A New Critical Plane Multiaxial Fatigue Criterion with an Exponent to Account for High Mean Stress Effect
Abstract
:1. Introduction
2. Materials and Methods
2.1. Critical Plane Methods
2.2. New Critical Plane Method
2.3. Experimental Database and Numerical Implementation
Reference | Number of Data Items | Material | Reason for the Selection |
---|---|---|---|
Papuga [3] | 15 | Various | Mean compressive loads applied |
Sauer [23] | 8 | 14S-T aluminium | Static bending or static torsion stresses |
O’Connor [41], Chodorowski [42] | 10 | NiCrMo steel | High values of mean axial tension and compressive loads |
Ukrainetz [43] | 6 | 0.1 C steel | Mean axial tension loads. Static shear stresses on torsional fatigue loading |
Grün et al. [44] | 5 | 25CrMo4 steel | High values of mean axial tension and compression loads |
Lüpfert et al. [45] | 8 | 20MnCr steel | High values of static compressive loads. Only biaxial loadings considered. |
Rausch [46] | 14 | EN-GJV-450 cast iron | High values of mean axial tension and compression loads. Static shear stresses on torsional fatigue loading |
Tovo [47] | 6 | EN-GJS-400-18 ductile cast iron | Mean axial tensile and compressive loads. Static shear stresses on torsional fatigue loading |
Pallarés-Santasmartas [48,49] | 6 | 34CrMo6 steel | Mean axial tensile and compressive loads. Static shear stresses on torsional fatigue loading |
3. Results and Discussion
3.1. General Results for the Complete Database
3.2. Results for Uniaxial Load Cases
3.3. Results for Load Cases with No Mean Stress
3.4. Results for Load Cases with Mean Stress
3.5. Results for Torsional Load Cases
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
a, b, c, d | parameters of the critical plane criteria |
κ | fatigue limit ratio κ = σ−1/τ−1 |
σ0 | fatigue limit in repeated axial loading |
σ−1 | fully reversed axial fatigue limit |
σu | ultimate tensile strength |
σnn,a | normal stress amplitude on the critical plane |
σnn,m | mean normal stress on the critical plane |
σeq | equivalent normal stress amplitude |
τ−1 | fully reversed torsional fatigue limit |
τnt,a | alternating shear stress on the critical plane |
R | load ratio |
Appendix A
Appendix A.1. Static Tensile Test
Appendix A.2. Repeated Axial Loading Fatigue Test
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Criterion | Equation (No Failure Condition) | Parameter Values |
---|---|---|
Findley (F) [9] | ||
Robert (R) [17] | ||
Papuga (P) [28] | ||
Abasolo (A) * | ||
for | ||
Complete Database: 485 Experiments | Findley | Robert | Abasolo | Papuga |
---|---|---|---|---|
Mean value of the error | 8.4 | 3.5 | 3.9 | −0.6 |
Standard deviation | 17.6 | 10.3 | 9.7 | 7.4 |
Maximum value of the error | 147.0 | 77.3 | 43.9 | 42.6 |
Minimum value of the error | −38.7 | −36.4 | −32.1 | −36.4 |
Range of the error | 185.7 | 113.7 | 76.0 | 78.9 |
Mean absolute value of the error | 12.4 | 7.0 | 7.2 | 5.2 |
“Accurate” results (error range ± 5%) | 40.5 | 49.6 | 49.6 | 63.4 |
