_{2}AlNb Alloy Subcomponents

_{2}AlNb Alloy Subcomponents

_{2}AlNb Alloy Subcomponents

Many titanium alloy subcomponents are subjected to fatigue loading in aerospace engineering, resulting in fatigue failure. The fatigue behavior of Ti_{2}AlNb alloy subcomponents was investigated based on the Seeger fatigue life theory and the improved Lemaitre damage evolution theory. Firstly, the finite element models of the standard open-hole specimen and Y-section subcomponents have been established by ABAQUS. The damage model parameters were determined by fatigue tests, and the reliability of fatigue life simulation results of the Ti_{2}AlNb alloy standard open-hole specimen was verified. Meanwhile, the fatigue life of Ti_{2}AlNb alloy Y-section subcomponents was predicted. Under the same initial conditions, the average error of fatigue life predicted by two different models was 20.6%. Finally, the effects of loading amplitude, temperature, and Y-interface angle on fatigue properties of Ti_{2}AlNb Y-section subcomponents were investigated. These results provide a new idea for evaluating the fatigue life of various Ti_{2}AlNb alloy subcomponents.

_{2}AlNb alloy

Advances in the aerospace industry require new lightweight materials and complex integral component forming technologies to improve fuel efficiency and payloads. Ti_{2}AlNb alloy has good plasticity and fracture toughness at room temperature, creep and fatigue resistance at a high temperature, high Young’s modulus, and specific strength. Compared with the traditional high-temperature titanium alloy, the upper limit of application temperature of Ti_{2}AlNb alloy exceeds 600°C and reaches 650°C∼700°C [

Many titanium alloy subcomponents are subjected to fatigue loading in aerospace engineering, resulting in fatigue failure. The fatigue behavior of Ti_{2}AlNb alloy subcomponents is fundamental. The fatigue properties of Ti_{2}AlNb alloy were mainly studied by analyzing the influence of microstructure, alloy composition and surface treatment. Through the study of the Orthorhombic structure (O phase), the formation mechanism of Ti_{2}AlNb alloy is diverse and complex, and the formation of the material is strongly dependent on the thermal machining process [_{2}AlNb alloy, such as strength, plasticity, oxidation resistance and creep resistance, have been significantly changed [_{2}AlNb alloy from 752 to 1123 MPa [_{2}AlNb alloy. Chen et al. [_{2}AlNb. They measured the residual stress of the specimen after glass fine shot peening by X-ray diffraction and electropolishing. Based on the image crystal plasticity model, Fu et al. [_{2}AlNb superalloy. After shot peening, residual compressive stress was introduced into the surfaces of samples, which offset part of the tensile stress, delayed the initiation and propagation of cracks, and significantly increased the fatigue strength limit from 170 to 360 MPa and the high cycle fatigue life is prolonged more than 25 times [_{2}AlNb alloy focuses on the material parts, and the fatigue behavior of subcomponents needs further study.

The fatigue life prediction of titanium alloy can be divided into three main criteria: stress criteria [

To sum up, the fatigue behavior of Ti_{2}AlNb alloy subcomponents is still an open question. Seeger fatigue life theory and the improved Lemaitre damage evolution theory are used to predicting the fatigue life of Ti_{2}AlNb alloy standard open-hole specimen and Y-section subcomponents. The research method has a particular reference significance for predicting the fatigue life of Ti_{2}AlNb alloy subcomponents and provides a new idea for evaluating the fatigue life of various engineering structures.

Seeger theory has been widely used to estimate the elastic-plastic stress and strain of notched parts under uniaxial or multiaxial stress (monotone and cyclic loading). Its accuracy has also been verified in relevant experiments [

The relation between the real local stress amplitude and durability is:

The true fracture strength (or stress) is shown to be:

The fatigue ductility coefficient,

Fatigue life can also be approximated by

The fatigue strength exponent will usually be between −0.05 and −0.12. The fatigue ductility exponent,

From

Seeger theory involves fatigue parameters as shown in

1.67 |
0.35 | −0.095 | −0.69 | 0.11 | 1.61 |

In the framework of CDM, damage is defined as the development of pores in microscopic, submicroscopic, and macroscopic fracture processes of materials, which is accompanied by the deterioration of the mechanical properties of materials. The ‘damage’ does not correspond to the actual crack. In metallic materials, the damage usually has no directivity, called isotropic damage, and can be expressed as a scalar quantity.

According to the equivalent strain hypothesis proposed by Lemaitre and Desmorat, the effective stress acting on the effective area can be defined as:

According to the constitutive damage model proposed by Krajcinovic and Lemaitre, the fatigue damage of metal materials in LCF is mainly caused by accumulated plastic strain. The greater the cumulative plastic deformation, the more excellent the energy dissipation caused by damage.

