PSI - Issue 75

Lewis Milne et al. / Procedia Structural Integrity 75 (2025) 419–425 L.Milne et al. / Structural Integrity Procedia 00 (2025) 000–000

424

6

LFT Data

LFT Curve

UFT Curve

LFT Data

LFT Curve

UFT Curve

450

500

HSE Model 1 - Ymin HSE Model 2 - Ymin

HSE Model 1 - Ypl HSE Model 2 - Ypl

HSE Model 1 - UTS HSE Model 2 - UTS

HSE Model 1 - Ymin HSE Model 2 - Ymin

HSE Model 1 - Ypl HSE Model 2 - Ypl

HSE Model 1 - UTS HSE Model 2 - UTS

450

JC-Method 1

JC-Method 2

JC-Method 1

JC-Method 2

400

400

350

350

300

300

250

250

a

Stress Amplitude (MPa)

b

Stress Amplitude (MPa)

200

200

150

150

1.00E+04

1.00E+05

1.00E+06

1.00E+07

1.00E+08

1.00E+09

1.00E+04

1.00E+05

1.00E+06

1.00E+07

1.00E+08

1.00E+09

No. of cycles to failure

No. of cycles to failure

Fig. 5. Strain rate corrected USF testing SN curves for (a)S275J2 and (b) C45 steels.

S275J2 and S275JR, an increase in σ pl of 100-150 MPa was observed, being slightly higher but of similar magnitude to the increase in UTS. For the C45, however, a much greater strain rate sensitivity was observed for σ pl , with an increase of over 300 MPa across the test range. This is unexpected, as the strain rate sensitivity is understood to be caused by the BCC ferrite regions of which the C45 has a much lower % than the other steels and thus it should be expected that the strain rate sensitivity of this material should be much lower than the others. Along with the quasistatic tensile results, we can use these values to fit strain rate sensitivity models to the tested steels. Several di ff erent strain rate models were selected for evaluation with these test results. First is the Johnson-Cook (J-C) plasticity model, which was previously applied by Hu et al. (2018) to quantify the strain rate and temperature sensitivity of a high-strength steel in USF testing, this model is yet to be applied to USF testing of ferritic steels. Alternatively to J-C model, a constitutive equation for the influence of strain rate on the yield strength of BCC metals was proposed by Milella (2002). This equation introduces the relation between the dynamic yield strength σ Y , D and strain rate / temperature on other side using the material coe ffi cients A , B , and C to be determined by fitting to the test data. In a report produced at the British HSE by Burdekin et al. (2004), two relations for the influence of strain rate on the yield strength for structural steel S355 are given. To evaluate the applicability of HSE models (“HSE-1” and “HSE-2”) for each material, each of them was fitted to the σ min , σ pl and UTS values obtained across the full range of strain rates. Model coe ffi cients were evaluated using the sum of least squares regression to achieve the best fit. The resultant model fits for S275JR are presented in Fig. 4. In all cases, it can be seen that the Millela model provided a poor correlation: underestimating the strength at low strain rates and overestimating the strength at moderate strain rates. As such, the Millela model was excluded from further analysis. For σ pl and UTS, HSE-1 and HSE-2 both provide similar accurate fits to the test data. HSE-2 provides a slightly more accurate prediction at lower strain rates as HSE-1 overestimates the yield strength from the quasistatic stress. When fitted to the σ min values, however, HSE-2 does not su ffi ciently capture the curvature in the results, leading to an overestimation of the strength at moderate strain rates. HSE-1, however, remains within the region of scatter for all of the σ min test values and is therefore more accurate for fitting against this parameter. These observations are consistent across all of the tested materials. Based on these observations, it is proposed to use HSE Model 2 based on σ pl as the primary model of strain rate sensitivity for these steels. For the HSE-1 and HSE-2 models, the 20 kHz SN curve was normalised using the predicted strength at the strain rates corresponding to the USF testing frequency. These normalised values were then multiplied by the predicted strength at the low frequency (LF) equivalent strain rate. This process was carried out for each material, using the trends for HSE-1 and HSE-2 fitted to σ pl , σ min and UTS. For the J-C model, the 20 kHz curve was simply divided by the frequency sensitivity factor η . The resultant corrected USF curves for all of the models are presented in Fig. 5, alongside LF SN curves for comparison. From Fig. 5, the corrected curves can be split into two groups. The J-C model alongside the HSE-1 and HSE-2 models fitted using σ pl all provide similar results, which are closer to matching the LF behaviour than the other models. Even still, these corrected curves are not su ffi ciently shifted down to match up with the conventional frequency results. As the USF SN curve is shifted directly downwards, any change in gradient with the test frequency is unaccounted for. It is therefore apparent that correcting for the increase in yield strength with strain rate is not su ffi cient to evaluate the discrepancy in fatigue behaviour between the two frequencies. This points to the existence of some other factor beyond the strain rate influence which is driving the frequency e ff ect.