The volume fraction of the fibers present in commercial filament wound structures, formed from either epoxy-impregnated tapes (“prepreg”) or fiber strands pulled through an epoxy bath, approaches 60 percent. Such close-packed structures are near the region that may cause dependent scattering effects to be important; that is, the scattering characteristics of one fiber may be affected by the presence of nearby fibers. This dependent scattering may change the single-fiber extinction coefficient and phase function, and thus may change the radiative transfer in such materials. This effect is studied for unidirectional fibers dispersed in a matrix with nonunity refractive index, and with large size parameter (fiber diameter to wavelength ratio) typical of commercial fiber–matrix composites. Only the case of radiation incident normal to the cylinder axes is considered, as this maximizes the dependent effects. The dependent extinction efficiency is found by solving the dispersion relations for the complex effective propagation constant of the composites. An estimation of this dependent scattering effect on the infrared in-situ curing of thermoset-hoop-wound structures is also conducted. It is found that the wave interference effect is significant for S-glass/3501-6 composite, and neglect of this effect tends to overestimate the temperature and cure state within the materials during IR in-situ curing.

Issue Section:
Radiative Transfer
Keywords:
Materials Processing and Manufacturing Processes, Radiation, Radiation Interactions
Topics:
Electromagnetic scattering, Hardening (Curing), Heating, Radiation (Physics), Radiation scattering, Scattering (Physics), Thermal analysis, Fibers, Composite materials, Epoxy adhesives, Epoxy resins, Cylinders, Dispersion relations, Glass, Manufacturing, Materials processing, Radiative heat transfer, Refractive index, Temperature, Wave interference, Wavelength
1.
Alder
B. J.
, and
Wainwright
T. E.
,
1962
, “
Phase Transition in Elastic Disks
,”
Physical Review
, Vol.
127
, No.
2
, pp.
359
–
361
.
2.
Balanis, C. A., 1989, Advanced Engineering Electromagnetics, Wiley, New York.
3.
Chae
D. G.
,
Ree
F. H.
, and
Ree
T.
,
1969
, “
Radial Distribution Functions and Equation of State of the Hard-Disk Fluid
,”
Journal of Chemical Physics
, Vol.
50
, No.
4
, pp.
1581
–
1589
.
4.
Chern, B.-C., Moon, T. J., and Howell, J. R., 1994, “Dependent Scattering Effects on Wave Propagation Through Filament-Wound Composites,” Radiative Heat Transfer: Current Research ASME HTD-Vol. 276, pp. 15–20.
5.
Chern
B. C.
,
Moon
T. J.
, and
Howell
J. R.
,
1995
, “
Thermal Analysis of In-Situ Curing for Thermoset, Hoop-Wound Structures Using Infrared Heating: Part I—Numerical/Experimental Investigation
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
117
, this issue, pp.
674
–
680
.
6.
Foldy
L. L.
,
1945
, “
The Multiple Scattering of Waves. General Theory of Isotropic Scattering by Randomly Distributed Scatterers
,”
Physical Review
, Vol.
67
, No.
3
, pp.
107
–
119
.
7.
Houston, R. L., and Korpela, S. A., 1981, “Heat Transfer Through Fiberglass Insulation,” Proceedings of 7th International Heat Transfer Conference, Vol. 2, pp. 499–504.
8.
Kerker, M., 1969, The Scattering of Light, Academic Press, New York.
9.
Kamiuto
K.
,
1990
, “
Study of the Scattering Regime Diagrams
,”
Journal of Thermophysics and Heat Transfer
, Vol.
4
, No.
4
, pp.
432
–
435
.
10.
Kumar, S., and White, S., 1990, “Scattering Properties of Woven Fibrous Insulations: Effects of Interference for Normal Incidence,” AIAA Paper No. 90-1674.
11.
Lado
F.
,
1968
, “
Equation of State of the Hard-Disk Fluid From Approximation Integral Equations
,”
Journal of Chemical Physics
, Vol.
49
, No.
7
, pp.
3092
–
3096
.
12.
Lax
M.
,
1952
, “
Multiple Scattering of Waves. II. The Effective Field in Dense Systems
,”
Physical Review
, Vol.
85
, No.
4
, pp.
621
–
629
.
13.
Lee
S. C.
,
1989
, “
Effect of Fiber Orientation on Thermal Radiation in Fibrous Media
,”
International Journal of Heat and Mass Transfer
, Vol.
32
, No.
2
, pp.
311
–
319
.
14.
Lee
S. C.
,
1990
, “
Dependent Scattering of an Oblique Incident Plane Wave by a Collection of Parallel Cylinders
,”
Journal of Applied Physics
, Vol.
68
, No.
10
, pp.
4952
–
4957
.
15.
Lee
S. C.
,
1992
a, “
Effective Propagation Constant of Fibrous Media Containing Parallel Fibers in the Dependent Scattering Regime
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
114
, pp.
473
–
478
.
16.
Lee, S. C., 1992b, “Extinction and Refraction of Radiation in High-Density Fibrous Composites Containing Nonhomogeneous Fibers,” AIAA Paper No. 92-2892.
17.
Ma
Y.
,
Varadan
V. K.
, and
Varadan
V. V.
,
1990
, “
Enhanced Absorption Due to Dependent Scattering
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
112
, pp.
402
–
407
.
18.
Varadan
V. K.
,
Bring
V. N.
, and
Varadan
V. V.
,
1979
, “
Coherent Electromagnetic Wave Propagation Through Random Distributed Dielectric Scatters
,”
Physical Review D
, Vol.
19
, No.
8
, pp.
2480
–
2489
.
19.
Varadan
V. V.
,
Varadan
V. K.
, and
Ma
Y.
,
1987
, “
Effects of Nonspherical Statics on EM Wave Propagation in Discrete Random Media
,”
Radio Science
, Vol.
22
, No.
4
, pp.
491
–
498
.
20.
White, S., and Kumar, S., 1989, “Interference Effects on Scattering by Parallel Fibers at Normal Incidence,” AIAA Paper No. 89-1717.
21.
Wood
W. W.
,
1968
, “
Monte Carlo Calculations for Hard Disks in the Isothermal-Isobaric Ensemble
,”
Journal of Chemical Physics
, Vol.
48
, No.
1
, pp.
415
–
434
.
22.
Wood
W. W.
,
1970
, “
NPT-Ensemble Monte Carlo Calculations for the Hard-Disk Fluid
,”
Journal of Chemical Physics
, Vol.
52
, No.
2
, pp.
729
–
741
.
23.
Zhu
P. Y.
,
Fung
A. K.
, and
Wong
K. W.
,
1987
, “
Effective Propagation Constants in Dense Random Media Under Effective Medium Approximation
,”
Radio Science
, Vol.
22
, No.
2
, pp.
234
–
250
.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.