A phenomenological model for fiber tow saturation of dual scale fabrics in liquid composite molding

Advanced composites are manufactured by liquid composite molding by impregnating a thermoset resin into a stationary woven or stitched preform. For a successful injection, the manufactured part should fill all the empty spaces between the fiber tows and inside the fiber tows with the resin. The fiber tows in such preforms have orders of magnitude lower permeability than the regions between the fiber tows, which makes them difficult to fill and hence susceptible to formation of microvoids. Numerical simulations can address the filling of fiber tows but it is difficult to capture the essential physics of their filling in a model created entirely from first principles due to the complexity of the flow which involves anisotropic permeability of flow along and across a fiber tow, uneven packing, fiber sizing, capillarity and the treatment of entrapped air. Hence, in this article we adopt a phenomenological approach in which we compare some of the possible models with an experimental procedure. The experimental procedure provides a quantitative measure of the filling of fiber tows during the impregnation process. A numerical simulation based on the dual scale flow was developed with different constitutive models that described the filling of the fiber tows. The predictions of the different models are compared with the experimental results under different processing conditions to select the model that most accurately describes the tow filling behavior. POLYM. COMPOS., 31:1881–1889, 2010. © 2010 Society of Plastics Engineers.     

Compressibility and relaxation of a new sandwich textile preform for liquid composite molding

In liquid composite molding, such as RTM or SRIM, the dry reinforcement is first compressed in the mold, and then the resin is injected into the mold cavity and cured. Knowledge of the compressibility of the reinforcement is important in order to estimate the mold closing force and the attainable range of fiber volume fraction. Moreover, in a lay-up composed of several types of fabrics, the compressibility of each fabric should be known to predict the thickness of each fabric layer, which is a prerequisite for the mold filling simulation. In this work, the relaxation and compressibility of a new sandwich fabric, Multimat®, and its components (a weft knit and a random mat) were studied and compared with a woven fabric. The different fabric relaxation behavior is explained in terms of fabric stiffness and volumetric dissipation energy. Fabric compression tests were performed by taking the fabric relaxation behavior into account. Fabric compression curves are fitted with the power law equation and agree well with the clamping pressure experimentally measured with a pressure transducer in an RTM mold. The influence of the number of layers was also investigated. Finally the compressibility of the Multimat is correlated to its components with a simple model.     

A new approach for kinetic modeling and optimization of rubber molding

Although extensive research has been carried out on the understanding of the complex vulcanization process, the influence of reversion through exposure time and temperature on the vulcanization degree remains unclear. Therefore, the main aim of this study was a novel optimization approach that can help the industrial practitioners to select the optimal operating parameters, exposure time, and molding temperature, to achieve desired vulcanization degree of selected product. Spheres of four different diameters (2.5, 5, 10, and 20 cm) were selected as test geometry for simulation and optimization of rubber molding. Obtained vulcanization rheometer data for commercially available rubber blend (NR/SBR) were fitted by a new modeling approach, dividing vulcanization curve into two fitting sets: curing and reversion. The heat transfer equations for chosen geometry were coupled with proposed kinetic model. A new temperature-dependent kinetic parameter x, as the maximal reversion degree, was introduced, enabling determination of the lowest operating molding temperature (T_min = 132.36 °C), preventing high reversion and overheating of the rubber product. The final optimization goal was assessment of the optimal temperature and vulcanization time dependence on the rubber products dimensions. Proposed models have precise prediction with R² values greater than 0.8328 and MAPE less than 2.3099%.     

Analysis of an injection/compression liquid composite molding process

The injection/compression liquid composite molding (LCM) process is simulated by using the control/volume finite element method (CV/FEM). The flow in the runner and the fiber-free areas is simplified by using an equivalent permeability approach. Several molding experiments were conducted using a tub-shaped mold and the structural reaction injection molding (SRIM) process for a poly(urethane/isocyanurate) matrix and a glass fiber preform. Good agreement is found between the experimental results and the simulation.     

Flow and cure phenomena in liquid composite molding

Liquid molding processes including resin transfer molding (RTM) and structural reaction injection molding (SRIM) continue to attract attention due to their potential for high volume manufacture. This paper examines and compares the pressuare and temperature histories observed in mold cavities during impregnation, heating, and polymerization for both RTM and SRIM using polyester, vinyl ester, and polyurethane resins in combination with continuous strand mats. Experimental results are related to thermal, chemical and rheological effects. Factors which influence materials behavior and process control and the implications for mold design are discussed.     

