Orientation Tensor Components Research Articles

A constitutive equation for fiber suspensions in viscoelastic media

A viscosity overshoot of fibers filled in a polymer melt under a shear flow is much tougher to predict via the existing constitutive equations of suspension rheology in a viscous media, owing to the effect of fiber orientation on the viscoelastic behavior. The WMT-X (White–Metzner model eXtended by Tseng) viscoelastic fluid model coupled with the typical Dinh–Armstrong fiber suspension model, known as the suspended WMT-X model, is proposed herein. The primary procedure involves verifying the lower viscosity of the completely aligned suspension compared to that of the randomly oriented suspension. In addition, the viscosity overshoot depends on the off-diagonal orientation tensor component in the flow-gradient plane. As a validation, the numerical predictions of transient shear viscosity are in good agreement with the related experimental data.

Probing the Rheological Properties of Liquids Under Conditions of Elastohydrodynamic Lubrication Using Simulations and Machine Learning

In elastohydrodynamic lubrication (EHL), the lubricant experiences pressures in excess of 500 MPa and strain rates larger than 10^5 text{s}^{-1}. The high pressures lead to a dramatic rise in the Newtonian viscosity and the high rates lead to large shear stresses and pronounced shear thinning. The extraction of accurate rheological properties using non-equilibrium molecular dynamics simulations (NEMD) has played a key role in improving our understanding of lubricant flow in EHL conditions. However, the high dimensionality of the output data generated by NEMD simulations often makes a deeper interrogation of the link between molecular-scale features and rheological properties challenging. In this paper, we explore the use of machine learning to analyze and visualize the high-dimensional output data generated in typical NEMD simulations. We show that dimension reduction of NEMD simulation data describing the shear flow of squalane enables a clear visualization of the transition from Newtonian to non-Newtonian shear thinning with increasing shear rate and provides a reliable assessment of the correlation between shear thinning and the evolution in molecular alignment. The end-to-end atom pairs dominate the largest variations in pair orientation tensor components for low-pressure systems (0.1, 100 MPa) and provide the clearest separation of the orientation tensors with rate. On the other hand, the side atom pairs dominate the largest variation in the tensor components for the high-pressure systems (Pge 400 MPa) which exhibit an overall limited evolution in orientation tensors as a function of rate. Dimension reduction using all the six components of the orientation tensors of all 435 pairs associated with a squalane molecule shows that the decrease in viscosity with rate for low pressures is strongly correlated with changes in molecular alignment. However, for high pressures, shear thinning occurs at saturated orientational order.

Investigation on the Coupling Effects between Flow and Fibers on Fiber-Reinforced Plastic (FRP) Injection Parts.

Glass or carbon fibers have been verified that can enhance the mechanical properties of the polymeric composite injection molding parts due to their orientation distribution. However, the interaction between flow and fiber is still not fully understood yet, especially for the flow–fiber coupling effect. In this study, we have tried to investigate the flow–fiber coupling effect on fiber reinforced plastics (FRP) injection parts utilizing a more complicated geometry system with three ASTM D638 specimens. The study methods include both numerical simulation and experimental observation. Results showed that in the presence of flow–fiber coupling effect, the melt flow front advancement presents some variation, specifically the “convex-flat-flat” pattern will change to a “convex-flat-concave” pattern. Furthermore, through the fiber orientation distribution (FOD) study, the flow–fiber coupling effect is not significant at the near gate region (RG). It might result from the strong shear force to repress the appearance of the flow–fiber interaction. However, at the end of filling region (ER), the flow–fiber coupling effect tries to diminish the flow direction orientation tensor component A11 and enhance the cross-flow orientation tensor component A22 simultaneously. It results in the dominance in the cross-flow direction at the ER. This orientation distribution behavior variation has been verified using a micro-computerized tomography (micro-CT) scan and image analysis technology.

