0
Research Papers

Steady-State Kink Band Propagation in Layered Materials

[+] Author and Article Information
Simon P. H. Skovsgaard

Department of Engineering,
Aarhus University,
Inge Lehmanns Gade 10,
Aarhus C 8000, Denmark
e-mail: sphs@eng.au.dk

Henrik Myhre Jensen

Professor
Department of Engineering,
Aarhus University,
Inge Lehmanns Gade 10,
Aarhus C 8000, Denmark
e-mail: hmj@eng.au.dk

Manuscript received January 22, 2018; final manuscript received March 5, 2018; accepted manuscript posted March 30, 2018; published online March 30, 2018. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 85(6), 061005 (Mar 30, 2018) (11 pages) Paper No: JAM-18-1046; doi: 10.1115/1.4039573 History: Received January 22, 2018; Revised March 05, 2018

Failure by steady-state kink band propagation in layered materials is analyzed using three substantially different models. A finite element model and an analytical model are developed and used together with a previously introduced constitutive model. A novel methodology for simulating an infinite kink band is used for the finite element model using periodic boundary conditions on a skewed mesh. The developed analytical model results in a transcendental equation for the steady-state kink band propagation state. The three models are mutually in good agreement and results obtained using the models correlate well with the previous experimental findings.

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

References

Fleck, N. , 1997, “ Compressive Failure of Fibre Composites,” Adv. Appl. Mech., 33, pp. 43–117.
Bishara, M. , Vogler, M. , and Rolfes, R. , 2017, “ Revealing Complex Aspects of Compressive Failure of Polymer Composites—Part II: Failure Interactions in Multidirectional Laminates and Validation,” Compos. Struct., 169, pp. 116–128. [CrossRef]
Budiansky, B. , 1983, “ Micromechanics,” Comput. Struct., 16(1–4), pp. 3–12. [CrossRef]
Jensen, H. M. , and Christoffersen, J. , 1997, “ Kink Band Formation in Fiber Reinforced Materials,” J. Mech. Phys. Solids, 45(7), pp. 1121–1136. [CrossRef]
Vogler, T. , and Kyriakides, S. , 1997, “ Initiation and Axial Propagation of Kink Bands in Fiber Composites,” Acta Mater., 45(6), pp. 2443–2454. [CrossRef]
Evans, A. G. , and Adler, W. F. , 1978, “ Kinking as a Mode of Structural Degradation in Carbon Fiber Composites,” Acta Metall., 26(5), pp. 725–738. [CrossRef]
Moran, P. M. , Liu, X. H. , and Shih, C. F. , 1995, “ Kink Band Formation and Band Broadening in Fiber Composites Under Compressive Loading,” Acta Metall. Mater., 43(8), pp. 2943–2958. [CrossRef]
Vogler, T. J. , and Kyriakides, S. , 1999, “ On the Axial Propagation of Kink Bands in Fiber Composites—Part I: Experiments,” Int. J. Solids Struct., 36(4), pp. 557–574. [CrossRef]
Hsu, S.-Y. , Vogler, T. J. , and Kyriakides, S. , 1999, “ On the Axial Propagation of Kink Bands in Fiber Composites—Part II: Analysis,” Int. J. Solids Struct., 36(4), pp. 575–595. [CrossRef]
Attwood, J. P. , Fleck, N. A. , Wadley, H. N. G. , and Deshpande, V. S. , 2015, “ The Compressive Response of Ultra-High Molecular Weight Polyethylene Fibres and Composites,” Int. J. Solids Struct., 71, pp. 141–155. [CrossRef]
Byskov, E. , Christoffersen, J. , Dencker Christensen, C. , and Sand Poulsen, J. , 2002, “ Kinkband Formation in Wood and Fiber Compositesmorphology and Analysis,” Int. J. Solids Struct., 39(13–14), pp. 3649–3673. [CrossRef]
Nizolek, T. , Begley, M. , McCabe, R. , Avallone, J. , Mara, N. , Beyerlein, I. , and Pollock, T. , 2017, “ Strain Fields Induced by Kink Band Propagation in Cu-Nb Nanolaminate Composites,” Acta Mater., 133, pp. 303–315. [CrossRef]
Jensen, H. M. , 1999, “ Analysis of Compressive Failure of Layered Materials by Kink Band Broadening,” Int. J. Solids Struct., 36(23), pp. 3427–3441. [CrossRef]
Prabhakar, P. , and Waas, A. M. , 2013, “ Interaction Between Kinking and Splitting in the Compressive Failure of Unidirectional Fiber Reinforced Laminated Composites,” Compos. Struct., 98, pp. 85–92. [CrossRef]
Skovsgaard, S. P. H. , and Jensen, H. M. , 2018, “ Constitutive Model for Imperfectly Bonded Fibre-Reinforced Composites,” Compos. Struct., 192, pp. 82–92. [CrossRef]
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]
Christoffersen, J. , and Jensen, H. M. , 1996, “ Kink Band Analysis Accounting for the Microstructure of Fiber Reinforced Materials,” Mech. Mater., 24(4), pp. 305–315. [CrossRef]
Sørensen, K. D. , Mikkelsen, L. P. , and Jensen, H. M. , 2009, “ User Subroutine for Compressive Failure of Composites,” Simulia Customer Conference, London, May 18–21, pp. 618–632.
Davidson, P. , and Waas, A. M. , 2014, “ Mechanics of Kinking in Fiber-Reinforced Composites Under Compressive Loading,” Math. Mech. Solids, 21(6), pp. 667–684. [CrossRef]
Wind, J. L. , Steffensen, S. , and Jensen, H. M. , 2014, “ Comparison of a Composite Model and an Individually Fiber and Matrix Discretized Model for Kink Band Formation,” Int. J. Non-Linear Mech., 67, pp. 319–325. [CrossRef]
Fleck, N. A. , and Budiansky, B. , 1991, “ Compressive Failure of Fibre Composites Due to Microbuckling,” Third Symposium on Inelastic Deformation of Composite Materials, Troy, NY, May 29–June 1, pp. 235–273.
Stören, S. , and Rice, J. R. , 1975, “ Localized Necking in Thin Sheets,” J. Mech. Phys. Solids, 23(6), pp. 421–441. [CrossRef]
Jensen, H. M. , 1999, “ Models of Failure in Compression of Layered Materials,” Mech. Mater., 31(9), pp. 553–564. [CrossRef]
Budiansky, B. , and Fleck, N. , 1993, “ Compressive Failure of Fibre Composites,” J. Mech. Phys. Solids, 41(1), pp. 183–211. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) Geometry of the micromechanical finite element model. The darker regions represent the fiber constituent. (b) Sketch of overall deformation.

