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。     

Relationship between isothermal and dynamic cure of thermosets via the isoconversion representation

This study deals with the cure of thermoset resins used in the pultrusion of fiber reinforced composites. The objective was to predict the degree of cure under non‐uniform time‐temperature profiles. A simple procedure using differential scanning calorimetry results was developed for predicting the degree of cure vs. time under isothermal conditions from dynamic DSC tests and vice versa. The principal feature of the procedure is the transformation of the degree of cure vs. time curves obtained under isothermal or dynamic DSC conditions into isoconversion curves as time vs. temperature or time vs. heating rate diagrams. The proposed procedure is validated with isothermal and dynamic DSC results from epoxy and polyester resin formulations used in the pultrusion of fiber reinforced composites. The agreement between predictions and experiments was very good and the extension of the procedure for predicting the cure under non‐uniform temperature profiles as in pultrusion seems to be feasible.     

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     

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     

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.     

Influence of heat transfer and curing on the quality of pultruded composites. I: Experimental

Blister formation, a major concern in pultrusion, has not been studied in detail. The objective of this study is to investigate the mechanism of blister formation and the effect of process variables such as die temperature, pulling speed, die length, and composite thickness on blister formation. Dies with different length and a stop-start method were used to investigate blister formation. The results show that for a given die and resin system, low temperature and a higher pulling speed lead to blister formation. Longer dies can prevent blister formation. Based on the experimental results, process windows for 4-mm-thick and 6-mm-thick composites are established for a vinyl ester resin. This study suggests that heater power input should be optimized in high-speed pultrusion.     

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.     

Cure characterization of soybean oil—Styrene—Divinylbenzene thermosetting copolymers

Bio‐based resins are an alternative to petroleum‐based resins in the production of fiber‐reinforced polymers (FRPs) by processes such as pultrusion. A detailed understanding of the cure behavior of the resin is essential to determine the process variables for production of FRPs. In this work, the cure kinetics of soybean oil‐styrene‐divinylbenzene thermosetting polymers is characterized by differential scanning calorimetry (DSC) measurements. By varying the concentration of the cationic initiator from 1 to 3 weight percent (wt %), the most viable resin composition for pultrusion is identified. The ability of phenomenological reaction models to describe the DSC measurements for the optimum resin composition is tested and kinetic equations, which can be used to determine the degree of cure at any temperature and time, are determined. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

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.     

Numerical and experimental analysis of resin flow and cure in resin injection pultrusion (RIP)

This work presents the results of modeling, numerical simulation, and experimental study of resin flow and heat transfer in the resin injection pultrusion (RIP) process. A control volume/finite element method (CV/FEM) was used to solve the flow governing equations, together with heat transfer and chemical reaction models. Resin viscosity, degree of cure, and fiber stack compressibility and permeability were measured in order to understand their influences on the process. An analytical flow model has also been develped based on the one‐dimensional flow approximation for the resin flow in the injection die. A high‐pressure small‐taper injection die was tested with different line speeds. Experimental data were used to verify the simulation results and the analytical solutions.     

The Effect of Processing Parameters on the Crystalline,Orientation, and Mechanical Properties of Two‐Stage Die‐Drawn Polypropylene

An investigation specifically focusing on the relationship among processing parameters, structure, and mechanical properties of solid two‐stage die‐drawn polypropylene (PP) has been done in this study, which aimed at providing a reliable reference in the choose of appropriate conditions that can be able to meet a specific processing requirement. PP sheets were drawn through a self‐design solid two‐stage die‐drawing apparatus to various drawing ratios (DRs) at different speeds and with different die‐exit thicknesses. The results showed that tensile strength, modulus, and the degree of orientation significantly increased with the nominal DR and could be further improved by increasing the drawing speed. While the crystallinity increased prior and decreased to near a constant value when the drawing speed was over 150 mm/min in the researched scope. Larger the die‐exit thickness was, lower the orientation degree was but higher the crystallinity could be obtained. Compared with crystallinity, orientation degree plays a leading role in the final product properties during a two‐stage solid die‐drawing process. POLYM. ENG. SCI., 59:2347–2355, 2019. © 2019 Society of Plastics Engineers     

Modeling of three‐dimensional flow and heat transfer in polystyrene foam extrusion dies

