# In metalmatrix and polymer matrix composites this

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Unformatted text preview: ber strength is 2000 MPa. Solution 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: Vcrit 482 2000 400 400 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 mixtures: 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 is pre...
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## This note was uploaded on 02/25/2013 for the course PHYS 2202 taught by Professor Sowell during the Spring '10 term at Georgia Institute of Technology.

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