Grahic Jump Location
Fig. 2

Illustration of mesh used in the finite element simulations. The coupling of the nodes locks the deformation in an orientation β.

Grahic Jump Location
Fig. 6

Nondimensional stress versus normalized end displacement u/L0 and fiber rotation ϕ for two simulations with 1 and 4 matrix element layers: (a) stress versus displacement and (b) stress versus fiber rotation

Grahic Jump Location
Fig. 5

Applied normalized stress −σ11/G as a function of fiber rotation ϕ for simulation with a band orientation β=10deg. The five deformation stages in Fig. 3 are designated.

Grahic Jump Location
Fig. 7

Assumed deformation of the constituents based on overall deformations of the composite. For illustrative purpose, the gray constituent reacts stiffer, as in the case of a fiber embedded in a polymer matrix.

Grahic Jump Location
Fig. 4

Applied normalized stress −σ11/G as a function of normalized end shortening u/L0 for simulation with a band orientation β=10deg. The five deformation stages in Fig. 3 are designated.

Grahic Jump Location
Fig. 3

Shear strain in matrix constituent, ε12, for five deformation stages during simulation for a geometry with an initial imperfection ϕ0=2deg and a band orientation β=10deg for a single strip as shown in Fig. 1(a)

Grahic Jump Location
Fig. 8

Kink band geometry with two coordinate systems, one inside the band and one outside represented with (•)i and (•)o respectively

Grahic Jump Location
Fig. 10

Illustration of steady-state kink band propagation in the case of inextensible fibers. The geometry with dashed lines represents a propagated configuration.

Grahic Jump Location
Fig. 9

External WE and internal work WI per unit volume as a function of fiber rotation ϕ for the semi-analytical model. The band orientation is set to β=20deg in the current simulation. The lock-up condition, WI=WE, is marked in the figure.

Grahic Jump Location
Fig. 11

Strain state outside (state 1) and inside the kink band (state 2). The strain state inside the kink band is rotated 60deg on the configuration to the right.

Grahic Jump Location
Fig. 12

Stress–strain relation for the semi-analytical and analytical models. The bilinear curve represents the response used for the analytical model.

Grahic Jump Location
Fig. 13

External, WE, and internal work WI done per unit volume as a function of the fiber rotation ϕ for the analytical model. The band orientation is set to β=20deg. The lock-up condition, WI=WE, is marked in the figure.

Grahic Jump Location
Fig. 14

Steady-state lock-up angle ϕss as a function of initial kink band orientation β0. Results are shown for the three models presented. Additionally, the conventional assumption of fiber lock-up ϕ=2β is included for comparison.

Grahic Jump Location
Fig. 15

Normalized steady-state kink band propagation stress −σ11ss/G as a function of initial kink band orientation β0. Results are shown for the three models presented.

Grahic Jump Location
Fig. 16

Steady-state lock-up angle ϕss as a function of Poisson's ratio for the matrix constituent νm. The initial band orientation is β0=10deg. Results are shown for the three models presented.

Grahic Jump Location
Fig. 17

Normalized steady-state kink band propagation stress −σ11ss/G as a function of Poisson's ratio for the matrix constituent νm. The initial band orientation is β0=10deg. Results are shown for the three models presented.

Grahic Jump Location
Fig. 18

Normalized steady-state kink band propagation stress −σ11ss/G as a function of normalized minimum tangent modulus for the matrix constituent Et,minm/Em. Results are shown for the semi-analytical and analytical models.

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