Influence of heat transfer and curing on the quality of pultruded composites. II: Modeling and simulation

In this study, a computer simulation code is developed to predict the dynamics of heat transfer in the pultrusion process. The die block and heater arrangement are included in the heat transfer analysis so that the simulation can provide the temperature profile at the interface between the die and the composite. The measured interface temperature profiles are then used to validate the simulation code. Energy management, i.e. heater power control along the heating die, is also considered in the simulation code. The code is capable of carrying out transient thermal analysis for both start-up and steady-state operation of the pultrusion process. From the experimental observations on the part quality in terms of blister formation, a processing window was obtained by showing the relation of the die length and the line speed to the part quality. The processing window is then generated numerically using the computer code based on the definition of a critical die length proposed in this work, and the result shows good agreement with the experimental data.     

Heat transfer for pultrusion of a modified acrylic/glass reinforced composite

Experimental values of the temperature on the wall and into the die were obtained for the pultrusion of a modified acrylic resin. The equation of continuity, and energy balance, coupled with a kinetic expression for the curing system, are solved using difference method to calculate the temperature and the conversion profiles in the thickness direction in a rectangular pultrusion die. The effects of the process variables (e.g. pulling rate, die temperature, die thickness and content of fibers) on the performance of the pultrusion are evaluated.     

复合材料拉挤成型过程中温度和固化度的数值模拟研究

本文对拉挤成型过程中热传导方程和固化度动力学方程进行了数值分析，确定了拉挤模具内温度和固化度属于强耦合关系。使用有限元软件IFEPG和FORTRAN语言为平台开发出一计算机程序，并使用该程序模拟出在一定工艺参数下拉挤模具内温度和固化度的分布，着重探讨了拉挤速度对模具内温度和固化度分布的影响。     

Fiber reinforced nylon-6 composites produced by the reaction injection pultrusion process

Reaction injection pultrusion (RIP) combines the injection pultrusion process with reaction injection molding (RIM) techniques to yield one of the more novel methods of thermoplastic matrix pultrusion. An experimental set-up was designed and built to pultrude nylon-6 RIM material and continuous E-glassfiber. Well-impregnated nylon-6 composites with 66.5, 68.8, 71.1, and 73.3 vol% fiber were produced. Internal temperature profile within the die was recorded during the process, and physical properties of resulting composites were measured. This paper presents results of the effect of fiber content, die temperature profile and pulling speed variations on internal temperature profile, monomer conversion, and physical properties. The study showed that increasing pulling speed lowered both peak temperature and monomer conversion. Higher die temperatures accelerated the reaction, resulting in a higher exotherm, a higher peak temperature, and a higher monomer conversion within the range investigated. Shear strength, flexual strength, flexual modulus, and transverse tensile strength were proportional to monomer conversion. Flexual modulus increased with higher fiber content within the range observed. Data allow the proper combination of die temperature profile and pulling speed to be selected to achieve a desired level of monomer conversion and physical properties. Results of this study provide basic information required for product design with nylon-6 composites as well as tool design, selection of processing conditions, and quality control for the process.     

Development of a mathematical model for the pultrusion process

A mathematical model has been developed to simulate the pultrusion process, namely the profiles of temperature and the degree of cure in both the axial and radial directions in a pultrusion die of cylindrical shape. For the study, the equations of continuity and energy transport, coupled with a kinetic expression for the curing reaction, were solved numerically, using a finite difference method. For the kinetic expression, we used an empirical expression of the form dα/dt = (k₁ + k₂α^m)(1 ? α)ⁿ to describe the curing behavior of both unsaturated polyester and epoxy resins. Differential scanning calorimetry (DSC) was used to investigate the curing behavior of the following systems: unsaturated polyester resin/glass fiber, epoxy resin/glass fiber, and epoxy resin/carbon fiber. The results of DSC runs were used to determine the kinetic parameters, which enabled us to predict the effects on the pultrusion characteristics of the following variables: (1) the type of initiator; (2) the type of fiber reinforcement; (3) the type of resin; and (4) the pulling speed and hence the residence time.     

Development of a mathematical model for the pultrusion of unsaturated polyester resin

A mathematical model is developed for simulating the pultrusion process of unsaturated polyester resin, using a mechanistic kinetic model based on free radical polymerization. In their previous publications (Refs. 1 and 7), Han and Lee used the mechanistic model to simulate the curing behavior of unsaturated polyester resins under isothermal conditions, employing the differential scanning calorimetry data obtained for a range of single initiators and multiple initiator systems. For the sake of mathematical convenience, a pultrusion die of cylindrical geometry was considered. The mathematical model developed permits one to choose any number of initiators when predicting the distributions of the degree of cure and temperature in both the radial and axial directions of the die. The effects of material variables (e.g., the type and concentration of mixed initiators) and processing conditions (e.g., pulling speed and die temperature distribution) on the performance of the pultrusion are evaluated.     

