Unformatted text preview: strength and the advantages of strengthening
bonded or joined together by atomic m
by the ﬁbers will be less than fully realized.
critical nucleus Nucleus of therequired for effective strengthening is interface accomplished by solidstate
size such that either
The minimum or critical ﬁber length lc
a
growth or dissolution will decrease its free ﬁber d,
function of several variables including the diameter of the energy.the ultimate tensile
conditions of high temperature and pr
critical resolved shear stress ( CRSS) The shear stress
diffusion coefﬁcient The constant i
resolved in the slip plane in the slip direction at which
relating mass ﬂux per unit area to the
gradient. It obeys an Arrheniustype e
plastic deformationMenu  Textbook Table of Contents
 eText Main occurs.
such is strongly temperaturedepende
crosslinks Primary bonds formed between adjacent
coefﬁcient describes the ease of atom
polymer chains. These atomic “bridges” are often
the solid state.
composed of small chains of either oxygen or sulfur but
can be composed of many other small groups of atoms.
direct dissolution mechanism A d
mechanism in which the solid dissolve
crystal lattice The framework on which atoms are
surrounding liquid without substantial
placed in periodic threedimensional structures.
dislocation A linear defect in a cry
crystalline Having atoms or ions arranged on a
responsible for plastic deformation.
threedimensional lattice having longrange order. pg583 [R] G1 727060 / IRWIN / Schaffer iq Chapter 14 12.01.98 plm QC3 rps MP Composite Materials 583
FIGURE 14.3–1
(a) Isolated ﬁber embedded
in a matrix, (b) the distortions associated with
tensile loading of the
composite in part a, and
(c) the distribution of shear
and normal stresses on the
outer ﬁber surface (also the
interface region) along the
ﬁber length in response to
the loading. (a) σ σ (b) l
lc /2 σ max = ε Ef lc /2
σ τ (c) strength of the ﬁbers f u , and the matrix shear yield strength my . The second factor sets
the limit on the load carried by the ﬁbers, and the third factor describes the ability of the
matrix to transmit the load from one ﬁber to the next. The relationship among these
variables is found using a force balance. The force carried by the ﬁbers is equal to the
normal stress in the ﬁbers multiplied by their crosssectional area. This force is transferred to the ﬁbers via a shear stress acting on the ﬁber surface. Mathematically, the force
balance is:
d lc
2 d2
4 my (14.3–1) fu or, equivalently,
lc
d fu 2 (14.3–2) my The quantity lc d is known as the critical aspect ratio. Typically, the critical aspect ratio
ranges from 20 to 150 for most ﬁber and matrix materials. Since a typical ﬁber diameter
is between 10 and 30 m, critical ﬁber lengths are on the order of 0.2–4.5 mm. In most
practical instances, the ﬁber length l is much larger than lc . 14.3.2 Characteristics of Fiber Materials  v v The most common geometrical shape for the reinforcing phase in a highperformance
structural composite is a ﬁber. The reason for this is that the strength of a brittle material
is inversely related to the sq...
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 Spring '10
 sowell
 Physics, The Crucible, ........., Tensile strength, IRWIN / Schaffer

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