Research Papers

Lamination Theory for the Strength of Fiber Composite Materials

[+] Author and Article Information
Richard M. Christensen

Professor Research Emeritus
Aeronautics and Astronautics Department,
Stanford University,
Stanford, CA 94305
e-mail: christensen@stanford.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 19, 2017; final manuscript received May 21, 2017; published online June 6, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(7), 071007 (Jun 06, 2017) (5 pages) Paper No: JAM-17-1264; doi: 10.1115/1.4036825 History: Received May 19, 2017; Revised May 21, 2017

Building upon the previous work for the failure of quasi-isotropic fiber composite laminates, the much more difficult and more important general case of orthotropic laminates is now taken up. The full and complete failure criterion is derived for fiber dominated, general 0, 90, ±45-deg laminated materials, with the relative volume fractions to be specified for each direction. Quasi-isotropy is a special case of the orthotropic formalism, and the general orthotropic results are just as rigorous as the previous specialized quasi-isotropic results. The orthotropic failure criterion results are of direct and immediate relevance in composite materials applications.

Copyright © 2017 by ASME
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Christensen, R. M. , and Lonkar, K. , 2017, “ Failure Theory/Failure Criteria for Fiber Composite Laminates,” ASME J. Appl. Mech., 84(2), p. 021009. [CrossRef]
Hinton, M. J. , and Kaddour, A. S. , 2013, “ The Second World-Wide Failure Exercise: Part B,” J. Compos. Mater., 47(6–7), pp. 641–966. [CrossRef]
Christensen, R. M. , 2014, “ Completion and Closure on Failure Criteria for Unidirectional Fiber Composite Materials,” ASME J. Appl. Mech., 81(1), p. 011011. [CrossRef]
Kirane, K. , Salviato, M. , and Bazant, Z. P. , 2016, “ Microplane-Triad Model for Elastic and Fracturing Behavior of Woven Composites,” ASME J. Appl. Mech., 83(4), p. 041006. [CrossRef]
Van Otterloo, D. L. , and Dayal, V. , 2003, “ How Isotropic Are Quasi-Isotropic Laminates,” Composites, Part A, 34(1), pp. 93–103. [CrossRef]


Grahic Jump Location
Fig. 1

Lamination pattern

Grahic Jump Location
Fig. 2

Failure for fiber-dominated unidirectional, intermediate, and quasi-isotropic laminates



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