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Research Papers

Evaluating Rigid and Semiflexible Fiber Orientation Evolution Models in Simple Flows

[+] Author and Article Information
Gregory M. Lambert

Department of Chemical Engineering,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
e-mail: s1lverch@vt.edu

Donald G. Baird

Department of Chemical Engineering,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
e-mail: dbaird@vt.edu

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received August 17, 2016; final manuscript received August 31, 2016; published online October 6, 2016. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 139(3), 031012 (Oct 06, 2016) (7 pages) Paper No: MANU-16-1438; doi: 10.1115/1.4034664 History: Received August 17, 2016; Revised August 31, 2016

As American vehicle fuel efficiency requirements have become more stringent due to the CAFE standards, the auto industry has turned to fiber reinforced polymer composites as replacements for metal parts to reduce weight while simultaneously maintaining established safety standards. Furthermore, these composites may be easily processed using established techniques such as injection molding and compression molding. The mechanical properties of these composites are dependent on, among other variables, the orientation of the fibers within the part. Several models have been proposed to correlate fiber orientation with the kinematics of the polymer matrix during processing, each using various strategies to account for fiber interactions and fiber flexing. However, these all require the use of empirical fitting parameters. Previous work has obtained these parameters by fitting to orientation data at a specific location in an injection-molded part. This ties the parameters to the specific mold design used. Obtaining empirical parameters is not a trivial undertaking and adds significant time to the entire mold design process. Considering that new parameters must be obtained any time some aspect of the part or mold is changed, an alternative technique that obtains model parameters independent of the mold design could be advantageous. This paper continues work looking to obtain empirical parameters from rheological tests. During processing, the fiber–polymer suspension is subjected to a complex flow with both shear and extensional behavior. Rather than use a complex flow, this study seeks to isolate and compare the effects of shear and extension on two orientation models. To this end, simple shear and planar extension are employed, and the evolution of orientation from a planar random initial condition is tracked as a function of strain. Simple shear was imparted using a sliding plate rheometer designed and fabricated in-house. A novel rheometer tool was developed and fabricated in-house to impart planar extension using a lubricated squeeze flow technique, where a low-viscosity Newtonian lubricant is applied to the solid boundaries to minimize the effect of shearing due to the no-slip boundary condition. The Folgar–Tucker model with a strain reduction factor is used as a rigid fiber model and compared against a bead–rod model (a semiflexible model) proposed by Ortman. Both models are capable of predicting the data, with the bead–rod model performing slightly better. Orientation occurs at a much faster rate under startup of planar extension and also attains a much higher degree of flow alignment when compared with startup of steady shear.

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Figures

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Fig. 1

Using the p vector to describe a rigid fiber's orientation

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Fig. 2

Describing fiber orientation using the two vectors p andq

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Fig. 3

Fiber length distribution in the composite used in this study

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Fig. 4

Fixture used for startup of constant planar extension

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Fig. 5

Stress growth under startup of steady shear (a) and startup of steady planar extension (b). Shear rate used was 0.1 s−1 and the Hencky strain rate used was 0.05 s−1 in compression. Error bars are the standard deviation.

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Fig. 6

Orientation evolution under startup of steady shear (a) and startup of constant planar extension (b). Shear rate used was 0.1 s−1 and the Hencky strain rate used was 0.05 s−1 in compression. Error bars are the standard deviation. Solid lines correlate to predictions of the Folgar–Tucker model, and dashed lines correlate to predictions by the bead–rod model.

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