# Low-Cycle Fatigue Behavior of 10CrNi3MoV High Strength Steel and Its Undermatched Welds

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Procedure

## 3. Results

#### 3.1. Monotonic Tensile Results and Micro-Hardness Analysis

_{YS}) and the ultimate tensile strength (σ

_{UTS}) is high for 10CrNi3MoV steel, which is 1.07. It means that the capability for hardening is limited. Compared with base metal, the undermatched welds have a higher T/Y ratio, which is 1.12. The mechanical properties of these materials under monotonic tension loading are summarized in Table 3.

#### 3.2. Fatigue Tests Results

_{f}, for each specimen. The stabilized hysteresis loops were used to determine the plastic strain and corresponding energy density values directly.

#### 3.3. The Analysis of Hysteresis Loops

_{p}, is the area of the hysteresis loop. The total damage under fatigue loading, ΔW

_{T}, are the plastic strain energy and the tension part of the elastic strain energy. As for the calculation of ΔW

_{p}, they can be conducted by a “master curve” for both non-Masing and ideal Masing material description [33]. The curve is different from the defined cyclic stress-strain curve. We can match the upper branches of half-life hysteresis loops under many strain amplitudes by translating the locations along its linear response portion. The relationship for the master curve with the origin at the tip of the smallest plastic strain hysteresis loop is proposed as follows:

_{p}) due to the plastic deformation can be calculated by the area of hysteresis loop. For a Masing-type material, it can be expressed as [34]:

_{p}can be calculated from the equation as following [28]:

#### 3.4. Low Cycle Fatigue Life

#### 3.5. Energy-Life Relationships

_{f}) can be compared with a log-log scale, which is determined by the measuring area of hysteresis loops, Masing-type Equation (3), and non-masing type Equation (4). Table 6 exhibits the values of $\Delta {W}_{P}$ with the corresponding strain amplitudes based on different equations. Seen from values in Table 6, the results of different methods are quite close. It is worthy to note that these values can be fitted by a linear relationship. Further, the stable linear relationship realizes the quantity of fatigue life by a proper damage parameter. The evolution of $\Delta {W}_{P}$ from experiments against fatigue life, which is shown as dashed line in Figure 11, can be fitted by a power law function from Equation (8). Figure 12 shows the comparison of plastic strain energy density ΔW

_{p}between 10CrNi3MoV high strength steel and its undermatched welds. The fitting linear relationship agrees well the experimental data for base metal and weld metal. In this manner, the stable trends give to the quantity the attribute of a proper fatigue damage parameter for fatigue assessment. From the results in Figure 13, the fatigue life of weld metal is longer than the base metal under the same plastic strain energy density values. It further illustrates that undermatched welds show better fatigue behaviors than the base metal.

#### 3.6. The Failure Location of Welded Joints

#### 3.7. The Fatigue Fracture Morphology

## 4. Conclusions

- (1)
- The cyclic strength mismatch ratio showed some discrepancy with the mismatch ratio under monotonic loading for these materials.
- (2)
- A gradual cyclic softening behavior under different strain amplitudes was observed for the two materials. Moreover, the soften behavior mainly appeared in the beginning cyclic stage, which took nearly 5–15% of fatigue life ratio.
- (3)
- The fatigue results show low strength weld metal exhibit a higher fatigue resistance than 10CrNi3MoV steel for all the range of total strain amplitudes, it illustrates that the enhancement of material strength cannot guarantee the proper improvement of fatigue properties.
- (4)
- According to the hysteresis loops under different strain amplitudes, 10CrNi3MoV high strength steel demonstrated almost ideal Masing-type behavior, whereas the undermatched weld metal exhibited non-Masing-type behavior.
- (5)
- The relationship between plastic strain energy density at half-life cycle against the number of reversals to failure is fitted satisfactorily by the power-low equation. The total strain energy density is an adequate parameter for both high- and low-cycle fatigue regimes.
- (6)
- The fatigue assessment for these two materials based on the plastic and total strain energy density all shows that the undermatched weld metal has better fatigue resistance than base metal.

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Microstructures of the investigated materials: (

**a**) 10CrNi3MoV high strength steel; (

**b**) undermatched welds.

**Figure 2.**(

**a**) Orientation of monotonic tension and fatigue test specimens with respect to the welded joints; (

**b**) Schematic of LCF test specimens about base metal and weld metal.

**Figure 3.**Monotonic stress-strain curves of 10CrNi3Mov high strength steel and its undermatched welds.

**Figure 5.**Evolution of the maximum and minimum stress with life ratio for different values of strain amplitudes: (

**a**) 10CrNi3MoV steel; (

**b**) Undermatched welds.

**Figure 6.**Stabilized stress-strain hysteresis loops and cycle Ramberg-Osgood relationships under different amplitudes: (

**a**) 10CrNi3MoV steel; (

**b**) Undermatched welds.

**Figure 7.**Stress-strain comparison between monotonic tension and cycle Ramberg-Osgood relationships: (

**a**) 10CrNi3MoV steel; (

**b**) Undermatched welds.

**Figure 8.**Superposition of the stable hysteresis loops at half-life along the linear portion to match upper branches, and corresponding master curves: (

**a**) 10CrNi3MoV steel; (

**b**) Undermatched welds.

**Figure 10.**Comparison between Manson-Coffin curves of materials from test and reference [38].

**Figure 11.**Comparison of Plastic strain energy density ΔW

_{p}between 10CrNi3MoV high strength steel and undermatched welds.

