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Elastic moduli of transversely isotropic graphite fibers and their composites

Equations used to calculate the complete set of elastic transversely isotropic properties for unidirectional fiber-reinforced materials having transversely isotropic fibers are experimentally verified by using improved ultrasonic techniques

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Abstract

This paper demonstrates that it is possible to calculate the complete set of elastic mechanical properties for graphite-epoxy fiber-reinforced materials at any fiber-volume fraction by modifying equations previously developed to include transversely isotropic graphite-fiber properties. Experimental verification of the modified equations is demonstrated by using these equations to curve fit elastic-property data obtained ultrasonically over a range of fiber-volume fractions. Material systems under consideration are T300/5208, AS-3501 and Modomor II/LY558 graphite epoxy. Using the modified equations it is possible to extrapolate for fiber properties. From Modomor II/LY558 ultrasonic data, it is shown that five out of seven extrapolated graphite-fiber properties are consistent with the assumption that graphite fibers are transversely isotropic. Elastic properties for T300/5208 and AS-3501 are ultrasonically evaluated by propagating stress waves through six individual specimens but at various angles from a block of unidirectional material. Particular attention is devoted to specimen dimensions. To demonstrate the need for accurately calculating or experimentally measuring all lamina elastic properties, a brief discussion is included on the effect that variations in lamina elastic properties have on calculating interlaminar stresses.

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Abbreviations

A :

unidirectional block dimensions, m

C ij :

material stiffnesses, contracted notation (i,j=1,2,3,4,5,6), Pa

c i :

wave-phase speeds (i=1,2,3), m/s

D :

transducer diameter, m

E i :

Young's moduli along lamina coordinates (i=1,2,3), Pa

E b :

matrix Young's modulus, Pa

E f L :

fiber longitudinal Young's modulus, Pa

E f T :

fiber Young's modulus in the transverse plane, Pa

G ij :

shear moduli in the laminai-j plane (i,j=1,2,3), Pa

G b :

matrix shear modulus, Pa

G f LT :

fiber shear modulus in the longitudinal-transverse plane, Pa

G f TT :

fiber shear modulus in the transverse plane, Pa

K b :

matrix plane-strain bulk modulus, Pa

K f TT :

fiber plane-strain bulk modulus, Pa

L :

specimen length, m

M :

margin, m

QL :

quasi-longitudinal wave

QT :

quasi-transverse wave

S :

time separatingQL andQT waves, s

T max :

specimen thickness necessary to separateQL andQT waves, m

T min :

specimen thickness satisfying energy-flux requirements, m

b :

matrix-volume fraction

V f :

fiber-volume fraction

W :

transmitted pulse width, s

θ:

angular deviation of energy flow from the wave normal, deg

ν b :

matrix Poisson's ratio

ν f LT :

fiber Poisson's ratio in the longitudinal-transverse plane

ν f TT :

fiber Poisson's ratio in the transverse plane

ϱ:

lamina mass density, kg/m3 (N-sec2/m4)

References

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Authors and Affiliations

  1. Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, 24061, Blacksburg, VA

    R. D. Kriz (Research Fellow and Associate Professor) & W. W. Stinchcomb (Research Fellow and Associate Professor)

Authors
  1. R. D. Kriz
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  2. W. W. Stinchcomb
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Kriz, R.D., Stinchcomb, W.W. Elastic moduli of transversely isotropic graphite fibers and their composites. Experimental Mechanics 19, 41–49 (1979). https://doi.org/10.1007/BF02324524

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  • DOI: https://doi.org/10.1007/BF02324524

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