Damage increment,

Damage strain energy release rate,

Substitute

According to the study of Zhou et al. [

For the LCF behavior of metal materials, the Ramberg-Osgood cycle is usually adopted. Within a stable cycle, the plastic strain can be expressed as:

The equivalent stress difference,

Assuming that the damage changes very little in a cycle, it can be approximated that the damage variable

By using the established damage constitutive relation

In order to calculate

Within a cycle, the damage changes,

When

By differentiating both ends of

For symmetric fatigue cycles, the hysteresis loop is central symmetry:

By substituting _{2}AlNb alloy in each loading cycle is:

Material parameters involved in the damage model are shown in

77.62 | 0.0023 | 2104 | 0.133 | 4.1 | 0.06 |

In order to measure the Elastic modulus and Poisson’s ratio of Ti_{2}AlNb alloy, the bar specimens were tested using the dynamic (acoustic resonance) method according to ASTM E1875-20. The data required for the excerpt is shown in

Temperature, ^{o}C) |
|||
---|---|---|---|

24 | 113.2 | 43.5 | 0.301 |

500 | 103.7 | 39.5 | 0.313 |

600 | 99.7 | 37.9 | 0.315 |

700 | 95.0 | 36.1 | 0.316 |

As the operating temperature range of Ti_{2}AlNb alloy subcomponents includes 500°C∼700°C, the standard open-hole specimen was selected for the test, as shown in _{2}AlNb alloy standard open-hole specimens are all lower than 10^{4}.

^{o}C) |
||||
---|---|---|---|---|

550 | −1 | 12.84 | 1.353 | 492 |

10.52 | 1.057 | 1357 | ||

9.25 | 0.931 | 2467 | ||

7.16 | 0.718 | 5298 | ||

6.73 | 0.592 | 7627 | ||

650 | −1 | 8.56 | 0.992 | 714 |

7.75 | 0.668 | 1861 | ||

6.41 | 0.616 | 3634 | ||

6.05 | 0.583 | 6923 |

Numerical methods to simulate the behavior of materials can reduce the design and experimental costs, and the combination of experimental and simulated data is more consistent with the actual situation [_{2}AlNb alloy standard open-hole specimens were analyzed for grid convergence. Then, the fatigue life of Ti_{2}AlNb alloy standard open-hole specimens was predicted. The reliability of the two theoretical methods was analyzed and the fatigue parameters were determined. Finally, the two theoretical methods were used to predict the fatigue life of Ti_{2}AlNb alloy Y-section subcomponents.

The FEM model of Ti_{2}AlNb alloy standard open-hole specimen was established in ABAQUS software. Three-dimensional four-node linear solid elements (C3D4) were used in the model. The element is defined by four nodes with three degrees of freedom for each node: translations in the nodal directions,

The convergence solution independent of the mesh size is obtained in the numerical calculation after the mesh sensitivity analysis, as shown in

Seeger method is to directly predict the fatigue life through empirical formulas based on the stress calculation results, so selecting finer grid elements is useful to improve the accuracy. The improved Lemaitre method calculates the cumulative damage according to the average stress of the grid. If the grid elements are selected too fine, the grid stiffness at the stress concentration will degrade rapidly until failure, leading to a large error in the predicted fatigue life. Therefore, selecting an appropriate grid element density can reduce the error.

Based on Seeger fatigue life theory, the static tensile results of the Ti_{2}AlNb alloy standard open-hole specimen of FEM were post-processed in FE-SAFE software. The fatigue cloud diagram of the FEM was generated, and showed the predicted fatigue life of a finite element structure at different positions. According to ^{2.782}, that is, failure after 605 cycles. According to ^{3.908}, that is, failure after 8,090 cycles.

Seeger theoretical error

The fatigue life of Ti_{2}AlNb alloy standard open-hole specimens was calculated at 550°C under five different forces: 12.84, 10.52, 9.25, 7.16 and 6.73 kN. When the temperature is 650°C, the fatigue life was calculated under five forces: 8.56, 7.75, 6.41 and 6.05 kN. Seeger fatigue life prediction value (Seeger) and test fatigue life value (Test) are summarized, as shown in

Although Seeger theory can predict the fatigue life of Ti_{2}AlNb alloy specimens within the allowable error range, there are still some defects. Seeger theory gives fatigue parameters based on many fatigue tests of Al-Ti alloy. Still, it is not rigorous enough to adopt uniform titanium alloy parameters for Ti_{2}AlNb alloy. Seeger theory read the equivalent stress of all grids in a static tensile process of the FEM. It calculates the fatigue life by using titanium alloy’s approximate fatigue life formula, which could not show the complete stiffness degradation process.

The FEM of Ti_{2}AlNb alloy standard open-hole specimen is subjected to axial loads on both cross-sections. The periodic, constant amplitude load adopts the loading method of the triangular wave, and each analysis step carries out a complete tension and compression process. The specific amplitude is shown in

The improved Lemaitre damage evolution theory is coupled to ABAQUS through the UMAT subroutine to simulate the low cycle fatigue damage of Ti_{2}AlNb alloy standard open-hole specimen. Firstly, the stress-strain field is calculated, and then the damage of elements is calculated according to the global element stress. With the increase in the number of cycles, the damage to elements accumulates continuously. When the damage of elements reaches critical damage (

When the initial condition is _{2}AlNb alloy standard open-hole specimen under cyclic loading.