Spatially homogeneous gelation in liquid composite molding

On‐line mixing of the resin with its curing agents prior to injection into a mold is a common industrial technique for fabricating composite parts. For vinyl‐ester resins that cure via free radical polymerization, the concentrations of retarder, accelerator, and initiator are pre‐selected and cannot be changed during the injection. Hence, the resin that enters the mold the earliest has cured longer than the resin that enters the mold later, since the gel time for the resin is the same, owing to the fixed ratio of the curing agents. This approach leads to inhomogeneous cure of the resin and consequently to longer residence time of the resin in the mold. It requires an additional 50 to 75 percent of the filling time before a part can be de‐molded. In this study, it is shown that by adjusting the concentration of curing agents during the injection, a more homogeneous gel time throughout the mold can be achieved. The time to de‐mold is reduced to 18‐24 percent of the filling time. Sensors that measure the conductivity of the resin were used to detect the location and monitor the cure of vinyl‐ester. This approach could be extended to other resin systems to control the spatial curing of the resin in the mold.     

Key issues in numerical simulation for liquid composite molding processes

Polymer-based composites have a great potential for the manufacture of energy-efficient vehicles. Because of this growing usage and also because mold cost increases with part complexity, numerical simulation of Liquid Composite Molding Processes such as Resin Transfer Molding (RTM) and Structural Reaction Injection Molding (SRIM) are becoming more important. To succeed in that venture, reliable input data as well as a numerical model able to simulate specific molding difficulties and complex shapes must be used. In this paper, several issues are discussed and a computer software is presented. Among them, permeability measurement is discussed. Concerning specific molding difficulties, simulation results compared with experimental data are presented for edge effects, flow in multilayers and flow in ribbed structures. Finally, nonisothermal filling is discussed. Experimental data showing how the temperature boundary layer is developed during the filling of a heated mold are presented.     

Heat transfer and reaction issues in liquid composite molding

This paper surveys current issues in the modeling of heat transfer and chemical reaction in resin transfer molding and structural reaction injection molding. The discussion is organized around four steps of modeling: incorporating the physical phenomena into a model, gathering material data, analyzing the model to provide physical understanding, and solving the model for relevant cases. The local volume averaging approach is summarized as a method for deriving appropriate balance equations. The resulting equations are analyzed using dimensional analysis, and analytical solutions are presented for several special cases. These include steady heat transfer for small and large Graetz numbers, and a transient solution for heat transfer during filling at large Graetz numbers. This latter solution explains why preheating the fibers does not heat the resin uniformly. Numerical solution methods are discussed, with emphasis on upwinding techniques for hyperbolic problems. The paper concludes with a summary of research achievements and needs.     

Mold filling and curing analysis in liquid composite molding

Non-isothermal mold filing and curing experiments of liquid composite molding were carried out in this work. To compare the experimental results with a previously developed numerical simulation model, measurements of volumetric heat transfer coefficient between the resin and the fiber, and characterization of resin kinetics and rheological changes were also conducted. Combined with the previously measured fiber perform permeability, the numerical model provided a good prediction of temperature profiles during molding for a polyurethane/glass fiber composite.     

In-plane permeability measurement and analysis in liquid composite molding

This work presents methods to measure and analyze in-plane permeabilities of various fabric reinforcements. The principal flow directions need to be determined first by conducting flow visualization. From the flow front pattern, the ratio of the permeabilities in the two principal directions can be determined. The pressure and the flow rate relationship from both radial and unidirectional flow measurement methods are then used to calculate the values of the permeabilities. By the use of the unidirectional flow measurement method, the edge flow effect can also be estimated.     

Construction of an ab initio kinetic model for industrial ethane pyrolysis

The industrial steam cracking of ethane was simulated using an ab initio kinetic model. The reaction network consists of 20 species and 150 reversible elementary reactions. The thermodynamic and kinetic parameters were obtained from ab initio CBS‐QB3 and W1U calculations and agree well with available experimental data. Predicted C₂H₆, C₂H₄, and H₂ yields are within 5% of experimental data for the three sets of conditions tested. Though CH₄ yields and outlet temperatures are particularly sensitive to the accuracy of the kinetic parameters, they are simulated with an accuracy of better than 10%. Larger deviations for the C₃H₆ and C₂H₂ yields are attributed to the limited size of the reaction network. The effect of total pressure on the rate coefficients was evaluated using Quantum Rice‐Ramsberger‐Kassel theory with the Modified Strong‐Collision approximation, and was found to be relatively minor for the reaction conditions tested. This study hence demonstrates the feasibility of simulating complex radical reactions using a predictive kinetic model derived from state‐of‐the‐art quantum chemical calculations. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Analysis of two-regional flow in liquid composite molding

This study investigates the two-regional flow in Liquid Composite Molding (LCM) with emphasis on the race tracking phenomenon. An equivalent permeability is introduced to describe the flow capacity in the fiber free region. A lumped permeability is also used to further simplify the flow modeling by averaging the flow across the flow direction. Both the equivalent permeability approach and the lumped permeability approach were verified with experiments. It is found that they are capable of modeling the race tracking effects in LCM.     

A new kinetic model for wool dyeing

Previous kinetic models of the dyeing process are reviewed in an attempt to describe the exhaustion profile of acid dyes on wool fibres. A new kinetic model is proposed that describes the dye uptake throughout the whole kinetic period, and that takes into account the amount of dye and acid supplied at the beginning of dyeing. The equation is used to achieve isoreactive dyeing by calculating the amount of dye to add during the dyeing process.     