Fiber Orientation Distribution Predictions for an Injection Molded Venturi-Shaped Part Validated Against Experimental Micro-Computed Tomography Characterization

Fil: Quintana, Maria Camila. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnologia de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingenieria. Instituto de Investigaciones en Ciencia y Tecnologia de Materiales; Argentina

The rotation of rigid spheroids in a viscous fluid under mean-field effects

An analytical model capturing the effects of mean-field considerations on the orientation evolution of a plurality of rigid spheroids suspended in a Newtonian matrix is developed. Three approaches are taken with increasing sophistication: a mesoscale view involving the analysis of several distinct layers of material subjected to simple shear flow, a traditional micromechanics inspired approach involving the Reuss assumption that each heterogeneity sees an equivalent stress, and the application of the Mori-Tanaka assumption in the viscous inclusion framework of Wetzel and Tucker (JFM 426, 2001). The resulting model behaviors are explored in simple shear flow and extensional flow. The behavior of the Mori-Tanaka model is qualitatively equivalent to that seen in a recent investigation by Gilormini and Chinesta (JNNFM 270, 2019) which considered the effects of the suspending medium being anisotropic in nature. With increase in concentration, the rate of orientation evolution towards collimation is increased as compared to the dilute case, but the relevant fourth-order orientation tensor component in simple shearing flow is shown to see an increased peak value.

Microstructure-mechanical properties relationships in vibration welded glass-fiber-reinforced polyamide 66: A high-resolution X-ray microtomography study

The effect of initial fiber orientation and welding conditions on the mechanical properties and microstructure of 30 wt% glass-fiber-reinforced polyamide 66 was systematically evaluated. For all conditions studied no significant change in the polymer matrix was evidenced. However, fibers in the welded zone were reoriented toward the squeeze and vibration flows and this reorientation is related to the appearance of cavities, as evidenced by high-resolution synchrotron-based X-ray microtomography. It is shown that stress at break values of the welded samples increase with the thickness of the weld zone together with the minimum value of the fiber orientation tensor component in the tensile direction. A drop of strain at break is also related to an increase in the fibers’ concentration in the weld. The maximum void volume fraction being measured on samples which have the thickest welded zones, counterintuitively it does not induce lower stress at break.

Smoothed particle hydrodynamics (SPH) modeling of fiber orientation in a 3D printing process

We present a numerical study of the fused deposition modeling 3D printing process of fiber-reinforced polymers by means of Smoothed Particle Hydrodynamics (SPH). For this purpose, a classical microstructure-based fiber suspension model coupled with a constitutive model for the suspending polymer is implemented within an SPH framework. The chosen model is reviewed, together with the details and specificities of its implementation in SPH. The results for several representative cases are then presented, mainly in terms of contours of fiber orientation tensor components and orientation distributions across the deposited layer thickness. The impact of the fiber concentration and its aspect ratio in a semi-concentrated regime and the effect of the ratio between extrusion and substrate velocities are investigated. Some insights into the link between the flow field and fiber orientation evolution within the printing head and as the material exits the nozzle are given. The main findings lie in the prediction of a skin/core structure in the deposited layer in which the skin regions exhibit a higher fiber alignment with respect to the core region. This effect is found to be enhanced by an increase in fiber concentration and to be sensitive to the substrate-to-extrusion velocity ratio. It is indeed enhanced in cases where the substrate velocity is low compared to the extrusion velocity and accompanied by a larger swelling of the deposit at the nozzle exit.

Measurement of fiber orientation distribution in injection-molded short-glass-fiber composites using X-ray computed tomography

