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Study on Creep-Fatigue Mechanical Behavior and Life Prediction of Ti_{2}AlNb-Based Alloy

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## Abstract

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_{2}AlNb-based alloy were carried out at 550 °C. Compared with low-cycle fatigue, a creep-fatigue hysteresis loop has larger area and smaller average stress. The introduction of creep damage will greatly reduce the cycle life, and change the fatigue crack initiation point and failure mechanism. Based on the linear damage accumulation rule, the fatigue damage and creep damage were described by the life fraction method and the time fraction method, respectively, and the creep-fatigue life of the Ti

_{2}AlNb-based alloy is predicted within an error band of ±2 times.

## 1. Introduction

_{2}AlNb-based alloy is an intermetallic compound. Its long-range ordered super-lattice structure has the effect of weakening dislocation diffusion and high-temperature diffusion, which makes the alloy have the advantages of high specific strength, specific stiffness, creep resistance, fracture toughness and excellent oxidation resistance [4,5]. As a new generation of aerospace lightweight high-temperature structural materials, Ti

_{2}AlNb-based alloy is expected to partially replace Ni-based alloy for the manufacture of aeroengine structural parts to reduce the weight of the engine [6,7]. At present, creep-fatigue related research mainly focuses on nickel-based alloy, 316 stainless steel and P91 steel and other traditional high- temperature structural materials [8,9,10,11,12]. There are few public reports on creep-fatigue studies of Ti

_{2}AlNb-based alloys. Therefore, it is urgently needed to study the creep-fatigue behavior of Ti

_{2}AlNb-based alloy and evaluate its creep-fatigue life.

_{2}AlNb-based alloy and predict its creep-fatigue life. Firstly, low-cycle fatigue, creep and creep-fatigue tests of Ti

_{2}AlNb-based alloy were carried out at 550 °C to analyze the effect of creep damage on the cyclic deformation and damage accumulation of materials. Then, based on the linear cumulative damage criterion, a life prediction model was established to predict the creep-fatigue life of Ti

_{2}AlNb-based alloy.

## 2. Experimental Materials and Design

_{2}AlNb-based alloy is cut from the combustion chamber casing blank. The microstructure of the initial Ti

_{2}AlNb-based alloy was characterized at room temperature, and the results are shown in Figure 1. EBSD and EDS analyses were performed using a ZEISS Sigma 300 scanning electron microscope, which was equipped with an electron backscatterer and an energy spectrometer. It can be seen from the metallographic photograph that the grain size of the alloy is between 100 um and 500 um. The black acicular O phase is distributed in the grey β phase. It can be seen that the distribution of the O phase in different grains is not uniform. The black spots in Figure 1a are defects in the preparation process of metallographic samples, not the microstructure characteristics of the material. According to the results of EBSD analysis, Ti

_{2}AlNb-based alloy is composed of the O phase, the $\beta $ phase and the ${a}_{2}$ phase, accounting for 52%, 30% and 7% of the area, respectively, and the unresolved rate is 11%. EDS analysis results show that the main components of the alloy are Ti, Al, Nb and Zr, and the atomic content ratio is 55:21:23:1.

_{2}AlNb-based alloy. In addition, low-cycle fatigue and creep tests provide necessary data support for parameter fitting of the creep-fatigue life prediction model. Figure 2 shows the sample sizes of different tests. Low-cycle fatigue tests and creep-fatigue tests were carried out on the Instron-8802 fatigue testing machine. When the sample fracture or the stress of the testing machine decreased by 25% instantaneously, the failure of the sample was judged. As shown in Figure 3, the loading waveforms of low-cycle fatigue and creep-fatigue tests are triangular wave and trapezoidal wave, respectively, and the strain ratio is −1. Creep tests were carried out on a GNCJ-100E creep testing machine. The equipment, manufactured by GangYanNaKe Testing Technology Co., LTD., can perform creep tests of 1~100 kN. When the sample was broken, the failure of the sample was judged. Table 1 gives the specific test parameters. The sample processing and tests were carried out according to GB/T 38822-2020, GB/T 15248-2008 and GB/T 2039-2012.

## 3. Creep-Fatigue Life Prediction Modeling

_{2}AlNb- based alloy can be obtained by combining Equations (2)–(7):

## 4. Results and Discussion

#### 4.1. Creep-Fatigue Behavior

_{2}AlNb-based alloy. It can be seen that the curve gradually widens with the increase in strain range. The area surrounded by the hysteresis loop represents the difference between the absorbed energy at loading and the released energy at unloading, which can be used to characterize the dissipation of strain energy. The larger the area enclosed by the hysteresis loop, the more fatigue damage accumulated per cycle. Figure 4b shows the steady-state hysteresis loop of creep-fatigue of Ti

_{2}AlNb-based alloy. Stress relaxation occurs during the holding period. With the increase in holding time, the area surrounded by the hysteresis loop increases, and the hysteresis loop moves downward. Low-cycle fatigue and creep-fatigue steady-state hysteresis loops have no obvious boundary between linear and nonlinear segments. This is caused by the Bauschinger effect in the continuous loading–unloading–reverse loading process, and the elastic limit decreases continuously under reverse loading.

