Packing mechanics of fiber reinforcements

• Published in: Polymer engineering and science Vol. 38; no. 8; pp. 1337 - 1350
• Main Author: Toll, Staffan
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01-08-1998; Blackwell Publishing Ltd
• Subjects: Composite micromechanics; Contact point statistics; Fiber packing; Fiber reinforced materials; Mathematical models; Statistical methods; Volume fraction
• ISSN: 0032-3888; 1548-2634; 1548-2634
• DOI: 10.1002/pen.10304

Theories of fiber packing, of use in manufacturing composite materials, are developed. The maximum packing fraction of force free fibers is estimated based on a statistical analysis of the distribution of fiber‐fiber contact points. The new expressions are more general than previous ones by allowing for a distribution in fiber length and orientation. The forced packing beyond this limit is governed by the bending of fiber segments between contact points. A micromechanical theory is developed for this, again based on the contact point statistics, and equations relating the force response per unit area of a fiber bed to the fiber volume fraction are derived for three basic types of assembly: a general 3D wad, a planar mat of dispersed fibers, and a bundle of almost parallel fibers. Other types of reinforcement structure, such as woven fabrics, and the effect of lubrication are also treated briefly.