Transient Rheology of Polypropylene Melt Reinforced · PDF fileTransient Rheology of...

1
Transient Rheology of Polypropylene Melt Reinforced with Long Glass Fibers Kevin C. Ortman 1 ; Neeraj Agarwal 1 ; Donald G. Baird 1 ; Peter Wapperom 2 , Jeffrey Giacomin 3 Chemical Engineering 1 , Mathematics 2 , Virginia Tech, Blacksburg, VA; Mechanical Engineering 3 , University of Wisconsin-Madison, Madison, WI Motivation for Research DA Dt = A κ T + κ A [( κ + κ T ): A ]A 2k[B A tr(B )] + 2C 1 II D ( δ 3A ) DB Dt = B κ T + κ B [( κ + κ T ): A ]B 2k[ A B tr(B )] + 2C 1 II D ( tr(B ) δ 3B ) R = r r tr(r r ) 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 DA Dt = A κ T + κ A [( κ + κ T ): A ]A + 2C 1 II D (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 Celstra n Azdel Orientation Representation and Theory Experimental Methods and Results Lipscomb Stress Model Π = Pδ + σ σ = η s (κ + κ T ) + c 1 ϕη s (κ + κ T ) + ϕη s N(κ + κ T ):( A A ) η + = σ 12 γ . = η s + c 1 ϕη s + 2ϕη s NA 12 2 (Stress Growth) Model Parameters: c 1 steady-state viscosity enhancement N magnitude of the viscosity overshoot C I 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 flexibilityShould this be accounted for in an orientation model? A = p p ψ( p , q , t ) dp dq B = p q ψ( p , q , t ) dp dq A = p p ψ( p , t ) dp Strautins and Latz, Rheol Acta, 2007 x 1 x 2 !"#$% x 3 ’())*+), ’())*+)- ) ’) ,) -) .) /) 0) 1) 2) ! #$%&’( ) )(. . " # (s $1 ) ) )(’ )(, )(- )(. )(/ )(0 )(1 )(2 )(3 )()) ’()) ,()) -()) .()) /()) *+,-./%01. 23-%+ 4%/- 567’8 4’’ 4,, 4-- ) )(), )(). )()0 )()2 )(’ )()) ’()) ,()) -()) .()) /()) *+,-./%01. 23-%+ 4%/- 567’8 4’, x 1 x 2 !"#$% x 3 ’())*+), ’())*+)- ) ’) ,) -) .) /) 0) 1) 2) ! #$%&’( ) )(. . " # ( s $1 ) ) )(’ )(, )(- )(. )(/ )(0 )(1 )(2 )(3 )()) ’()) ,()) -()) .()) /()) *+,-./%01. 23-%+ 4%/- 567’8 4’’ 4,, 4-- ) )(), )(). )()0 )()2 )(’ )()) ’()) ,()) -()) .()) /()) *+,-./%01. 23-%+ 4%/- 567’8 4’, x 1 x 2 !"#$% x 3 ’())*+), ’())*+)- ) ’) ,) -) .) /) 0) 1) 2) ! #$%&’( ) )(. . " # ( s $1 ) ) )(’ )(, )(- )(. )(/ )(0 )(1 )(2 )(3 )()) ’()) ,()) -()) .()) /()) *+,-./%01. 23-%+ 4%/- 567’8 4’’ 4,, 4-- ) )(), )(). )()0 )()2 )(’ )()) ’()) ,()) -()) .()) /()) *+,-./%01. 23-%+ 4%/- 567’8 4’, γ . = 1 0 10 20 30 40 50 60 70 Γ 0.2 0.4 0.6 0.8 1.0 Aii,Rii !"#$%&’()*+,& .,%/ 0"/ =A 11 =A 22 =A 33 10 20 30 40 50 60 70 Γ 600 800 1000 1200 1400 Η Pa Sec !"#$%&’()*+,& .,%/ 0"/ = Data Points = FT = BR γ . = 1 A = 1 0 0 0 0 0 0 0 0 A = 1/3 0 0 0 1/3 0 0 0 1/3 Randomly Oriented Fully Oriented

Transcript of Transient Rheology of Polypropylene Melt Reinforced · PDF fileTransient Rheology of...

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

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

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

Π = −Pδ +σ

σ =ηs(κ +κT ) + c1ϕηs(κ +κT ) +ϕηsN(κ +κT ) : (AA)

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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B = pq∫ ψ(p,q,t)dpdq

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