Issue34

S. Kikuchi et alii, Frattura ed Integrità Strutturale, 34 (2015) 261 - 270; DOI: 10.3221/IGF-ESIS.34.28 268 where d is an average grain size of the bulk homogeneous material (m). The gradient obtained from the data of R = 0.1 was higher than that of the R = 0.5. This result means that effect of grain size on the value of  K th is remarkable at low stress ratio. Furthermore, the  K th value of the Harmonic series was estimated. Fig. 12 shows a schematic diagram explaining the estimation of threshold stress intensity range,  K th , of the Harmonic series based on the data of the bulk homogeneous materials. Assuming that the threshold stress intensity range decreases linearly with decreasing the square root of the grain size, we obtain the estimated  K th by substituting the grain size of fine-grained structure, d min , of the Harmonic series into the Eqs. (3) and (4) for each R : Estimated values of  K th of the Harmonic series are shown in Tab. 3. Comparing to values of  K th estimated and obtained by tests for each R , there were no obvious differences. This result indicates that the value of  K th of the Harmonic series can be estimated based on the fatigue crack propagation of the bulk homogeneous material and was determined by the crack propagation behavior of the fine-grained structure in the harmonic structure. Consequently, a bimodal harmonic structure reduced the fatigue crack propagation resistance of Ti-6Al-4V alloy due to the existence of the fine-grained structure, which decreased the closure intensity factor, K cl . However, there were little differences in  K eff,th values between the Harmonic series and the IP series so that additional mechanisms and factors may exist. This reason should be clarified in future works. 0 1 2 3 4 2 3 4 5 Square root of grain size d 1/2 , × 10 -3 m 1/2  K th , MPam 1/2 R = 0.1 R = 0.5 Bulk Ti-6Al-4V with homogeneous microstructure 1 0.578 1 0.259 0 0 Square root of grain size d 1/2 , × 10 -3 m 1/2  K th , MPam 1/2 Regression line determined by the data of specimens with homogeneous microstructure   1  K th =  +  d 1/2 Estimated  K th ( d min in the harmonic structure) 1/2 Figure 11 : Relationship between threshold stress intensity range and grain size for the bulk specimen with homogeneous microstructure. Figure 12 : Schematic diagram explaining the estimation of threshold stress intensity range of the Harmonic series based on the data of the bulk specimen with homogeneous microstructure.  K th (MPam 1/2 ) R = 0.1 R = 0.5 Experimental 3.62 ± 0.16 ( n = 3) 2.73 ± 0.17 ( n = 2) Estimated ( d min = 1.1  m) 3.47 2.88 Table 3 : Comparison of the values of  K th estimated and obtained by tests of the Harmonic series (Ave. ± S.D.) .