摘要
This paper presents a macroscopic constitutive model reproducing the hysteretic behaviors of the superelastic shape memory alloy (SMA) under cyclic loading. The progressive increase of residual strain with the increased cycle number in such materials is assumed to be a consequence of the progressive increase of residual stress-induced martensitic volume fraction upon the cyclic effects. The progressive decrease of phase transformation critical stresses with the increased cycle number in such materials is assumed to be a result from the progressive increase of phase transformation critical temperatures upon the cyclic effects. A cyclic evolution equation is supposed to describe the influences of cycle effects on the material properties of the SMA under cyclic loading. A phase transformation equation expressing the phase transformation behaviors of the SMA under cyclic loading is established based on the differential relationship between martensitic volume fraction and the free energy increment of phase transformation. A mechanical constitutive equation predicting the mechanical characteristics of the SMA under cyclic loading is developed on the basis of thermodynamics and continuum mechanics. The cyclic evolution equation, phase transformation equation, and mechanical constitutive equation together compose the presented macroscopic constitutive model considering cyclic effects. Results of the numerical simulations illustrate that it can well reproduce the superelastic hysteretic behaviors of the SMA under cyclic loading.
This paper presents a macroscopic constitutive model reproducing the hysteretic behaviors of the superelastic shape memory alloy （SMA） under cyclic loading. The progressive increase of residual strain with the increased cycle number in such materials is assumed to be a consequence of the progressive increase of residual stress-induced martensitic volume fraction upon the cyclic effects. The progressive decrease of phase transformation critical stresses with the increased cycle number in such materials is assumed to be a result from the progressive increase of phase transformation critical temperatures upon the cyclic effects. A cyclic evolution equation is supposed to describe the influences of cycle effects on the material properties of the SMA under cyclic loading. A phase transformation equation expressing the phase transformation behaviors of the SMA under cyclic loading is established based on the differential relationship between martensitic volume fraction and the free energy increment of phase transformation. A mechanical constitutive equation predicting the mechanical characteristics of the SMA under cyclic loading is developed on the basis of thermodynamics and continuum mechanics. The cyclic evolution equation, phase transformation equation, and mechanical constitutive equation together compose the presented macroscopic constitutive model considering cyclic effects. Results of the numerical simulations illustrate that it can well reproduce the superelastic hysteretic behaviors of the SMA under cyclic loading.
基金
supported by the Fundamental Research Funds for Central Universities of China (Grant Nos. HEUCFZ1004, HEUCF110202 andHEUCF110204)
the Harbin Talent Foundation of Scientific and Technical Innovation of China (Grant No. RC2009QN0170046)
the Foundation for Returned Overseas Scholars from the Ministry of Education of China (Series 37)
the National Postdoctoral Science Foundation of China(Grant No. 20080430933)
