PSI - Issue 35

Martin Ferreira Fernandes et al. / Procedia Structural Integrity 35 (2022) 141–149 Martin Ferreira Fernandes et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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The plastic deformation accumulation observed in dwell-fatigue tests could result from the stress redistribution mechanism in the α phase grains that leads to slip of dislocations and, consequently, early plastic deformation processes that instigate crack nucleation. To summarize, the dwell-fatigue tested specimens fractured at a high cumulated plastic strain and a significantly lower fatigue life than at pure fatigue tests, indicating a substantial dwell life debit of the Ti-6Al-4V alloy. 3.2. Weibull and Statistical analysis The Weibull distribution was applied to verify the reliability of the dwell-fatigue data and to estimate the fatigue life for several reliabilities. Table 2 shows the Weibull model parameters of the dwell-fatigue data at maximum stress levels of 950, 975, and 1000 MPa. The shape parameter ( n ) was higher than 1 for all stress levels tested, which means that the fatigue data has low variability. The scale parameter ( m ) corresponds to the dwell-fatigue life at a given stress level with a failure probability of 63.2% (Fernandes et al., 2020). Table 3 shows the dwell-fatigue life for different reliabilities, representing the percentage of specimens expected to withstand at least the corresponding fatigue life. The dwell-fatigue test scattering was much smaller at a stress level of 950 MPa. As a result, the shape parameter value was 9.21 at 950 MPa. This is the reason for the outstanding difference in the number of cycles to failure for a reliability of 90% at 950 MPa compared to 975 MPa and 1000 MPa. At the stress level of 950 MPa, the Weibull distribution predicted a smaller fatigue life reduction. The reliability increased due to little scattering at this stress level. Moreover, the number of cycles to failure substantially reduces as the stress level of the dwell-fatigue test approaches the yield strength of the material. For example, for a 70% reliability, the expected lifetime of the material is 17298 cycles at a stress level of 950 MPa, compared to only 1074 and 714 cycles at stress levels of 975 MPa and 1000 MPa, respectively. Table 2 . Weibull parameters α and β for d well-fatigue tests. (MPa) m (scale parameter) n (shape parameter) 950 19347 9.21 975 2868 1.05 1000 1453 1.45

Table 3. Weibull analysis.

Number of cycles to failure Reliability 950 MPa 975 MPa 1000 MPa 50 % 18593 2023 1128 70 % 17298 1074 714 90 % 15153 336 308

Fig. 4 displays the statistical analysis of the linear regression model for the dwell-fatigue data. The normality of dwell-fatigue data was proven with a Ryan-Joiner coefficient of 0.962. In the normality plot (Fig. 4a), it was possible to verify the proximity of results to the normal distribution line. The analysis of variance (ANOVA), supported by the normality test results, revealed a P-value of about 0.000 and an F-value of 21.12, which proves the statistical significance of the experimental results. The linear model presented a reasonable adjustment of 75.2% in the linear regression plot (Fig. 4b), and most points are within the 90% confidence bands (6 out of 9 points). The analysis showed the statistical significance of the dwell-fatigue data.