A three‐dimensional mathematical model was developed to investigate the nonisothermal, non‐Newtonian polymer flow through the dies used in the polystyrene foam extrusion process. The model, based on the computational fluid dynamics (CFD) code, Polyflow, allowed for the shear rate and temperature dependence of the shear viscosity of the blowing agent laden polystyrene melt. The model also accounted for viscous heating. The shear viscosity of the polystyrene‐blowing agent mixture was measured experimentally at several temperatures. The model was used to calculate pressure, flow, and temperature distributions in two different dies used for industrial‐scale extrusion of polystyrene foams. The article presents a selection of computed results to illustrate the effect of die design on uniformity of flow at the die exit, the overall pressure drop in the die, relative magnitudes of pressure drop in the land section versus the rest of the die, and temperature distribution in the die. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

Thermo‐chemical response of vinyl‐ester resin

This paper presents the thermo‐chemical characterization of Dow Derakane 411‐C50 commercial vinyl‐ester resin at low temperatures (20°C to 40°C). Differential Scanning Calorimetry (DSC) and Torsional Braid Analysis (TBA) are the experimental techniques used to characterize the material behavior. The cure kinetics are studied using DSC and are modeled using a modified autocatalytic equation with a maximum degree‐of‐cure term. Also, the effect of inhibitors in the resin system is accounted for by an inhibitor depletion model. The glass transition temperature (T^g) is also characterized using TBA and related to the degree of cure. It was found that the T_g and the degree of cure do not exhibit a linear relationship for this resin system. The findings presented in this work provide information for accurate cure modeling and process simulation of vinyl‐ester materials.     

Optimal design of the coat‐hanger die used for producing melt‐blown fabrics by finite element method and evolution strategies

In this article, an optimal design procedure that improves the uniformity of flow rate distribution at the outlet of the coat‐hanger die is proposed. The two‐membered evolution strategy was combined with the finite element method to optimize the design parameters of an initial coat‐hanger die geometry designed by analytical method based on one‐dimensional lubrication method. The slot gap and the manifold angle were chosen to be the optimized design parameters, and the coefficient of variation (CV) value of the flow velocity at the die outlet is regarded as the objective function. The optimal results were achieved in the 22nd generation after 100 generations' evolution, which show that the CV% value of the flow velocity at the die outlet is only 1.3631% and decreases by 68% of the initial value caused by unoptimizable die geometry. POLYM. ENG. SCI., 2009. © 2008 Society of Plastics Engineers     

Modeling of injected pultrusion processes: A numerical approach

Injected pultrusion (IP) is an attractive process for high volume, high performance, and low cost manufacture of continuous fiber reinforced polymer matrix composites. In this work we focus our attention on development of a computer simulation model for the IP process. First, the governing equations for conservation of mass, momentum, and energy are developed using a local volume averaging approach. In turn, a computer simulation model of the IP process is developed using finite element/control volume (FE/CV) and finite difference techniques. Specifically, the equation of continuity and conservation of momentum are solved in 2-D using a Galerkin FE/CV technique. The energy and chemical species balance equations are solved in 3-D, where streamline upwind Petrov-Galerkin (SUPG) or streamline upwind (SU) FE/CV are used to discretize the equations in two dimensions while finite differences have been used in the third dimension. The chemical species balance equation is solved in the Lagrangian frame of reference using finite differences. Different numerical formulations (Galerkin, Lagrangian, SU, and SUPG) are used to solve a number of benchmark problems to determine the best numerical formulation. It is shown that for coarse discretization, Streamline Upwind methods perform consistently better than the other methods. However, for refined meshes, the Lagrangian method produces the best solution for a given CPU time. Also, using the simulation model, the effect of fiber pull speed, reinforcement anistropy, and taper of the die on the quality of the product is studied. It is shown that the simulation model can be effectively used to design the die geometry as well as to optimize the operating conditions for a given product.     

Influence of cure conditions on out‐of‐autoclave bismaleimide composite laminates

Bismaleimides (BMI) are thermosetting polymers that are widely used in the aerospace industry due to their good physical properties at elevated temperatures and humid environments. BMI‐based composites are used as a replacement for conventional epoxy resins at higher service temperatures. Out‐of‐Autoclave (OOA) processing of BMI composites is similar to that of epoxies but requires higher cure temperatures. Polymer properties such as degree of cure and crosslink density are dependent on the cure cycle used. These properties affect mechanical strength as well as glass transition temperature of the composite. In the current research, carbon fiber/BMI composite laminates were manufactured by OOA processing. The void content was measured using acid digestion techniques. The influence of cure cycle variations on glass transition temperature and mechanical strength was investigated. Properties of manufactured specimens were compared with that of conventional autoclave cured BMI composites. Laminates fabricated via OOA processing exhibited properties comparable to that of autoclave cured composites. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43984.     

