Statistical bounding approach to study of filamentary composites provides understanding of their fracture mechanics. Comparison shows that bounds are in good agreement with data from several fiber-matrix systems, and that they can be used to interpret strength data and provide fracture behavior information leading to improved strength

Zweben, C.

English

NASA Technical Reports Server

June 1971	 Brief 71-10161 
NASA TECH BRIEF 
NASA Pasadena Office 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield; Virginia 22151. Requests for individual copies or questions relating to the. Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.F. 20546. 
New Understanding of Fiber Composite Materials 
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Recent contributions have been made to the 
theoretical and empirical understanding of composite 
materials—fibers of suitable materials embedded in 
a plastic or metal matrix—which comprise a new area 
	
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Test Temperature, °C 
	
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Tensile Strength of Alumina Whisker - Aluminum 
Composites as a Function of Temperature 
of materials technology, with important potential for 
materials chemists and mechanical and structural 
engineers. 
The high tensile strength and ease of forming are 
important advantages of filamentary composites. How-
çver, an understanding of their fracture mechanics 
is basic to safe, efficient utilization in structural
design. A statistical bounding approach to the prob-
lem provides this understanding. Comparison shows 
that the bounds are in good agreement with data from 
a variety of fiber-matrix systems, and that they can 
be used to interpret strength data and to provide 
information on fracture behavior leading to im-
proved strength. 
The nonuniform strength of the commonly used 
fibers (such as boron, graphite, glass, alumina, sili-
con carbide, etc.) has significant effects on the 
strength of composite materials. The fracture of a 
single fiber can result in matrix cracks which may 
propagate through surrounding fibers, triggering a 
"weakest link" mode of failure. The expected stress 
at which the first fiber break will occur is there-
fore a lower bound on expected composite strength. 
Many materials do not fail in the weakest link 
mode. In such materials, each scattered fiber break 
can be thought of as a nucleus for the propaga-
tion of fiber breaks. The stress concentration factors 
increase with the number of broken fibers, and the 
composite enters a "fiber break propagation" mode 
of failure. A lower bound on this failure mode is 
the expected stress at which the first overstressed 
fiber will break. 
Another failure mode, associated with the inability 
of an entire cross-section to resist an applied load, 
can be used as an upper bound on composite tensile 
strength. 
At least for certain fiber-matrix systems studied, 
a strong bond may result in a lower tensile 
strength than that obtained with a weaker bond. Pre-
sumably, a strong bond will result in improved 
transverse properties, indicating that there may have 
to be a tradeoff between tensile strength and trans-
verse strength for some fiber-matrix systems. 
(continued os etleal) 
This document was prepared under the sponsorship of the National 	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 . information contained in this document, or warrants that such use 
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https://ntrs.nasa.gov/search.jsp?R=19710000160 2020-03-17T02:23:44+00:00Z
The figure shows the experimental and predicted 
strength as a function of the temperature of an 
alumina-whisker-in-aluminum composite. Note that 
the slope of the experimental data follows that of 
the lower bound more closely than that of the upper 
bound. 
The classical Griffith-Irwin-Orowan theory of crack 
propagation, which is concerned only with homogene-
ous materials, is apparently not adequate for explain-
ing the mechanics of failure in a notched unidirec-
tional composite subjected to tensile load in the fiber 
direction. In composites, fiber debonding, matrix and 
fiber plasticity, and scatter in fiber strength all affect 
crack propagation. 
Since the fibers are the main load carrying elements, 
a composite can carry load even though the matrix 
is completely fractured. Many fibers in a matrix 
can be fractured while the matrix remains intact. 
In either case, crack length is essentially undefined. 
Cracks in the matrix parallel to the fibers, and de-
bonding of fibers, often present a failure mode not 
covered by the conventional approach. 
If a fiber breaks in a thin plate consisting of 
a single layer of unidirectional fibers in an elastic 
matrix, the load is transmitted through the matrix 
to adjacent fibers. These are subjected to an increase 
in the average stress: When this stress reaches the 
ultimate strength of the fibers (assumed to be uni-
form), the one at the root of the notch will fail. The 
stress in the next intact fiber becomes greater than 
the ultimate fiber strength, it too fails, and a chain 
reaction failure occurs. 
Studies indicate a drastic reduction in the strength 
of such composites if only a few fibers are cut. 
For example, a central notch that cuts only four 
fibers in an infinite sheet reduces the strength by 
over 50%, and only two fibers cut at the edge 
of a sheet will produce the same effect. 
Not all fiber composites fall within the elastic 
matrix category. Where an inelastic matrix is used, 
stress concentrations in the vicinity of the notch 
root may cause .fiber debonding or matrix fracturing 
parallel to the fibers. Once this phenomenon begins, 
small increments of applied load result in a large 
debonded or fractured region. Such debonding or 
cracking results in a drastic reduction of the maxi-
mum load concentration factor in adjacent, unbroken 
filaments. 
The notch sensitivity of a material can be sig-
nificantly reduced by providing a .fiber-matrix bond 
that will fail before adjacent fibers are broken due 
to load concentrations. However, the adverse effects 
of fiber debonding on transverse properties must be 
taken into account. 
Brief 71-10161
The effect of matrix plasticity on load con-
centrations in a monolayer composite with one broken 
filament was investigated, with the matrix assumed to 
be elastic perfectly-plastic. The results indicate that, 
for the same load ratio, fiber debonding or matrix 
splitting results in a greater reduction in the maxi-
mum load concentration factor than does matrix 
yielding. 
In the foregoing cases, in which the fibers have 
a unique ultimate strength, the failure of the notch-
root fiber results in the propagation of fiber breaks, 
unless debonding occurs. However, if there is scatter 
in fiber strength, this is not necessarily true. When 
one of the notch-root fibers breaks, there is a finite 
probability that a nearby fiber will be able to resist 
both the steady state and dynamic stress concen-
trations resulting from the fracture of the first 
fiber. The probability of such failure constitutes a 
lower bound on the probability of failure due to 
crack propagation from a central or edge notch. 
Although matrix plasticity results in a greater 
probability of failure than does matrix elasticity, 
this negative effect is generally overshadowed by 
the reduction in load concentration factor. In the 
case of debonding or matrix splitting, this reduc-
tion is even more pronounced. In the limiting case, 
the notch-root fiber has the same probability of 
failure as any fiber in the composite; i.e., there is 
no tendency for the notch to propagate. 
The stress necessary to propagate a notch may 
be higher than the failure stress level at which an 
unnotched composite will fail. A long specimen with 
many fibers and a shallow notch will probably not 
fail as a result of a crack propagating from the 
notch. To the contrary, it can be expected that a 
fiber will break at some arbitrary point in the speci-
men, triggering failure,. before a stress. level is 
reached that is high enough to propagate a crack 
from the notch. 
Note: 
Requests for further information may be directed 
to:•
Technology Utilization Officer 
NASA Pasadena Office 
4800 Oak Grove Drive 
Pasadena, California 91103 
Reference: TSP71-10161 
Patent status: 
No patent action is contemplated by NASA. 
Source: Carl Zweben, formerly of 
Caltech /JPL 
under contract to.: 
NASA Pasadena Office 
(N PO-11605) 
Category 04.


New understanding of fiber composite materials

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