“Acceptable” results (error range ± 15%) | 70.0 | 87.4 | 86.0 | 94.4 |
Conservative results (error range + 5% + 40%) | 41.6 | 36.0 | 36.8 | 17.1 |
Non-conservative results (error range − 5% − 40%) | 12.6 | 13.8 | 13.4 | 19.3 |
Pure Axial Cases: 76 Experiments | Goodman | Gerber | Marin | Findley | Robert | Abasolo | Papuga |
---|---|---|---|---|---|---|---|
Mean value of the error | 50.3 | 9.5 | −8.4 | 8.3 | 4.1 | 2.6 | −2.6 |
Standard deviation | 109.4 | 52.0 | 23.2 | 28.0 | 16.6 | 10.4 | 10.7 |
Maximum value of the error | 596.0 | 268.4 | 68.3 | 147.0 | 77.3 | 38.9 | 42.6 |
Minimum value of the error | −39.1 | −52.9 | −57.5 | −38.7 | −27.4 | −25.9 | −36.4 |
Range of the error | 635.2 | 321.3 | 125.9 | 185.7 | 104.6 | 64.7 | 78.9 |
Mean absolute value of the error | 58.9 | 25.5 | 17.6 | 19.0 | 8.8 | 6.6 | 7.7 |
“Accurate” results (error range ± 5%) | 5.3 | 26.3 | 21.1 | 30.3 | 61.8 | 56.6 | 46.1 |
“Acceptable” results (error range ± 15%) | 26.3 | 59.2 | 67.1 | 50.0 | 84.2 | 86.8 | 89.5 |
Conservative results (error range + 5% + 40%) | 42.1 | 28.9 | 13.2 | 31.6 | 22.4 | 31.6 | 17.1 |
Non-conservative results (error range − 5% − 40%) | 21.1 | 34.2 | 50.0 | 26.3 | 11.8 | 11.8 | 35.5 |
Pure Axial Cases with High Mean Stress (0.05 ≤ R < 1): 35 Experiments | Goodman | Gerber | Marin | Findley | Robert | Abasolo | Papuga |
---|---|---|---|---|---|---|---|
Mean value of the error | 94.8 | 18.2 | −14.9 | 18.4 | 10.8 | 8.0 | −2.0 |
Standard deviation | 147.6 | 73.5 | 27.7 | 35.3 | 21.4 | 11.2 | 14.5 |
Maximum value of the error | 596.0 | 268.4 | 68.3 | 147.0 | 77.3 | 38.9 | 42.6 |
Minimum value of the error | −32.6 | −52.9 | −57.5 | −38.7 | −14.9 | −9.7 | −36.4 |
Range of the error | 628.6 | 321.3 | 125.9 | 185.7 | 92.1 | 48.6 | 78.9 |
Mean absolute value of the error | 100.4 | 41.2 | 24.9 | 27.3 | 14.0 | 9.4 | 10.8 |
“Accurate” results (error range ± 5%) | 2.9 | 11.4 | 11.4 | 25.7 | 45.7 | 37.1 | 25.7 |
“Acceptable” results (error range ± 15%) | 20.0 | 40.0 | 48.6 | 34.3 | 74.3 | 80.0 | 80.0 |
Conservative results (error range + 5% + 40%) | 22.9 | 31.4 | 5.7 | 28.6 | 37.1 | 57.1 | 25.7 |
Non-conservative results (error range − 5% − 40%) | 14.3 | 37.1 | 51.4 | 20.0 | 8.6 | 5.7 | 45.7 |
No Mean Stress Cases: 172 Experiments | Findley | Robert | Abasolo | Papuga |
---|---|---|---|---|
Mean value of the error | 1.6 | 1.6 | 1.6 | 1.1 |
Standard deviation | 5.0 | 5.0 | 5.0 | 3.7 |
Maximum value of the error | 16.1 | 16.1 | 16.1 | 12.4 |
Minimum value of the error | −12.4 | −12.4 | −12.4 | −9.7 |
Range of the error | 28.4 | 28.4 | 28.4 | 22.1 |
Mean absolute value of the error | 4.1 | 4.1 | 4.1 | 3.1 |
“Accurate” results (error range ± 5%) | 70.5 | 70.5 | 70.5 | 81.5 |
“Acceptable” results (error range ± 15%) | 98.8 | 98.8 | 98.8 | 100.0 |
Conservative results (error range + 5% + 40%) | 21.4 | 21.4 | 21.4 | 13.9 |
Non-conservative results (error range − 5% − 40%) | 8.1 | 8.1 | 8.1 | 4.6 |
