Numerical Evaluation of Single Fiber Motion for Short-Fiber-Reinforced Composite Materials Processing

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Dongdong Zhang ◽  
Douglas E. Smith ◽  
David A. Jack ◽  
Stephen Montgomery-Smith
Keyword(s):  
Aspect Ratio ◽  
Original Work ◽  
Polymer Melt ◽  
Short Fiber ◽  
Single Fiber ◽  
Runge Kutta Method ◽  
Reinforced Composite ◽  
Fiber Motion ◽  
Angular Velocities

This paper presents a computational approach for simulating the motion of a single fiber suspended within a viscous fluid. We develop a finite element method (FEM) for modeling the dynamics of a single rigid fiber suspended in a moving fluid. Our approach seeks solutions using the Newton–Raphson method for the fiber’s linear and angular velocities such that the net hydrodynamic forces and torques acting on the fiber are zero. Fiber motion is then computed with a Runge-Kutta method to update the fiber position and orientation as a function of time. Low-Reynolds-number viscous flows are considered since these best represent the flow conditions for a polymer melt within a mold cavity. This approach is first used to verify Jeffery’s orbit (1922) and addresses such issues as the role of a fiber’s geometry on the dynamics of a single fiber, which were not addressed in Jeffery’s original work. The method is quite general and allows for fiber shapes that include, but are not limited to, ellipsoidal fibers (such as that studied in Jeffery’s original work), cylindrical fibers, and bead-chain fibers. The relationships between equivalent aspect ratio and geometric aspect ratio of cylindrical and other axisymmetric fibers are derived in this paper.

Numerical Evaluation of Single Fiber Motion for Short Fiber Composites Materials Processing

2010 ◽  
Author(s):  
Dongdong Zhang ◽  
Douglas E. Smith ◽  
David A. Jack ◽  
Stephen Montgomery-Smith
Keyword(s):  
Original Work ◽  
Polymer Melt ◽  
Numerical Approach ◽  
Short Fiber ◽  
Single Fiber ◽  
Axis Ratio ◽  
Runge Kutta Method ◽  
Composites Materials ◽  
Fiber Motion ◽  
Angular Velocities

This paper presents a numerical approach for calculating the single fiber motion in a viscous flow. This approach addresses such issues as the role of axis ratio and fiber shape on the dynamics of a single fiber, which was not addressed in Jeffery’s original work. We develop a Finite Element Method (FEM) for modeling the dynamics of a single rigid fiber suspended in a moving fluid. Low Reynolds number viscous flows are considered since these best represent the flow conditions for a polymer melt within a mold cavity. Our approach seeks the fiber angular velocities that zero the hydrodynamic torques acting on the fiber using the Newton-Raphson method. Fiber motion is then computed with a Runge-Kutta method to update the position, i.e. the angle of the fiber as a function of time. This method is quite general and allows for fiber shapes that include, but are not limited to, ellipsoidal fibers (such as that studied in Jeffery’s original work), cylindrical fibers and beads-chain fibers. The relationships between equivalent axis ratios and geometrical axis ratios for cylindrical and beads-chain fibers are derived in this paper.

Application of Embedded Element in the Short Fiber Reinforced Composite

2018 ◽  
Vol 774 ◽  
pp. 241-246
Author(s):  
Jian Hong Gao ◽  
Xiao Xiang Yang ◽  
Li Hong Huang
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Aspect Ratio ◽  
Volume Fraction ◽  
Element Model ◽  
Short Fiber ◽  
Fiber Reinforced ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
Edge Size

The finite element analysis (FEA) is a numerical method for predicting the mechanical property of short fiber reinforced composite usefully. However, as we know, there is always a “jamming” limit when generating fiber architecture expecially in the cases of high volume fraction and high aspect ratio of short fiber. Even if the volume fraction and aspect ratio in finite element model meet the practical requirements, the problem of mesh deformity will always occur which would lead to unconverge of numerical computation. In this work, embedded element technique which will help to reduce the probability of the above two problems is employed to establish the finite element model of short fiber reinforced composite. The effect of edge size, thickness and mesh density of FE models on the elastic modulus were investigated. Numerical results show that the value of elastic modulus mainly depend on the edge size and fiber amount of FE model while the effect of thickness can be neglected. The elastic modulus takes to converge for high element number. An inverse method is proposed to calculate volume fraction of short fibers, by which numerical results agree well with the calculation results of empirical formula based on Halpin-Tsai equation.