Being able to measure the fiber orientation distribution in the injection-molded composite parts is of considerable importance, since the distribution locally affects the mechanical and physical properties of the final part such as its strength, impact toughness, internal stress, and fatigue properties. In this study, we experimentally measured the fiber orientations in two injection-molded specimens produced from 30wt% short-glass-fiber-reinforced polyamide 6 using plate-shaped cavities with and without a weld-line. The fiber orientation distributions were observed directly using a high-resolution three-dimensional (3D) X-ray computed tomography (CT) system XVA-160α. A simple method based on a series of X-ray CT images was developed to measure the orientation angles of the individual fibers. Further, precise 3D calculations of the fiber orientations related to the second-order orientation tensor components were performed to obtain a consistent description of the observed behavior. Consequently, this study explored a potential application of X-ray CT imaging, a novel and powerful technique for observing and measuring fiber orientation. Further, the software CIMP-PACK3DM was employed to analyze the resin flow in the mold cavity using the finite element method (FEM). The filling patterns of the injection-molded plates with and without a weld-line as determined using FEM were in good quantitative agreement with the X-ray CT imaging analysis results. It was found that the fiber 3D orientation distributions of the injection-molded plates with and without a weld-line could be obtained with precision by combining the high-resolution 3D X-ray CT system XVA-160α with the resin flow analysis software CIMP-PACK3DM using FEM.

Phenomenological improvements to predictive models of fiber orientation in concentrated suspensions

The standard Folgar-Tucker (FT) orientation equation is a useful method for theoretically determining isotropic fiber orientation in concentrated suspensions. However, when quantitatively compared with related experimental observations, this equation demonstrates an over-prediction inaccuracy. Recently, the Phelps-Tucker anisotropic rotary diffusion (ARD) model has shown an ability to handle primary anisotropic fiber orientation. Nevertheless, the ARD tensor depending upon Hand's tensor is difficult to apply in general, because numerous parameters themselves are so sensitive as to affect the stability of any numerical results. To address these critical problems in predicting fiber orientation, this study proposes an improved ARD tensor combined with a new retardant principal rate (iARD-RPR) model. The RPR model is a coaxial correction of the orientation tensor for the FT equation. In addition, the iARD tensor, consisting of an identity tensor and a dimensionless fiber-rotary-resistance tensor, is more concise with two available parameters. As a validation, the iARD-RPR model nicely fits the orientation tensor components measured in transient simple shear flows. Of particular importance is the good agreement between the predictive fiber orientation distribution and the practical core-shell structure for the center-gated disk of injection molding of fiber-reinforced thermoplastics.

Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials

Diffraction contrast tomography is a near-field diffraction-based imaging technique that provides high-resolution grain maps of polycrystalline materials simultaneously with the orientation and average elastic strain tensor components of the individual grains with an accuracy of a few times 10−4. Recent improvements that have been introduced into the data analysis are described. The ability to process data from arbitrary detector positions allows for optimization of the experimental setup for higher spatial or strain resolution, including high Bragg angles (0 < 2θ < 180°). The geometry refinement, grain indexing and strain analysis are based on Friedel pairs of diffraction spots and can handle thousands of grains in single- or multiphase materials. The grain reconstruction is performed with a simultaneous iterative reconstruction technique using three-dimensional oblique angle projections and GPU acceleration. The improvements are demonstrated with the following experimental examples: (1) uranium oxide mapped at high spatial resolution (300 nm voxel size); (2) combined grain mapping and section topography at high Bragg angles of an Al–Li alloy; (3) ferrite and austenite crystals in a dual-phase steel; (4) grain mapping and elastic strains of a commercially pure titanium sample containing 1755 grains.

Effect of macromolecular entanglement on the simple shear flow of viscoelastic fluid

We investigate the stationary shear flow of an incompressible fluid described by the non-linear differential-vector model proposed by Remmelgassom, Harrison and Lill (RHL-model). In the absence of macromolecular entanglements, analytical expressions for orientation tensor components and material functions are derived, and the effect of the parameters of the model on their form is studied. The ranges of model parameters, in which the examined relations show ambiguity, are determined. The influence of macromolecular length limitation on the form of tensor components and material functions is studied numerically.