_{f}and N/N

_{c–f}). The cyclic soft/hardening behavior is characterized by the evolution of the maximum tensile stress of each cycle with the normalized life. It can be seen in Figure 5a that the specimens at different strain levels show slight cyclic hardening in the front and middle stages of low-cycle fatigue, which is caused by strain hardening during cyclic deformation. At the end of the curve, there is obvious cyclic softening, because the initiation and propagation of fatigue cracks reduce the effective bearing area, resulting in the decrease in tensile stress. It can be seen from Figure 5b that there is a significant softening at the beginning of creep-fatigue and no rapid softening at the end of the curve. This indicates that under creep-fatigue load, the crack expands rapidly after initiation and causes the failure of the specimen in one cycle.

_{2}AlNb-based alloy. At 400~600 MPa creep stress levels, there is only an initial creep stage and a steady creep stage before creep rupture, and the steady creep rate increases with the increase in creep stress level.

_{2}AlNb-based alloy at 550 °C. It can be found that the low-cycle fatigue and creep life generally decrease with the increase in strain range and stress level. But creep-fatigue life does not monotonically decrease with the increase in holding time. It can be seen from Figure 7 that after creep damage is introduced into low-cycle fatigue, the cycle life decreases significantly. When the holding time increases from 50 s to 100 s, the cycle life increases. In addition, when the holding time increases from 50 s to 100 s, the average stress of the steady-state hysteresis loop decreases significantly, which leads to the increase in life. The creep-fatigue life of Ti

_{2}AlNb-based alloy is affected by the holding time and average stress. The larger the holding time and average stress, the lower the creep-fatigue life of the sample.

#### 4.2. Creep-Fatigue Fracture

_{2}AlNb-based alloy specimens is observed to analyze the failure mode. By comparing the failure modes under different loading conditions, the effect of creep damage on fatigue failure of Ti

_{2}AlNb-based alloy is investigated.

_{2}AlNb-based alloy changes from transgranular fracture to transgranular and intergranular mixed fracture.

_{2}AlNb-based alloy consists of an intergranular fracture zone and a transgranular fracture zone. Affected by creep damage, voids are formed near the grain boundary of Ti

_{2}AlNb-based alloy, and the voids grow up to form intergranular cracks. The growth of creep cavities and the propagation of intergranular cracks lead to the decrease of the effective bearing area of the sample, and the actual stress on the effective bearing surface will continue to increase, resulting in the crack. In addition, it can be seen in Figure 9 that there are a large number of secondary cracks between the intergranular fracture zone and the transgranular fracture zone of the fracture surface. This part is the interface between the cracked zone and the uncracked zone when the specimen is about to undergo creep failure. Severe geometric discontinuity leads to stress concentration and promotes secondary crack propagation.

_{2}AlNb-based alloy is shown in Figure 10. The creep-fatigue test fracture with 50~100 s holding time is composed of small planes in different directions, which is a typical intergranular brittle fracture. When the holding time increases to 150~300 s, the fracture is similar to a creep fracture. Figure 11 shows the fracture comparison of fatigue, creep, and creep-fatigue tests. After creep damage was introduced into the fatigue test of Ti

_{2}AlNb based alloy, the fracture morphology obviously changed. The fatigue crack of Ti

_{2}AlNb-based alloy initiates at the edge of the sample, and the final fracture is a transgranular and intergranular mixed fracture. After adding strain holding, the failure mode in the early stage of the test changed into intergranular fracture. The transgranular fracture zone in Figure 10c,d is formed at the moment of specimen fracture. Most importantly, the crack source can no longer be observed at the fracture edge. The introduction of creep damage changes the location of fatigue crack initiation. Based on the above experimental phenomena, the creep-fatigue failure process of Ti

_{2}AlNb-based alloy is judged as follows: creep damage leads to voids near the grain boundary, resulting in stress concentration, and fatigue cracks initiate near the grain boundary. Guided by the stress concentration at the grain boundary, the cracks propagate along the grain boundary, resulting in intergranular fracture. When the holding time increases to more than 150 s, the reason for the occurrence of the tearing fracture zone is the same as that in the creep test, which is caused by the decrease in effective bearing surface during the holding process.

