# Effect of Carbide Precipitation on the Evolution of Residual Stress during Tempering

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Non-Isothermal Tempering Test

#### 2.3. Measurement of Residual Stress

^{3}) were taken from the middle of the steel plate with a wire cutter. One of these specimens was used to measure the residual stress before tempering. The remaining seven pieces were placed in a box furnace, heated to 100–700 °C (temperature increment being 50 °C), taken out after 30 min, and then subjected to measurement of residual stress using the crack compliance method [16]. The crack compliance method is based on the principle of elastic fracture mechanics. It is a technique capable of measuring residual stress along the thickness direction of a material. Specifically, the method introduces a slit with progressively increasing depth to release the residual stress on the test plane, and the deformation induced by the release of residual stress is recorded as a function of the slit depth and used to determine the preexisting residual stress. The strain measurements are shown in Figure 2. The determination of residual stress from measured strain is an inverse mechanics problem, and residual stress is computed through the least-squares inversion of a linear system called the compliance matrix, which is determined from finite element analysis. The specific stress computation procedure employed is described in detail by Prime [16,17].

#### 2.4. TEM Analysis

^{3}) was cut from a heat-treated specimen, and the thickness was ground to 80 μm or less on sandpaper with different grit numbers. Then, a small disk (diameter of Φ3 mm) was punched out on a special punching machine. Thin TEM foils were prepared by a twin-jet electrochemical polisher at 50 V in a 4 vol.% perchloric acid alcohol electrolyte at −30 °C, and then investigated with a JSM2100F (JSOL Corp. Kyoto, Japan) field emission electron microscope operated at 200 kV.

#### 2.5. Vickers Micro-Hardness

## 3. Results

#### 3.1. Evolution of 700L Microstructure during Tempering

#### 3.1.1. Stages in the Tempering Process

#### 3.1.2. Evolution of Dislocation during Tempering

#### 3.2. Residual Stress Test

#### 3.2.1. Characterization Parameters of Residual Stress

_{RS}). The absolute value of residual stress ($\left|{\sigma}_{RS}\right|$) is the difference between the maximum and minimum residual stress of a point on the material in the thickness direction, which can be used to evaluate the uniformity of residual stress in the thickness direction of the point; this is shown in Equation (1):

_{RS}) is the integral of the absolute value of the residual stress, which can be used to measure the mean level of the residual stress in the thickness direction, as shown in Equation (2):

_{RS}is the unit elastic strain energy of residual stress in MPa∙mm.

#### 3.2.2. Measurement Result of Residual Stress

#### 3.3. Effect of Evolution of Microstructure on Residual Stress

## 4. Discussion

#### 4.1. Transformation Plasticity during Tempering

#### 4.2. Effect of Carbides Precipitation on Residual Stress

^{−1}. Even if the temperature difference between the surface of the strip and the core was up to 300 °C, the temperature stress in the strip was only 467.64 MPa, which was lower than the yield strength of the material at this temperature. Therefore, at this stage, the initial residual stress cannot be improved by decreases in the elastic modulus or the yield strength [7]. Moreover, the tempering temperature at this time was lower than 0.3 Tm. Therefore, the creep is not enough to bring about a significant improvement in residual stress during this stage. Interestingly, it can be seen from Figure 8a, the trends of residual stress on the material’s surface and in the core were opposite during tempering at temperatures below 300 °C, showing clear directionality. It can be inferred from these observations that the precipitation plasticity dominates the evolution of residual stress at this stage.

#### 4.3. Regulation of Residual Stress by High-Temperature Creep

## 5. Conclusions

- (1)
- The tempering process of low-carbon 700 L included the following six stages—carbon segregation and cementite I precipitation, retained austenite decomposition, cementite II precipitation, cementite dissolution, alloy carbide precipitation, and Mn partitioning. In addition, three hardness peaks appeared in the cementite II precipitation, alloy carbide precipitation, and Mn partitioning stages.
- (2)
- 700 L has two distinct residual stress adjustment stages during tempering, which are related to the transformation of the microstructure. The first stage overlapped with cementite II precipitation, and the absolute value of residual stress was reduced from 487 MPa to 200 MPa; however, the elastic deformation energy remained unchanged. The second stage was for temperatures of 450–650 °C, and the absolute value of residual stress was reduced to 174 MPa. During this stage, the elastic deformation energy was reduced by 72.72%.
- (3)
- Precipitation plasticity was the main reason for the adjustment of residual stress during the first stage. The direction of the initial residual stress determined the direction of the precipitation plastic strain caused by the precipitation of carbides. This led to different trends in residual stress on the material’s surface and in the core during tempering. The adjustment of the residual stress at this stage reduced the micro-stress formed from the volume mismatch during the quenching process but had limited ability to adjust the macroscopic residual stress.
- (4)
- Although the second residual stress adjustment stage overlapped with the alloy carbide precipitation and Mn partitioning stages, the carbide precipitation only reduced the elastic strain energy by 8.7%. It is inferred that the activation energy for creep was the main driving force for the adjustment of the residual stress during the second stage. The initial residual stress provided an applied stress that generated creep, and the tempering temperature enhanced the driving force generated by the creep. Tempering at 600 °C could improve both the micro-stress and macro-stress in 700 L steel.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Changes in length during non-isothermal tempering of 700L. (

