# On the Influence of Control Type and Strain Rate on the Lifetime of 50CrMo4

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## Abstract

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## 1. Introduction

## 2. Effects of Strain Rate on Deformation and Fatigue

#### 2.1. Intrinsic Effects

#### 2.2. Extrinsic Effects

## 3. Experimental Foundation

## 4. Method

#### 4.1. Correction for Control Type

#### 4.2. Statistical Analysis

## 5. Results

## 6. Analysis

## 7. Summary

## 8. Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Do Models Assuming Log-Normal Distributions Describe the Data Sets Well?

**Figure A1.**Estimated and observed accumulated failure rates for 50CrMo4 specimens in laboratory air; 919 MPa ultimate tensile strength; ${K}_{t}=1$.

**Figure A2.**Estimated and observed accumulated failure rates for 50CrMo4 specimens in laboratory air; 919 MPa ultimate tensile strength; ${K}_{t}=1.75$.

**Figure A3.**Estimated and observed accumulated failure rates for 50CrMo4 specimens in argon; 919 MPa ultimate tensile strength; ${K}_{t}=1.75$.

**Figure A4.**Estimated and observed accumulated failure rates for 50CrMo4 specimens in laboratory air; 919 MPa ultimate tensile strength; ${K}_{t}=2.06$.

**Figure A5.**Estimated and observed accumulated failure rates for 50CrMo4 specimens in laboratory air; 1096 MPa ultimate tensile strength; ${K}_{t}=1.2$.

**Figure A6.**Estimated and observed accumulated failure rates for 50CrMo4 specimens in laboratory air; 1726 MPa ultimate tensile strength; ${K}_{t}=2.06$.

**Figure A7.**Quantile-quantile plots for 50CrMo4 specimens in laboratory air; 919 MPa ultimate tensile strength; ${K}_{t}=1$.

**Figure A8.**Quantile-quantile plots for 50CrMo4 specimens in laboratory air; 919 MPa ultimate tensile strength; ${K}_{t}=1.75$.

**Figure A9.**Quantile-quantile plots for 50CrMo4 specimens in argon; 919 MPa ultimate tensile strength; ${K}_{t}=1.75$.

**Figure A10.**Quantile-quantile plots for 50CrMo4 specimens in laboratory air; 919 MPa ultimate tensile strength; ${K}_{t}=2.06$.

**Figure A11.**Quantile-quantile plots for 50CrMo4 specimens in laboratory air; 1096 MPa ultimate tensile strength; ${K}_{t}=1.2$.

**Figure A12.**Quantile-quantile plots for 50CrMo4 specimens in laboratory air; 1726 MPa ultimate tensile strength; ${K}_{t}=2.06$.

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**Figure 4.**Geometry of specimens with ultimate tensile strength 919 as well as 1726 MPa and K = 2.06 [6].

**Figure 5.**This figure shows 0.2% offset yield depending on the strain rate, for the 919 MPa ultimate tensile strength (

**left**) and for the batches 919 MPa, 1170 MPa and 1475 MPa (

**right**).

**Figure 6.**Cyclic stress strain curves. (

**First row**): 919 MPa and 1096 MPa ultimate tensile strength. (

**Second row**): 1726 MPa ultimate tensile strength (left) and comparison of batches with 919 MPa, 1096 MPa, 1170 MPa, 1475 MPa and 1726 MPa ultimate tensile strength.

**Figure 8.**Fatigue behavior of 50CrMo4 in laboratory air; 919 MPa ultimate tensile strength; ${K}_{t}=1$; Curves of 10, 50 and 90% probability of survival; run-outs are marked with an arrow; left side: before correction; right side: after correction; top: only HCF region; bottom: including VHCF region.

**Figure 9.**Fatigue behavior of 50CrMo4 in laboratory air; 919 MPa ultimate tensile strength; ${K}_{t}=1.75$; Curves of 10, 50 and 90% probability of survival; run-outs are marked with an arrow; left side: before correction; right side: after correction; top: only HCF region; bottom: including VHCF region.

**Figure 10.**Fatigue behavior of 50CrMo4 in argon; 919 MPa ultimate tensile strength; ${K}_{t}=1.75$; Curves of 10, 50 and 90% probability of survival; run-outs are marked with an arrow; left side: before correction; right side: after correction; top: only HCF region; bottom: including VHCF region.

**Figure 11.**Fatigue behavior of 50CrMo4 in laboratory air; 919 MPa ultimate tensile strength; ${K}_{t}=2.06$; run-outs are marked with an arrow; left side: before correction; right side: after correction; top: only HCF region; bottom: including VHCF region.

**Figure 12.**Fatigue behavior of 50CrMo4 in laboratory air; 1096 MPa ultimate tensile strength; ${K}_{t}=1.2$; run-outs are marked with an arrow; left side: before correction; right side: after correction; top: only HCF region; bottom: including VHCF region.

**Figure 13.**Fatigue behavior of 50CrMo4 in laboratory air; 1726 MPa ultimate tensile strength; ${K}_{t}=2.06$; run-outs are marked with an arrow; left side: before correction; right side: after correction; top: only HCF region; bottom: including VHCF region.

