin is used. The preheating of mold and fiber was conducted to shorten the filling time compared with that of quick process. Quick-post process with a post cure stage was investigated to verify the composite properties fabricated by quick process. The cycle time was 16 min for preheating process, about 30% shorter than that of quick process, simultaneously, flexural strength and interlaminar shear strength (ILSS) were respectively improved by 29% and 7% compared with those of quick process. The non-uniformity of mechanical properties at different positions along resin flow direction under preheating process was found, but the processing quality of composite was good. The preheating process is confirmed to be suitable for the improvement of processing efficiency of VARIM with good mechanical properties. In addition, the composite fabricated by quick-post process has better mechanical properties, which is attributed to the alleviation of residual stress during post curing process.     

Use of Centroidal Voronoi Diagram to find optimal gate locations to minimize mold filling time in resin transfer molding

In Resin Transfer Molding (RTM) processes, liquid resin is injected into a dry reinforcement structure to create a composite part within given time limits. To reduce the fill time, resin may be injected into the mold through multiple gates. The minimum number of gates and their locations needs to be determined. To reduce the number of scenarios to be simulated, an iterative method is implemented for multiple-gate injection optimization. The inlet nodes on the mesh surface are used to generate a Voronoi Diagram of the mold geometry. Then the optimal Centroidal Voronoi Diagram (CVD) of the mold surface is searched iteratively. It is shown that the generation points associated with the optimal CVD correspond with the gate locations that yield the shortest fill time. The results are compared with exhaustive search and genetic algorithms results to illustrate the efficiency and accuracy of CVD method.