Abstract
The fracture investigations of the planar lattices made of ductile cell walls are currently limited to bending-dominated hexagonal honeycomb. In this paper, the plastic zones of stretching-dominated lattices, including Kagome and triangular lattices, are estimated by analyzing their effective yield loci. The normalized in-plane yield loci of these two lattices are almost identical convex curves enclosed by 4 straight lines, which is almost independent of the relative density but is highly sensitive to the principal stress directions. Therefore, the plastic zones around the crack tip of Kagome and triangular are estimated to be quite different to those of the continuum solid and also hexagonal lattice. The plastic zones predictions by convex yield surfaces of both lattices are validated by FE calculations, although the shear lag region caused by non-local bending effect in the Kagome lattice enlarges the plastic zone in cases of small ratio of r p /l.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Evans, A.G., Lightweight materials and structures. Materials Research Bulletin, 2001, 26(10): 790–797.
Gibson, L.J. and Ashby, M.F., Cellular Solids: Structure and Properties. Cambridge: Cambridge University Press, 1997.
Wang, A.J. and McDowell, D.L., In-plane stiffness and yield strength of periodic metal Honeycombs, ASME Journal of Engineering Materials and Technology, 2004, 126: 137–156.
Hutchinson, R.G., Wicks, N. and Evans, A.G., et al., Kagome Plate Structures for Actuation. International Journal of Solids and Structures, 2003, 40: 6969–6980.
Fleck, N.A and Qiu, X., The damage tolerance of elastic-brittle, two dimensional isotropic lattices. Journal of the Mechanics and Physics of Solids, 2007, 55: 562–588.
Alonsoa, I.Q. and Fleck, N.A., Damage tolerance of an elastic-brittle diamond-celled honeycomb. Scripta Materialia, 2007, 56: 696–696.
Romijn, N.E.R. and Fleck, N.A., The fracture toughness of planar lattices: imperfection sensitivity. Journal of the Mechanics and Physics of Solids, 2007, 55(12): 2538–2564.
Schmidt, I. and Fleck, N.A., Ductile fracture of two-dimensional cellular structures. International Journal of Fracture, 2001, 111: 327–342.
Chen, C., Lu, T.J. and Fleck, N.A., Effect of imperfections on the yielding of two-dimensional foams. Journal of the Mechanics and Physics of Solids, 1999, 47: 2235–2272.
Hutchinson, R.G., Mechanics of Lattice Materials, P.H.D. thesis, Cambridge University, UK, 2004.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (No.10502027) and the National Fundamental Research Program of China (No.G2006CB601202).
Rights and permissions
About this article
Cite this article
Qiu, X., He, L., Qian, Y. et al. Plastic zone of semi-infinite crack in planar Kagome and triangular lattices. Acta Mech. Solida Sin. 22, 213–225 (2009). https://doi.org/10.1016/S0894-9166(09)60268-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S0894-9166(09)60268-8