PSI - Issue 36

Volodymyr Iasnii et al. / Procedia Structural Integrity 36 (2022) 284–289 Volodymyr Iasnii, Lukasz Sobaszek, Petro Yasniy / Structural Integrity Procedia 00 (2021) 000 – 000

287

4

a)

b)

0,0 0,5 1,0 1,5 2,0 -0,10 -0,05 0,00 0,05 0,10 0,15 P, kN

0,0 0,5 1,0 1,5 2,0

-0,20

-0,10

0,00

0,10

0,20

-2,0 -1,5 -1,0 -0,5

-2,0 -1,5 -1,0 -0,5

P, kN

 , %

ε , %

Fig. 3. Summary of the results for 7 tested frequencies 0.001 Hz (а) and 0.1 Hz (d). The hysteresis loops represent SMA wire response for different displacement amplitudes.

Dissipated energy and loss factor were calculated by formula (1). Their dependencies on the displacement amplitude at loading frequency 0.1 Hz are shown on Fig. 4 and Fig. 5. In general, in the studied frequencies ranges the dissipation energy increase with the increasing in displacement amplitude of the device rod (Fig. 4). The loss factor could be described by a monotonic decreasing function on the amplitude. The exceptions are for the load frequencies of 0.001 Hz and 2 Hz, so the loss factor is in the range from 0.1 to 0.19 at = 3 mm and from 0.07 to 0.16 at S a =8 mm (Fig. 5). This can be caused by heating of the SMA wire while increase frequency (a change in frequency from 0.1 to 0.5 Hz leads to an increase in temperature by up to 3 °C). According to the Clausis -Clapeyron relation, the martensitic stress transformation increases with increasing of temperature.

0 1 2 3 4 5 6 7 8

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4

0,001 Hz 0,005 Hz 0.01 Hz

0,001 Hz 0,005 Hz 0,01 Hz

0.1 Hz 0,5 Hz

0,1 Hz 0,5 Hz

1 Hz 2 Hz

1 Hz 2 Hz

η =Δ W/2 π W

Δ W, J

2

4

6

8

10

2

4

6

8

10

S a , mm

S a , mm

Fig. 4. Dependence of dissipation energy on the amplitude.

Fig. 5. Dependence of loss factor on the amplitude.

System stiffness was measured on the area of forward transformation as the slope of linear dependency P - f(S). Approximation of numerical results was performed using the least squares method. Fig. 6 shows the dependences of the device stiffness on the displacement amplitude on the forward transformation region. The evolution of device stiffness with increasing of amplitude significantly depends on the loading frequency. The stiffness decreases continuously with increase of amplitude from 3 to 9 mm at frequency range of