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Unformatted text preview: ber strength is 2000 MPa.
Since the matrix yields at the strain when ﬁber fracture occurs, we can take
of the matrix 400 MPa. Thus, from Equation 14.5–15, we ﬁnd:
400 m yield strength 0.051 Hence, ﬁber strengthening should occur in this system for a ﬁber volume fraction as little as 5.1%. .......................................................................................................................................
14.5.3 Estimation of the Coefﬁcient of Thermal Expansion
The coefﬁcient of thermal expansion is an important design parameter for all structural
materials subjected to even modest variations in temperature during service. As a ﬁrst
estimate, the expansion coefﬁcient of the composite, c , can be obtained by the rule of
Vm c | v v 600 iq | m Vf (14.5–16) f e-Text Main Menu | Textbook Table of Contents pg601 [R] G1 7-27060 / IRWIN / Schaffer iq Chapter 14 Composite Materials where m and f are the expansion coefﬁcients of the matrix and ﬁber materials. In most
common composites, m
f , so in a uniaxial composite, the ﬁbers constrain the
expansion of the matrix in the longitudinal direction. This causes the composite to expand
less in the longitudinal direction and more in the transverse direction than predicted by
Equation 14.5–16. More accurate expressions for estimating the expansion coefﬁcients in
the longitudinal and transverse directions have been derived, but are outside the scope of
this introductory chapter. 14.5.4 Fracture Behavior of Composites
Fracture in composites usually begins with cracking of the most brittle phase. In metalmatrix and polymer-matrix composites this usually means cracking begins in the brittle
ﬁbers; in ceramic-matrix composites this usually means cracking begins in the matrix.
The manner in which this initial fracture progresses determines the toughness of the
composite. To illustrate this point, consider a system of brittle ﬁbers in a ductile matrix.
When fracture occurs in an isolated ﬁber at any point along its length, the stresses carried
by the ﬁber in the vicinity of the crack must be transferred to the surrounding matrix and
the other ﬁbers. If the surrounding matrix and ﬁbers are able to withstand the stresses, the
fracture will stabilize at that location.
Interfaces play a major role in stabilizing fractures. If delamination occurs at the interface, effective blunting of the crack occurs and the fracture is stabilized. Crack blunting
also occurs because of plastic deformation in the ductile matrix. If the fracture is stabilized at one location, it will begin at other locations if the deformation is continued. This
process will continue until the damage is so widely spread that the stress originally carried
by the fractured ﬁbers can no longer be carried by the uncracked matrix. At this point,
ultimate fracture of the composite occurs. This process is schematically illustrated in
Figure 14.5–6a along with an accompanying stress-strain diagram. Such a fracture mode
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