# Experiment and Modeling on Macro Fiber Composite Stress-Induced Actuation Function Degradation
## 3 Results and Discussion  
Free end resonant displacement response time history graphs of the MFC piezoelectric beams actuated by MFC actuators are shown in Figures 5-7. Reduction of the displacement amplitude can be clearly observed after a certain number of cyclic loads has been imposed on the MFC actuator. These test results evidently show the actuation function degradation of the MFC actuator undergoing cyclic loads with stress amplitudes of 18 MPa, 24 MPa and 30 MPa, respectively. Figure 4: Actuation function test set up for the MFC actuator: (**a**) DC power; (**b**) Signal generator; (**c**) High voltage amplifier; (**d**) Laser sensor; (**e**) Steel beam with MFC; (**f**) Signal acquisition system (**g**) PC. Figure 5: Tip displacement time history of the beam specimen actuated by MFC under cyclic load (stress amplitude 18 MPa). The resonant displacement response amplitudes in the free end of the beam actuated by the MFC actuator undergoing different amplitudes of cyclic load versus the loading cycles are shown in Figure 8. As it can be seen from Figure 8a, when the stress amplitude of the cyclic load is 12 MPa, the resonant displacement amplitude of the piezoelectric cantilever beam actuated by MFC does not degenerate with the increase of load cycles. It indicates that the actuation function of the MFC actuator does not degenerate undergoing cyclic loads whose stress amplitude is less than 12 MPa. The experimental results in Figure 8b-d show that for the cyclic loads whose stress amplitudes are 18 MPa, 24 MPa and 30 MPa, respectively, degradation of the free end resonant displacement amplitude of the beam specimen actuated by the MFC actuator can be visibly observed with the increase of the loading cycles. These results evidently indicate that the actuation function of the MFC actuator does degenerate with the increase of loading cycles for some stress amplitude level. It can also be seen, from the slope change of the amplitude degenerate curves, that the actuation function degradation rate increases significantly with the increase of the stress amplitude. By using the calculation formula of the actuation function index \(A\)\((\sigma,N)\), the variation curves of the MFC piezoelectric actuation function index \(A\)\((\sigma,N)\) versus loading cycles have been plotted for cyclic loading stress amplitudes of 30 MPa, 24 MPa, 18 MPa and 12 MPa, respectively, which can be seen in Figure 9.  
Figure 6: Tip displacement time history of the beam specimen actuated by MFC under cyclic load (stress amplitude 24 MPa). Figure 7: Tip displacement time history of the beam specimen actuated by MFC under cyclic load (stress amplitude 30 MPa). As can be seen from the variation curves of the actuation function index \(A\)\((\sigma,N)\) shown in Figure 9, for the cyclic loads with stress amplitudes 30 MPa, 24 MPa and 18 MPa, the MFC piezoelectric actuation function gradually degenerates with the increase of the cyclic load cycles, and the degree of actuation function degradation is independent from the amplitude of the excitation voltage applied to the MFC actuator. As it can be seen from Figure 9a that the actuation function of MFC degenerates rapidly within the first \(4\times 10^{5}\) cycles of cyclic load with stress amplitude 30 MPa. For example, when the number of cycles only reaches the first 250,000, the MFC piezoelectric actuation function has already degenerated to 66% of its intact level. The fitting curve of the MFC actuation function index \(A\)\((\sigma,N)\) versus load cycles demonstrates that the actuation function degradation process of the MFC actuator undergoing cyclic load is a nonlinear process. From the slope change of the actuation function degradation curve, it can be found that, within the first \(4\times 10^{5}\) cycles, the actuation function of MFC degrades rapidly, then after \(8\times 10^{5}\) cycles the degenerate rate gradually slows down with the increase of the loading cycles.