A new empirical viscosity model for ceramic suspensions

This paper presents a new predictive viscosity model for ceramic suspensions. Starting from Einstein's model (1906), various theoretical, empirical, and phenomenological models have been proposed for different suspension systems. However, there is still a lack of reliable model for ceramic suspensions used in colloidal ceramic shape-forming methods. Here, the rheological properties of ceramic suspensions comprising NiO/YSZ (nickel oxide/yttria stabilized zirconia) as the ceramic powder, and furfuryl alcohol as the suspending media were measured over a range of shear-rates (between 1 and 1000 s⁻¹) and different solid volume fractions from 0 to 0.4010. An empirical equation was then developed for the ceramic suspensions using the mobility parameter (?/(?_m−?)), which links Einstein's model with the more recent relative viscosity models. The proposed model was used to predict the relative viscosity data, showing excellent agreement to the experimental data from this study and with reported data in literature for other ceramic systems. The model was also used to estimate the maximum solid volume fraction for the ceramic suspensions (?_m=0.571), with better accuracy than those estimated by existing models.     

Sensor placement study for online flow monitoring in liquid composite molding

On‐line sensing can play an important part in controlling the quality of the final product in any manufacturing environment, including liquid composite molding (LCM). Having a sensor embedded within the part itself is often the most effective means of monitoring its condition at various stages of manufacturing and even throughout its useful life. However, given their intrusive nature, there are practical limitations imposed upon their size, quantity and trajectory within the part. This study explores the possibility of using a single lineal sensor to monitor the resin flow front during the mold filling stage of LCM, and to detect the onset of void formation and the presence of dry spots within the mold. Experiments were conducted to characterize the response of a fiber optic system previously developed for cure monitoring. Simulations were then performed to determine the optimal placement of just one such sensor in a mold to demonstrate that sufficient information on the mold filling process could be obtained. The purpose of the simulation work was to learn how to interpret the sensor response and, subsequently, use it to control the LCM process.     

A local composition model for multicomponent liquid mixture shear viscosity

A local composition model for multicomponent, nonaqueous, liquid mixture shear viscosity has been developed and tested. Only binary equilibrium thermodynamic information is used in the model in addition to pure component data. No mixture shear viscosities and no adjustable parameters are required. Predictions based on this model were compared to experimental data obtained from the literature and in this laboratory, yielding an average absolute deviation of 1.1% for ln(ηV) for 47 binary and 0.8% for seven ternary systems.     

A new one parameter viscosity model for binary mixtures

The Grunberg & Nissian equation with one parameter is widely recommended in the viscosity calculation. However, it is demonstrated that this equation fails to generate satisfactory results for size‐asymmetric mixtures containing large and small molecules. In this work, a new one parameter viscosity model for binary mixtures has been developed on the basis of Eyring's absolute reaction rate theory and the Flory‐Huggins equation. The concept of molecular surface fraction is introduced for modeling liquid mixture viscosities. The viscosity calculations of the new equation are compared with the Grunberg & Nissian equation for a broad range of chemical mixtures including 527 binary systems (containing 63 binary ionic liquid cosolvent systems) and total 17,268 viscosity points. The new equation was found to have an improved performance over the frequently employed Grunberg & Nissian equation, especially for size‐asymmetric mixtures containing large and small molecules. © 2010 American Institute of Chemical Engineers AIChE J, 57: 517–524, 2011     

Trans-plane fluid permeability measurement and its applications in liquid composite molding

This work discusses tow independent methods to measure and analyze the trans-plane fjuid permeability of various fiber reinforcements. In the unidirectional flow method, the measured injection pressure and flow rate, together with a one-dimensional Darcy's law were used to calculate the trans-plane permeability of fiber mats was independent of flow rate only at low injection pressure. Flow-induced fiber mat permeability change occurred when the injection pressure exceeded the clamping pressure. Measured permeability in conjunction with a three-dimensional mold filling computer program was used to simulate the effect of stacking sequence for a combination of different fiber mats on the mold filling pattern. Finally, a method is proposed to simplify the simulation of a three-dimensional flow through the fiber perform.     

A comparison between experiments and predictions for the blow molding of an industrial part

We present a numerical simulation for the blow molding of an industrial high density polyethylene part. The rheology of the polymeric material is described by means of an integral viscoelastic fluid model with a multi-mode relaxation spectrum. A membrane element is applied for performing the blow molding simulation of geometrically complex objects such as a bottle with a handle; the motion governing equations are described by means of a Lagrangian representation. The contact between the parison and the moving mold is handled by means of a robust algorithm. The numerical tool is applied for the production of a bottle with a handle. The predicted results are compared with their experimental counterparts. In particular, we focus on the thickness distribution of the blow product.