Critical Frequency of Self-Heating in a Superelastic Ni-Ti Belleville Spring: Experimental Characterization and Numerical Simulation

Sensors (Basel). 2021 Oct 27;21(21):7140. doi: 10.3390/s21217140.


The mechanical loading frequency affects the functional properties of shape memory alloys (SMA). Thus, it is crucial to study its effect for the successful use of these materials in dynamic applications. Based on the superelastic cyclic behavior, this work presents an experimental methodology for the determination of the critical frequency of the self-heating of a NiTi Belleville conical spring. For this, cyclic compressive tests were carried out using a universal testing machine with loading frequencies ranging from 0.5 Hz to 10 Hz. The temperature variation during the cyclic tests was monitored using a micro thermocouple glued to the NiTi Belleville spring. Numerical simulations of the spring under quasi-static loadings were performed to assist the analysis. From the experimental methodology applied to the Belleville spring, a self-heating frequency of 1.7 Hz was identified. The self-heating is caused by the latent heat accumulation generated by successive cycles of stress-induced phase transformation in the material. At 2.0 Hz, an increase of 1.2 °C in the average temperature of the SMA device was verified between 1st and 128th superelastic cycles. At 10 Hz, the average temperature increase reached 7.9 °C and caused a 10% increase in the stiffness and 25% decrease in the viscous damping factor. Finally, predicted results of the force as a function of the loading frequency were obtained.

Keywords: Ni-Ti Belleville spring; dynamic loading; self-heating frequency; shape memory alloys; superelasticity.

MeSH terms

  • Alloys
  • Elasticity
  • Heating*
  • Materials Testing
  • Nickel*
  • Temperature
  • Titanium


  • Alloys
  • titanium nickelide
  • Nickel
  • Titanium