Modeling of stress relaxation process, case study: Shape setting heat treatment of a Ni rich-NiTi alloy

[Display omitted] •Stress relaxation phenomenon was modeled during shape setting process of NiTi alloy.•Continuum mechanics was utilized for determination of a with-box model.•Relaxation process depends on shape setting temperature and chemical composition. Shape setting (stress relaxation) process which is generally defined by heating an elastically constrained material is used as an industrial technique for fixing accuracy of shape, and sometimes deformation of some materials specially those which have high spring back property. The present study attempts to explore stress relaxation process during heating an elastically constrained material using basic concepts of continuum mechanics, and lumped element modeling. Hence, Ni rich-NiTi wires were deformed elastically and their fixed strain during heat treatment (ε) was measured gradually by increasing the stress relaxation time (t). The ε–t curve was found to be a possible answer for a differential equation between discreet elements of the continuum specimen (NiTi wire). Ultimately, a white box model was expanded for predicting this phenomenon using general concepts of diffusion in solids. Results of the investigation illustrate that stress relaxation process depends on the temperature of shape setting process, chemical composition of the material, the amount of strain fixed in the material and also activation energy of diffusion.