# Investigation of Size Effects Due to Different Cooling Rates of As-Quenched Martensite Microstructures in a Low-Alloy Steel

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## Abstract

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## Featured Application

**The results of this work will be used to develop simulation models that will be applied in the early development stages of highly stressed components. A further aim is that these investigations might contribute to a better understanding of the martensite transformation mechanism.**

## Abstract

## 1. Introduction

## 2. Experimental Setup and Methodology

## 3. Experimental Results

#### 3.1. Heat Treatment

#### 3.2. Hardness

#### 3.3. Microstructure Analyses

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CPP | Close packet plane |

EBSD | Electron backscatter diffraction |

ECDF | Empirical cumulative distribution function |

PAG | Prior austenite grain |

## Appendix A. Reconstructed Martensite Close Packet Plane Packets

**Figure A1.**EBSD map in an inverse pole figure color scheme with superimposed prior austenite grain boundaries, recrystallization twin boundaries (black) and close packet plane packets (white). (

**a**) A1, (

**b**) A2, (

**c**) A3, (

**d**) A4.

## Appendix B. Number of Close Packet Plane Packets and Blocks in Prior Austenite Grains

**Figure A2.**Number of blocks in (

**a**), and packets in (

**b**) depending on the prior austenite grain (PAG) cross-section area.

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**Figure 1.**Specimen geometry and measurement methodology, (

**a**) Specimen types with nominal dimensions of material 50CrMo4 (SAE 4150); specimen type C is only used for temperature measurement. (

**b**) Specimen handling after heat treatment. EBSD: electron backscatter diffraction.

**Figure 2.**Heat treatment of the specimens, (

**a**) dilatation curves of SAE 4150 during heating, (

**b**) dilatation curves of SAE 4150 during cooling, (

**c**) temperature profile during cooling. Note that temperature curves are time-shifted so that $T(t=0)=800{\phantom{\rule{3.33333pt}{0ex}}}^{\circ}\mathrm{C}$.

**Figure 3.**Variation of the hardness measurements by indicating the deviation from the mean value of the individual samples (

**a**) A1, (

**b**) A2, (

**c**) A3, (

**d**) A4.

**Figure 4.**Correlation between measured hardness and cooling time; numbers above data points indicate cooling rates.

**Figure 5.**EBSD map in an inverse pole figure color scheme with superimposed prior austenite grain boundaries (black) and recrystallization twin boundaries (white): (

**a**) A1, (

**b**) A2, (

**c**) A3, (

**d**) A4.

**Figure 6.**Comparison of mean and median prior austenite grain cross-section areas in the measured EBSD domain; numbers above bars indicate the number of evaluable grains in the domain.

**Figure 7.**Empirical cumulative distribution function: (

**a**) normalized packet cross section areas, (

**b**) normalized block cross section areas.

**Figure 8.**Packet cross-section area depending on the prior austenite grain (PAG) cross-section area: (

**a**) measured data, (

**b**) representation of measured data with fitted curves.

**Figure 9.**Martensite block cross-section area depending on the prior austenite grain (PAG) cross-section area: (

**a**) measured data, (

**b**) representation of measured data with fitted curves.

**Table 1.**Chemical composition of the investigated material 50CrMo4 (SAE 4150) in wt.%; the remainder is Fe.

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

50CrMo4 [1] | 0.52 | 0.26 | 0.74 | 0.014 | 0.008 | 1.31 | 0.18 |

**Table 2.**Relevant measured quenching parameters and martensite start temperatures of EBSD-analyzed specimens; parameters for A4 refer to measuring point ①.

Analysis | A1 | A2 | A3 | A4 |
---|---|---|---|---|

Specimen Type | A | A | B | A |

${T}_{\mathrm{MS}}$ in ${}^{\circ}\mathrm{C}$ | 279.3 | 277.1 | 286.8 | - |

${t}_{85}$ in s | 20.0 | 6.3 | 4.9 | 0.62 |

${t}_{{T}_{\mathrm{MS}}\to 100{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}}$ in s | 18.1 | 20.1 | 15.3 | 0.47 * |

${t}_{81}$ in s | 52.8 | 33.5 | 25.0 | 1.9 |

${\dot{\tilde{T}}}_{85}$ in ${}^{\circ}{\mathrm{Cs}}^{-1}$ | 15.0 | 47.6 | 61.2 | 484 |

${\dot{\tilde{T}}}_{{T}_{\mathrm{MS}}\to 100{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}}$ in ${\mathrm{Ks}}^{-1}$ | 9.9 | 8.8 | 12.2 | 383 * |

${\dot{\tilde{T}}}_{81}$ in ${}^{\circ}{\mathrm{Cs}}^{-1}$ | 13.3 | 20.9 | 28.0 | 368 |

**Table 3.**Comparison of relative differences between the equilibrium temperature and martensite start temperature $\frac{{T}_{0}-{T}_{\mathrm{MS}}}{{T}_{0}}$, differences of Gibbs free energies at the martensite start temperature $\Delta {G}_{\mathrm{chem}}^{\mathrm{MS}}$ and size effects of several materials.

Material (Name) | ${\mathit{T}}_{\mathbf{MS}}$ in ${}^{\circ}\mathbf{C}$ | Obvious Size Effect | Reference | $\frac{{\mathit{T}}_{0}-{\mathit{T}}_{\mathbf{MS}}}{{\mathit{T}}_{0}}$ | $\mathbf{\Delta}{\mathit{G}}_{\mathbf{chem}}^{\mathbf{MS}}$ in ${\mathbf{Jmol}}^{-1}$ |
---|---|---|---|---|---|

(Thermo-Calc TCFE 8) | |||||

Fe-22 wt.% Ni | 240 | Yes | [23] | 0.22 | $-416$ * |

Fe-24 wt.% Ni | 187 | Yes | [21] | 0.29 | $-461$ * |

Fe-18 wt.% Ni | 297 | Yes | [21] | 0.25 | $-615$ * |

18% Ni maraging steel | 217 | Yes | [21] | 0.44 | $-1120$ |

WHT1500HF | 382 | Yes | [27] | 0.45 | $-1718$ |

50CrMo4 | 280 | No | 0.52 | $-1875$ | |

AISI 630 | 140 | No | [25] | 0.76 | $-2400$ |

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**MDPI and ACS Style**

Graf, M.; Kuntz, M.; Autenrieth, H.; Müller, R.
Investigation of Size Effects Due to Different Cooling Rates of As-Quenched Martensite Microstructures in a Low-Alloy Steel. *Appl. Sci.* **2020**, *10*, 5395.
https://doi.org/10.3390/app10155395

**AMA Style**

Graf M, Kuntz M, Autenrieth H, Müller R.
Investigation of Size Effects Due to Different Cooling Rates of As-Quenched Martensite Microstructures in a Low-Alloy Steel. *Applied Sciences*. 2020; 10(15):5395.
https://doi.org/10.3390/app10155395

**Chicago/Turabian Style**

Graf, Marius, Matthias Kuntz, Hermann Autenrieth, and Ralf Müller.
2020. "Investigation of Size Effects Due to Different Cooling Rates of As-Quenched Martensite Microstructures in a Low-Alloy Steel" *Applied Sciences* 10, no. 15: 5395.
https://doi.org/10.3390/app10155395