Micromechanical simulations of biaxial yield, hardening and plastic flow in short glass fiber reinforced polyamide

Mean-field homogenization (MFH) is used to predict the biaxial yield behavior, hardening and plastic flow of composite materials made of an elasto-plastic matrix reinforced with misaligned short fibers. The procedure is applied to short glass fiber reinforced polyamide, which represents an important industrial application of those composites. First, MFH is verified against full-field accurate finite element simulations of representative volume elements with multiple fibers. Next, a parametric study is carried out with MFH in order to predict the biaxial plastic behavior of numerous microstructures corresponding to various values of volume fraction, aspect ratio and second-rank orientation tensor components of the glass fibers. Results demonstrate the loss of both isotropic hardening and plastic flow normality, except for 2D random orientation. For illustration, a fit of Hill's orthotropic plasticity criterion is conducted for several orientation tensors.

Quantitative 3D measurement of the nanostructural features that dictate mesoscale performance properties of nanocomposites

Mesoscale performance properties of nanocomposites are dictated by the nanoscale structure developed in the composite during processing, combining nanoscale contributions over a mesoscale volume. In this artilce, for the first time, we present a procedure that deduces the fully 3D process-induced nanostructural features of carbon nanofiber/polymer composites responsible for the mesoscale performance. In particular, we have developed a method for obtaining the nanofiber orientation in 3D Euclidean space from 2D projections provided by a transmission electron microscope. The 3D Euler angles we obtain are used to construct orientation tensors, the measure of nanostructure that has the most significant influence on mesoscale performance properties. Our measurement method is benchmarked by using numerically generated 3D samples to compare orientation tensor components known a priori with those generated using our procedure. A significant contribution of the procedure is its ability to produce quantitative 3D measurements of the evolution of nanostructure in space and time. The method is successfully applied to observe the effect of extensional rheology on nanofiber orientation. It is shown that orientation tensor data obtained from our experimental method accurately fits the predictions of the fiber orientation evolution equation proposed by Folgar and Tucker. POLYM. COMPOS., 31:1495–1503, 2010. © 2009 Society of Plastics Engineers

Numerical solution of the Fokker–Planck equation for fiber suspensions: Application to the Folgar–Tucker–Lipscomb model

The probability distribution function for fiber orientation under flow (Fokker–Planck equation) is numerically solved using a finite volume method. Different time and spatial schemes have been tested to reduce considerably the computational time and to cover a wide range of the Peclet ( Pe) number. For Pe ≤ 10 3, the results are compared with data available in the literature and for Pe ≥ 10 3, the numerical schemes are assessed using an analytical solution. Excellent agreement was observed and the method allowed us to describe the evolution of the fourth-order orientation tensor components of fibers in transient simple shear (forward and reverse) flows, and compare with the predictions of an orthotropic closure approximation. In addition, the Folgar–Tucker–Lipscomb (FTL) model was used with no closure approximation to predict the rheological behavior of a short fiber-filled polypropylene in simple shear flow. The accuracy of commonly used closure approximations is discussed, and key aspects of the FTL model that still need to be improved are highlighted in the scope of this work.

Study on Fiber Weight Fraction Effect on Tensile Modulus of Polystyrene (PS) Composites Reinforced with Short Glass Fiber (SGF) Based on Their Fiber Orientation

In this study, the tensile modulus of injection molded SGF/PS composites is investigated. The experimental and simulation results show, increasing of tensile modulus of these composites, is inconsistent with increasing of fiber content in high fiber weight fraction. This inconstancy is more distinguishable for fiber weight fractions greater than 40%wt of GF. To explain away this observation, the fiber orientation tensor of molded part is simulated. The behavior of a11, the first orientation tensor component in filling flow direction, through the thickness of the part is obtained for different SGF/PS compositions. The consequent curves can explain the unexpected behavior and support this idea that the effects of fiber orientation should be considered in calculation of SFG composite properties.

