Application and evaluation of the method of ellipses for measuring the orientation of long,semi‐flexible fibers

The method of ellipses (MoE) is a common experimental technique utilized to quantitatively determine the orientation state of a population of rigid fibers within a fiber–polymer composite. In this research, the validity of applying the MoE to long, semi‐flexible fiber systems in which the majority of fibers are flexible is discussed. The components of the orientation tensor were first determined for a composite formed by a homogenous, simple shear field. The minimum acceptable image analysis width, or bin width, for the selected geometry was found to be ∼5.5 mm, or 1.4 times the average fiber length. This modified bin width was then used to determine the orientation at multiple percentages of flow within an injection‐molded, center‐gated disc, and compared to orientation values obtained utilizing the traditional, 0.7‐mm bin width. The results show that the traditional, 0.7‐mm bin width is sufficient for analysis of the center‐gated geometry. This fortuitous result is attributed to the axisymmetric nature of the center‐gated geometry, and the highly transverse fiber alignment seen within the samples, especially at moderate to high percentages of flow. In more complex flows, it is expected that the conventional bin width will not apply. POLYM. COMPOS., 2013. © 2013 Society of Plastics Engineers     

Modeling of fiber–polymer coupling for suspensions of mono‐modal fibers

The rheology of suspensions of fibers in polymer solutions is strongly dependent on fiber–fiber and fiber–polymer interactions. To model these interactions and their dependence on the flow and suspension properties, the steady shear viscosity of glass fibers in a polyethylene oxide polymer solution are measured for different fiber volume fractions and aspect‐ratios. The measurements are conducted for well characterized fiber samples that have a uniform and well defined aspect‐ratio and for moderate volume fractions. The results of the experimental study are used to correlate the polymer–fiber coupling factor and the fiber–fiber interaction coefficient using a mathematical model based on a modified FENE‐P (finitely extensible nonlinear elastic) constitutive equation. It was found that both parameters are strongly dependent on the characteristics of the suspension, but also depend on the flow shear rate that determines the degree of fiber orientation. In general, fiber–fiber and polymer–fiber interactions increase with both the aspect‐ratio and the volume fraction and are more important when the fibers are not fully oriented. POLYM. COMPOS., 27:82–91, 2006. © 2005 Society of Plastics Engineers     

Rheology of LDPE‐based semiflexible fiber suspensions

Molten LDPE suspensions containing fibers of different flexibilities have been investigated in simple shear and small and large amplitude oscillatory shear (LAOS) flow. The suspensions exhibited viscosity and normal stress overshoots in stress growth experiments, and the magnitude and width of the overshoots became larger as the fiber flexibility increased. LAOS was used to help understanding the relationship between stress growth and fiber orientation. For all composites, the stress signal decreased with time in LAOS, and this behavior was more pronounced in the case of the more rigid fibers. The energy dissipated per LAOS cycle was evaluated for each composite, and it showed that less energy was dissipated as fiber flexibility decreased. In addition, the dissipated energy decreased with time and this has been interpreted in terms of a reduction of fiber contacts. The first normal stress difference showed a nonsinusoidal periodic response, and fast Fourier transform analysis indicated the presence of a first harmonic corresponding to the applied frequency for the fiber‐filled systems, in addition to the second harmonic observed for the neat LDPE. It resulted in asymmetrical strain‐normal force Lissajou curves for the suspensions, with this asymmetry being more pronounced in the case of the more rigid fibers. This has been attributed to a more extensive fiber orientation for the latter. POLYM. COMPOS., 31:1474–1486, 2010. © 2009 Society of Plastics Engineers     

Improved through‐plane electrical conductivity in a carbon‐filled thermoplastic via foaming

Flow‐induced orientation of the conductive fillers in injection molding creates parts with anisotropic electrical conductivity where through‐plane conductivity is several orders of magnitude lower than in‐plane conductivity. This article provides insight into a novel processing method using a chemical blowing agent to manipulate carbon fiber (CF) orientation within a polymer matrix during injection molding. The study used a fractional factorial experimental design to identify the important processing factors for improving the through‐plane electrical conductivity of plates molded from a carbon‐filled cyclic olefin copolymer (COC) containing 10 vol% CF and 2 vol% carbon black. The molded COC plates were analyzed for fiber orientation, morphology, and electrical conductivity. With increasing porosity in the molded foam part, it was found that greater out‐of‐plane fiber orientation and higher electrical conductivity could be achieved. Maximum conductivity and fiber reorientation in the through‐plane direction occurred at lower injection flow rate and higher melt temperature. These process conditions correspond with foam flow during filling of the mold cavity, indicating the importance of shear stress on the effectiveness of a fiber being rotated out‐of‐plane during injection molding. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Experimental characterization of traditional composites manufactured by vacuum‐assisted resin‐transfer molding