**a**) The changes in specimen length during the two tempering processes and the corresponding differences; (

**b**) The first derivative of the difference between the changes in the length for the first and second tempering steps.

**Figure 4.**TEM images during tempering at different temperatures. (

**a**) TEM image before tempering; (

**b**)TEM image at 200 °C—precipitation of cementite I; (

**c**) TEM image at 300 °C—decomposition of retained austenite; (

**d**) TEM image at 300 °C—precipitation of cementite II; (

**e**) TEM image at 550 °C—alloy carbide precipitation; (

**f**) TEM image at 650 °C—Mn partitioning.

**Figure 6.**TEM images in the tempering process. (

**a**) TEM image before tempering; (

**b**) TEM image after tempering at 200 °C for 30 min; (

**c**) TEM images after tempering at 300 °C for 30 min. (

**d**) TEM images after tempering at 600 °C for 30 min.

**Figure 7.**Comparisons of residual stress distribution before tempering of 700 L with that after tempering at 200 °C, 300 °C, and 600 °C for 30 min. (

**a**) Tempering at 200 °C for 30 min; (

**b**) Tempering at 300 °C for 30 min; (

**c**) Tempering at 600 °C for 30 min.

**Figure 8.**Evolution of residual stress during tempering. (

**a**) Evolution of residual stress on the surface and in the core; (

**b**) Evolution of residual stress and elastic strain energy along the thickness direction.

**Figure 9.**The true stress-strain, elastic modulus, and yield strength curves of 700 L at different temperatures. (

**a**) The true stress-strain curves; (

**b**) The elastic modulus and yield strength curves.

C | Si | Mn | P | S | Nb | Al | Ti | Fe |
---|---|---|---|---|---|---|---|---|

0.079 | 0.072 | 1.460 | 0.011 | 0.002 | 0.051 | 0.039 | 0.095 | Bal. |

Residual Stress | Before Tempering | After 200 °C Tampering | After 300 °C Tampering | After 600 °C Tampering |
---|---|---|---|---|

${\mathsf{\sigma}}_{\mathrm{RSmax}}$ (MPa) | 287 | 218 | 0 | 113 |

${\mathsf{\sigma}}_{\mathrm{RSmin}}$ (MPa) | −200 | −242 | −200 | −61 |

${\mathsf{\sigma}}_{\mathrm{RSmax}}-{\mathsf{\sigma}}_{\mathrm{RSmin}}$ (MPa) | 487 | 460 | 200 | 174 |

% | 100% | 94.45% | 41.07% | 35.73% |

Elastic Strain Energy | Before Tempering | After 200 °C Tampering | After 300 °C Tampering | After 600 °C Tampering |
---|---|---|---|---|

style="border-bottom:solid thin">Elastic strain energy (MPa∙mm) | 1609 | 1657 | 1572 | 439 |

% | 100% | 102.98% | 97.70% | 27.28% |

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**MDPI and ACS Style**

Ding, W.; Liu, Y.; Xie, J.; Sun, L.; Liu, T.; Yuan, F.; Pan, J.
Effect of Carbide Precipitation on the Evolution of Residual Stress during Tempering. *Metals* **2019**, *9*, 709.
https://doi.org/10.3390/met9060709

**AMA Style**

Ding W, Liu Y, Xie J, Sun L, Liu T, Yuan F, Pan J.
Effect of Carbide Precipitation on the Evolution of Residual Stress during Tempering. *Metals*. 2019; 9(6):709.
https://doi.org/10.3390/met9060709

**Chicago/Turabian Style**

Ding, Wenhong, Yazheng Liu, Jianxin Xie, Li Sun, Tianwu Liu, Fei Yuan, and Jin Pan.
2019. "Effect of Carbide Precipitation on the Evolution of Residual Stress during Tempering" *Metals* 9, no. 6: 709.
https://doi.org/10.3390/met9060709