Acta Mechanica Solida Sinica

, Volume 22, Issue 3, pp 276–282

# Stochastic elasto-plastic fracture analysis of aluminum foams

Article

## Abstract

Model I quasi-static nonlinear fracture of aluminum foams is analyzed by considering the effect of microscopic heterogeneity. Firstly, a continuum constitutive model is adopted to account for the plastic compressibility of the metallic foams. The yield strain modeled by a two-parameter Weibull-type function is adopted in the constitutive model. Then, a modified cohesive zone model is established to characterize the fracture behavior of aluminum foams with a cohesive zone ahead of the initial crack. The tensile traction versus local crack opening displacement relation is employed to describe the softening characteristics of the material. And a Weibull statistical model for peak bridging stress within the fracture process zone is used for considering microscopic heterogeneity of aluminum foams. Lastly, the influence of stochastic parameters on the curve of stress-strain is given. Numerical examples are given to illustrate the numerical model presented in this paper and the effects of Weibull parameters and material properties on J-integral are discussed.

## Key words

aluminum foams cohesive zone model continuum constitutive model fracture Weibull distributions J-integral

## References

1. [1]
Gibson, L.J. and Ashby, M.F., Cellular Solids: Structures and Properties, Seconded. Cambridge: Cambridge University Press, 1997.
2. [2]
Guo, R.P., Mai, Y.W., Fan, T.Y., Liu, G.T. and Maier, M., Plane stress crack growing steadily in metal foams. Materials Science and Engineering A, 2004, 381: 292–298.
3. [3]
Blazy, J.S, Marie-Louise, A., Forest, S., Chastel, Y., Pineau, A., Awade, A., Grolleron, C. and Moussy, F., Deformation and fracture of aluminium foams under proportional and non proportional multi-axial loading: statistical analysis and size effect. International Journal of Mechanical Sciences, 2004, 46: 217–244.
4. [4]
Olurin, O.B., Fleck, N.A. and Ashby, M.F., Deformation and fracture of aluminium foams. Materials Science and Engineering A, 2000, 291: 136–146.
5. [5]
Elices, M., Guinea, G.V., Gomez, J. and Planas, J., The cohesive zone model: advantages, limitations and challenges. Engineering Fracture Mechanics, 2002, 69: 137–163.
6. [6]
Li, H. and Chandra, N., Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models. International Journal of Plasticity, 2003, 19: 849–882.
7. [7]
Chen, C, Fleck, N.A and Lu, T.J., The mode I crack growth resistance of metallic foams. Journal of the Mechanics and Physics of Solids, 2001, 49: 231–259.
8. [8]
Sun, S.Y. and Chen, H.R., Application of a continuum constitutive model for fracture analysis of metallic foam with element-free Galerkin method. In: Proceedings of the 5th International Conference on Nonlinear Mechanics, edited by Chien Wei-zang, Shanghai University Press, Shanghai, 2007, 262–266.Google Scholar
9. [9]
Triantafillou, T.V. and Gibson, L.J., Constitutive modeling of elastic-plastic open-cell foams. Journal of Engineering Mechanics, 1990, 116: 2772–2778.
10. [10]
Muhlich, U. and Brocks, W., On the numerical integration of a class of pressure-dependent plasticity models including kinematic hardening. Computational Mechanics, 2003, 31: 479–488.
11. [11]
You, X.M., Zhao, H.F. and Wei, Y.G., Determination of interfacial mechanical parameters for an Al/Eproxy/Al2O3 system by using peel test simulations. Acta Mechanica Solida Sinica, 2008, 20(3): 198–206.
12. [12]
Han, F.S. and Zhu, Z.G., The mechanical behavior of foamed aluminum. Journal of Materials Science, 1999, 34: 291–299.
13. [13]
Wang, X. and Yu, J.L., Uniaxial mechanical behavior of aluminum foam. Journal of Experimental Mechanics, 2001, 16: 438–443 (in Chinese).Google Scholar
14. [14]
Wicklein, M. and Thoma, K., Numerical investigations of the elastic and plastic behaviour of an open-cell aluminium foam. Materials Science and Engineering A, 2005, 397: 391–399.

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2009

## Authors and Affiliations

• Shiyong Sun
• 1
• Haoran Chen
• 1
• Xiaozhi Hu
• 2
• Zhanjun Wu
• 1
1. 1.State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianChina
2. 2.School of Mechanical EngineeringThe University of Western AustraliaPerthAustralia