New book details now-ubiquitous fiber modeling developed decades ago in MechSE

7/14/2022 Julia Park

Prof. Emeritus Charles L. Tucker has published a new book, "Fundamentals of Fiber Orientation--Description, Measurement and Prediction" that describes the development of the models used to predict fiber orientation, an important part of the process of molding plastics.

Written by Julia Park

Chuck Tucker with his new book.Professor Emeritus Charles L. Tucker III has published a new book, “Fundamentals of Fiber Orientation—Description, Measurement and Prediction,” that describes the development of the models used to predict fiber orientation – an important part of the process of molding plastics.

Many of the plastic parts used in everyday life are reinforced with tiny glass or carbon fibers.  The individual fibers, finer than a human hair and often less than a millimeter long, are mixed with the plastic before it is molded into shape.  During molding, the flow orients the fibers, so the resulting material has different properties in different directions, much like a piece of wood.  Engineers use computer simulations to help design the tooling and get the properties right.  The models that are used all over the world to predict fiber orientation came from the MechSE department. 

Tucker and his graduate students developed and refined these models over more than 40 years. Tucker’s new book explains the technology.  Aimed at engineers who use the software and researchers who need a concise overview, the book covers how fiber orientation is described mathematically, how it is measured experimentally, and how it is predicted in software. 

Tucker said the technology has a deeper connection to MechSE too. He credits his former colleague Professor Fred Leckie with one of the key ideas that made the solution practical: the use of tensors to describe fiber orientation. 

“Fred’s office was next to mine, and when my students and I were solving fiber orientation distribution functions in 2D, Fred said, ‘You should use these tensors that Turan Onat and I are using for microscopic damage in metals.’ At first I was unable to grasp the idea,” Tucker said.  “However, one day Fred came in and said, ‘I was at home sick yesterday so I made some notes about how you could use tensors for your fibers.’ He handed me one sheet of paper with equations and sketches, and from that I was able to understand the concept. My paper with Suresh Advani (which now has more than 1,000 citations) was the eventual result. Orientation tensors have since become the standard way to predict, measure, or even talk about fiber orientation, but without Fred’s generosity and persistence we might not have them today.”

Polymers reinforced with discontinuous fibers have a wide range of important applications such as in automotive parts and business machines. The flow that occurs during processing of these materials creates a complex but repeatable pattern of fiber orientation, which plays a key role in achieving the desirable mechanical properties these materials can offer. 

For practicing engineers, the book teaches the fundamentals needed to understand data, set up meaningful simulations, and interpret results. It provides a thorough, organized overview of the field, and will also be a valuable resource to those undertaking research in this area. Free MATLAB software implementing the models discussed in the book is provided online.  

Fundamentals of Fiber Orientation—Description, Measurement and Prediction (Munich: Hanser Publishers, 2022, ISBN 978-1-56990-875-4 (E-Book ISBN 9781-56990-876-1)).

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This story was published July 14, 2022.