Development of an isothermal lubricating layer model for injection pultrusion of electronic prepregs

The current process for manufacturing electronic prepregs uses solvent‐based resin systems. Solvents are environmentally unfriendly and contribute to voids in the pre‐preg, which are a source of product variability. Prepreg inconsistencies are one of the major sources of scrap on the board shops. To overcome these drawbacks, a solvent‐less process is currently being developed in our laboratory. The process is based on the concept of injection pultrusion or continuous resin transfer molding (RTM). The centerpiece of the process is an impregnation die. Glass fabric and resin are fed into the die where fiber impregnation and partial resin cure occurs depending on the material chemo‐rheology. The B‐staging is finished in an oven located immediately after the die. A key to the success of the process is being able to predict the pulling force. Fabrics used in electronic prepreg manufacturing are relatively fragile; they could be damaged if the pulling force is too high. A model to predict the pulling force, based on the formation of a continuous lubricating layer between the die surface and the moving fabric, has been developed and experimentally tested using model fluids.     

Resin flow in a pultrusion process

A simple model for the resin flow in a pultrusion die based on the theory of lubrication has been developed. The velocity field in the pultrusion die has been calculated together with the pressure drop. A useful tool to evaluate the energy loss due to the viscosity dissipation along the die has been developed. Model results have been evaluated, by using chemorheological submodels, in terms of the contribution to the pulling force due to the viscous drag.     

An optimization procedure for the pultrusion process based on a finite element formulation

Composite materials are manufactured by different processes. In all, the process variables have to be analyzed in order to obtain a part with uniform mechanical properties. In the pultrusion process, two variables are the most important: the pulling speed of resin‐impregnated fibers and the temperature profile (boundary condition) imposed on the mold wall. Mathematical modeling of this process results in partial differential equations that are solved here by a detailed procedure based on the Galerkin weighted residual finite element method. The combination of the Picard and Newton‐Raphson methods with an analytical Jacobian calculation proves to be robust, and a mesh adaptation procedure is presented in order to avoid integration errors during the process optimization. The two earlier‐mentioned variables are optimized by the Simulated Annealing method with some constraints, such as a minimum degree of cure at the end of the process, and the resin degradation (the part temperature cannot be higher than the resin degradation temperature at any time during the whole process). Herein, the proposed objective function is an economic criterion instead of the pulling speed of resin‐impregnated fibers, used in the majority of papers.     

Pultruded fiber-reinforced poly(methyl methacrylate) composites. I. Effect of processing parameters on mechanical properties

A feasibility study of pultrusion of fiber-reinforced thermoplastic PMMA composite has been conducted using a proprietary method. Effect of processing parameters, preparation of methyl methacrylate (MMA) prepolymer on the mechanical properties (tensile, flexural strength and modulus, impact strength, etc.) of fiber-reinforced PMMA composites by pultrusion has been studied. Processing parameters investigated included pulling rate, die temperature, postcure time and temperature, and filler content. From the study of Brookfield viscometer and FTIR spectrum the processing conditions can be defined. It was found from SEM photographs that the wetting out of fibers by PMMA resin was complete, and the fiber bundles were distributed evenly in the PMMA matrix. From the study of ¹H-NMR, GPC, and Brookfield viscometer, the conversion, molecular weight, and viscosity of MMA prepolymer data were obtained. From the DSC diagram, molecular weight measurement, and the rule of polymerization rate, the optimum die temperature was determined. It was found that the mechanical properties increase with increasing filler content and postcure temperature, and with decreasing die temperature and pulling rate.     

Mathematical model for the pultrusion of blocked PU–UP matrix composites

The thermokinetic behavior of blocked polyurethane (PU)–unsaturated polyester (UP)–based composites during the pultrusion of glass‐fiber‐reinforced composites was investigated utilizing a mathematical model that accounted for the heat transfer and heat generation during curing. The equations of continuity and energy balance, coupled with a kinetic expression for the curing system, were solved using a finite difference method to calculate the temperature profiles and conversion profiles in the thickness direction in a rectangular pultrusion die. A kinetic model, dP/dt = A exp(?E/RT)P^m(1 ? P)ⁿ, was proposed to describe the curing behavior of a blocked PU–UP resin. Kinetic parameters for the model were obtained from dynamic differential scanning calorimetry scans using a multiple regression technique, which was able to predict the effects of processing parameters on the pultrusion. The effects of processing parameters including pulling speed, die wall temperature, and die thickness on the performance of the pultrusion also were evaluated. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 1996–2002, 2003     

In‐situ pultrusion of urea‐formaldehyde matrix composites. II: Effect of processing variables on mechanical properties

