Transient Rheology of Polypropylene Melt Reinforced with Long Glass Fibers Kevin C. Ortman1; Neeraj Agarwal1; Donald G. Baird1; Peter Wapperom2, Jeffrey Giacomin3
Chemical Engineering1, Mathematics2, Virginia Tech, Blacksburg, VA; Mechanical Engineering3, University of Wisconsin-Madison, Madison, WI
Motivation for Research
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DADt
= A ⋅ κT +κ ⋅ A − [(κ +κT ) : A]A
− 2k[B − A tr(B)] + 2C1IID (δ − 3A)
DBDt
= B ⋅ κT +κ ⋅ B − [(κ +κT ) : A]B− 2k[A − B tr(B)] + 2C1IID (tr(B)δ − 3B)
R = rrtr(rr)
where r = (p − q)
Create long fiber reinforced thermoplastic (LFT) materials as a function of processing design for: Increased strength properties Production of light weight materials More energy efficient transportation
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DADt
= A •κT +κ • A − [(κ +κT ) : A]A
+ 2C1IID (δ − 3A)
3 mm 1 mm
Improve the accuracy of currently available LFT orientation simulations for molding processes by using/modifying current fiber orientation theory in combination with using state-of-the-art numerical techniques. Establish a method for characterizing long fiber composite fluids based on rheology (independent of molding processes). Evaluate the accuracy of the simulations by comparing numerical predictions with experimentally determined orientations in simple and complex flows.
Scope of Research
Folgar-Tucker Orientation Model Generalized Jefferyʼs for Fibers
Folgar-Tucker Term
Bead-Rod Orientation Model
Acknowledgments NSF: DMI-0853537 Saibic and RTP for material Aning Lab Davis Lab (Adam Larkin, Dr. Will Miles)
Conclusions and Future Work
Celstran Azdel
Orientation Representation and Theory Experimental Methods and Results
Lipscomb Stress Model
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Π = −Pδ +σ
σ =ηs(κ +κT ) + c1ϕηs(κ +κT ) +ϕηsN(κ +κT ) : (AA)
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η+ =σ12γ. =ηs + c1ϕηs + 2ϕηsNA12
2 (Stress Growth)
Model Parameters: c1 steady-state viscosity enhancement N magnitude of the viscosity overshoot CI isotropic rotary diffusion term k flexibility term in Bead-Rod
Sliding Plate Rheometer: Rectilinear and homogenous flow Reduces unwanted fiber/fiber and fiber/wall contacts Localized stress measurements reduce edge effects Fiber Orientation Analysis: Digital imaging method of Leedʼs
Long fibers are observed to exhibit flexibility Sliding Plate efficiently allows for the study of LFT rheology Long Fibers orient in the direction of simple shear, despite their initial orientation. Flexibility theory can be used to delay orientation but rheology predictions, using the chosen orientation and stress models, are not consistent with experiment. Future desire to track more fibers from shear startup Future investigation of Bead-Rod behavior in complex flow
Long fibers exhibit flexibility… Should this be accounted for in an orientation model?
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A = pp∫ ψ(p,q,t)dpdq
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B = pq∫ ψ(p,q,t)dpdq
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A = pp∫ ψ(p, t)dp
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