Determining the 3D permeability of fibrous media using the Newton method

This work explores the reliability and sensitivity of using the Newton method to determine the elements of a fiber mat's permeability tensor. The goal of this work is to determine the extent to which experimental errors affect the numerical results and to provide general guidelines on which types of fiber materials are appropriate for this method. The sensitivity analysis reveals that employing the Newton method is a rather robust approach, applicable to a wide range of materials. The sensitivity analysis also reveals robustness with regard to experimental error as well.     

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).     

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.     

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.     

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.     

Longitudinal permeability determination of dual-scale fibrous materials

In this work, the longitudinal permeability of squarely packed dual-scale fiber preforms is studied theoretically. These fiber preforms are composed of aligned porous tows and the tows are tightly packed. The effective permeability is calculated as a parallel-like network of intra-tow permeability and inter-tow permeability, which are quantified by Darcy’s law and the inscribed radius between tows, respectively. The jump velocity at the interface between inter-tow fluids and porous tows is considered, as derived by substituting Beavers and Joseph’s correlation into Brinkman’s equation. We further examine the effects of intra-tow permeability on the effective permeability of the fibrous system with three interface conditions: (1) interface velocity = 0, (2) interface velocity = mean intra-tow velocity, and (3) interface velocity = jump velocity. The jump-velocity-based model is found to be closest to numerical data. The influence of the fiber volume fraction of tows on the effective permeability is also analyzed.     

An analytical model for the longitudinal permeability of aligned fibrous media

This paper presents an analytical series solution of the longitudinal fluid flow in porous media consisting of aligned rigid fibers, which, in turn, is used to establish a relationship for the longitudinal permeability as a function of the fiber packing geometry, fiber volume fraction and the fiber radius. The analytical series solution is developed for rectangular and staggered packing arrangements of the fibers using the boundary collocation method where the constants in the series solution are solved for numerically. As the number of boundary collocation points is increased, the analytical solution is shown to converge with a finite element solution of the identical flow situation for all fiber volume fractions and packing arrangements. In addition, the permeability results are presented in a dimensionless form as a function of the fiber volume fraction and fiber packing arrangement for a general applicability and easy use of the results for predicting the longitudinal permeability of fiber tows consisting of aligned rigid fibers.     

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.     

“Equivalent” permeability and flow in compliant porous media

Resin flow modeling for liquid composite molding processes is generally based on assumptions of rigid porous media. This is invalid for process variations utilizing compliant mold. Yet the models built on rigid porous media assumption are used with some success in analyzing such infusions.Previous work showed that for certain porous media the one dimensional flow patterns are similar to those in rigid porous media and the deformation effects can be included in a scaling factor for permeability.This note analyzes the one-dimensional linear and radial flows in porous media with generic constitutive relations between resin pressure, thickness and permeability. It shows that as long as the deformation remains moderate, the effect of deforming porous medium may be incorporated in a single scaling factor for material permeability. This scaling factor depends on material and applied injection pressure, but does not change with time, flow-front position or type of infusion (linear or radial).     

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.     

Characterization of preform permeability in the presence of race tracking

For realistic simulation of resin flow in a stationary fibrous porous preform during Liquid Composite Molding (LCM) processes, it is necessary to input accurate material data. Of great importance in simulating the filling stage of the LCM process is the preform permeability; a measure of the resistance the preform poses to the flowing fluid. One method to measure permeability values is by conducting one-dimensional flow experiments, and matching the flow behavior to known analytical models. The difficulty is the edge effects such as race tracking disrupt the flow and violate the one-dimensional flow assumption. The new approach outlined in this paper offers a methodology to obtain accurate bulk permeability values despite any race tracking that may be present along the edges of the mold containing isotropic fabrics. Further, a method of approximate equivalent isotropic scaling is explained to extend the use of this method to determine permeability of anisotropic materials with race tracking present. Both approaches are validated with computer simulations, and then utilized in laboratory experimentation. The values calculated from this approach compare well with permeability values obtained from one-dimensional permeability experiments without the presence of race tracking.     

Study of nesting induced scatter of permeability values in layered reinforcement fabrics

Time consumption is the major drawback of many existing set-ups for permeability measurement. This drawback has prevented many researchers from studying the statistical distribution of experimentally obtained permeability values. To overcome this problem—while maintaining the necessary accuracy—an automated central injection rig for permeability identification called ‘PIERS set-up’ (permeability identification using electrical resistance sensors) was developed. The PIERS set-up was used to characterize two typical glass fiber reinforcements. The test results demonstrated the presence of large scatter in the identified permeability values and hence the necessity to consider a statistical distribution of permeability values. The existence of a permeability distribution implies that a small number of measurements will not be sufficient to fully characterize the material. This paper discusses the necessary number of measurements to adequately characterize the statistical distribution and investigates the origins of the observed scatter. The paper also shows that the nesting of layers during stacking and mold closing is a major source of the observed variations in permeability values.     

