Mechanics of Natural Composites
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MECHANICS OF NATURAL COMPOSITES
Dr. Joseph E. Saliba, Rebecca C. Schiavone, Stephen L. Gunderson, and Denise G. Taylor. University of Dayton Research Institute, Dayton, Ohio 45469 ABSTRACT This study was initiated to investigate the structural response of the bessbeetle to determine potential advantageous ramifications and effects on the optimization of synthetic composite materials. The result of the micromechanics sensitivity study of various parameters are presented. Variables such as fiber size and shape, fiber volume fraction, ratio of modulus of elasticity of fiber over matrix, are changed one variable at a time, and the response quantities such as stress and tranverse modulus are presented. BACKGROUND The cuticle, or exoskeleton, of the bessbeetle (Odontotaenius disjunctus) is a natural polymeric composite that is structurally similar to man-made fiber reinforced composites. However, the insect cuticle uses fibers which vary in cross sectional size and shape (see Figure 1) through the thickness. The reason for the variation is uncertain. This paper attempts to determine the effects of fiber shape variation, volume fraction, and modulus ratio of the constituents (Ef/E.) on individual ply properties.
Figure 1.
Schematics diagram of the bessbeetle cuticle.
Information was limited on the micromechanics of elliptical fiber reinforced composites which resulted in a low degree of confidence in the results. The lack of information caused problems when it came time to use classical laminate theory for computing or approximating the modulus of elasticity in the lateral direction. Methods were therefore developed for the necessary calculations. PROBLEM DESCRIPTION The approximation of the transverse (E22 ) modulus for a single lamina can be accomplished using two different techniques. The
Mat. Res. Soc. Symp. Proc. Vol. 218. @1991 Materials Research Society
216
first method based on the rule of mixtures of elementary mechanics of materials and deals with unidirectional continuous fiber. Ef Em E22
-
EfVm + EVf
The subscripts f and m represent fiber and matrix while V and E are the volume fraction and modulus of elasticity. The transverse modulus does not take into consideration the shape of the fiber and geometrically speaking is only a function of the volume fraction. The second approach is which can be written as:
based
on the Halpin-Tsai
equations
l+Cl7Vf E2 2 = Em
1-7 Vf
with Ef/Em-l
7Ef/Em+C
C=
w 2 - + 40 Vf1 0 t
where w = reinf. width t = reinf. thick.
The above Halpin-Tsai approach was developed to model a wide array of possible reinforcement geometries and in that sense is very global. Our literature review reveals very limited experimental validation for elliptical fibers, thus the need for a micromechanics sensitivity study to better understand the modeling of E..2 Once the transverse modulus is determined we can study with a high degree of confidence the advantages of variable size, and shaped fiber, as well as the double helical stacking. OBJECTIVE The main objective of this study can b
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