An invariant based fitted closure of the sixth-order orientation tensor for modeling short-fiber suspensions

Jack, David A.; Smith, Douglas E.

doi:10.1122/1.2000970

Cited by 38 publications

(31 citation statements)

References 25 publications

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“…Our work utilizes the invariant-based INV 6 closure approximation of Jack and Smith [19]. In order to explore the effectiveness of this model, the orientation tensor C may be incorporated into a model forȦ d , the diffusive contribution ofȦ.…”

Section: Previous Ard Models 241 the Koch Modelmentioning

confidence: 99%

An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics

Phelps

Tucker

2009

Journal of Non-Newtonian Fluid Mechanics

284

195

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Section: Previous Ard Models 241 the Koch Modelmentioning

confidence: 99%

An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics

Phelps

Tucker

2009

Journal of Non-Newtonian Fluid Mechanics

284

195

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“…Hinch & Leal 1976;Altan et al 1989Altan et al , 1990Verleye & Dupret 1993;Cintra & Tucker 1995;VerWeyst et al 1999;Chung & Kwon 2002;Han & Im 2002;Jack & Smith 2005;Jack, Schache & Smith 2010) have proposed closures, that is formulae to calculate the fourth-order moment tensor A from the second-order moment tensor A. Many of the approximate closures involve coefficients obtained by fitting numerical data found by solving (1.2) using a finite-element method (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Exact tensor closures for the three-dimensional Jeffery's equation

Montgomery‐Smith

Jack

et al. 2011

J. Fluid Mech.

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This paper presents an exact formula for calculating the fourth-moment tensor from the second-moment tensor for the three-dimensional Jeffery's equation. Although this approach falls within the category of a moment tensor closure, it does not rely upon an approximation, either analytic or curve fit, of the fourth-moment tensor as do previous closures. This closure is orthotropic in the sense of Cintra & Tucker (J.

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“…This necessitates the need for a closure by which the higher order orientation tensor is approximated as a function of a lower order tensor, i.e., A = f (A). There exist many closure approximations in the literature of A in terms of A (see e.g., [13,14,28,[40][41][42][43][44][45][46]] to list just a few) and several for the sixth-order orientation tensor (see e.g., [30,47,48]). Montgomery-Smith et al [45] demonstrated that the orthotropic fitted (ORT) closure implemented by VerWeyst and Tucker [28] and the fast exact closure (FEC) [45] are the most accurate.…”

Section: Fiber Orientation Modelingmentioning

confidence: 99%

Prediction of the Fiber Orientation State and the Resulting Structural and Thermal Properties of Fiber Reinforced Additive Manufactured Composites Fabricated Using the Big Area Additive Manufacturing Process

et al. 2018

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Recent advances in Fused Filament Fabrication (FFF) include large material deposition rates and the addition of chopped carbon fibers to the filament feedstock. During processing, the flow field within the polymer melt orients the fiber suspension, which is important to quantify as the underlying fiber orientation influences the mechanical and thermal properties. This paper investigates the correlation between processing conditions and the resulting locally varying thermal-structural properties that dictate both the final part performance and part dimensionality. The flow domain includes both the confined and unconfined flow indicative of the extruder nozzle within the FFF deposition process. The resulting orientation is obtained through two different isotropic rotary diffusion models, the model by Folgar and Tucker and that of Wang et al., and a comparison is made to demonstrate the sensitivity of the deposited bead's spatially varying orientation as well as the final processed part's thermal-structural performance. The results indicate the sensitivity of the final part behavior is quite sensitive to the choice of the slowness parameter in the Wang et al. model. Results also show the need, albeit less than that of the choice of fiber interaction model, to include the extrudate swell and deposition within the flow domain.

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An invariant based fitted closure of the sixth-order orientation tensor for modeling short-fiber suspensions

Cited by 38 publications

References 25 publications

An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics

An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics

Exact tensor closures for the three-dimensional Jeffery's equation

Prediction of the Fiber Orientation State and the Resulting Structural and Thermal Properties of Fiber Reinforced Additive Manufactured Composites Fabricated Using the Big Area Additive Manufacturing Process

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