Life assessment method considering multi-axial thermomechanical fatigue damage mechanism

Abstract

The application discloses a life evaluation method considering multi-axial thermal mechanical fatigue damage mechanism, utilizes equivalent temperature to grasp characteristic information of temperature load in multi-axial thermal mechanical fatigue load history, and provides a temperature dependence influence factor calculation model based on hyperbolic tangent function, and the influence of temperature on damage is considered. The influence of longer cycle period and the introduction of holding time on failure life is considered by utilizing time dependence influence factor. The influence of non-proportional additional hardening on fatigue and oxidation damage is considered by adopting Shang-Wang multi-axial damage model. The influence of material rapid cracking on failure life caused by the comprehensive action of high temperature, tensile stress and shear stress is considered by utilizing rapid cracking influence factor. The failure life results of uniaxial isothermal fatigue test with and without holding time, uniaxial and multi-axial thermal mechanical fatigue test are utilized to verify the proposed method, and the prediction error is within 2 times factor, and the method is applied to failure life prediction of actual high-temperature structure.

Description

Technical Field

[0001] This invention belongs to the field of multiaxial thermomechanical fatigue strength, and particularly relates to a life assessment method that takes into account the multiaxial thermomechanical fatigue damage mechanism. Background Technology

[0002] Major components of aero-engines are frequently subjected to combined thermal and mechanical loads during operation. The mechanical loads typically involve multiple directions, leading to multiaxial thermomechanical fatigue at critical locations on these components. Multiaxial loading makes the thermomechanical cyclic deformation behavior and fatigue damage mechanisms more complex than under uniaxial loading; therefore, multiaxial thermomechanical fatigue has become a significant limiting factor for the failure life of engineered components at high temperatures. Developing robust life prediction methods under multiaxial thermomechanical loading is essential and crucial for assessing the structural integrity of these high-temperature components.

[0003] Recently, our latest work systematically investigated the fatigue behavior of TC4 titanium alloy under multiaxial thermomechanical loading and summarized five main damage mechanisms that can reasonably explain the life law. Mechanism 1 is the temperature dependence of damage, that is, damage caused by high temperature increases with increasing temperature. Mechanism 2 is the time dependence of damage, that is, the introduction of longer cycle periods and residence times will increase oxidation damage. Mechanism 3 is the effect of tensile mean stress. In the presence of tensile mean stress, a larger tensile peak stress can increase fatigue damage by increasing the crack propagation rate, and oxidation damage will also increase because more oxygen enters the metal through surface cracks. Mechanism 4 is the effect of non-proportional additional hardening, which leads to a larger equivalent stress amplitude response and further increases fatigue and oxidation damage. Mechanism 5 is the rapid cracking of the material, activated by the combined effect of high temperature, tensile stress, and shear stress, resulting in a significant shortening of the failure life. In order to reasonably predict the fatigue life of TC4 titanium alloy under multiaxial thermomechanical loading, it is necessary to consider the above damage mechanisms when constructing the damage model. Summary of the Invention

[0004] This invention aims to address the design requirements of multiaxial thermomechanical fatigue strength by proposing a life assessment method that considers the damage mechanism of multiaxial thermomechanical fatigue. The invention utilizes equivalent temperature to capture the characteristic information of temperature load in the multiaxial thermomechanical fatigue load history and provides a temperature-dependent influence factor calculation model based on the hyperbolic tangent function, considering the influence of temperature on damage. A time-dependent influence factor is used to consider the impact of longer cycle periods and the introduction of hold time on failure life. The Shang-Wang multiaxial damage model is employed to consider the influence of non-proportional additional hardening on fatigue and oxidation damage. A rapid cracking influence factor is used to consider the impact of rapid material cracking caused by the combined effects of high temperature, tensile stress, and shear stress on failure life. The proposed method is validated using failure life results from uniaxial isothermal fatigue tests with and without hold time, as well as uniaxial and multiaxial thermomechanical fatigue tests. The prediction error is within 2 factors, and this method can be applied to the failure life prediction of actual high-temperature structures.