Mean Stress Cases: 313 Experiments | Findley | Robert | Abasolo | Papuga |
---|---|---|---|---|
Mean value of the error | 12.1 | 4.6 | 5.1 | −1.5 |
Standard deviation | 20.7 | 12.1 | 11.4 | 8.7 |
Maximum value of the error | 147.0 | 77.3 | 43.9 | 42.6 |
Minimum value of the error | −38.7 | −36.4 | −32.1 | −36.4 |
Range of the error | 185.7 | 113.7 | 76.0 | 78.9 |
Mean absolute value of the error | 17.3 | 9.0 | 9.3 | 6.5 |
“Accurate” results (error range ± 5%) | 24.0 | 38.0 | 38.0 | 53.4 |
“Acceptable” results (error range ± 15%) | 54.0 | 81.2 | 78.9 | 91.4 |
Conservative results (error range + 5% + 40%) | 52.7 | 44.1 | 45.4 | 18.8 |
Non-conservative results (error range − 5% − 40%) | 15.0 | 16.9 | 16.3 | 27.5 |
High Mean Stress Cases (0.05 ≤ RvM < 1): 110 EXPERIMENTS | Findley | Robert | Abasolo | Papuga |
---|---|---|---|---|
Mean value of the error | 19.5 | 6.5 | 8.2 | −2.3 |
Standard deviation | 27.9 | 15.7 | 13.2 | 11.7 |
Maximum value of the error | 147.0 | 77.3 | 43.9 | 42.6 |
Minimum value of the error | −38.7 | −18.0 | −16.6 | −36.4 |
Range of the error | 185.7 | 95.2 | 60.5 | 78.9 |
Mean absolute value of the error | 25.8 | 11.7 | 12.1 | 9.0 |
“Accurate” results (error range ± 5%) | 17.3 | 28.2 | 27.3 | 37.3 |
“Acceptable” results (error range ± 15%) | 35.5 | 74.5 | 69.1 | 82.7 |
Conservative results (error range + 5% + 40%) | 43.6 | 47.3 | 55.5 | 24.5 |
Non-conservative results (error range − 5% − 40%) | 17.3 | 21.8 | 16.4 | 37.3 |
Mean Stress Cases, Pure Torsion: 33 Experiments | Findley | Robert | Abasolo | Papuga |
---|---|---|---|---|
Mean value of the error | −0.7 | −4.7 | −5.4 | −7.5 |
Standard deviation | 11.0 | 6.3 | 5.6 | 8.3 |
Maximum value of the error | 29.1 | 5.8 | 5.4 | 7.7 |
Minimum value of the error | −31.0 | −18.0 | −16.6 | −31.3 |
Range of the error | 60.1 | 23.7 | 22.0 | 39.0 |
Mean absolute value of the error | 7.4 | 5.9 | 5.9 | 8.1 |
“Accurate” results (error range ± 5%) | 54.5 | 51.5 | 45.5 | 45.5 |
“Acceptable” results (error range ± 15%) | 87.9 | 90.9 | 93.9 | 84.8 |
Conservative results (error range + 5% + 40%) | 24.2 | 3.0 | 3.0 | 3.0 |
Non-conservative results (error range − 5% − 40%) | 21.2 | 45.5 | 51.5 | 51.5 |
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Abasolo, M.; Pallares-Santasmartas, L.; Eizmendi, M. A New Critical Plane Multiaxial Fatigue Criterion with an Exponent to Account for High Mean Stress Effect. Metals 2024, 14, 964. https://doi.org/10.3390/met14090964
Abasolo M, Pallares-Santasmartas L, Eizmendi M. A New Critical Plane Multiaxial Fatigue Criterion with an Exponent to Account for High Mean Stress Effect. Metals. 2024; 14(9):964. https://doi.org/10.3390/met14090964
Chicago/Turabian StyleAbasolo, Mikel, Luis Pallares-Santasmartas, and Martin Eizmendi. 2024. "A New Critical Plane Multiaxial Fatigue Criterion with an Exponent to Account for High Mean Stress Effect" Metals 14, no. 9: 964. https://doi.org/10.3390/met14090964