#### 4.3. Creep-Fatigue Life Prediction

_{2}AlNb-based alloy, and the stress relaxation parameters were fitted based on the creep-fatigue steady-state hysteresis loop data. The fitting results are shown in Figure 12. The above parameter fitting process was carried out in Matlab.

_{2}AlNb-based alloy.

## 5. Conclusions

_{2}AlNb-based alloy at 550 °C are systematically designed, and the creep-fatigue mechanical behavior and damage mechanism of Ti

_{2}AlNb based alloy are explored. On this basis, the creep-fatigue life prediction model of Ti

_{2}AlNb-based alloy is established, which provides technical support for the creep-fatigue service performance evaluation of Ti

_{2}AlNb-based alloy. The paper is summarized as follows:

_{2}AlNb-based alloy exhibits slight cyclic hardening during the low-cycle fatigue test. Since the load holding is increased at the maximum tensile strain, the maximum tensile stress of creep-fatigue decreases with the cycle times, and the maximum compressive stress increases, showing that the hysteresis loop moves downward with the cycle times. The Bauschinger effect occurs in Ti

_{2}AlNb-based alloy during low cycle fatigue and creep-fatigue cyclic deformation, resulting in no obvious boundary between elastic and inelastic segments in the steady-state hysteresis loop.

_{2}AlNb based alloy is significantly reduced. When the strain range is constant, the creep-fatigue life is mainly affected by holding time and average stress. The increase in holding time and average stress will lead to the decrease in creep-fatigue life.

_{2}AlNb-based alloy, creep damage leads to voids near the grain boundary, and causes stress concentration. Cracks initiate near the grain boundary and propagate along the grain boundary, resulting in fracture of the specimen.

_{2}AlNb based alloy was predicted by the time fraction method, and the predicted results were within ±2 times error band.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Microstructure characterization and element proportion of Ti

_{2}AlNb-base alloy: (

**a**) OM (200×); (

**b**) OM (1000×); (

**c**) EBSD; (

**d**) EDS.

**Figure 2.**Shape and dimensions of the tested specimens: (

**a**) low-cycle fatigue and creep-fatigue; (

**b**) creep.

Test | Loading Rate/s^{−1} | Strain Range/% | Stress Level/MPa | Hold Time/s |
---|---|---|---|---|

Fatigue | 0.005 | 1.2 | \ | \ |

1.3 | ||||

1.4 | ||||

1.6 | ||||

Creep | \ | \ | 400 | \ |

450 | ||||

500 | ||||

550 | ||||

600 | ||||

Creep-fatigue | 0.005 | 1.4 | \ | 50 |

100 | ||||

150 | ||||

200 | ||||

300 |

Test | Strain Range/% | Stress Level/MPa | Hold Time/s | Life |
---|---|---|---|---|

Fatigue | 1.2 | \ | \ | 9660/cycle |

1.3 | 1081/cycle | |||

1.4 | 742/cycle | |||

1.6 | 482/cycle | |||

Creep | \ | 400 | \ | 548/h |

450 | 195/h | |||

500 | 201/h | |||

550 | 78/h | |||

600 | 9/h | |||

Creep-fatigue | 1.4 | \ | 50 | 385/cycle |

100 | 493/cycle | |||

150 | 428/cycle | |||

200 | 254/cycle | |||

300 | 272/cycle |

Fatigue Damage | Creep Damage | Stress Relaxation |
---|---|---|

$\Delta {\epsilon}_{0},m,c$ | $a,b$ | $K$ |

**Table 4.**${\sigma}_{0}$ of creep-fatigue steady-state hysteresis loop under different holding times.

${t}_{h}$/s | 50 | 100 | 150 | 200 | 300 |

${\sigma}_{0}$/MPa | 621.890 | 615.718 | 560.482 | 542.131 | 550.315 |

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**MDPI and ACS Style**

Wang, Y.; Wang, X.; Yang, Y.; Lan, X.; Zhang, Z.; Li, H. Study on Creep-Fatigue Mechanical Behavior and Life Prediction of Ti_{2}AlNb-Based Alloy. *Materials* **2022**, *15*, 6238.
https://doi.org/10.3390/ma15186238

**AMA Style**

Wang Y, Wang X, Yang Y, Lan X, Zhang Z, Li H. Study on Creep-Fatigue Mechanical Behavior and Life Prediction of Ti_{2}AlNb-Based Alloy. *Materials*. 2022; 15(18):6238.
https://doi.org/10.3390/ma15186238

**Chicago/Turabian Style**

Wang, Yanju, Xinhao Wang, Yanfeng Yang, Xiang Lan, Zhao Zhang, and Heng Li. 2022. "Study on Creep-Fatigue Mechanical Behavior and Life Prediction of Ti_{2}AlNb-Based Alloy" *Materials* 15, no. 18: 6238.
https://doi.org/10.3390/ma15186238