[0005] The technical solution adopted in this invention is a life assessment method that considers the multiaxial thermomechanical fatigue damage mechanism. The implementation steps of this method are as follows:

[0006] Step (1): Calculate the equivalent temperature T of the temperature load in the multiaxial thermomechanical fatigue load history. e :

[0007]

[0008] Among them, T e It is the equivalent temperature of the temperature load, T(t) i ) is t i The temperature at time t, where i is the temperature load data point count variable, and t is the temperature at time t. i It is the time corresponding to the i-th data point, where n is the number of temperature load data points, and T th It is the critical temperature;

[0009] Step (2): Based on the T calculated in step (1) e Calculate the temperature-dependent influence factor D T :

[0010]

[0011] Among them, T m It is the melting temperature of the material, α T It is a material constant expressing temperature dependence, and tanh is the hyperbolic tangent function;

[0012] Step (3): Calculate the time-dependent influence factor D t :

[0013] D t =1+αt t cyc

[0014] Among them, t cyc It is the cycle period, α t It is a material constant that expresses time dependence;

[0015] Step (4): Calculate the rapid cracking influence factor M:

[0016]

[0017] Where, σ eq For von Mises equivalent stress, σ b σ is the tensile strength of the material. x For axial stress, τ xy Shear stress;

[0018] Step (5): Based on the parameters obtained in steps (2), (3), and (4), calculate the multiaxial thermomechanical fatigue life N. f :

[0019]

[0020] Where, Δγ max It is the range of maximum shear strain on the critical surface. It is the normal strain range between the maximum shear strain reversal points on the critical surface. It is the normal mean stress on the critical surface, E is Young's modulus, σ' f ε' is the fatigue strength coefficient, b is the fatigue strength exponent, and ε' is the fatigue strength coefficient. f Here, c is the fatigue plasticity coefficient, c is the fatigue plasticity index, and < > are Macaulay brackets. The expression is: <x>=max{0,x}, where positive values ​​in parentheses are equal to the value itself, and negative values ​​are equal to 0.

[0021] Compared with existing technologies, this invention proposes a life assessment method that considers the multiaxial thermomechanical fatigue damage mechanism. First, the proposed method captures the characteristic information of temperature load in the multiaxial thermomechanical fatigue loading process using equivalent temperature, and proposes a temperature-dependent influence factor calculation model based on the hyperbolic tangent function, considering the influence of temperature on material damage at high temperatures. Second, a time-dependent influence factor is proposed to consider the impact of longer cycle periods and the introduction of hold time on failure life. Third, the Shang-Wang multiaxial damage model is used as the basic model to consider the influence of non-proportional additional hardening on fatigue and oxidation damage. Then, a rapid cracking influence factor is proposed to consider the influence of rapid material cracking caused by the combined effects of high temperature, tensile stress, and shear stress on multiaxial thermomechanical fatigue life. Finally, the proposed method is validated using failure life results from uniaxial isothermal fatigue tests with and without hold time, as well as uniaxial and multiaxial thermomechanical fatigue tests. The prediction error is within 2 factors, indicating that the proposed method has the potential to be applied to the failure life prediction of practical high-temperature structures, which is of great significance. Attached Figure Description

[0022] Figure 1 Geometry and dimensions of thin-walled tube specimens (all dimensions are in mm).

[0023] Figure 2 The fatigue testing system includes a heated specimen, induction coil, cooling pipe, thermocouple, and extensometer.

[0024] Figure 3 Comparison of predicted and tested lifespan results. Detailed Implementation

[0025] The present invention will be described in conjunction with the accompanying drawings.

[0026] The invention is further illustrated by the life prediction process of TC4 titanium alloy under uniaxial isothermal fatigue tests with and without holding time, as well as uniaxial and multiaxial thermomechanical fatigue tests.

[0027] The materials and testing equipment are described below:

[0028] TC4 is a medium-strength α-β titanium alloy, widely used in the manufacture of compressor disks, blades, and fans for aero engines due to its excellent overall performance. The chemical composition of TC4 material is shown in Table 1, and the heat treatment conditions are as follows: annealing at 580℃ for 2 hours; air cooling to room temperature.

[0029] Table 1. Chemical composition (wt.%) of TC4 titanium alloy

[0030]

[0031] Figure 1 The geometry and dimensions of the thin-walled tube specimens used are shown, with a straight section length of 30 mm and a wall thickness of 1 mm. All fatigue tests were conducted on an axial-torsional closed-loop servo-hydraulic testing system, such as... Figure 2 As shown. Heating of the temperature load was achieved by an RF induction coil, and cooling was achieved by a forced-air cooling pipe. Additionally, a type K thermocouple welded to the middle of the outer surface of the gauge length was used to measure temperature, and a high-temperature axial-torsional extensometer with a gauge length of 25 mm was used to measure strain. All tests were conducted in air.