Material Batch | C | Cr | Mo | Mn | P | S |
---|---|---|---|---|---|---|

919 MPa [5] | 0.53 | 1.06 | 0.19 | 0.69 | <0.01 | <0.01 |

1096 MPa [8] | 0.48 | 1.00 | 0.18 | 0.71 | 0.013 | 0.010 |

1170 MPa [10] | 0.49 | 1.01 | 0.19 | 0.69 | <0.01 | 0.011 |

1475 MPa [10] | 0.48 | 1.06 | 0.19 | 0.68 | 0.01 | 0.012 |

1726 MPa [6] | 0.51 | 1.09 | 0.19 | 0.73 | 0.016 | <0.01 |

Material Batch | Young’s Modulus E in GPa | 0.2% Offset Yield Strength ${\mathit{\sigma}}_{0.2}$ in MPa | Ultimate Tensile Strength ${\mathit{\sigma}}_{\mathit{u}}$ in MPa |
---|---|---|---|

919 MPa [5] | 206 | 842 | 919 |

1096 MPa [8] | 202 | 1000 | 1096 |

1170 MPa [10] | 208 | 1025 | 1170 |

1475 MPa [10] | 204 | 1345 | 1475 |

1726 MPa [6] | 215 | 1544 | 1726 |

Material Batch | Young’s Modulus E in GPa | Hardening Coefficient ${\mathit{K}}^{\prime}$ in MPa | Hardening Exponent ${\mathit{n}}^{\prime}$ |
---|---|---|---|

919 MPa | 206 | 1341 | 0.135 |

1096 MPa | 202 | 2816 | 0.237 |

1170 MPa | 204 | 1162 | 0.068 |

1475 MPa | 204 | 1436 | 0.073 |

1726 MPa | 215 | 1687 | 0.060 |

**Table 4.**Parameters, log-likelihood values of fitted fatigue curves as well as number of specimens and p-values obtained in t-test.

${\mathit{\sigma}}_{\mathit{u}}$ | ${\mathit{K}}_{\mathit{t}}$ | Atmosphere | Corrected? | ${\mathit{\sigma}}_{\mathbf{ref}}$ | ${\mathit{N}}_{\mathbf{ref}}$ | ${\mathit{k}}_{1}$ | $\mathbf{SD}$ | ${\mathit{L}}_{\mathbf{log}}$ | $\begin{array}{c}\#\mathbf{Specimens}\\ \mathit{p}-\mathbf{Value}\end{array}$ | |
---|---|---|---|---|---|---|---|---|---|---|

Figure 8 | 919 MPa | 1 | lab air | no | 512 MPa | 6.0×10${}^{5}$ | 12.0 | 0.43 | −28.4 | 50 |

Figure 8 | 919 MPa | 1 | lab air | yes | 512 MPa | 7.0×10${}^{5}$ | 20.0 | 0.24 | −0.4 | $7.5\times {10}^{-6}\%$ |

Figure 9 | 919 MPa | 1.75 | lab air | no | 630 MPa | 3.3×10${}^{5}$ | 11.9 | 0.20 | 3.2 | 16 |

Figure 9 | 919 MPa | 1.75 | lab air | yes | 574 MPa | 3.4×10${}^{5}$ | 8.5 | 0.16 | 6.5 | $28.8\%$ |

Figure 10 | 919 MPa | 1.75 | argon | no | 630 MPa | 1.1×10${}^{6}$ | 13.7 | 0.27 | −1.5 | 16 |

Figure 10 | 919 MPa | 1.75 | argon | yes | 574 MPa | 1.1×10${}^{6}$ | 10.3 | 0.11 | 11.2 | $3.5\%$ |

Figure 11 | 919 MPa | 2.06 | lab air | no | 618 MPa | 3.8×10${}^{5}$ | 5.8 | 0.39 | −16.1 | 41 |

Figure 11 | 919 MPa | 2.06 | lab air | yes | 566 MPa | 4.7×10${}^{5}$ | 6.3 | 0.30 | −7.2 | $1.3\%$ |

Figure 12 | 1096 MPa | 1.2 | lab air | no | 500 MPa | 3.6×10${}^{5}$ | 2.3 | 0.37 | −12.34 | 30 |

Figure 12 | 1096 MPa | 1.2 | lab air | yes | 500 MPa | 5.1×10${}^{5}$ | 5.2 | 0.34 | −10.2 | $12.2\%$ |

Figure 13 | 1726 MPa | 2.06 | lab air | no | 876 MPa | 4.8×10${}^{5}$ | 9.2 | 0.22 | 3.6 | 32 |

Figure 13 | 1726 MPa | 2.06 | lab air | yes | 875 MPa | 4.8×10${}^{5}$ | 9.4 | 0.22 | 3.6 | $30.6\%$ |

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**MDPI and ACS Style**

Geilen, M.B.; Schönherr, J.A.; Klein, M.; Leininger, D.S.; Giertler, A.; Krupp, U.; Oechsner, M. On the Influence of Control Type and Strain Rate on the Lifetime of 50CrMo4. *Metals* **2020**, *10*, 1458.
https://doi.org/10.3390/met10111458

**AMA Style**

Geilen MB, Schönherr JA, Klein M, Leininger DS, Giertler A, Krupp U, Oechsner M. On the Influence of Control Type and Strain Rate on the Lifetime of 50CrMo4. *Metals*. 2020; 10(11):1458.
https://doi.org/10.3390/met10111458

**Chicago/Turabian Style**

Geilen, Max Benedikt, Josef Arthur Schönherr, Marcus Klein, Dominik Sebastian Leininger, Alexander Giertler, Ulrich Krupp, and Matthias Oechsner. 2020. "On the Influence of Control Type and Strain Rate on the Lifetime of 50CrMo4" *Metals* 10, no. 11: 1458.
https://doi.org/10.3390/met10111458