**Figure 12.**Comparison of Plastic strain energy density ΔW

_{p}from different equations: (

**a**) 10CrNi3MoV high strength steel; (

**b**) undermatched welds.

**Figure 13.**Comparison of total strain energy density ΔW

_{t}between 10CrNi3MoV high strength steel and undermatched welds.

**Figure 14.**Comparison of total strain energy density ΔW

_{t}from different equations: (

**a**) 10CrNi3MoV high strength steel; (

**b**) undermatched welds.

**Figure 15.**LCF fracture location of the welded joint under different strain amplitudes: (

**a**) Macro morphology; (

**b**) Optical images for microstructure.

**Figure 16.**SEM fracture images, under strain amplitudes 0.4% and 0.8% of base metal (10NiCr3MoV). (

**a**) over fracture surface under 0.4%; (

**b**) over fracture surface under 0.8%; (

**c**) crack propagation near crack origin under 0.4%; (

**d**) crack origin under 0.4%.

**Figure 17.**SEM fracture images, under strain amplitudes 0.4% and 0.8% of undermatched welds. (

**a**) over fracture surface under 0.4%; (

**b**) over fracture surface under 0.8%; (

**c**) crack propagation near crack origin under 0.4%; (

**d**) crack origin under 0.8%.

Steel | C (%) | Si (%) | Mn (%) | Cr (%) | Mo (%) | Ni (%) | Cu (%) | V (%) | S (%) | P (%) |
---|---|---|---|---|---|---|---|---|---|---|

10CrNi3MoV | 0.09 | 0.29 | 0.48 | 0.94 | 0.4 | 2.88 | - | 0.06 | 0.005 | 0.011 |

U-Welds | 0.027 | 0.243 | 1.3 | 0.051 | - | 1.09 | 0.05 | - | 0.0073 | 0.011 |

Current | Voltage | Welding Speed | Electrode Diameter | Shielding Gas 80%Ar-20%CO_{2} | Heat Input | Interpass Temperature |
---|---|---|---|---|---|---|

(A) | (V) | (mm/s) | (mm) | (L/min) | (KJ/mm) | (°C) |

140–190 | 24–28 | 4.5–5.3 | 1.2 | 20 | 0.7–0.85 | <80 |

Steel | Yield Strength (MPa) | Tensile Strength (MPa) | Young’s Modulus (GPa) | Poisson’s Ratio | Kv (J) −20 °C |
---|---|---|---|---|---|

10CrNi3MoV | 693 | 741 | 205 | 0.3 | 280 |

U-Welds | 498 | 559 | 195 | 0.3 | 260 |

Specimens Reference | Total Strain Amplitude, Δε/2 (%) | Elastic Strain Amplitude, Δε_{e}/2 (%) | Plastic Strain Amplitude, Δε_{p}/2 (%) | Stress Amplitude, Δσ/2 (MPa) | Plastic Strain Energy Density ΔW_{p} (MJ/m^{3}) | Total Strain Energy Density ΔW_{T} (MJ/m^{3}) | Number of Cycle to Failure, N_{f} |
---|---|---|---|---|---|---|---|