Unidirectional fiber reinforced urea‐formaldehyde (UF) composites have been prepared by the pultrusion processes. The effects of the processing parameters on the mechanical properties (flexural strength and flexural modulus, etc.) of the glass fiber reinforced UF composites by pultrusion has been studied. The processing variables investigated included die temperature, pulling speed, postcure temperature and time, filler type and content, and glass fiber content. The die temperature was determined from differential scanning calorimetry (DSC) diagram, swelling ratio, and mechanical properties tests. It was found that the mechanical properties increased with increasing die temperature and glass fiber content, and with decreasing pulling rate. The die temperature, pulling speed, and glass fiber content were determined to be 220°C, 20–80 cm/min, and 60–75 vol%, respectively. The mechanical properties reached a maximum value at 10, 5, 5, and 3 phr filler content corresponding to the kaolin, talc, mica, and calcium carbonate, respectively, and then decreased. The mechanical properties increase at a suitable postcure temperature and time. Furthermore, the properties that decreased due to the degradation of composite materials for a long postcure time are discussed. POLYM. COMPOS., 27:8–14, 2006. © 2005 Society of Plastics Engineers     

Fluid mechanics analysis of a two-dimensional pultrusion die inlet

Fluid mechanics plays an important role in many manufacturing processes including the pultrusion of composite materials. The analysis of fluid mechanics problems generally involves determination of quantities such as pressure and velocity. During the pultrusion process, the short, tapered inlet region of the pultrusion die experiences a significant amount of fluid resin pressure rise. The quality of a pultruded product can be affected by the amount of pressure rise in the pultrusion die inlet. Void formation can be suppressed and good fiber “wet out” achieved by a sufficiently high pressure rise in the pultrusion die inlet region. In this study the change in fluid resin pressure rise as a function of die entrance geometry is investigated by developing a finite element model based on the assumptions of Darcy's law for flow in porous media. The momentum equations are combined with the continuity equation to save computational time and memory. A Galerkin weighted residual based finite element method is developed to solve the resulting equation. This model is capable of predicting the pressure rise in the tapered inlet region of the pultrusion die as well as the straight portion of the die. By varying the size of the preform plates the thickness of the fiber/resin matrix approaching the die inlet can be varied. The finite element model predicts the impact of changing the preform plate size on the fluid resin pressure rise in the pultrusion die. The effect of varying the wedge angle for a linearly tapered die inlet region is also studied using this model. The results in this work can be useful for designing a pultrusion die system.     

The development of glass fiber reinforced polystyrene for pultrusion. I: Process feasibility,dynamic mechanical properties,and postformability

A feasibility study on the pultrusion of a glass fiber reinforced polystyrene (PS) has been conducted using a proprietary method. The styrene prepolymer synthesized in this study was prepared from blends of styrene monomer and benzoyl peroxide (BPO). The process feasibility, dynamic mechanical properties, and postformability of the glass fiber reinforced PS by pultrusion have been investigated. By means of gel permeation chromatography, ¹H nuclear magnetic resonance (¹H-NMR), and a Brookfield viscometer, the molecular weight, conversion, and viscosity of the styrene prepolymer were obtained. From the investigations of the long pot life of styrene prepolymer, the high reactivity of styrene prepolymer, and excellent fiber wet-out, it was found that the PS resin showed excellent process feasibility for pultrusion. The dynamic storage modulus (E') of pultruded glass fiber reinforced PS composites increased with increasing die temperature, filler content, postcuring and glass fiber content, and with decreasing pulling rate. The composite can be postformed by thermoforming under pressure, and mechanical properties of postformed composites can be improved.     

The development of a mathematical model for the pultrusion of blocked polyurethane composites

The thermokinetic behavior of blocked polyurethane-based composites during the pultrusion of glass-fiber reinforced composites is investigated utilizing a mathematical model accounting for the heat transfer and the heat generation during curing. The equations of continuity and energy balance, coupled with a kinetic expression for the curing system, are solved using a finite difference method to calculate the temperature and conversion profiles in the thickness direction in a rectangular pultrusion die. A kinetic model, dP/ dt = A exp(?E/RT) (1?P)ⁿP^m, was proposed to describe the curing behavior of a blocked polyurethane resin. Kinetic parameters for the model were obtained from dynamic differential scanning calorimetry (DSC) scans using a multiple regression technique, which was able to predict the effects of processing variables on the pultrusion. The effects of process variables (e.g., pulling rate, die temperature, and die thickness) on the performance of the pultrusion are also evaluated. © 1993 John Wiley & Sons, Inc.     

