PSI - Issue 75

Robert Goraj et al. / Procedia Structural Integrity 75 (2025) 691–708 Goraj/ Structural Integrity Procedia (2025)

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( ) 109 109 MPa SOL101 ±30.7 ±30.7 Hz SOL107 2 ( ) ±121.3 ±121.2 Hz SOL107 HCF (2 2 , ) 26.8 30.7 dB SOL108 HCF (2 , ) 10.8 10.9 dB SOL108 max[ ( , )] 201 199 MPa SOL109 min[ ( , )] -89 -90 MPa SOL109 1 ( )

static normal stress

natural frequency (mode 1) natural frequency (mode 2)

high cycle fatigue high cycle fatigue maximal tension

maximal compression

7. Verification of the degree of material utilization with RIFEST The results presented in section 4 are verified with the commercial fatigue software WIAM ® fatigue RIFEST version 3.0.8 distributed by the company Applus+ IMA Dresden. The stress amplitude and the stress mean value are analytically estimated for = using (23) and (24) accordingly. The obtained values: | ( )| = 145 MPa and ̅ ( ) = 56 MPa are set to RIFEST as inputs. The characteristic stress amplitude returned by RIFEST is identical (excluding the output rounding error) to the analytical value of ,1 ( ) = 160 MPa estimated using (29). However, the design factor returned by RIFEST: K WK = 1.42 is slightly (~4%) lower than the value estimated by (31). This is because of the incorporation of the Neuber’s micro-support effect in the RIFEST algorithm, which cannot be deactivated by the user. The lower K WK results in a higher component fatigue limit σ WK = 301 MPa (cf. analytical value (32)). Consequently, the degree of material utilization a BK returned by RIFEST is slightly smaller than the optimal value of 1.0, which is required in the analytical approach. It equals 0.968 for 1E7 load cycles. An excerpt from the RIFEST output report is present in Appendix C. For the objective of results comparison, the cyclic degree of material utilization a BK is shown in Fig. 12 as a function of the number of load cycles N .

Fig. 12. Number of load cycles dependent cyclic degree of material utilization

The solid line indicates the a BK obtained using the analytical method. For N = 1E7, the chosen material reaches its optimal utilization, which was required in the analytical approach (i. e. 1.0). The a BK obtained by RIFEST is plotted using a dashed line. The logarithmic slope of a BK is a reciprocal of k for N < 1E6 and equals 1/5. The slope decreases to 1/9 in the range 1E6 ≤ N < ∞ accordingly to the approach used in (33). The slopes in different regions are shown in the box. Appendix A. Laplace transform of the function (1) The time dependent function (1): ( ) = ( ℎ + ( )) ∑ [ ( − ) − ( − 2 2+ 1 )] ∞ =0 , ≥0 (38)