Value Meanings of the Modern Textbook of the Russian Language

2018 ◽  
Vol 79 (8) ◽  
pp. 7-10 ◽  
Author(s):  
A. D. Deikina
Keyword(s):  
Original Work ◽  
School Education ◽  
Russian Language ◽  
Educational Strategy ◽  
Personal Meanings ◽  
Current Trends ◽  
Modern Textbook ◽  
The Russian Language

Analysis of the current trends in the teaching of the Russian language allows to assert the value of the category of values in the educational strategy. In the context of orientation of the textbook to modern requirements the role of the text in the characteristic of language as an expression of value and personal meanings is emphasized. Providing personal and humanistic thinking and the formation of value view of students in the Russian language is more successful on a wide background of text material by stimulating a variety of ways of original work of students. Its predicted results are closely related to the awareness of the value of the Russian language. Attention is paid to the resources associated with the organization of open educational space on the basis of axiological ideas as the leading in the theory of school education and textbook.

»Gott segne Kupfer« Goethes Kunstbeschreibungen im Zeitalter der semitechnischen Reproduzierbarkeit

2017 ◽  
Vol 80 (3) ◽  
pp. 392-417
Author(s):  
Mattias Pirholt
Keyword(s):  
Crucial Role ◽  
Original Work ◽  
Continuous Process ◽  
Work Experiences ◽  
Autobiographical Accounts ◽  
Plaster Casts

Abstract This study investigates how the experience of reproductions – drawings, copperplate engravings, woodcuts, lithography, plaster casts, and so forth – influenced Johann Wolfgang von Goethe’s conception of art in general and his descriptions of art (e.g., ekphrases, reviews, and autobiographical accounts) in particular. Well acquainted with the technologies of reproduction of his time, Goethe, often in collaboration with Johann Heinrich Meyer, acknowledged the crucial role of reproductions for the understanding of the productive idea of the original work. Experiences of reproductions and comparisons between copies, drafts, and the original enabled Goethe to grasp the idea as an ever-transforming productive constant of the continuous process of becoming of the work.

Investigation into the role of poly(vinylpyrrolidone) in the growth of high aspect ratio silver nanowires

2021 ◽  
Vol 128 ◽  
pp. 108558
Author(s):  
Yuyue Guo ◽  
Yangfei Hu ◽  
Xiaojiong Luo ◽  
Shudong Lin ◽  
Jiwen Hu ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Silver Nanowires

Anisotropic Effective Moduli of Cracked Short-Fiber Reinforced Composites

1999 ◽  
Vol 66 (3) ◽  
pp. 709-713 ◽  
Author(s):  
R. S. Feltman ◽  
M. H. Santare
Keyword(s):  
Short Fiber ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Effective Moduli ◽  
Fiber Reinforced ◽  
Fiber Fracture ◽  
Composite Systems ◽  
Reinforced Composite ◽  
Anisotropic Elastic ◽  
Energy Dissipated

A model is presented to analyze the effect of fiber fracture on the anisotropic elastic properties of short-fiber reinforced composite materials. The effective moduli of the material are modeled using a self-consistent scheme which includes the calculated energy dissipated through the opening of a crack in an arbitrarily oriented elliptical inclusion. The model is an extension of previous works which have modeled isotropic properties of short-fiber reinforced composites with fiber breakage and anisotropic properties of monolithic materials with microcracks. Two-dimensional planar composite systems are considered. The model allows for the calculation of moduli under varying degrees of fiber alignment and damage orientation. In the results, both aligned fiber systems and randomly oriented fiber systems with damage-induced anisotropy are examined.

Flow Measurements in a Nozzle Guide Vane Passage With a Low Aspect Ratio and Endwall Contouring

2000 ◽  
Author(s):  
Steven W. Burd ◽  
Terrence W. Simon
Keyword(s):  
Aspect Ratio ◽  
Flow Field ◽  
Guide Vane ◽  
Flow Measurements ◽  
Vast Number ◽  
Aspect Ratios ◽  
Nozzle Guide Vane ◽  
Endwall Contouring ◽  
Nozzle Guide

The vast number of turbine cascade studies in the literature has been performed in straight-endwall, high-aspect-ratio, linear cascades. As a result, there has been little appreciation for the role of, and added complexity imposed by, reduced aspect ratios. There also has been little documentation of endwall profiling at these reduced spans. To examine the role of these factors on cascade hydrodynamics, a large-scale nozzle guide vane simulator was constructed at the Heat Transfer Laboratory of the University of Minnesota. This cascade is comprised of three airfoils between one contoured and one flat endwall. The geometries of the airfoils and endwalls, as well as the experimental conditions in the simulator, are representative of those in commercial operation. Measurements with hot-wire anemometry were taken to characterize the flow approaching the cascade. These measurements show that the flow field in this cascade is highly elliptic and influenced by pressure gradients that are established within the cascade. Exit flow field measurements with triple-sensor anemometry and pressure measurements within the cascade indicate that the acceleration imposed by endwall contouring and airfoil turning is able to suppress the size and strength of key secondary flow features. In addition, the flow field near the contoured endwall differs significantly from that adjacent to the straight endwall.

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