13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- elastic region and the sensor is perfectly bonded on the plate. If thickness of the sensor is enough thin, strain distribution in the plate is uniform regardless of the presence of the sensor, and structure is described as follows: L u Estrucutre structure , (7) where Estrucuture is Young's modulus of structure, u is the displacement on the sensor and L is gauge length of the sensor, respectively. Using Walker equation, the fatigue cycles, N, is represented as the function of the normalized crack length, , and the maximum strain, max, as: 2 0,2 2 2 d 1 2 2 2 max 2 2 m m f E R W C W N W . (8) Furthermore, when two sensors of different properties are employed, simultaneous equation are given as follows, 1 0,1 1 1 1 d 1 1 1 max 1 m m f E R W C W N W , 2 0,2 2 2 d 1 2 2 2 max 2 2 m m f E R W C W N W . (9) Indexes 1 and 2 represent sensor 1 and 2, respectively. From these equations, the fatigue cycles and the stress amplitude of structure, strucuture, are obtained as: 2 1 1 2 1 2 1 2 2 1 1 2 2 1 1 1 2 1 2 2 1 1 2 1 m m mm m m m m F F W W E E R W W C C N W W , 1 2 1 1 2 2 1 2 2 1 1 1 1 2 2 2 1 1 2 structure structure 1 1 1 m m m m F F E R W E R W W W C C R E W W . (10) In the case that the steel structure (Estrucuture = 200 GPa) is subjected to cyclic loading with the stress ratio of 0.1, the fatigue cycles and the stress amplitude were calculated by eqs. (10) and experimental parameters of ED-Cu and ED-Ni, as shown in Fig. 8. Stress amplitude can be estimated from crack length detected from two sensors with different characteristics. Therefore, it was shown that fatigue cycles on structures can be estimated using smart patch. Evaluation of fatigue damage of structure is important to avoid the rapture caused by cyclic loading. Cumulative fatigue damage is commonly determined using the Palmgren-Miner rule [15]. In this rule, the amount of fatigue damage, D, is given as the ratio of cyclic number of N / Nf, where Nf is the number of cycles to failure. Based on many studies about fatigue life of structural components, relationship between stress amplitude and the number of cycles to failure is generally characterized by S-N curve in high-cycle fatigue situations as: SN m SN f N C , (11) where CSN and mSN is material constants and Δσ is stress amplitude [16]. Using the fatigue cycles calculated by smart patch and S-N curve (as shown in Fig. 9(a)), the amount of fatigue damage can be evaluated as shown in Fig. 9 (b). Therefore, it was demonstrated that the health of structure can be estimated using smart patch. 5.3. Estimation of fatigue damage using single material Another equation for estimating fatigue cycles and stress amplitude from fatigue crack length of two specimens can be derived using near-threshold fatigue crack behavior as shown in Fig. 10. Using Kohout equation, the fatigue cycles, N, is represented as:
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