A multiscale model based on the framework of microplane theory is developed to predict the elastic and fracturing behavior of woven composites from the mesoscale properties of the constituents and the weave architecture. The effective yarn properties are obtained by means of a simplified mesomechanical model of the yarn, based on a mixed series and parallel coupling of the fibers and of the polymer within the yarns. As a novel concept, each of the several inclined or aligned segments of an undulating fill and warp yarn is represented by a triad of orthogonal microplanes, one of which is normal to the yarn segment while another is normal to the plane of the laminate. The constitutive law is defined in terms of the microplane stress and strain vectors. The elastic and inelastic constitutive behavior is defined using the microplane strain vectors which are the projections of the continuum strain tensor. Analogous to the principle of virtual work used in previous microplane models, a strain energy density equivalence principle is employed here to obtain the continuum level elastic and inelastic stiffness tensors, which in turn yield the continuum level stress tensor. The use of strain vectors rather than tensors makes the modeling conceptually clearer as it allows capturing the orientation of fiber failures, yarn cracking, matrix microcracking, and interface slip. Application of the new microplane-triad model for a twill woven composite shows that it can realistically predict all the orthotropic elastic constants and the strength limits for various layups. In contrast with the previous (nonmicroplane) models, the formulation can capture the size effect of quasi-brittle fracture with a finite fracture process zone (FPZ). Explicit finite-element analysis gives a realistic picture of progressive axial crushing of a composite tubular crush can initiated by a divergent plug. The formulation is applicable to widely different weaves, including plain, twill, and satin weaves, and is easily extensible to more complex architectures such as hybrid weaves as well as two- and three-dimensional braids.
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April 2016
Research-Article
Microplane-Triad Model for Elastic and Fracturing Behavior of Woven Composites
Kedar Kirane,
Kedar Kirane
Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60201
e-mail: kedarkirane2011@u.northwestern.edu
Northwestern University,
Evanston, IL 60201
e-mail: kedarkirane2011@u.northwestern.edu
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Marco Salviato,
Marco Salviato
Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60201
e-mail: marco.salviato@northwestern.edu
Northwestern University,
Evanston, IL 60201
e-mail: marco.salviato@northwestern.edu
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Zdeněk P. Bažant
Zdeněk P. Bažant
Distinguished McCormick Institute Professor and
W.P. Murphy Professor
ASME Honorary Member
Civil and Environmental Engineering and
Materials Science,
Northwestern University,
Evanston, IL 60201
e-mail: z-bazant@northwestern.edu
W.P. Murphy Professor
ASME Honorary Member
Civil and Environmental Engineering and
Materials Science,
Northwestern University,
Evanston, IL 60201
e-mail: z-bazant@northwestern.edu
Search for other works by this author on:
Kedar Kirane
Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60201
e-mail: kedarkirane2011@u.northwestern.edu
Northwestern University,
Evanston, IL 60201
e-mail: kedarkirane2011@u.northwestern.edu
Marco Salviato
Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60201
e-mail: marco.salviato@northwestern.edu
Northwestern University,
Evanston, IL 60201
e-mail: marco.salviato@northwestern.edu
Zdeněk P. Bažant
Distinguished McCormick Institute Professor and
W.P. Murphy Professor
ASME Honorary Member
Civil and Environmental Engineering and
Materials Science,
Northwestern University,
Evanston, IL 60201
e-mail: z-bazant@northwestern.edu
W.P. Murphy Professor
ASME Honorary Member
Civil and Environmental Engineering and
Materials Science,
Northwestern University,
Evanston, IL 60201
e-mail: z-bazant@northwestern.edu
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 15, 2015; final manuscript received December 14, 2015; published online January 25, 2016. Editor: Yonggang Huang.
J. Appl. Mech. Apr 2016, 83(4): 041006 (14 pages)
Published Online: January 25, 2016
Article history
Received:
November 15, 2015
Revised:
December 14, 2015
Citation
Kirane, K., Salviato, M., and Bažant, Z. P. (January 25, 2016). "Microplane-Triad Model for Elastic and Fracturing Behavior of Woven Composites." ASME. J. Appl. Mech. April 2016; 83(4): 041006. https://doi.org/10.1115/1.4032275
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