Numerical simulation of metal matrix composites and polymer matrix composites processing by infiltration: a review

The injection of a liquid metal through a fibrous preform is one of the techniques used to manufacture metal matrix composites (MMCs). The flow of metal through fibrous preform is a problem of fluid mechanics in porous medium. Numerical simulations of this process were developed in particular for non-isothermal infiltrations which take into account the phenomena of phase change. In addition, numerical models were developed to predict the appearance of defects in the end product and to study the evolution of the deformation of the fibrous preform during metal infiltration. After pointing out the analogous numerical studies devoted to the Resin Transfer Moulding (RTM) process, we give a progress report on the models developed to date for MMCs.     

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.     

Evaluation of through-thickness permeability and the capillary effect in vacuum assisted liquid molding process

Through-thickness penetration under vacuum assistance is crucial for resin film infusion (RFI) and vacuum assistant resin transfer molding (VARTM) process. In this paper, values of the through-thickness unsaturated permeability (TTUP) and capillary pressure (P_c) are estimated based on the infiltration velocity in preforms of carbon fiber fabric and glass fiber fabric, respectively, measured by a specially designed apparatus. It reveals that, for the through-thickness permeation, the P_c values generally decrease with increasing fiber content. Relatively accurate TTUP can be obtained by counting P_c into the permeation dynamics. If P_c is neglected, liquids with good-wettability, such as silicone oil, tend to result in larger TTUPs. The corrected TTUPs show good agreement according to Carman–Kozeny, Gutowski modified Carman–Kozeny equation, and Gebart model, respectively. The resultant permeability resistance parameters of the preforms indicate that the penetration in carbon fabric bed is slower than in glass fabric bed. However, for fiber volume fraction more than 60%, the corrected TTUPs show no significant difference for all the preforms.     

An optically-based inverse method to measure in-plane permeability fields of fibrous reinforcements

Structural composite manufacturing relying on Liquid Composite Molding technologies is strongly affected by local variability of the fibrous reinforcement. Optical techniques using light transmission are used and allow field measurements of areal weight (and fibre volume fraction) of glass fibre reinforcement. The coupling of obtained areal weight mappings along with injection flow fronts is used to extract in-plane permeability fields. The current work presents results with a focus on glass random mats, but the method can be adapted to any glass fibrous medium. A study of convergence and error due to discretization is performed. Also the influence of the stacking of fibrous layers on the preform variability is analyzed. The major advantage of the proposed technique is a relatively fast acquisition of statistical data on reinforcement variability, which can be later utilized in stochastic based process simulations.     

Characterization of textile permeability as a function of fiber volume content with a single unidirectional injection experiment

Textile permeability is a fundamental property to describe preform impregnation in Liquid Composite Molding (LCM) processes. It depends on textile architecture and fiber volume content (FVC). Conventional methods to measure in-plane permeability are based on radial or unidirectional injection experiments performed at fixed FVC. A complete characterization involves a series of tests and requires several material samples. This study presents a novel approach to characterize permeability as a function of FVC through a unique unidirectional injection experiment with a preform containing different FVC sections. The same experimental set-up as in conventional unidirectional unsaturated permeability measurements is used with a second pressure transducer embedded in the mold in addition to the one located at the inlet gate. A fast algorithm is developed to exploit the data from the two sensors and automatically derive the permeability distribution without any need of visual flow front observations. The methodology is validated with a random fiber mat and a woven fabric. Results show that accurate permeability characterization can be achieved for both kinds of textiles.     

Investigation on the spring-in phenomenon of carbon nanofiber-glass fiber/polyester composites manufactured with vacuum assisted resin transfer molding

Process-induced residual stress arises in polymer composites as a result of mismatched resin contraction and fiber contraction during the cure stage. When a curved shell-like composite part is de-molded, the residual stress causes the spring-in phenomenon, in which the enclosed angle of the part becomes smaller than the angle of its mold. In this paper, a new approach is presented to control and reduce the spring-in angle by infusing a small amount of carbon nanofibers (CNFs) together with liquid resin into the glass fiber preform using vacuum assisted resin transfer molding (VARTM) process. The experimental results showed that the spring-in angles of the L-shaped composite specimens were effectively restrained by the CNFs. An analytical model and a 3-D FEA model were developed to predict the spring-in phenomenon and to understand the role of CNFs in reducing the spring-in angle. The models agreed with the experimental results reasonably well. Furthermore, the analytical model explains how the CNF-enhanced dimensional tolerance control is accomplished through the reductions in the matrix’s equivalent coefficient of thermal expansion and linear crosslinking shrinkage.     

Vacuum-assisted resin infusion (VARI) and hot pressing for CaCO3 nanoparticle treated kenaf fiber reinforced composites

This work was to apply the vacuum-assisted resin infusion (VARI) process and use calcium carbonate inorganic nanoparticle impregnation (INI) to improve the mechanical properties and water resistance of the kenaf fiber/polyester composites. The results show that the modulus of elasticity (MOE), modulus of rapture (MOR), tensile modulus (TE) and tensile strength (TS) of the composites made with INI-treated fibers are increased by 33.1%, 64.3%, 22.3% and 67.8%, respectively, compared with the composites made with un-treated fibers. The thickness swelling of 24-h water submersion is reduced from 19.7% to 1.9%. The moisture contents of the composites after the conditioning and water submersion are reduced from 5.8% to 1.5% and 18.3% to 2.2%, respectively, when INI-treated fibers are employed. The improvement makes the kenaf fiber/polyester composites possible to replace the glass fiber SMC for the automobile application.     

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.