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NSF-CMMI-MPM #0720399 - Phenomenological-Based Constitutive Model and Simulation of Fiber Interaction for Short Fiber Composite Processing
Objective and Background
Short-fiber polymer composites enjoy widespread industrial application due in part to their high strength to weight ratios. Finished product performance is largely dictated by processing conFiber Motionditions, ergo it is essential to have a complete understanding of the flow kinematics/fiber orientation coupling to obtain an accurate representation of final part behavior. Unfortunately, recent research has exposed the propensity of current models for fiber collisions to over-predict the fiber alignment rate. To promote the advancement of lightweight, high strength composites, a new fundamental approach is needed to better capture fiber interactions in polymer composite melt flow. The collaborative work between the investigators at the University of Missouri - Columbia and Baylor University is unique in that we propose to develop industrially applicable representations for fiber interaction behavior beginning at the discrete fiber level. This is in stark contrast to existing methods which incorporate fiber collision effects by introducing a Brownian-like component to Jeffery's equation of motion for rigid ellipsoids in a dilute suspension (Jeffery, 1923), neglecting the underlying physical phenomena.
Developed Results
Transient solution of A_{ij} in simple shear flow from the Folgar-Tucker model
  • Developed a directionally dependant diffusion model to capture discrete fiber collisions.
  • Formulated a spherical harmonic expansion of the fiber orientation distribution function, and demonstrated this approach provided numerically exact solutions of the fiber orientation distribution requiring computational efforts several orders of magnitude less than that of the often employed control volume approach.
  • Analyzed the currently available diffusion models, and provided the first results for these models that did not rely on a closure (a numerical approximation).
  • Developed the Exact Closure, which exactly closes the orientation tensor equation of motion for pure Jeffery's motion
  • Developed the Fast Exact Closure, the first closure for the orientation tensor equation of motion that does not rely on any type of numerical fitting proccedure and results demonstrate accuracies better then that of the orthotropic closures
  • Compared the stiffness results one would obtain from the classical closures, and those of the exact closures.  Results were compared to the numerically exact spherical harmonic solutions, and demonstrated that the FEC closure was the most accurate orthotropic closure.
Journal Publications From This Work
Fiber Collision Schematic
  • Discontinuous Long Fiber Reinforced Composite Stiffness Predictions for Injection Molded Parts. C. Zhang and D.A. Jack. Under review, Composites, Part B, 2011.
  • Effectiveness of Recent Fiber-interaction Diffusion Models for Orientation and the Part Stiffness Predictions in Injection Molded Short-Fiber Reinforced Composites. B.A. Agboola, D.A. Jack and S. Montgomery-Smith. Under review, Composites, Part A, 2011.
  • Numerical Evaluation of Single Fiber Motion for Short-Fiber-Reinforced Composite Materials Processing. D. Zhang, D.E. Smith, D.A. Jack and S. Montgomery-Smith. Journal of Manufacturing Science and Engineering, 133(5):051002-9 2011.
  • The Fast Exact Closure for Jeffery's Equation with Diffusion S. Montgomery-Smith, D.A. Jack and D.E. Smith. Journal of Non-Newtonian Fluid Mechanics, 166:343-353, 2011.
  • Exact Tensor Closures for the Three Dimensional Jeffery's Equation. S. Montgomery-Smith, W. Hei, D.A. Jack and D.E. Smith. Journal of Fluid Mechanics, 680:321-335, 2011.
  • Neural Network Based Closure for Modeling Short-Fiber Suspensions. D.A. Jack, B.K. Schache, and D.E. Smith. Polymer Composites, 31(7):1125-1141, 2010.
  • A Systematic Approach to Obtaining Numerical Solutions of Jefferys Type Equations Using Spherical Harmonics. S. Montgomery-Smith, D.A. Jack and D.E. Smith. Composites, Part A, 41:827-835, 2010.
  • Modeling Fibre Orientation in Short Fibre Suspensions Using the Neural Network-Based Orthotropic Closure. N. Qadir and D.A. Jack. Composites: Part A, 40:1524- 1533, 2009.