Pultruded fiber reinforced blocked polyurethane (PU) composites. II. Processing variables and dynamic mechanical properties

Unidirectional fiber reinforced blocked polyurethane (PU) composites have been prepared by the pultrusion process. The effects of processing variables on the mechanical properties and dynamic mechanical properties of fiber reinforced PU composites by pultrusion have been studied. The processing variables investigated included pulling rate (in-line speed), die temperature, postcure time and temperature, and filler type and content. The dynamic mechanical properties of the composites produced by the process were studied utilizing dynamic mechanical spectrometer. Results show that the composites possessed various optimum pulling rates at different die temperatures. From the DSC data analysis, swelling ratio, and mechanical properties, the optimum die temperature was determined. It was found that the mechanical properties increase with filler content for various types of filler. The increasing of mechanical properties depends on the optimum postcure temperature and time. However, the properties decreased for longer postcure times since the composite materials were degraded. The glass-transition temperature (T_g) increased slightly and the damping peak (tan δ) was broadened due to fiber reinforcement. The dynamic mechanical moduli (G′, G″) of pultruded PU composites are apparently higher than those of the matrices. The moduli (G′, G″) increase with increasing fiber and filler content, and the damping peak becomes broad. Effect of postcuring on the degree of crosslinking, T_g, and dynamic modulus will be discussed.     

In situ pultrusion of urea–formaldehyde matrix composites. I. Processability,kinetic analysis,and dynamic mechanical properties

We conducted a feasibility study on the pultrusion of a glass‐fiber‐reinforced urea–formaldehyde (UF) composite using a proprietary method. The UF prepolymer synthesized in this study was prepared from blends of UF monomer and a curing agent (NH₄Cl).The process feasibility, kinetic analysis, and dynamic mechanical properties of the glass‐fiber‐reinforced UF composites by pultrusion were investigated. From investigations of the long pot life of the UF prepolymer, the high reactivity of the UF prepolymer, and excellent fiber wet‐out, we found that the UF resin showed excellent process feasibility for pultrusion. A kinetic model, dα/dt = A exp(?E/RT)α^m(1 ? α)ⁿ, is proposed to describe the curing behavior of a UF resin. Kinetic parameters for the model were obtained from dynamic differential scanning calorimetry scans with a multiple‐regression technique. The dynamic storage modulus of the pultruded‐glass‐fiber‐reinforced UF composites increased with increasing die temperature, filler content and glass‐fiber content and with decreasing pulling rate. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 1242–1251, 2002     

Pultrusion die pressure response to changes in die inlet geometry

Pultrusion is a process of manufacturing composites that requires a high resin pressure rise in the tapered die inlet region. A sufficiently high pressure rise is important for a good quality pultruded product, thereby necessitating a study of the mechanisms affecting the die inlet pressure rise. Various process control parameters affect the resin pressure rise in the die inlet. The geometry of the tapered die inlet region can have a significant effect on the pressure rise in the pultrusion die. In this study a finite element model was developed to predict this pressure rise as a function of the tapered die inlet geometry. The composite matrix being pultruded was modeled on the assumptions of Darcy's laws for flow in porous media. A Galerkin's weighted residual based finite element technique was used to solve the governing equations. The pressure rise in the tapered inlet region of the die, as well as in the straight portion of the die, is predicted by this finite element model. Circular, parabolic, and wedge shaped die inlets have been modeled to compare their shapes on the resin pressure rise in the pultrusion die. Different angles for wedge shapes, different radii for circular shapes, and different foci for parabolic shapes were modeled to predict the influence of varying key geometrical parameters for each die inlet contour on pressure rise. The finite element model developed provides insight as to how to design the die inlet to produce a suitable pressure rise in the pultrusion die inlet.     

Development of an environmentally friendly solventless process for electronic prepregs

The most common commercial processes for manufacturing prepregs for electronic applications use solvent‐based resin systems. Solvents are not environmentally friendly and contribute to voids in prepregs and laminates. The resin impregnation process is performed in an open resin bath. This low‐pressure impregnation is conducive to voids in prepregs. Voids cause product variability, which is a major source of scrap in board shops. To eliminate these drawbacks, a solventless process, based on the concept of injection pultrusion, has been developed. The impregnation is performed in a die under pressure to minimize voids. In previous work, chemorheological and kinetic measurements were used to identify a potential epoxy‐based resin system. In addition, flow visualization with model fluids was used to establish the basic flow mechanism. Here we use the previous results to develop a mathematical model for the B‐staging process. A prototype B‐staging die has been built and used to verify the mathematical model. The results show that the model agrees well with the experimental data for low pulling speeds and slightly underpredicts the runs at high pulling speeds. The properties of the prepregs, the dielectric constant (DK) and dielectric loss (DF), have also been measured in this research. The measurements show that the solventless prepregs have acceptable DK and DF values according to the Institute for Printed Circuits FR‐4 designation (a permittivity and tangent loss standard). A microscope has been used to observe the void contents of the prepregs. The solventless prepregs have been compared against standard FR‐4 prepregs and shown qualitatively to have fewer voids. Based on the mathematical model, two potential process alternatives for the manufacture of solventless prepregs have been developed and analyzed. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 1136–1146, 2004