Mean Stress Effect on the Axial Fatigue Strength of DIN 34CrNiMo6 Quenched and Tempered Steel
Abstract
:1. Introduction
1.1. Historical Background
1.2. Empirical Methods
1.3. Methods Based on Physical Principles
- Gough hypothesis [7]: This theory states that effect of the mean stresses is due only to the damage produced by the maximum stress reached during the cycle, with no regard for the mean stress itself. This assumption led to the Crossland method [30], which uses the maximum hydrostatic stress during the cycle as the damage parameter.
- Distortion energy theory [17]: In a theoretical material of von Mises, the effect of the normal stress to the critical plane is quadratic, without any influence of the hydrostatic stress. Moreover, equating the energies produced in N cycles in the case of completely reversed alternating stresses and the case of superimposed static stresses to a variable stress, an elliptic relationship between the mean and alternating stresses is obtained. This theory can be expressed analytically through the Marin multiaxial fatigue method.
- Total strain energy theory [31]: The effect of the mean stresses is related to the total elastic deformation energy stored. This hypothesis leads to the Froustey method, which leads to an elliptic relationship between the mean and alternating stresses, as in the Marin method.
- Findley critical plane [32]: The normal stress to high shear stress amplitudes planes allow the propagation of a micro-crack initiated by shear stresses. As Findley remarks [33], this effect is approximately linear in some materials, being clearly non-linear in others. For simplicity purposes, a linear normal maximum stress to the critical plane was selected by Findley as one of the damage parameters for the formulation of the Findley critical plane method.
2. Testing Procedure
2.1. Material
2.2. Specimens and Testing Machine
3. Results and Experimental Correlation with Empirical and Physical Models
3.1. Fatigue Test Results
3.2. Fractographic Analysis of the Specimens
3.3. Correlation of the Experimental Results with Empirical and Physical Models
3.3.1. Empirical Models
3.3.2. Physical-Based Models
4. Development of an Energetic Fatigue Criterion for a DIN 34CrNiMo6 Quenched and Tempered Steel
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Derivation of the Parameters of the Proposed Physical Method
Appendix A.1. Fully Reversed Torsion Fatigue Test
Appendix A.2. Repeated Torsion Fatigue Test
Appendix A.3. Fully Reversed Axial Fatigue Test
Appendix A.4. Repeated Axial Fatigue Test
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Element | C | Cr | Ni | Mo | Mn | Si | P | S | Fe |
---|---|---|---|---|---|---|---|---|---|
Weight (%) | 0.345 | 1.565 | 1.565 | 0.237 | 0.710 | 0.275 | 0.0075 | 0.003 | Balance |
Monotonic Properties | Symbol | Value |
---|---|---|
Yield strength | σyp | 1084 MPa |
Ultimate tensile strength | σuts | 1210 MPa |
Reduction of area | Z | 60.2% |
Elongation at fracture | A | 12.2% |
σm (MPa) | σa (MPa) | R (Stress Ratio) | α | β |
---|---|---|---|---|
−216 | 647 | −2 | 1.14 × 1048 | −15.000 |
0 | 615 | −1 | 4.61 × 1042 | −13.220 |
181 | 542 | −0.5 | 1.79 × 1031 | −9.338 |
522 | 472 | 0.05 | 6.37 × 1077 | −26.889 |
R (σmin/σmax) | σm (MPa) | Gerber | Goodman | Morrow | Dietmann |
---|---|---|---|---|---|
−2 | −216 | 8.0 | −12.0 | −8.3 | −3.2 |
−0.5 | 181 | −10.9 | 3.5 | −0.3 | −4.6 |
0.05 | 522 | −6.1 | −25.9 | 13.4 | 1.7 |
R (σmin/σmax) | σm (MPa) | Crossland | Marin, Froustey | Findley |
---|---|---|---|---|
−2 | −216 | −1.0 | 6.5 | −8.1 |
−0.5 | 181 | −7.5 | −12.2 | 0.6 |
0.05 | 522 | −10.5 | −17.6 | 20.5 |
Parameters | σ−1 | τ−1 | σ0 | τ0 | a | b | c | Λ |
---|---|---|---|---|---|---|---|---|
Values for 34CrNiMo6 steel | 615 | 433 | 961 | 765 | 433 | 819 | 4092 | 2337 |
R (σmin/σmax) | σm (MPa) | Proposed Theory (Equation (17)) |
---|---|---|
−2 | −216 | 2.6 |
−0.5 | 181 | −7.5 |
0.05 | 522 | 2.6 |
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Pallarés-Santasmartas, L.; Albizuri, J.; Avilés, A.; Avilés, R. Mean Stress Effect on the Axial Fatigue Strength of DIN 34CrNiMo6 Quenched and Tempered Steel. Metals 2018, 8, 213. https://doi.org/10.3390/met8040213
Pallarés-Santasmartas L, Albizuri J, Avilés A, Avilés R. Mean Stress Effect on the Axial Fatigue Strength of DIN 34CrNiMo6 Quenched and Tempered Steel. Metals. 2018; 8(4):213. https://doi.org/10.3390/met8040213
Chicago/Turabian StylePallarés-Santasmartas, Luis, Joseba Albizuri, Alexander Avilés, and Rafael Avilés. 2018. "Mean Stress Effect on the Axial Fatigue Strength of DIN 34CrNiMo6 Quenched and Tempered Steel" Metals 8, no. 4: 213. https://doi.org/10.3390/met8040213