The primary purpose of this study is to investigate the anisotropic behavior of different glass‐fabric‐reinforced polyester composites. Two commonly used types of traditional glass fabrics, woven roving fabric and chopped strand mat, have been used. Composite laminates have been manufactured by the vacuum infusion of polyester resin into the fabrics. The effects of geometric variables on the composite structural integrity and strength are illustrated. Hence, tensile and three‐point‐bending flexural tests have been conducted at different off‐axial angles (0, 45, and 90°) with respect to the longitudinal direction. In this study, an important practical problem with fibrous composites, the interlaminar shear strength as measured in short‐beam shear tests, is discussed. The most significant result deduced from this investigation is the strong correlation between the changes in the interlaminar shear strength values and fiber orientation angle in the case of woven fabric laminates. Extensive photographs of fractured tensile specimens resulting from a variety of uniaxial loading conditions are presented. Another aim of this work is to investigate the interaction between the glass fiber and polyester matrix. The experiments, in conjunction with scanning electron photomicrographs of fractured surfaces of composites, are interpreted in an attempt to explain the interaction between the glass fiber and polyester. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Rheology of fiber filled polymer melts: Role of fiber‐fiber interactions and polymer‐fiber coupling

An experimental study and a numerical modeling analysis are carried out to examine the effects of fiber‐fiber interactions and coupling between fiber orientation and polymer chains conformation on the rheological properties of fiber suspensions. The experimental study allowed examination of large fiber volume fractions up to 35% over a range of shear rates that spans eight decades. This study confirmed already known results and led to new ones. In particular, a peak in the steady shear viscosity at the low shear rate region is observed at large volume fractions. Furthermore, new results regarding the applicability of the Cox‐Merz rule, the behavior of the damping factor, and the end pressure drops are reported, and physical interpretations are proposed. The results of the numerical modeling showed that it is necessary to account for the polymer‐fiber coupling factor to obtain a good fit between the model predictions and the experimental measurements. Comparisons between the model predictions and the experimental measurements allowed study of the variation of the parameters that govern the fiber‐fiber interactions and the polymer‐fiber coupling with the properties of the suspension and the flow. POLYM. ENG. SCI., 45:385–399, 2005. © 2005 Society of Plastics Engineers     

A simplified method to determine the 3D orientation of an injection molded fiber‐filled polymer

In short‐fiber reinforced composites, it is widely accepted that the fiber orientation plays an important role on their overall physical and thermomechanical properties. To predict the properties of such composite materials, a full 3D fiber orientation characterization is required. A variety of destructive and nondestructive techniques have been developed, but all the methods have the same common point that they are very tedious and time consuming. Knowing that the fiber orientation induced by the flow remains mainly in the flow plane, an easier method has been performed for injection molded fiber‐filled polymers. It is based on the simple 2D SEM image analysis of a specific 45°‐oblique section plane. Then, the indetermination of fiber orientation from an ellipse mark analysis does not exist anymore. This novelty also turns out to be much more accurate. To achieve measurements over large composite samples, the method has been fully automated. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Processing of short‐fiber reinforced polypropylene. I. Influence of processing conditions on the morphology of extruded filaments

An experimental investigation of the processing of glass fiber reinforced polypropylene is presented. Final fiber orientation distribution, fiber distribution in filament sections, rheological properties, final fiber length distribution and surface morphology were analyzed. This analysis was done taking into account the quantity of fibers and their interactions and flow conditions. The final fiber orientation increased when shear rate increased and fiber concentration decreased. Moreover, inhomogeneities in fiber distribution increased as the concentration of fibers decreased. The density profile showed a significant variation with fiber concentration, but it was not dependent on the shear rate applied. The viscosity showed a linear dependence with shear rate. The average fiber length and the breadth of this distribution decreased with the increasing fiber concentration and extrusion rate. The extruded filament surface showed minor roughness when the shear rate increased or when the fiber concentration decreased. The results of this experimental characterization give useful information to determine the influence of the processing variables on the final properties of short‐fiber reinforced polypropylene and constitutes the first part of a more ambitious project that also includes the development of a modeling strategy of the processing behavior for short‐fiber composites.     

