# Experiment and Modelling of the Pre-Strain Effect on the Creep Behaviour of P/M Ni-Based Superalloy FGH96

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Creep Model with Pre-Strain Effect

#### 3.1. Micro-Twinning-Based Creep Model

_{2}structure. These PTs have high energies and impede the movements of a/6<112> dislocations. Diffusion-mediated reordering near the {111} planes yielded twinned parts with the ideal L1

_{2}structure. The rearranged atomic lattice formed a mirror-image relationship with the original lattice before the PT formation, which meant that true twins (TT) were formed. The transformation from high-energy PTs to low-energy TTs made the a/6<112> dislocations slip again, leading to continuous creep deformation. Therefore, the formation of PTs was induced by the shear of dislocations, while the formation of TTs is thermally mediated.

#### 3.2. Creep Model with Pre-Strain Effect

_{1}is a temperature-independent parameter reflecting the dislocation accumulation, and k

_{2}is a temperature-dependent parameter describing the dislocation annihilation [34].

## 4. Result and Discussion

#### 4.1. Influence of Pre-Strain on the Creep Behaviour

#### 4.2. Influence of Pre-Strain on Microstructure

#### 4.3. Validation of the Creep Rate Model

_{tp}), the formation energy of two-layer PTs in secondary γ′ (Γ

_{pt}), the formation energy of two-layer TTs in secondary γ′ (Γ

_{tt}), the formation energy of two-layer TTs in the γ matrix (Γ

_{tm}), the diffusion coefficient for reordering (D

_{ord}), and the diffusion length (x). Reordering involves the diffusion of Ni and Al atoms; a definite value of D

_{ord}was still unavailable. The diffusion coefficient of Al atoms in Ni

_{3}Al was obtained as [36]:

_{3}Al was obtained as [37]:

_{ord}was set as the average value of the two diffusion coefficients [25], i.e., ${D}_{ord}=\frac{{D}_{Al}^{*}+{D}_{Ni}^{*}}{2}$. The diffusion length, x, was taken as twice the value of b

_{tp}[25].

_{1}, and k

_{2}were calibrated by experimental data; their values are listed in Table 2. These three parameters were determined as follows. According to Equation (11), ${\rho}_{tp-pre}^{0}$ was determined using the steady-state strain rates of the sample without pre-strain. Then, the values of k

_{1}and k

_{2}were calibrated according to Equation (13) using the steady-state strain rates of the pre-strained samples. Finally, Equation (14) was adopted to calculate the creep rates using the parameters shown in Table 1 and Table 2.

b_{tp}(Å) | Γ_{pt}(J/m ^{2}) | Γ_{tt}(J/m ^{2}) | Γ_{tm}(J/m ^{2}) | D_{ord} at 973 K(m ^{2}/s) | x |
---|---|---|---|---|---|

1.44 [38] | 0.7 [25] | 0.02 [25] | 0.03 [39] | 3.24 × 10^{−20} | 2 b_{tp} [25] |

^{13}m

^{−2}. Pre-strains of 6% had no obvious influence on the morphology and distribution of γ′ precipitates and pre-strains mainly affected the density of a/6<112> dislocations; therefore, an exponential function of dislocation density was adopted to identify the pre-strain effect.

## 5. Conclusions

- (1)
- The steady-state creep rate and 70 h creep strain continuously increased with the increase in pre-strains. Compared with an unstrained specimen, the creep strain of pre-strained specimens accumulated rapidly in the first few hours, followed by a higher steady-state creep rate. For specimens with more than 1% pre-strain, the steady-state creep rate was more than 10 times greater than that of the unstrained specimen.
- (2)
- Room-temperature pre-tension within 6.04% plastic strain had no obvious influence on the morphology and distribution of γ′ precipitates, whereas the dislocation density continuously increased with the increase in pre-strains. The increases in mobile dislocation density after pre-strain were the main reasons for the increase in creep rates of FGH96 alloys.
- (3)
- The predicted steady-state creep rates showed good agreement with the experimental data; the creep model proposed in this study could capture the pre-strain effect while considering the micro-twinning mechanism.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**The grain morphology (

**a**,

**b**) and γ′ distribution (

**c**,

**d**) of FGH96 before and after pre-strains: (

**a**) OM unstrained, (

**b**) OM 6.04% pre-strained, (

**c**) SEM unstrained, and (

**d**) SEM 6.04% pre-strained.

**Figure 5.**TEM analysis of the FGH96 alloy after various degrees of pre-strains: (

**a**) un-strained, (

**b**) 0.33% pre-strain, (

**c**) 1.01% pre-strain, and (

**d**) 6.04% pre-strain.

**Figure 6.**TEM analysis of the FGH96 alloy after 70 h creep: (

**a**) 0.34% pre-strained sample, (

**b**) 1.05% pre-strained sample.

**Figure 7.**Predicted (

**a**) steady-state creep rates and (

**b**) dislocation density under different pre-strains.

${\mathit{\rho}}_{\mathit{t}\mathit{p}-\mathit{p}\mathit{r}\mathit{e}}^{0}$ (m^{−2})
| k_{1} (m^{−1}) | k_{2} |
---|---|---|

8.27 × 10^{11} | 1.7490 × 10^{8} | 41.83 |

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**MDPI and ACS Style**

Wang, H.; Zhang, J.; Shang, H.; Sha, A.; Cheng, Y.; Duan, H.
Experiment and Modelling of the Pre-Strain Effect on the Creep Behaviour of P/M Ni-Based Superalloy FGH96. *Materials* **2023**, *16*, 3874.
https://doi.org/10.3390/ma16103874

**AMA Style**

Wang H, Zhang J, Shang H, Sha A, Cheng Y, Duan H.
Experiment and Modelling of the Pre-Strain Effect on the Creep Behaviour of P/M Ni-Based Superalloy FGH96. *Materials*. 2023; 16(10):3874.
https://doi.org/10.3390/ma16103874

**Chicago/Turabian Style**

Wang, Hao, Jingyu Zhang, Huashan Shang, Aixue Sha, Yangyang Cheng, and Huiling Duan.
2023. "Experiment and Modelling of the Pre-Strain Effect on the Creep Behaviour of P/M Ni-Based Superalloy FGH96" *Materials* 16, no. 10: 3874.
https://doi.org/10.3390/ma16103874