[0032] Introduction to isothermal fatigue tests with and without load holding time:

[0033] Strain-controlled uniaxial fatigue tests were conducted at 200℃, 350℃, and 500℃, with and without holding time. Table 2 lists the test details and failure life results, where the axial strain amplitude Δε is... x The coefficient of performance (COP) was 1.2%, the cycle period (t) was 20 seconds, and the hold time was 120 seconds. The failure criterion for all tests was defined as a 30% reduction in the steady-state peak stress.

[0034] Table 2. Test details and life results of isothermal fatigue tests.

[0035]

[0036]

[0037] Introduction to uniaxial and multiaxial thermomechanical fatigue testing:

[0038] During multiaxial thermomechanical fatigue testing, the total axial strain and total shear strain were measured and controlled using a high-temperature axial-torsional extensometer. The total axial strain was calculated by adding the axial mechanical strain and the axial thermal strain (ε). t =ε m +ε th In this process, the axial thermal strain is calculated in real time as a function of temperature. That is, the axial mechanical strain waveform is first given, and the thermal strain at any given moment is calculated in real time based on temperature and thermal expansion. Then, the total axial strain is calculated and controlled in real time. The total shear strain is equal to the shear strain because the shear strain is unaffected by temperature changes. For uniaxial thermomechanical fatigue tests, it is necessary to control the thermal phase angle between the axial mechanical strain waveform and the temperature waveform. In multiaxial thermomechanical fatigue tests, it is necessary to control not only the thermal phase angle but also the mechanical phase angle between the axial mechanical strain waveform and the torsional shear strain waveform. The thermal phase angles are specified as 0°, 90°, and 180°, and the mechanical phase angles are specified as 0° and 90°. Therefore, three uniaxial thermomechanical fatigue loading paths are formed, including TIP, TOP, and TOP. 90 and TOP 180 And six axial-torsional thermomechanical fatigue loading paths, including MIPTIP, MIPTOP 90 MIPTOP 180 MOPTIP, MOPTOP 90 and MOPTOP 180 As shown in Table 3.

[0039] Table 3 Loading waveforms and paths of thermomechanical fatigue tests

[0040]

[0041]

[0042]

[0043] Table 4 lists the failure life results of uniaxial and multiaxial thermomechanical fatigue tests. The equivalent strain ε was calculated using the von Mises criterion. eq The equivalent amplitude Δε of all thermomechanical fatigue tests eq / 2 is 1.2%. The temperature load range is 200~500℃, the cycle period t is 120s, and the calculated temperature change rate is 5℃ / s, which can ensure the temperature uniformity of the specimen gauge length during the test.

[0044] Table 4. Test details and life results of thermomechanical fatigue tests.

[0045]

[0046]

[0047] A life assessment method considering multiaxial thermomechanical fatigue damage mechanism, the specific calculation process is as follows:

[0048] Step (1): Calculate the equivalent temperature T of the temperature load in the multiaxial thermomechanical fatigue load history. e :

[0049]

[0050] Among them, T e It is the equivalent temperature of the temperature load, T(t) i ) is t i The temperature at time t, where i is the temperature load data point count variable, and t is the temperature at time t. i It is the time corresponding to the i-th data point, where n is the number of temperature load data points, and T th It is the critical temperature;

[0051] Step (2): Based on the T calculated in step (1) e Calculate the temperature-dependent influence factor D T :

[0052]

[0053] Among them, T m It is the melting temperature of the material, α T It is a material constant expressing temperature dependence, and tanh is the hyperbolic tangent function;

[0054] Step (3): Calculate the time-dependent influence factor D t :

[0055] D t =1+α t t cyc

[0056] Among them, t cyc It is the cycle period, α t It is a material constant that expresses time dependence;

[0057] Step (4): Calculate the rapid cracking influence factor M:

[0058]

[0059] Where, σ eq For von Mises equivalent stress, σ b σ is the tensile strength of the material. x For axial stress, τ xy Shear stress;

[0060] Step (5): Based on the parameters obtained in steps (2), (3), and (4), calculate the multiaxial thermomechanical fatigue life N. f :

[0061]

[0062] Where, Δγ max It is the range of maximum shear strain on the critical surface. It is the normal strain range between the maximum shear strain reversal points on the critical surface. It is the normal mean stress on the critical surface, E is Young's modulus, σ' f ε' is the fatigue strength coefficient, b is the fatigue strength exponent, and ε' is the fatigue strength coefficient. f Here, c is the fatigue plasticity coefficient, c is the fatigue plasticity index, and <> represents Macaulay brackets. The expression is: <x>=max{0,x}, where positive values ​​in parentheses are equal to the value itself, and negative values ​​are equal to 0.

