Journal of Materials Engineering and Performance

, Volume 27, Issue 4, pp 2038–2048 | Cite as

An improved Armstrong–Frederick-Type Plasticity Model for Stable Cyclic Stress–Strain Responses Considering Nonproportional Hardening

  • Jing Li
  • Zhong-ping Zhang
  • Chun-wang Li


This paper modified an Armstrong–Frederick-type plasticity model for investigating the stable cyclic deformation behavior of metallic materials with different sensitivity to nonproportional loadings. In the modified model, the nonproportionality factor and nonproportional cyclic hardening coefficient coupled with the Jiang–Sehitoglu incremental plasticity model were used to estimate the stable stress–strain responses of the two materials (1045HR steel and 304 stainless steel) under various tension–torsion strain paths. A new equation was proposed to calculate the nonproportionality factor on the basis of the minimum normal strain range. Procedures to determine the minimum normal strain range were presented for general multiaxial loadings. Then, the modified model requires only the cyclic strain hardening exponent and cyclic strength coefficient to determine the material constants. It is convenient for predicting the stable stress–strain responses of materials in engineering application. Comparisons showed that the modified model can reflect the effect of nonproportional cyclic hardening well.


multiaxial fatigue nonproportional hardening nonproportionality factor plasticity incremental model stabilized stress–strain response 



The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (No. 51601221 and No. 51575524) and the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2015JM5240).


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Copyright information

© ASM International 2018

Authors and Affiliations

  1. 1.School of Mechatronic EngineeringXidian UniversityXi’anChina
  2. 2.The Science InstituteAir Force Engineering UniversityXi’anChina

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