# Deformation Behavior of C15E + C Steel under Different Uniaxial Stress Tests

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## Abstract

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## 1. Introduction

## 2. The Main Determinants of Research

## 3. Research Results

#### 3.1. Mechanical Behavior of Material at Different Temperatures

#### 3.2. Short-Time Creep Tests and Creep Simulation

#### 3.3. Testing the Energy of Impact Fracture of a Material and Fracture Toughness Assessment

#### 3.4. Uniaxial Fully Reversed Mechanical Fatigue of the Material

#### 3.4.1. Different Types of Material Fatigue

#### 3.4.2. Fatigue-Life (S-N) Diagram Based on Fully Reversed Mechanical Fatigue Tests

#### 3.4.3. Determination of Fatigue Limit Based on Modified Staircase Method

- ${k}_{\left(P,1-\alpha ,\nu \right)}$, the coefficient for the one-sided tolerance limit for a normal distribution, and
- ${\overline{\sigma}}_{y}$, the estimated standard deviation of the fatigue strength that can be calculated as:$${\overline{\sigma}}_{y}=1.62\times d\left(D+0.029\right).$$

- for $R=-1$ $\to $ ${\overline{\mu}}_{y}={\sigma}_{0}+d\left(\frac{A}{C}-\frac{1}{2}\right)$ = 250 + 10 (8/5 − 1/2) = 261 MPa,or, this can be obtained as (Table 3):for $R=-1$ $\to $ ${\overline{\mu}}_{y}$ = (250 + 260 + 270 + 260 + 270 + 260 + 270)/7 = 262.86 MPa, whose amount is similar to previously obtained ones.

- for $R=-1$ ${\overline{\sigma}}_{y}=1.62\times d\left(D+0.029\right)$ = 1.62$\times 10$ (0.24 + 0.029) = 4.36 MPa.

- for $R=-1$ $\to $ ${\sigma}_{f\left(0.1;0.9;6\right)}={\overline{\mu}}_{y}-{k}_{\left(P,1-\alpha ,\nu \right)}\times {\overline{\sigma}}_{y}$ = 261 –2.333 $\times $ 4.36 = 250.83 MPa.

#### 3.5. A Brief Analysis of the Microstructure of Material in State: As-Received, Previously Subjected to Creep, after Fracture Due to Fatigue

## 4. Conclusions

_{f(20°C,R = −1)}= 250.83MPa was determined. The strength of the material corresponding to the particular number of the cycles to failure can be monitored based on the stress—life (fatigue—life/$S\u2014N)$ diagram, and it is commonly referred to as fatigue life.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Equipment used in research. (

**a**) Materials testing machine, 400 kN. (

**b**) Dynamic testing machine, ±50 kN. (

**c**) Charpy impact machine, 300 J.

**Figure 2.**Test specimens used in research. (

**a**) Type of the specimen used in determination of engineering stress–strain curves and creep curves. (

**b**) Type of the specimen used in fatigue testing. (

**c**) Type of the specimen used in Charpy V-notch testing.

**Figure 3.**Engineering stress–strain diagrams and mechanical properties versus temperature. (

**a**) Engineering stress–strain diagrams, temperatures: 20, 100, 200, 250, and 300 °C. (

**b**) Engineering stress–strain diagrams, temperatures: 400, 500, and 600 °C. (

**c**) Ultimate tensile strength and yield strength versus temperature. (

**d**) Modulus of elasticity versus temperature.

**Figure 4.**Sort-time creep tests of C15E + C (1.1141) steel and creep modeling. (

**a**) Creep tests at 400 °C. (

**b**) Creep tests at 500 °C. (

**c**) Creep test at 600 °C. (

**d**) Creep modeling.

**Figure 5.**Measured impact fracture energy (CVN) and calculated fracture toughness (${K}_{Ic}$): C15E + C (1.1141) steel.

**Figure 6.**Fatigue life/stress-life (S—N) diagram; $\mathrm{stress}\text{}\mathrm{ratio}\text{}R=-1$; C15E + C (1.1141) steel.

**Figure 7.**Optical micrographs: As-received material (specimen 1), C15E + C (1.1141) steel, 3% nitric acid, and 97% alcohol, (500×). (

**a**) Cross-section of the specimen. (

**b**) Longitudinal section of the specimen.

**Figure 8.**SEM micrographs and the composition of the material at corresponding positions on SEM micrograph (3 and 4) marked in Figure 8a: Material previously subjected to creep (specimen 2), at 600 °C/8.6 MPa/1200 min, C15E + C (1.1141), steel, 3% nitric acid, and 97% alcohol. (

**a**) Cross-section, 3000×. (

**b**) Longitudinal section, 3000×. (

**c**) Composition-position 3 on the SEM micrograph (

**a**). (

**d**) Composition-position 4 on the SEM micrograph (

**a**).

**Figure 9.**SEM micrographs and the composition of the material at corresponding positions on SEM micrograph (4 and 5) marked in Figure 9a: Material fractured due to fatigue (specimen 3), fractured at 94979 cycles/$\pm 310\mathrm{MPa}$, C15E + C (1.1141) steel, 3% nitric acid, and 97% alcohol. (