[0063] To predict the failure life of TC4 titanium alloy under multiaxial thermomechanical loading using this method, the following material constants need to be determined: fatigue material constants at room temperature, and the material's critical temperature T. th Material constant α T Material constant α t The rapid cracking factor M is also shown. The fatigue material constants of TC4 titanium alloy at room temperature are shown in Table 5.

[0064] Table 5. Fatigue material constants of TC4 at room temperature.

[0065]

[0066] Critical temperature T of TC4 titanium alloy th The temperature is 250℃, and the material constant α T The value is 1150, and the material constant α is... t The value is 0.00115, and the material's melting temperature T is... m At 1650℃, the tensile strength σ b The pressure is 910 MPa, and the rapid cracking influence factor M is 1.82.

[0067] The failure life results of uniaxial constant-temperature fatigue tests with and without load holding time, as well as uniaxial and multiaxial thermomechanical fatigue tests, were used to validate the life prediction method. The prediction error was within a factor of 2. Figure 3 As shown, satisfactory prediction results were achieved.

[0068] This invention provides a life assessment method considering the multiaxial thermomechanical fatigue damage mechanism. First, this method utilizes equivalent temperature to capture the characteristic information of temperature load in the multiaxial thermomechanical fatigue loading process and provides a temperature-dependent influence factor calculation model based on the hyperbolic tangent function, considering the influence of temperature on damage. Second, a time-dependent influence factor is used to consider the impact of longer cycle periods and the introduction of hold time on failure life. Third, the Shang-Wang multiaxial damage model is adopted to consider the influence of non-proportional additional hardening on fatigue and oxidation damage. Then, a rapid cracking influence factor is used to consider the impact of rapid material cracking caused by the combined effects of high temperature, tensile stress, and shear stress on failure life. Finally, the proposed method is validated using failure life results from uniaxial isothermal fatigue tests with and without hold time, as well as uniaxial and multiaxial thermomechanical fatigue tests. The prediction error is within 2 factors, meaning that this method can be applied to the failure life prediction of actual high-temperature structures.< / x> < / x>

Claims

1. A life assessment method considering multiaxial thermomechanical fatigue damage mechanism, characterized in that: The implementation steps of this method are as follows: Step (1): Calculate the equivalent temperature T of the temperature load in the multiaxial thermomechanical fatigue load history. e : Among them, T e It is the equivalent temperature of the temperature load, T(t) i ) is t i The temperature at time t, where i is the temperature load data point count variable, and t is the temperature at time t. i It is the time corresponding to the i-th data point, where n is the number of temperature load data points, and T th It is the critical temperature; Step (2): Based on the T calculated in step (1) e Calculate the temperature-dependent influence factor D T : Among them, T m It is the melting temperature of the material, α T It is a material constant expressing temperature dependence, and tanh is the hyperbolic tangent function; Step (3): Calculate the time-dependent influence factor D t : D t =1+a t t cyc Among them, t cyc It is the cycle period, α t It is a material constant that expresses time dependence; Step (4): Calculate the rapid cracking influence factor M: Where, σ eq For von Mises equivalent stress, σ b σ is the tensile strength of the material. x For axial stress, τ xy Shear stress; Step (5): Based on the parameters obtained in steps (2), (3), and (4), calculate the multiaxial thermomechanical fatigue life N. f : Where, Δγ max It is the range of maximum shear strain on the critical surface. It is the normal strain range between the maximum shear strain reversal points on the critical surface. It is the normal mean stress on the critical surface, E is Young's modulus, σ' f ε' is the fatigue strength coefficient, b is the fatigue strength exponent, and ε' is the fatigue strength coefficient. f Here, c is the fatigue plasticity coefficient, c is the fatigue plasticity index, and < > are Macaulay brackets. The expression is: <x> =max{0,x}, where positive values ​​in parentheses are equal to the value itself, and negative values ​​are equal to 0.< / x>

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