Cure reaction of multi‐walled carbon nanotubes/diglycidyl ether of bisphenol A/2‐ethyl‐4‐methylimidazole (MWCNTs/DGEBA/EMI‐2,4) nanocomposites: effect of carboxylic functionalization of MWCNTs

BACKGROUND: The aim of this work was to study, using differential scanning calorimetry, the effect of carboxylic functionalization of multi‐walled carbon nanotubes (MWCNTs) on the cure reaction of MWCNTs/diglycidyl ether of bisphenol A/2‐ethyl‐4‐methylimidazole (MWCNTs/DGEBA/EMI‐2,4) nanocomposites. This is important for the practical design, analysis and optimization of novel materials processing. RESULTS: Comparing the influence of non‐functionalized MWCNTs and carboxyl‐functionalized MWCNTs, it was found that, at the initial curing stage, both MWCNTs act as catalyst and COOH functionalization of MWCNTs has a catalytic effect on the curing process. Then, at the later curing stage, non‐functionalized MWCNTs prevent the occurrence of vitrification, whereas COOH functionalization of MWCNTs promotes vitrification. Non‐functionalized MWCNTs decrease the degree of curing, as evidenced by lower total heat of reaction and lower glass transition temperatures of nanocomposites compared to neat epoxy; however, COOH functionalization of MWCNTs increases the degree of curing. CONCLUSION: For the development of composites, COOH functionalization of MWCNTs could bring a positive influence to the composite process. Its acceleration of cure could help shorten pre‐cure time or lower pre‐treatment temperature, and its effect of promoting vitrification could help shorten post‐cure time or lower post‐treatment temperature. Copyright © 2009 Society of Chemical Industry     

Visualization of initial expansion behavior of butane‐blown low‐density polyethylene foam at extrusion die exit

A charge‐coupled device (CCD) camera was used to observe n‐butane‐blown low‐density polyethylene (LDPE) foams at the extrusion die exit. The effects of butane content, nucleating‐agent (talc) content, aging modifier (glycerol monostearate), die temperature, and die geometry on the initial expansion behavior of the foam extrudate were studied. A transparent section of the foam extrudate was found at certain die temperatures. The reasons for the existence of this transparent section and its effect on the processing conditions and material formulations are discussed. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers     

Effects of postcure temperature variation on hygrothermal‐mechanical properties of an out‐of‐autoclave polymer composite

The effects of cure temperature variation on the properties of an out‐of‐autoclave polymer composite manufactured using Cycom 5320 8HS prepreg were investigated using different postcure temperatures of a two‐stage cure cycle. In addition, the effects of adverse environmental conditions on the cure temperature variation were studied by conditioning the samples in an environmental chamber until they reached moisture equilibrium. The state of cure was obtained using a differential scanning calorimeter and dynamic mechanical analyzer. The mechanical properties were obtained using short‐beam shear (SBS) and combined loading compression (CLC) test methods. The state of cure obtained showed increases in total heat of reaction, degree of cure, and glass transition temperature as the postcure temperature increased. The SBS and CLC strengths showed an increasing trend as postcure temperature increased. Good correlations were obtained between the material's cure temperatures, state of cure, and mechanical properties for room temperature dry and hot wet conditions. The study showed that the state of cure can be used to define, monitor, and verify the cure quality. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3090–3097, 2013     

Effect of long‐chain branches of polypropylene on rheological properties and foam‐extrusion performances

The effect of modifying polypropylene by the addition of long‐chain branches on the rheological properties and performance of foam extrusion was studied. Three polypropylenes, two long‐chain‐branched polypropylenes and a linear polypropylene, were compared in this study. The modification was performed with a reactive‐extrusion process with the addition of a multifunctional monomer and peroxide. The rheological properties were measured with a parallel‐plate and elongational rheometer to characterize the branching degree. The change from a linear structure to a long‐chain‐branched nonlinear structure increased the melt strength and elasticity of polypropylene. Also, there was a significant improvement in the melt tension and sag resistance for branched polypropylenes. Foaming extrusion was performed, and the effect of the process variables on the foam density was analyzed with Taguchi's experimental design method. For this study, an L₁₈(2¹3⁵) orthogonal array was used on six parameters at two or three levels of variation. The considered parameters were the polypropylene type, the blowing agent type, the blowing agent content, the die temperature, the screw speed (rpm), and the capillary die length/diameter ratio. As a result, the most significant factor that influenced the foam density was the degree of long‐chain branching of polypropylene. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 1793–1800, 2005