PSI - Issue 57

Jacopo Pelizzari et al. / Procedia Structural Integrity 57 (2024) 817–823 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

821

5

The plastic strain and the elastic strain components relevant to each strain-controlled tested specimen have been extracted from the half-life hysteresis loops, which correspond to the stabilized cycles. The strain components have been fitted and combined to obtain the fatigue design curve according to the Manson-Coffin equation (Eq. 2) and the resulting curve is reported in Fig. 5, where the experimental data are expressed as strain amplitude  a versus number of reversals to failure. The parameters  ' f , b ,  ' f and c, which define the Manson-Coffin curve, are listed in Table 2. Fig. 5 shows that the transition from the plastic material behavior and the linear elastic behavior occurs at around 700 reversals. = ′ (2 ) + ′ (2 ) (2) 1.E-01

1.E-02

1.E-03

ea, tot, machined ea, el, machined ea, pl, machined M-C machined NC  a total  a elastic  a plastic Manson-Coffin fitted curve

1.E-04

 a [mm/mm]

1.E-05

1.E-06

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

Number of reversals to failure, 2N f

Fig. 5. Manson-Coffin fatigue design curve of EN-GJS-500-7 for machined surface specimens tested under R  =-1 .

4. Comparison of the bench load spectrum with the fatigue design curve The simplified bench load spectrum is composed by three load steps, which turn into a local strain spectrum in the region of highest strains, where failure occurred at the end of the test in correspondence of a number of reversals equal to 606000. The strain values have been acquired by placing a strain gauge rosette Micro-measurements model C2A 06-031WW-120, which returned the three strain steps characterized by a given maximum principal strain amplitude and a strain ratio R  equal to zero   he maximum stress associated to each load step has been calculated adopting the CCS equation and the relevant maximum principal strain value. Subsequently, the strain amplitude, which is equal to half of the maximum principal strain value (being R  =0), and the maximum stress were multiplied together to obtain the Smith-Watson-Topper (SWT) fatigue design parameter relevant to each load step. As a result of the previous calculations, the local strain spectrum is reported in Fig. 6 in terms of the Smith-Watson Topper fatigue design parameter  which accounts for the mean stress effect on fatigue life. The figure reports also the fatigue design curve previously reported in Fig. 5, but expressed in terms of the SWT fatigue design parameter. The Palmgren-Miner damage index relevant to the axle fatigue test spectrum reported in Fig. 6 has been calculated according to Eq. 3, where n i is the experimental number of reversals while N i is the number of reversals estimated by entering the SWT fatigue design curve defined at survival probability equal to 50% (Fig. 6) with each i-th load level. The Palmgren-Miner damage index to failure resulted equal to 0.48 for the given bench load spectrum. This index has a paramount significance since it will be compared with that evaluated from actual spectra measured during in-field tests to evaluate if the bench load spectrum adopted for product validation properly simulates the fatigue damage generated by the in-field load spectra.