Rheological behavior of coir‐fiber‐filled polypropylene composites at constant shear stress

The rheological behavior of coir‐fiber‐filled polypropylene (PP) composite has been studied at constant shear stress. The shear stress versus shear rate relationship for the composite follows power law model of viscous flow. Unlike similar studies in the literature, the viscosity is treated as a stress‐independent parameter, which increases with the increase of fiber loading; but decreases with the rise of temperature. The SEM reveals that the fibers are loosely bound to the polymer matrix and the outer surface of the composite is rough and irregular, making it susceptible to high friction with the wall of the flow channel. With analogy to nth order chemical reaction, new formula has been derived for the activation energy of viscous flow, which is found to increase with the increase in the fiber content. The die‐swell ratio decreases with the increase of fiber loading, but increases with the rise of temperature. The elastics parameters of the composite such as the recoverable shear strain, the first normal stress difference, and the elastic strain induced by the stored energy in the capillary reservoir have been estimated based on the die‐swell data. POLYM. COMPOS., 36:51–61, 2015. © 2014 Society of Plastics Engineers     

Investigation of fiber orientation states in injection‐compression molded short‐fiber‐reinforced thermoplastics

Injection‐compression molding (ICM) has received increased attention because of its advantages over conventional injection molding (CIM). This article aims to investigate the effects of five dominating ICM processing parameters on fiber orientation in short‐fiber‐reinforced polypropylene (SFR‐PP) parts. A five‐layer structure of fiber orientation is found across the thickness under most conditions in ICM parts. This is quite different from the fiber orientation patterns in CIM parts. The fibers orient orderly along the flow direction in the shell region, whereas most fibers arrange randomly in the skin and the core regions. Additionally, the fiber orientation changes in the width direction, with most fibers arranging orderly along the flow direction at positions near the mold cavity wall. The results also show that the compression force, compression distance, and compression speed play important roles in determining the fiber states. Thicker shell regions, in which most fibers orient remarkably along the flow direction, can be obtained under larger compression force or compression speed. Moreover, the delay time has an obvious effect on the fiber orientation at positions far from the gate. However, the effect of compression time is found to be negligible. POLYM. COMPOS., 31:1899–1908, 2010. © 2010 Society of Plastics Engineers.     

Numerical simulation of three‐dimensional fiber orientation in injection molding including fountain flow effect

It is essential to predict the nature of flow field inside mold and flow‐induced variation of fiber orientation for effective design of short fiber reinforced plastic parts. In this investigation, numerical simulations of flow field and three‐dimensional fiber orientation were carried out in special consideration of fountain flow effect. Fiber orientation distribution was described using the second‐order orientation tensor. Fiber interaction was modeled using the interaction coefficient C_I. Three closure approximations, hybrid, modified hybrid, and closure equation for C_I=0, were selected for determination of the fiber orientation. The fiber orientation routine was incorporated into a previously developed program of injection mold filling (CAMPmold), which was based on the fixed‐grid finite element/finite difference method assuming the Hele‐Shaw flow. For consideration of the fountain flow effect, simplified deformation behavior of fountain flow was employed to obtain the initial condition for fiber orientation in the flow front region. Comparisons with experimental results available in the literature were made for film‐gated strip and centergated disk cavities. It was found that the orientation components near the wall were were accurately predicted by considering the fountain flow effect. Test simulations were also carried out for the filling analysis of a practical part, and it was shown that the currently developed numerical algorithm can be effectively used for the prediction of fiber orientation distribution in complex parts.     

Interfacial stress transfer in nylon‐6/E‐Glass microcomposites: Effect of temperature and strain rate

In this study, the interfacial properties between E‐glass fibers with different commercial sizings have been investigated on model composites with a nylon‐6 matrix. In particular, the fiber critical length was measured by means of the single‐fiber fragmentation test over a wide range of temperatures (from 25 to 175°C) and strain rates (from 0.0008 to 4 min⁻¹). The general trend observed is that the fiber critical aspect ratio increases as the temperature increases and it decreases as strain rate is increased. The fiber critical aspect ratio for unsized fibers resulted to be reasonably well linearly related to the square root of the fiber to matrix modulus ratio. This results is in accordance with the Cox's shear‐lag theoretical model and the Termonia's numerical simulations. Sized fibers display an higher deviation from the theoretical prevision probably because of the presence of interphases whose properties are different from the bulk matrix. As a consequence, the interfacial shear strength values resulted to be dependent on the fiber sizing. In particular, the fibers coated with an epoxy sizing showed a superior thermal stability of the fiber matrix‐interface with respect to the unsized or nylon compatible sized fibers.     

