Stochastic Geometry of Two-Dimensional Fiber Assemblies

Yamada, Kunihiro; Horikawa, Akira

doi:10.4188/transjtmsj.36.8_t111

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“…The constitutive equations for deformation of three--dimensionally oriented fibre assembly were discussed by Yamada and Horikawa [33,34]. They can be useful for discussion of the deformation and flow of fibre-filled polymer systems under low shear/strain rate.…”

Section: Three-dimensionally Oriented Fibre Assemblymentioning

confidence: 99%

“…we consider here the case in which all fibres are oriented two-dimensionally. (33) where: A ψ (2k) -Fourier cosine transformation of q(ψ). Fourier cosine transformation is given by: For two-dimensional deformation (λ 1 , λ 2 ), A ψ (2k) is given from eqs.…”

Section: Simple Shear Deformation Of Two-dimensionally Oriented Fibrementioning

confidence: 99%

“…(30), (31) and (34) as: (35) From eqs. (33) and (35), the shear modulus is (36) For the simplification of G relation, Hermanns's orientation coefficient (J) can be used. For two-dimensionally oriented fibre assembly it is defined by the following equation: (37) and also from eq.…”

Section: Simple Shear Deformation Of Two-dimensionally Oriented Fibrementioning

confidence: 99%

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Rheological behavior of fiber-filled polymer melts at low shear rate. Part. I. Modeling of rheological properties

Hausnerová

Honková²,

Lengalova³

et al. 2008

Polimery

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In this review the models applied for the description of non-Newtonian liquids were presented. Highly filled polymer melts showing distinct yield stress are such liquids. The effects of forces of geometrical and physical interactions among the filler particles on the properties were discussed. These interactions forces depend on the type, size and shape of filler particles and in case of fibers also on their orientation. The deformations and flow of fibers assemblies in the melt under shear stress were discussed. The equations used for description of three-or two-dimensionally oriented fibers sets are presented. Key words: polymer melt, filler, modeling of rheological properties, viscosity, yield stress, shear rate.CHARAKTERYSTYKA REOLOGICZNA W ZAKRESIE MA£YCH SZYBKOOECI OECINANIA STOPÓW POLIMERÓW NAPE£NIONYCH W£ÓKNAMI. Cz. I. MODELOWANIE W£AOECIWOOECI REOLO-GICZNYCH Streszczenie -W pracy przegl¹dowej przedstawiono modele stosowane do opisu w³aoeciwooeci reologicznych cieczy nienewtonowskich, którymi s¹ stopy polimerów o wysokim stopniu nape³nienia wykazuj¹ce wyraŸn¹ granicê plastycznooeci. Omówiono wp³yw na omawiane w³aoeciwooeci si³ oddzia-³ywañ geometrycznych i fizycznych miêdzy cz¹stkami nape³niacza. Si³y tych oddzia³ywañ zale¿¹ od rodzaju, wielkooeci i kszta³tu cz¹stek nape³niacza, a w przypadku w³ókien, tak¿e od ich orientacji. Przedyskutowano tak¿e deformacje i przep³yw zespo³ów w³ókien w stopie pod wp³ywem naprê¿eñ oecinaj¹cych. Przedstawiono równanie stosowane w przypadku zespo³ów w³ókien o orientacji trójwymiarowej oraz dwuwymiarowej. S³owa kluczowe: stop polimeru, nape³niacz, modelowanie w³aoeciwooeci reologicznych, lepkooeae, granica plastycznooeci, szybkooeae oecinania.

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Section: Three-dimensionally Oriented Fibre Assemblymentioning

confidence: 99%

Section: Simple Shear Deformation Of Two-dimensionally Oriented Fibrementioning

confidence: 99%