0
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

Professor
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.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Kyriakides, S. , Arseculeratne, R. , Perry, E. J. , and Liechti, K. M. , 1995, “ On the Compressive Failure of Fiber Reinforced Composites,” Int. J. Solids Struct., 32(6–7), pp. 689–738. [CrossRef]
Yerramalli, C. S. , and Waas, A. M. , 2004, “ The Effect of Fiber Diameter on the Compressive Strength of Composites—A 3D Finite Element Based Study,” Comput. Model. Eng. Sci., 6(1), pp. 1–16.
Kwon, Y. W. , and Berner, J. M. , 1995, “ Micromechanics Model for Damage and Failure Analyses of Laminated Fibrous Composites,” Eng. Fract. Mech., 52(2), pp. 231–242. [CrossRef]
Li, V. C. , Wang, Y. , and Backe, S. , 1991, “ A Micromechanical Model of Tension-Softening and Bridging Toughening of Short Random Fiber Reinforced Brittle Matrix Composites,” J. Mech. Phys. Solids, 39(5), pp. 607–625. [CrossRef]
Bažant, Z. P. , and Belytschko, T. B. , 1984, “ Continuum Theory for Strain Softening,” J. Eng. Mech., 110(12), pp. 1666–1692. [CrossRef]
Lasry, D. , and Belytschko, T. , 1988, “ Localization Limiters in Transient Problems,” Int. J. Solids Struct., 24(6), pp. 581–597. [CrossRef]
Triantafyllidis, N. , and Aifantis, E. C. , 1986, “ A Gradient Approach to Localization of Deformation. I. hyperelastic Materials,” J. Elasticity, 16(3), pp. 225–237. [CrossRef]
De Borst, R. , 1991, “ Simulation of Strain Localization: A Reappraisal of the Cosserat Continuum,” Eng. Comput., 8(4), pp. 317–332. [CrossRef]
Kafadar, C. B. , and Eingen, A. C. , 1971, “ Micropolar Media—I: the Classical Theory,” Int. J. Eng. Sci., 9(3), pp. 271–305. [CrossRef]
Steigmann, D. J. , 2012, “ Theory of Elastic Solids Reinforced With Fibers Resistant to Extension, Flexure and Twist,” Int. J. Non-Linear Mech., 47(7), pp. 734–742. [CrossRef]
Steigmann, D. J. , 2015, “ Effects of Fiber Bending and Twisting Resistance on the Mechanics of Fiber-Reinforced Elastomers,” Nonlinear Mech. Soft Fibrous Mater., 559, pp. 269–305.
Fleck, N. A. , and Shu, J. Y. , 1995, “ Microbuckle Initiation in Fiber Composites: A Finite Element Study,” J. Mech. Phys. Solids, 43(12), pp. 1887–1918. [CrossRef]
Sørensen, K. D. , Mikkelsen, L. P. , and Jensen, H. M. , eds., 2007, “ On the Simulation of Kink Bands in Fiber Reinforced Composites,” 28th Risø International Symposium on Materials Science: Interface Design of Polymer Matrix Composites—Mechanics, Chemistry, Modelling and Manufacturing, Risø, Denmark, pp. 281–288. http://orbit.dtu.dk/files/3699447/2008_46.pdf
Sørensen, K. D. , Mikkelsen, L. P. , and Jensen, H. M. , eds., 2009, “ User Subroutine for Compressive Failure of Composites,” Simulia Customer Conference, pp. 1–15. http://www.simulia.com/download/scc-papers/Energy/user-subroutine-compressive-failure-of-composites-2009-F.pdf
Prabhakar, P. , and Waas, A. M. , 2013, “ Upscaling From a Micro-Mechanics Model to Capture Laminate Compressive Strength Due to Kink Banding Instability,” Comput. Mater. Sci., 67, pp. 40–47. [CrossRef]
Ostoja-Starzewski, M. , 2008, Microstructural Randomness and Scaling in Mechanic of Materials, Chapman and Hall, London, Chap. 6.
Christensen, R. M. , 1979, Mechanics of Composite Materials, Wiley, New York. pp. 80–83.
Zhang, D. , and Waas, A. M. , 2014, “ A Micromechanics Based Multiscale Model for Nonlinear Composites,” Acta Mech., 225(4–5), pp. 1391–1417. [CrossRef]