BM1 | 1.2 | 0.469 | 0.731 | 595 | 18.546 | 19.940 | 163 |

BM2 | 0.8 | 0.296 | 0.504 | 566 | 9.667 | 10.487 | 361 |

BM3 | 0.8 | 0.290 | 0.510 | 565 | 9.799 | 10.618 | 405 |

BM4 | 0.6 | 0.291 | 0.309 | 567 | 5.787 | 6.613 | 585 |

BM5 | 0.6 | 0.286 | 0.314 | 561 | 5.759 | 6.561 | 571 |

BM6 | 0.5 | 0.280 | 0.220 | 537 | 3.812 | 4.564 | 820 |

BM7 | 0.4 | 0.331 | 0.069 | 510 | 2.500 | 3.345 | 1878 |

BM8 | 0.3 | 0.280 | 0.021 | 495 | 0.795 | 1.487 | 11,737 |

BM9 | 0.2 | 0.200 | - | 480 | 0 | 0.480 | 42,146 |

WM1 | 1.2 | 0.276 | 0.924 | 542 | 18.377 | 19.125 | 245 |

WM2 | 1 | 0.254 | 0.746 | 511 | 13.593 | 14.242 | 410 |

WM3 | 0.8 | 0.261 | 0.539 | 535 | 9.801 | 10.499 | 590 |

WM4 | 0.6 | 0.247 | 0.353 | 489 | 6.807 | 7.410 | 1048 |

WM5 | 0.5 | 0.298 | 0.202 | 435 | 4.084 | 4.733 | 1838 |

WM6 | 0.4 | 0.215 | 0.185 | 424 | 2.719 | 3.175 | 3412 |

WM7 | 0.3 | 0.198 | 0.102 | 386 | 1.181 | 1.662 | 14,389 |

WM8 | 0.21 | 0.2 | - | 370 | 0 | 0.470 | 109,640 |

Mechanical Properties | 10CrNi3MoV | Undermatched Welds |
---|---|---|

Young’s modulus (GPa) | 205 | 195 |

Cyclic hardening coefficient, K′ (MPa) | 857.16 | 1251.8 |

Cyclic hardening exponent, n′ | 0.079 | 0.172 |

Master curve hardening coefficient, K* (MPa) | 1113 | 685.99 |

Master curve hardening exponent, n* | 0.112 | 0.079 |

**Table 6.**Fatigue strength and fatigue ductility parameters of 10CrNi3MoV high strength steel and undermatched welds.

Mechanical Properties | 10CrNi3MoV | Undermatched Welds |
---|---|---|

Fatigue strength coefficient, ${\sigma}_{f}^{\prime}$ | 1386.4 | 896.9 |

Fatigue strength exponent, b | −0.108 | −0.067 |

Fatigue ductility coefficient, ${\epsilon}_{f}^{\prime}$ | 0.779 | 0.5351 |

Fatigue ductility exponent, c | −0.798 | −0.65 |

**Table 7.**Experimental and theoretical ΔW

_{p}values of 10CrNi3MoV high strength steel and undermatched welds.

Specimens Reference | Total Strain Amplitude, Δε/2 (%) | Plastic Strain Energy Density ΔW_{p} (MJ/m^{3}) from Experiments | Plastic Strain Energy Density ΔW_{p} (MJ/m^{3}) from Equation (3) | Plastic Strain Energy Density ΔW_{p} (MJ/m^{3}) from Equation (4) |
---|---|---|---|---|

BM1 | 1.2 | 18.546 | 14.850 | 13.599 |

BM2 | 0.8 | 9.667 | 9.740 | 8.909 |

BM3 | 0.8 | 9.799 | 9.838 | 8.999 |

BM4 | 0.6 | 5.787 | 5.982 | 5.472 |

BM5 | 0.6 | 5.759 | 6.014 | 5.500 |

BM6 | 0.5 | 3.812 | 4.034 | 3.685 |

BM7 | 0.4 | 2.500 | 1.201 | 1.096 |

BM8 | 0.3 | 0.795 | 0.355 | 0.324 |

BM9 | 0.2 | 0 | 0 | 0 |

WM1 | 1.2 | 18.377 | 14.153 | 17.943 |

WM2 | 1 | 13.593 | 10.773 | 13.697 |

WM3 | 0.8 | 9.801 | 8.149 | 10.338 |

WM4 | 0.6 | 6.807 | 4.878 | 6.216 |

WM5 | 0.5 | 4.084 | 2.483 | 3.185 |

WM6 | 0.4 | 2.719 | 2.217 | 2.847 |

WM7 | 0.3 | 1.181 | 1.113 | 1.437 |

WM8 | 0.21 | 0 | 0 | 0 |

Mechanical Properties | 10CrNi3MoV | Undermatched Welds |
---|---|---|

${k}_{p}$ (MJ/m^{3}) | 1162.1 | 1318.8 |

${\alpha}_{p}$ | −0.738 | −0.69 |

${k}_{T}$ (MJ/m^{3}) | 599.6 | 751.8 |

${\alpha}_{T}$ | −0.622 | −0.603 |

$\Delta {W}_{0}^{e+}$ | 0.213 | 0.382 |

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**MDPI and ACS Style**

Song, W.; Liu, X.; Berto, F.; Razavi, N.
Low-Cycle Fatigue Behavior of 10CrNi3MoV High Strength Steel and Its Undermatched Welds. *Materials* **2018**, *11*, 661.
https://doi.org/10.3390/ma11050661

**AMA Style**

Song W, Liu X, Berto F, Razavi N.
Low-Cycle Fatigue Behavior of 10CrNi3MoV High Strength Steel and Its Undermatched Welds. *Materials*. 2018; 11(5):661.
https://doi.org/10.3390/ma11050661

**Chicago/Turabian Style**

Song, Wei, Xuesong Liu, Filippo Berto, and Nima Razavi.
2018. "Low-Cycle Fatigue Behavior of 10CrNi3MoV High Strength Steel and Its Undermatched Welds" *Materials* 11, no. 5: 661.
https://doi.org/10.3390/ma11050661