Publications From This Work
Fiber Collision Schematic
  • Rheological Study on Multiple Fiber Suspensions for Fiber Reinforced Composite Materials Processing. D. Zhang*, D.E. Smith, and D.A. Jack. Proceedings of ASME IMECE'11, Denver, Colorado, November, 2011.
  • Observed Deviations between Classical and Novel Mathematical Models for Predicting Fiber Orientation in Injection Molded Composites. B.A. Agboola* and D.A. Jack. Early Career Technical Conference, Fayetteville, Arkansas, March 2011, Received Best Presentation.
  • Flexible Fiber Waviness as a Role in Fiber Motion Simulation and Material Property Prediction. C. Zhang* and D.A. Jack. Early Career Technical Conference, Fayetteville, Arkansas, March 2011.
  • Fiber Orientation for Suspensions of Long Fibers: Comparison of Rigid and Flexible Models. C. Zhang* and D.A. Jack. Proceedings of the Society of Rheology's 82nd Annual Meeting, Santa Fe, New Mexico, October, 2010 Accepted for presentation.
  • Fiber Orientation and Stiffness Predictions for Thin Geometries Using the Fast Exact Closure. B. Agboola* and D.A. Jack. Proceedings of the Society of Rheology's 82nd Annual Meeting, Santa Fe, New Mexico, October, 2010 Accepted for presentation.
  • Numerical Evaluation of Single Fiber Motion for Short Fiber Composites Materials Processing. D. Zhang*, D.E. Smith, D.A. Jack and S. Montgomery-Smith. Proceedings of ASME IMECE'10, Vancouver, British Columbia, Canada, November, 2010.
  • Fast Solutions for the Fiber Orientation of Concentrated Suspensions of Short-Fiber Composites Using the Exact Closure Methods. S. Montgomery-Smith, D.A. Jack, and D.E. Smith. Proceedings of ASME IMECE'10, Vancouver, British Columbia, Canada, November, 2010.
  • Modeling of Flexible Fiber Motion and Orientation in Simple Shear Flow: A Comparison between Rod-Chain Model and Jeffery's Equation. C. Zhang* and D.A. Jack. Proceedings of ASME IMECE'10, Vancouver, British Columbia, Canada, November, 2010.
  • Investigation of the Effectiveness and Efficiency of the Exact Closures: Comparison with Industrial Closures and Spherical Harmonic Solutions. B. Agboola*, D.A. Jack and S. Montgomery-Smith. Proceedings of ASME IMECE'10, Vancouver, British Columbia, Canada, November, 2010.
  • Flexible Fiber Suspension Orientation Model Predictions: Comparison Between Rod-Chain Model and Classical Jeffery's Rigid Ellipsoid Model. C. Zhang* and D.A. Jack. Early Career Technical Conference, Tulsa, Oklahoma, March 2010.
  • Comparison of Short-Fiber Orientation and Predicted Materials Properties from Closure Approximations and Spherical Harmonics. B. Agboola* and D.A. Jack. Early Career Technical Conference, Tulsa, Oklahoma, March 2010, Received Best Presentation.
  • Modeling Orientational Diffusion in Short Fiber Composite Processing Simulations. D.E. Smith*, S. Montgomery-Smith, D.A. Jack. National Science Foundation CMMI Engineering Research and Innovation Conference, Honolulu, Hawaii, June 2009.
  • Neural Network-Based Closure Approximation for Short-Fiber Suspension Simulations. D.E. Smith* and D.A. Jack. The Annual Mtg of the Polymer Processing Society, PPS 24, Salerno, Italy, June 2008.
  • Anisotropic Diffusion Model for Suspensions of Short-Fiber composite Processes. D.A. Jack*, S. Montgomery-Smith, and D.E. Smith. The XVth International Congress on Rheology, the Society of Rheology 80th Annual Meeting, Monterey, California, August, 2008.
  • Spherical Harmonic Solutions of Fiber Orientation Probability Distributions for Composite Processes. S. Montgomery-Smith*, D.A. Jack, and D.E. Smith. The XVth International Congress on Rheology, the Society of Rheology 80th Annual Meeting, Monterey, California, August, 2008.
Baylor University School of Engineering and Computer Science Department of Mechanical Engineering Sic'Em - Scientific Innovations in Composites and Engineering Materials