Data‐Driven Subgrid‐Scale Modeling for Convection‐Dominated Concentration Boundary Layers

A flexible modeling approach for the accurate approximation of convection‐dominated reactive‐species boundary layers is introduced. A substitute problem is solved numerically and analyzed by employing statistical methods. The numerical data are then used to train a machine learning model that can be used to approximate the reactive mass transfer locally if a direct resolution of the concentration boundary layer is infeasible. Compared to previous modeling approaches, the machine learning model replaces the analytical solution of a simplified substitute problem, which makes it applicable to more complicated and general settings.     

Dynamic and capillary shear rheology of natural fiber‐reinforced composites

An extended dynamic and capillary rheological study of molten flax and sisal polypropylene (PP) composites was performed. Fiber concentration varied from 20 to 50 wt% and shear rate from 0.1 rad s^?1 to 10,000 s^#142;?1. Maleic anhydride‐grafted‐PP was used as compatibilizer; it strongly reduces PP and composite viscosity. Composites are yield‐stress shear‐thinning fluids with solid‐like behavior being more pronounced at high fiber content. Composites do not obey Cox–Merz rule, which was explained by different macrostructures of the molten composites in parallel plates and capillary die geometries: random fiber orientation versus strong alignment in the flow direction, respectively. Theories describing the viscosity of suspensions of solid particles were applied to the composites studied and rheological parameters and maximal packing fiber volume fraction were calculated. POLYM. ENG. SCI., 53:2582–2593, 2013. ©2013 Society of Plastics Engineers.     

Modeling and simulation of fiber‐reinforced polymer mold‐filling with phase change

A gas‐solid‐liquid three‐phase model for the simulation of fiber‐reinforced composites mold‐filling with phase change is established. The influence of fluid flow on the fibers is described by Newton's law of motion, and the influence of fibers on fluid flow is described by the momentum exchange source term in the model. A revised enthalpy method that can be used for both the melt and air in the mold cavity is proposed to describe the phase change during the mold‐filling. The finite‐volume method on a non‐staggered grid coupled with a level set method for viscoelastic‐Newtonian fluid flow is used to solve the model. The “frozen skin” layers are simulated successfully. Information regarding the fiber transformation and orientation is obtained in the mold‐filling process. The results show that fibers in the cavity are divided into five layers during the mold‐filling process, which is in accordance with experimental studies. Fibers have disturbance on these physical quantities, and the disturbance increases as the slenderness ratio increases. During mold‐filling process with two injection inlets, fiber orientation around the weld line area is in accordance with the experimental results. At the same time, single fiber's trajectory in the cavity, and physical quantities such as velocity, pressure, temperature, and stresses distributions in the cavity at end of mold‐filling process are also obtained. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 42881.     

Short‐beam and three‐point‐bending tests for the study of shear and flexural properties in unidirectional‐fiber‐reinforced epoxy composites

The bending properties of composite materials are often characterized with simply supported beams under concentrated loads. The results from such tests are commonly based on homogeneous beam equations. For laminated materials, however, these formulas must be modified to account for the stacking sequence of the individual plies. The horizontal shear test with a short‐beam specimen in three‐point bending appears suitable as a general method of evaluation for the shear properties in fiber‐reinforced composites because of its simplicity. In the experimental part of this work, the shear strength of unidirectional‐glass‐fiber‐reinforced epoxy resin composites was determined in different fiber directions with the short‐beam three‐point‐bending test. Also, the elastic constants and flexural properties of the same materials were determined from bending experiments carried out on specimens in the 0, 15, 30, 45, 60, 75, and 90° fiber directions with high span–thickness ratios. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 63–74, 2004     

Measurement and numerical simulation of three‐dimensional fiber orientation states in injection‐molded short‐fiber‐reinforced plastics

To determine three‐dimensional fiber orientation states in injection‐molded short‐fiber composites, a confocal laser scanning microscope (CLSM) is used. Since the CLSM optically sections the specimen, more than two images of the cross sections on and below the surface of the composite can be obtained. Three‐dimensional fiber orientation states can be determined by using geometric parameters of fiber images obtained from two parallel cross sections. For experiments, carbon‐fiber‐reinforced polystyrene is examined by the CLSM and geometric parameters of fibers on each cross‐sectional plane are measured by an image analysis. In order to describe fiber orientation states compactly, orientation tensors are determined at different positions of the prepared specimen. Three‐dimensional orientation states are obtained without any difficulty by determining the out‐of‐plane angles utilizing fiber images on two parallel planes acquired by the CLSM. Orientation states are different at different positions and show the shell–core structure along the thickness of the specimen. Fiber orientation tensors are predicted by a numerical analysis and the numerically predicted orientation states show good agreement with measured ones. However, some differences are found at the end of cavity. They may result from the fountain flow effects, which are not considered in the numerical analysis. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 500–509, 2003