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For stiffness predictions of short fiber reinforced polymer composites, it is essential to understand the orientation during processing. This is often performed through the equation of change of the fiber orientation tensor to simulate the fiber orientation during processing. Unfortunately this approach, while computationally efficient, requires th...
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... from the solutions of the equation of motion for a ij are provided in Figure 1 from each of the aforementioned closure methods. A look at the second order orientation tensor results shows that the FEC and the ORT yield numerically identical results (out to the third significant digit), with the Hybrid performing the poorest and the neural network closures with the most accurate results. ...
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... Only the even order tensor survived due to the fact that the probability distribution function is an odd function. A code that evaluates the Bays method can take several weeks to months to reach the steady state orientation [6,[14][15][16] whereas solutions using the SPH approach will require several minutes [16,17]. Solutions of the orientation tensor equation of motion for the same flows can be solved in a matter of seconds [16]. ...
... Only the even order tensor survived due to the fact that the probability distribution function is an odd function. A code that evaluates the Bays method can take several weeks to months to reach the steady state orientation [6,[14][15][16] whereas solutions using the SPH approach will require several minutes [16,17]. Solutions of the orientation tensor equation of motion for the same flows can be solved in a matter of seconds [16]. ...
... A code that evaluates the Bays method can take several weeks to months to reach the steady state orientation [6,[14][15][16] whereas solutions using the SPH approach will require several minutes [16,17]. Solutions of the orientation tensor equation of motion for the same flows can be solved in a matter of seconds [16]. ...
There is a need for physics-based mathematical models for the design of indus-trial short-fiber reinforced composites (SFRC) to predict the fiber orientation within the part. Traditional models for fiber interactions use the isotropic rotary diffusion model of Folgar and Tucker, but there is considerable interest to use the Phelps and Tucker anisotropic rotary diffusion model. Both models predict the flow induced ori-entation, which directly determines the resulting stiffness of an injection molded part. These two models are investigated in the present work. A number of fourth order orientation tensor closure approximations are investigated for both diffusion models, with the goal being to suggest the more effective and efficient closure approxima-tion for a variety of flow conditions. Differences in the resulting elastic properties predicted from the two rotary diffusion models are observed. These observations raise questions as to which diffusion model should be used commercially for injection molded SFRCs.