Patel, D. K. , Hasanyan, A. D. , and Waas, A. M. , 2016, “ N-Layer Concentric Cylinder Model (NCYL): An Extended Micromechanics-Based Multiscale Model for Nonlinear Composites,” Acta Mech., 228(1), pp. 275–306. [CrossRef]
Onck, P. R. , 2002, “ Cosserat Modeling of Cellular Solids,” C. R. Méc., 330(11), pp. 717–722. [CrossRef]
Trovalusci, P. , Ostoja-Starzewski, M. , De Bellis, M. L. , and Murrali, A. , 2015, “ Scale-Dependent Homogenization of Random Composites as Micropolar Continua,” Eur. J. Mech.-A/Solids, 49, pp. 396–407. [CrossRef]
Forest, S. , and Sab, K. , 1998, “ Cosserat Overall Modeling of Heterogeneous Materials,” Mech. Res. Commun., 25(4), pp. 449–454. [CrossRef]
De Bellis, M. L. , and Addessi, D. , 2011, “ A Cosserat Based Multi-Scale Model for Masonry Structures,” Int. J. Multiscale Comput. Eng., 9(5), pp. 543–563. [CrossRef]
Lee, S. H. , and Waas, A. M. , 1999, “ Compressive Response and Failure of Fiber Reinforced Unidirectional Composites,” Int. J. Fract., 100(3), pp. 275–306. [CrossRef]
Hsu, S. Y. , Vogler, T. J. , and Kyriakides, S. , 1998, “ Compressive Strength Predictions for Fiber Composites,” ASME J. Appl. Mech., 65(1), pp. 7–16. [CrossRef]
Davidson, P. , and Waas, A. M. , 2016, “ Mechanics of Kinking in Fiber-Reinforced Composites Under Compressive Loading,” Math. Mech. Solids, 21(6), pp. 667–684. [CrossRef]
NG, W. H. , Salvi, A. G. , and Waas, A. M. , 2010, “ Characterization of the in-Situ Non-Linear Shear Response of Laminated Fiber-Reinforced Composites,” Compos. Sci. Technol., 70(7), pp. 1126–1134. [CrossRef]
Alsaleh, M. I. , Voyiadjis, G. Z. , and Alshibli, K. A. , 2006, “ Modelling Strain Localization in Granular Materials Using Micropolar Theory: Mathematical Formulations,” Int. J. Numer. Anal. Methods Geomech., 30(15), pp. 1501–1524. [CrossRef]
Ramezani, S. , Naghdabadi, R. , and Sohrabpour, S. , 2008, “ Non-Linear Finite Element Implementation of Micropolar Hypo-Elastic Materials,” Comput. Methods Appl. Mech. Eng., 197(49–50), pp. 4149–4159. [CrossRef]
Schultheisz, C. R. , and Waas, A. M. , 1996, “ Compressive Failure of Composites—Part I: Testing and Micromechanical Theories,” Prog. Aerosp. Sci., 32(1), pp. 1–42. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Kinematics of a 2D micropolar volume element

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

Fiber-aligned coordinates x̂i

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 6

Concentric fiber-matrix cylinder under bending moment

Grahic Jump Location
Fig. 7

Isotropic matrix material nonlinearity [27]

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
Fig. 9

Isoparametric representation of a four-noded micropolar quadrilateral element

Grahic Jump Location
Fig. 10

Schematic of the micromechanics boundary value problem

Grahic Jump Location
Fig. 11

Schematic of the equivalent micropolar continuum boundary value problem

Grahic Jump Location
Fig. 12

Stress response of the micromechanics and micropolar continuum models

Grahic Jump Location
Fig. 13

Deformation history of the micromechanics model

Grahic Jump Location
Fig. 14

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

Grahic Jump Location
Fig. 15

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

Grahic Jump Location
Fig. 16

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

Grahic Jump Location
Fig. 17

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 19

Concentric cylinder representation of a fibrous composite

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In