An extension of the ZM model for shape memory alloys accounting for plastic deformation

Wael Zaki, Sorin Zamfir, Ziad Moumni

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In this paper, the ZM model for shape memory alloys (Zaki and Moumni, 2007a,b) is modified in order to account for irreversible plastic deformations that might occur when the material is subjected to severe mechanical loading. For this purpose, we follow the same procedure used for developing the original model, cast mainly within the framework of generalized standard materials with internal constraints. A first version based on the non-cyclic ZM model (Zaki and Moumni, 2007b) is developed and used to simulate the tensile behavior of a polycrystalline NiTi shape memory alloy. Comparison with experimental data shows the ability of the model to adequately predict the stress-strain behavior of the material, including plastic deformation of martensite beyond the point of plastic yield. The model fails, however, in providing a satisfactory estimate of the total inelastic deformation remaining after complete unloading. To overcome this issue, the cyclic version of the ZM model (Zaki and Moumni, 2007a) is generalized. The resulting model better fits experimental data.

Original languageBritish English
Pages (from-to)266-274
Number of pages9
JournalMechanics of Materials
Issue number3
StatePublished - Mar 2010


  • Generalized standard materials
  • Macroscale modeling
  • Plastic deformation
  • Shape memory alloys


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