Effects of Some Injection Molding Process Parameters on Fiber Orientation Tensor of Short Glass Fiber Polystyrene Composites (SGF/PS)

Calculation of fiber orientation distribution is the reference standard for determining the numerous physical and mechanical properties of injection molded short fiber reinforced thermoplastics. On the other hand, most of the properties of these composites depend on their fiber orientation pattern, which can be represented by tensorial notation, aij. This work focuses on numerical calculation of a fiber orientation tensor of an injection molded short glass fiber polystyrene (SGF-PS) composite part, shaped as a rectangular plate. In this study, the effects of some parameters of the injection molding process including injection flow rate, mold wall temprature, packing pressure and also fiber content on the changes of fiber orientations of this specimen are investigated. Our studies are concentrated on determining the changes of the first orientation tensor component in the flow direction due to different injection parameters. In addition, the changes on tensile modulus of the injected part are simulated in every condition. The simulations show how these molding parameters can influence both fiber orientation and tensile modulus of injection molded parts. At the first step, in order to be confident about the software results, they are validated by experimental data in two cases.

Simulation of Three-dimensional Fiber Orientation in Weldline Areas During Push-pull-processing

Push-pull-processing (PPP) is a live in-mold manipulation method of co-injection molding providing increased opportunities for controlling the melt flow during solidification. The mold has two gates connected to two synchronized injection units. During the packing phase, the melt moves through the mold several times. This modified filling process influences the orientation of fibers in a part significantly. In this work, a modified 3-D model for PPP has been developed and performed with the aid of a commercial software package (Moldflow) in order to predict the fiber orientation distribution within the weldline area of PPP parts. The predicted values of orientation tensor components (a11) are found to agree reasonably well with corresponding experimental measurements.

Fibre-orientation measurements in short-glass-fibre composites—II: a quantitative error estimate of the 2D image analysis technique

Fibre-orientation measurement by two-dimensional (2D) image analysis of polished cross-sections is a rapid and highly efficient method for determining the fibre orientation distribution over large sample areas. In a recent paper, a new technique was presented for measuring fibre orientation to a high level of accuracy by the use of a confocal microscope. In this paper, the confocal technique is used to evaluate independently the performance of the 2D image analysis technique and the errors are presented in full. The results reveal a significant systematic error in orientation measurements and the effect of image resolution is considered. A method is proposed for correcting this systematic error and its validity is verified experimentally. A technique for determining the sampling error of a fibre-orientation measurement is presented, enabling the calculation of confidence limits about the derived orientation tensor components. It is shown how confidence limits aid the comparison of two fibre-orientation measurements of similar samples. Furthermore, the sampling error should enable a more meaningful comparison of numerical simulation of injection moulded composites and their experimentally manufactured counterparts.

Analysis of knitted fabric reinforced composites: Part II. Stiffness and strength

Abstract The influence of the knit structure on the stiffness and strength in tensile and in share loading of glass warp knitted fabric epoxy composites is studied. The average strength depends on the fibre content and on the linear density of the yarn. The anisotropy in tensile and shear properties is related to the orientation tensor components a 1111 and a 1122 , respectively. By making use of these relationships, a knit structure can be evaluated with regard to the mechanical properties of its composite with only two measurements: (1) measurement of the achievable fibre content; and (2) measurement of the fibre orientations.

Determination of 3D fiber orientation distribution in thermoplastic injection molding

An automated optical section method for quantifying the orientation state of short fibers in injection molded parts is presented. The method is based on imaging tracer fibers in index of refraction-matched transparent composites. The experimental methods and performance characteristics of the method are described. The method is non-destructive, operator-independent, economical and rapid. Scanning to depths of about 1.3 mm without cutting is possible at 10 μm spatial resolution at processing rates of < 10 min mm −3. Straightforward modifications should allow processing rates >1 mm 3 min −1. Calibration tests suggest that fiber orientation is quantified to within the accuracy expected based on the degree of solid angle discretization chosen for analysis (5 ° here). Reproducible fiber orientation distributions are realized for sample domain sizes of about 2 mm × 2 mm × 0.15 mm. The orientation distribution function is quantified as well as the orientation tensor components. Convenient graphical visualizations of the 3D orientation distribution function and tensor representations are provided.