Research Papers

Compressive Failure of Fiber Composites: A Homogenized, Mesh-Independent Model

[+] Author and Article Information
Armanj D. Hasanyan

Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109

Anthony M. Waas

William E Boeing Department of Aeronautics
and Astronautics,
University of Washington,
Seattle, WA 98195

1Present address: Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 14, 2017; final manuscript received March 18, 2018; published online June 14, 2018. Assoc. Editor: George Kardomateas.

J. Appl. Mech 85(9), 091001 (Jun 14, 2018) (15 pages) Paper No: JAM-17-1679; doi: 10.1115/1.4039754 History: Received December 14, 2017; Revised March 18, 2018

Micromechanics models of fiber kinking provide insight into the compressive failure mechanism of fiber reinforced composites, but are computationally inefficient in capturing the progressive damage and failure of the material. A homogenized model is desirable for this purpose. Yet, if a proper length scale is not incorporated into the continuum, the resulting implementation becomes mesh dependent when a numerical approach is used for computation. In this paper, a micropolar continuum is discussed to characterize the compressive failure of fiber composites dominated by kinking. Kink banding is an instability associated with a snap-back behavior in the load–displacement response, leading to the formation of a finite region of localized deformation. The challenge in modeling this mode of failure is the inherent geometric and matrix material nonlinearity that must be considered. To overcome the mesh dependency of numerical results, a length scale is naturally introduced when modeling the composite as a micropolar continuum. A new approach is presented to approximate the effective transversely isotropic micropolar constitutive relation of a fiber composite. Using an updated Lagrangian, nonlinear finite element code, previously developed for incorporating the additional rotational degrees-of-freedom (DOFs) of micropolar theory, the simulation of localized deformation in a continuum model, corresponding to fiber kinking, is demonstrated and is found to be comparable with the micromechanics simulation results. Most importantly, the elusive kink band width is a natural outcome of the continuum model.

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Fig. 1

Kinematics of a 2D micropolar volume element

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Fig. 2

Two-dimensional micropolar volume element with asymmetric stresses Σij and couple stresses Mi3

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Fig. 3

Fiber-aligned coordinates x̂i

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Fig. 4

Schematic of external shear loads on a fiber and matrix layered composite: (a) Shear stress applied perpendicular to fibers and (b) Shear stress applied parallel to fibers

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Fig. 5

Deformation modes of the RVE: (a) Σ̂12=Σ applied on a 6 fiber volume element, (b) Σ̂21=Σ applied on a six fiber volume element, (c) Σ̂12=Σ applied on a 12 fiber volume element, (d) Σ̂21=Σ applied on a 12 fiber volume element, (e) Σ̂12=Σ applied on a 18 fiber volume element, (f) Σ̂21=Σ applied on a 18 fiber volume element, (g) Σ̂12=Σ applied on a 24 fiber volume element, and (h) Σ̂21=Σ applied on a 24 fiber volume element

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Fig. 6

Concentric fiber-matrix cylinder under bending moment

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Fig. 7

Isotropic matrix material nonlinearity [27]

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Fig. 8

Equivalent nonlinear material nonlinearity under different symmetric loading conditions [15]

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Fig. 9

Isoparametric representation of a four-noded micropolar quadrilateral element

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Fig. 10

Schematic of the micromechanics boundary value problem

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Fig. 11

Schematic of the equivalent micropolar continuum boundary value problem

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Fig. 12

Stress response of the micromechanics and micropolar continuum models

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Fig. 13

Deformation history of the micromechanics model

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Fig. 14

Deformation history of the 9 × 21 element mesh of the continuum model

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Fig. 15

Deformation history of the 14 × 31 element mesh of the continuum model

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Fig. 16

Deformation history of the 18 × 41 element mesh of the continuum model

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Fig. 17

Contour plots of (a) the micropolar couple stress and (b) curvature strain at 1% strain (frame 5), for 18 × 41 element mesh

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Fig. 18

Contour plots of (a) micropolar rotation and (b) classical rotation in a Cauchy continuum, at 1% strain (frame 5), for 18 × 41 element mesh

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Fig. 19

Concentric cylinder representation of a fibrous composite




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