**a**) Cross-section, 3000×, (

**b**) Composition-position 4 on the SEM micrograph. (

**c**) Composition–position 5 on the SEM micrograph.

**Figure 10.**Observation of fatigue fracture morphology, C15E + C (1.1141) steel. (

**a**) Fatigue streaks-back of fatigue fracture growth zone, 2000×. (

**b**) Front part of fatigue fracture growth zone, 3000×. (

**c**) Dimples in the last fracture zone of the fatigue fracture, 3000×. (

**d**) Brittle phase particles prone to crack formation, 3000×.

Material: C15E + C Steel (Special Nonalloyed-Case Hardening Steel) | |||||||
---|---|---|---|---|---|---|---|

Designation | |||||||

Steel name (type, grade, and quality)/i.e., letter mark of steel in accordance with the norm (country code): (EN, DIN, and other norms) | Steel number (Mat. No, W. Nr, and Mat. code)/i.e., numerical designation of steel | ||||||

(EN)/(DIN): (10084 (2008))/(17210 (1986)): C15E/C15, Ck15 England/ BS 080M15; France/AFNOR XC15; USA/AISI-ESA 1015 In accordance with above given norms that define technical delivery conditions, this steel belongs to the material group classified (named) as case hardening nonalloy special steels, which is confirmed by the below given chemical composition. | 1.1141 | ||||||

Chemical composition, Mass (%) | |||||||

C | Si | Mn | P | S | Cr | Ni | |

0.135 | 0.233 | 0.38 | 0.01 | 0.009 | 0.084 | 0.06 | |

Mo | Cu | Al | W | Sn | Rest | ||

0.019 | 0.027 | 0.035 | 0.006 | 0.007 | 98.99 |

Material | C15E + C (1.1141) | |
---|---|---|

Time–Stress Dependence Model: $\epsilon \left(t\right)=\epsilon \left(\sigma ,t\right)$; | ||

$T=const$ | ||

Equation | ||

$\epsilon \left(t\right)={D}^{-T}{\sigma}^{p}{t}^{r}$ and Time (min) = 1200 | ||

Creep processes were carried out at temperature and stresses listed below | ||

Constant temperature/$\mathrm{T}$°C | 400 | |

Applied constant stress level $\sigma \left({10}^{6}\mathrm{Pa}\right)$ | 107 | 178.5 |

$\sigma =x\times {\sigma}_{0.2}$ | $x=0.3$ | $x=0.5$ |

Parameters (according to Equation) | Parameters $\left(D,p,r\right)$ valid for | |

x = 0.3–0.5 | ||

D | 1.21913163202914 | |

p | 3.96411487762191 | |

r | 0.686440947878887 |

$\mathbf{Stress}\mathbf{Ratio}\mathit{R}=-1,\mathbf{Steel}\mathbf{C}15\mathbf{E}+\mathbf{C}\left(1.1141\right),\mathbf{Room}\mathbf{Temperature},$ Failed (◆), Unfailed (○) | |||||||
---|---|---|---|---|---|---|---|

Stress ${\sigma}_{i},$ max (MPa) | Specimen | ||||||

1 | 2 | 3 | 4 | 5 | 6 | 7 | |

270 | ♦ | ♦ | ♦ | ||||

260 | ♦ | ♦ | ○ | ||||

250 | ○ |

**Table 4.**Data Analysis Related to Table 3.

$\mathbf{Stress}\mathbf{Ratio}\mathit{R}=-1,\mathbf{Steel}\mathbf{C}15\mathbf{E}+\mathbf{C}\left(1.1141\right),\mathbf{F}-\mathbf{Failed},$ Room Temperature | ||||
---|---|---|---|---|

Stress ${\sigma}_{i}$/MPa | Stress level, i | f_{i} | if_{i} | i^{2}f_{i} |

270 | 2 | 3 | 6 | 12 |

260 | 1 | 2 | 2 | 2 |

250 | 0 | 0 | 0 | 0 |

$\sum}{f}_{i},i{f}_{i},{i}^{2}{f}_{i$ | 5 | 8 | 14 |

$\mathbf{Stress}\mathbf{Ratio}\mathit{R}=-1$ | |
---|---|

Formula | Material: C15E + C (1.1141) |

$A={\displaystyle \sum}i\times {f}_{i}$ | 8 |

$B={\displaystyle \sum}{i}^{2}\times {f}_{i}$ | 14 |

$C={\displaystyle \sum}{f}_{i}$ | 5 |

$D=\frac{B\times C-{A}^{2}}{{C}^{2}}$ | 0.24 |

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**MDPI and ACS Style**

Brnic, J.; Brcic, M.; Krscanski, S.; Niu, J.; Chen, S.; Gao, Z. Deformation Behavior of C15E + C Steel under Different Uniaxial Stress Tests. *Metals* **2020**, *10*, 1445.
https://doi.org/10.3390/met10111445

**AMA Style**

Brnic J, Brcic M, Krscanski S, Niu J, Chen S, Gao Z. Deformation Behavior of C15E + C Steel under Different Uniaxial Stress Tests. *Metals*. 2020; 10(11):1445.
https://doi.org/10.3390/met10111445

**Chicago/Turabian Style**

Brnic, Josip, Marino Brcic, Sanjin Krscanski, Jitai Niu, Sijie Chen, and Zeng Gao. 2020. "Deformation Behavior of C15E + C Steel under Different Uniaxial Stress Tests" *Metals* 10, no. 11: 1445.
https://doi.org/10.3390/met10111445