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The Theory of Materials Failure$
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Richard M. Christensen

Print publication date: 2013

Print ISBN-13: 9780199662111

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199662111.001.0001

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Micromechanics Failure Analysis

Micromechanics Failure Analysis

(p.177) 13 Micromechanics Failure Analysis
The Theory of Materials Failure

Richard M. Christensen

Oxford University Press

Micromechanics of failure treats local conditions of failure that occur at about the micron scale. Often, however, the term “micromechanics” is used much more broadly as occurring over quite a wide range of small scales, but certainly far above the atomic scale and far below the macroscopic scale. Three major problems of failure at small scales are considered. The first problem concerns the failure behavior of aligned fiber composites, as in Chapter 11. The distinction, however, is that a micromechanics failure analysis is used here to reduce the number of calibrating failure properties from six to five. In particular, the transverse shear strength is shown to be expressible in terms of the transverse uniaxial tensile and compressive strengths. It is a major advantage to eliminate this particular property, which is difficult to determine experimentally. The second problem concerns the failure conditions that surround a rigid spherical inclusion in an infinite elastic medium. A similar problem was considered in Chapter 10, but here the full solution is given and evaluated. Such inclusions are often at the micron size. Finally, the third problem involves the load transfer through the matrix phase around a broken fiber in aligned-fiber composites. Is the secondary failure most likely to occur in the matrix or in the surrounding overloaded fibers?

Keywords:   micromechanics, micron scale, macroscopic scale, fiber composites, transverse shear, spherical inclusion, load transfer, broken fiber

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