13th International Conference on Fracture June 16–21, 2013, Beijing, China —4— （ ）1 d ) -0.5006 d ) 4.1698(d d ) 1.7765(d -0.1186(d 0 2 0 3 0 = + + + + + = Δ R S S λ (7) From equation (7), we know, firstly, through a simple test, for each specimen, solve damage coefficient λ and material constant d0 , then, whatever equivalent length d of crack initiation is defined, △S/S will be calculated .Vice versa, we can get d from the known ΔS/S and corresponding cycle is crack initiation life. It could be seen from many tests, when ΔS/S reached 50% (corresponding equivalent crack length was 5mm), specimen fractured immediately. So, for formulas (6) and (7), the following boundary conditions will be satisfied: 0≤△S/S≤0.5, 0≤d≤r. 4. Verification of prediction model for low cycle fatigue crack initiation In order to ensure correctness of the built prediction model, related test were carried out, with the following test conditions: four pieces used with series of number 1 to 4, constant strain amplitude 0.6%, test frequency 0.2Hz; when percentage of stress attenuation increased to 5.33%, 9.35%, 14.0%, 19.17% respectively (corresponding equivalent crack length was 1.00mm, 1.50mm, 2.00mm and 2.50mm accordingly), test ended. Afterwards, the tested specimens were heated about 30 minutes at a temperature from 300℃ to 400℃ and then fatigued again, and finally all specimens were fractured into two parts. Adopting PHOTOSHOP tool software, daubing fatigue crack propagation district black and re-fatigue and fractured distracts white, see figure 3(a) and (b). Figure 3 showed that the specimen fracture appearance had different degree distortion, and measured area swept due to crack propagation was not uniform with the real area by reason of measurement error. So, it is necessary to correct the prediction model. Percentage of black distract to the entire fractured area was measured by OLYCIAm3 Image Analysis System, and equivalent crack length was calculated per equation (7). Relative errors of real crack length to calculated crack length from prediction model, λ value of each specimen, and corrected value d0 (difference between average of real equivalent crack length and that from prediction model) were listed in table1. (a) before (magnification 5×) (b) after (magnification 5×) (1) District of fatigue crack propagation (2) Districts of re-fatigue and fracture Fig.3 Fracture appearance of the specimen processed before and after Tab.1 Comparison of real value and calculated value from prediction model of equivalent length of crack initiation (1) (2) (1) (2)
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