The error of the improved Lemaitre damage evolution theory

The improved Lemaitre prediction value (Lemaitre) and test fatigue life value (Test) are summarized, as shown in

The difference between Seeger theory method and the improved Lemaitre damage evolution theory in predicting the fatigue life of structural parts can be understood through the simulation in

For feature extraction of structural parts of integral investment casting casing of Ti_{2}AlNb alloy, there are many Y-shaped areas with three interface interactions in the casing section, as shown in

The fatigue life of the Ti_{2}AlNb alloy Y-section subcomponents with the interface angle of 30° was calculated under five different loads: 22, 20, 18, 16 and 14 kN. The fatigue life of the Y-section subcomponents with the angle of 40° was calculated under five loads: 20, 18, 16, 14 and 12 kN. The fatigue life of the Y-section subcomponents with the angle of 60° was calculated under five loads: 18, 16, 14, 12 and 10 kN. Fatigue life values predicted by Seeger theory (Seeger) and fatigue life values predicted by the improved Lemaitre damage evolution theory (Lemaitre) are summarized, as shown in

The error between Seeger and the improved Lemaitre method,

When the initial conditions are identical,

_{2}AlNb alloy Y-section subcomponents at 650°C are all smaller than those carried at 550°C. Temperature is negatively correlated with the fatigue life of the subcomponents. When the temperature is constant, decreasing the load amplitude will increase the number of failure cycles of Ti_{2}AlNb alloy Y-section subcomponents. The load amplitude is negatively correlated with the fatigue life of the subcomponents.

The effect of interface angle on the fatigue life of Ti_{2}AlNb alloy Y-section subcomponents is studied by two theoretical methods. When the initial conditions are _{2}AlNb alloy Y-section subcomponents at different interface angles is shown in

When the improved Lemaitre damage evolution theory is used to predict the fatigue life of subcomponents, the maximum number of failure cycles is far less than expected, but the failure cycle cannot converge. At this point, stiffness degradation has just begun, so the number of cycles applied at each analysis step needs to be adjusted. In addition, the unscientific division of the FEM grid will also lead to the appearance of some defective data.

In this paper, the low cycle fatigue behaviour of Ti_{2}AlNb alloy Y-section subcomponents has been studied experimentally and numerically. The finite element simulation parameters of Ti_{2}AlNb alloy standard open-hole specimen were determined based on the fatigue test data. The fatigue life of Ti_{2}AlNb alloy Y-section subcomponents was predicted, which solved the problem that it was difficult to conduct conventional fatigue tests for complex Ti_{2}AlNb alloy subcomponents. Some critical conclusions are summarized as follows:

The convergence of the finite element model mesh of Ti_{2}AlNb alloy standard open-hole specimen was analyzed using fatigue test data at 550°C and 650°C. The optimal global mesh size of the Seeger theory and the improved Lemaitre theory is 2 mm, and the optimal local mesh size is 0.2 and 1 mm, respectively.

The fatigue life of the Ti_{2}AlNb alloy standard open-hole specimen was predicted. The average error of maximum failure cycles of Ti_{2}AlNb alloy standard open-hole specimen at 550°C and 650°C between Seeger theory and test is 12.4% and 15.2%, respectively. The nine-point average error between the Seeger theory and the test value is 13.8%. The average error of maximum failure cycles of Ti_{2}AlNb alloy standard open-hole specimen at 550°C and 650°C between improved Lemaitre damage evolution theory and test is 21.4% and 12.5%, respectively. The stiffness of the grid element degrades rapidly when the cyclic stress is high, resulting in a significant error at 550°C. The nine-point average error between the improved Lemaitre theory and the test value is 16.9%. The average errors of fatigue life predicted by the Seeger theory and the improved Lemaitre theory are 13.8% and 16.9%, respectively.

The load amplitude, temperature, and Y-interface angle are negatively correlated with the fatigue life of the Ti_{2}AlNb alloy Y-section subcomponents. The average error of fatigue life of Ti_{2}AlNb alloy Y-section subcomponents predicted by two theoretical methods is 20.6%. By observing the failure position of the structures, it is found that the increase of the angle of the interface area will amplify the stress concentration effect, thus reducing the fatigue life, which is consistent with the Seeger theory results.

The authors are grateful for the financial support provided by the

The authors declare that they have no conflicts of interest to report regarding the present study.

_{2}AlNb intermetallic fabricated by selective laser melting

_{2}AlNb-based alloy through double-wire arc additive manufacturing

_{2}AlNb-based alloy containing O +

_{2}AlNb based alloy

_{2}AlNb-based alloy

_{2}AlNb-based alloy at 800°C

_{2}AlNb-based titanium aluminide

_{2}AlNb based alloy

_{2}AlNb-based alloys

_{2}AlNb-based alloys

_{2}AlNb-based alloy

_{2}AlNb alloy

_{2}AlNb intermetallic alloy

_{2}AlNb superalloy by using image-based crystal plasticity modeling

_{2}AlNb intermetallic compound under shot peening