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Research Papers

Microplane-Triad Model for Elastic and Fracturing Behavior of Woven Composites

[+] Author and Article Information
Kedar Kirane

Civil and Environmental Engineering,
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

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

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 83(4), 041006 (Jan 25, 2016) (14 pages) Paper No: JAM-15-1617; doi: 10.1115/1.4032275 History: Received November 15, 2015; Revised December 14, 2015

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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References

Figures

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Fig. 1

Schematic representation of (a) the RUC of a 2 × 2 twill composite and its local coordinate system and (b) decomposition of the RUC into matrix, fill and warp yarn plates assumed to be in parallel coupling

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Fig. 2

(a) Example of discretization of the yarn into microplanes for a twill 2 × 2 and (b) projection of the strain tensor into the μ th microplane triad

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Fig. 3

Local coordinate system assigned to each yarn section

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Fig. 4

Schematic representation of (a) an RUC for a 2 × 2 twill weave composite and (b) the microplanes used for the discretization of the yarns

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Fig. 5

Evolution laws of (a) the fiber modulus degradation and (b) the matrix modulus degradation

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Fig. 6

(a) Degradation of fiber stress versus inelastic strain at one material point, calibrated for tension. (b) Comparison of the measured and predicted load displacement curve for a [0]8 coupon, under tension.

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Fig. 7

(a) Degradation of fiber stress versus inelastic strain at one material point, calibrated for compression. (b) Comparison of the measured and predicted load displacement curve for a [0]8 coupon, under compression.

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Fig. 8

(a) Material point stress strain curve in the [45]8 configuration, under tension. (b) Comparison of the measured and predicted load displacement curve for a [45]8 coupon, under tension.

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Fig. 9

Comparison of the measured and predicted load displacement curve for a quasi-isotropic coupon under (a) tension and (b) compression

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Fig. 10

Fractured specimen from the tests and predicted damage localization from simulations for (a) [45]8 coupon under tension, (b) QI coupon under tension, and (c) QI coupon under compression

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Fig. 11

Comparison of the measured and predicted size effect in SENT [0]8 coupons

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Fig. 12

Deformation patterns in (a) circular and (b) square crush cans under a plug-initiated crush and (c) geometry of the crush initiating plug

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Fig. 13

Force versus displacement for (a) circular and (b) square crush can under a plug-initiated crush

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