Function-based reconstruction of the fiber orientation distribution function of short-fiber-reinforced polymers

2022 ◽  
Vol 66 (1) ◽  
pp. 147-160
Author(s):  
Matija Nabergoj ◽  
Janez Urevc ◽  
Miroslav Halilovič
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Fiber Orientation ◽  
Orientation Distribution ◽  
Short Fiber ◽  
Fiber Reinforced Polymers ◽  
Fiber Reinforced ◽  
Reinforced Polymers ◽  
Fiber Orientation Distribution

A Statistical Method to Obtain Material Properties From the Orientation Distribution Function for Short-Fiber Polymer Composites

Materials ◽  
2005 ◽  
Author(s):  
David A. Jack ◽  
Douglas E. Smith
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Material Properties ◽  
Fiber Orientation ◽  
Orientation Distribution ◽  
Short Fiber ◽  
Expectation Values ◽  
Order Tensor ◽  
Fiber Orientation Distribution ◽  
Orientation Tensors

Material behavior of short-fiber composites can be found from the fiber orientation distribution function, with the only widely accepted procedure derived from the application of orientation/moment tensors. The use of orientation tensors requires a closure, whereby the higher order tensor is approximated as a function of the lower order tensor thereby introducing additional computational errors. We present material property expectation values computed directly from the fiber orientation distribution function, thereby alleviating the closure problem inherent to orientation tensors. Material properties are computed from statistically independent unidirectional fiber samples taken from the fiber orientation distribution function. The statistical nature of the distribution function is evaluated with Monte-Carlo simulations to obtain approximate stiffness tensors from the underlying unidirectional composite properties. Examples are presented for simple analytical distributions to demonstrate the effectiveness of expectation values and results are compared to properties obtained through orientation tensors. Results yield a value less than 1.5% for the coefficient of variation and suggest that the orientation tensor method for computing material properties is applicable only for the case of non-interacting fibers.

Fast Solutions for the Fiber Orientation of Concentrated Suspensions of Short-Fiber Composites Using the Exact Closure Method

2010 ◽  
Author(s):  
Stephen Montgomery-Smith ◽  
David A. Jack ◽  
Douglas Smith
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Fiber Orientation ◽  
Orientation Distribution ◽  
Equation Of Motion ◽  
Fiber Composites ◽  
Short Fiber ◽  
Second Order ◽  
Orientation Tensor ◽  
Kinetics Of

The kinetics of the fiber orientation during processing of short-fiber composites governs both the processing characteristics and the cured part performance. The flow kinetics of the polymer melt dictates the fiber orientation kinetics, and in turn the underlying fiber orientation dictates the bulk flow characteristics. It is beyond computational comprehension to model the equation of motion of the full fiber orientation probability distribution function. Instead, typical industrial simulations rely on the computationally efficient equation of motion of the second-order orientation tensor (also known as the second-order moment of the orientation distribution function) to model the characteristics of the fiber orientation within a polymer suspension. Unfortunately, typical implementation forms of any order orientation tensor equation of motion requires the next higher, even ordered, orientation tensor, thus necessitating a closure of the higher order expression. The recently developed Fast Exact Closure avoids the classical closure problem by solving a set of related second-order tensor equations of motion, and yields the exact solution for pure Jeffery’s motion as the diffusion goes to zero. Typical closures are obtained through a fitting process, and are often obtained by fitting for orientation states obtained from solutions of the full orientation distribution function, thus tying the closure to the flows from which it was fit. With the recent understandings of the limitations of the Folgar and Tucker (1984) model of fiber interactions during processing, it has become clear the importance of developing a closure that is independent of any choice of fitting data. The Fast Exact Closure presents an alternative in that it is constructed independent of any fitting process. Results demonstrate that when diffusion exists, the solution is not only physical, but solutions for flows experiencing Folgar-Tucker diffusion are shown to exhibit an equal to or greater accuracy than solutions relying on closures developed via a curve fitting approach.

Orientation Distribution of Fiber Suspensions in Extensional Flow

2013 ◽  
Vol 785-786 ◽  
pp. 981-984 ◽  
Author(s):  
Zan Huang ◽  
Jin Ping Qu ◽  
Ji Wei Geng ◽  
Shu Feng Zhai ◽  
Shi Kui Jia
Keyword(s):  
Differential Equation ◽  
Distribution Function ◽  
Orientation Distribution Function ◽  
Fiber Orientation ◽  
Extensional Flow ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Fiber Suspensions ◽  
Short Fibers ◽  
Fiber Orientation Distribution

An orientation distribution function is adopted to describe three-dimensional orientation distribution of short fibers suspensions in extensional flow. A mathematical model of evolution process on fiber orientation distribution function is established by analytical method. Numerical simulation is also used to describe two and three dimensional orientation distribution of fibers. Therefore, analytical solution of differential equation on forecast fiber orientation distribution is deduced.

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