CN113449431B - Unloading energy-based low cycle fatigue life prediction method - Google Patents
Unloading energy-based low cycle fatigue life prediction method Download PDFInfo
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Abstract
The invention provides a low cycle fatigue life prediction method based on unloading energy, and belongs to the field of metal material fatigue life prediction. The method comprises the following steps: step 1, obtaining a strain amplitude under a given condition; step 2, substituting the strain amplitude under the given condition into a pre-established low-cycle fatigue life prediction model of the metal material to be tested, and predicting to obtain the low-cycle fatigue life of the metal material to be tested; the low cycle fatigue life prediction model of the pre-established metal material to be tested is as follows:
in the formula, N f For cycle times, ε is the amplitude of strain, A SU 、B SU 、A TU And B TU Are all coefficients, obtained by fitting. The method can provide a low cycle fatigue life prediction model with simple structure and high accuracy.
Description
Technical Field
The invention relates to a low cycle fatigue life prediction method based on unloading energy, and belongs to the field of metal material fatigue life prediction.
Background
The prediction of the fatigue life of the engineering material has great significance to the design and the application thereof. As an important structural material, the fatigue performance of a metal material is influenced by various factors, such as grain size, a second phase, texture, temperature, plastic strain amplitude, cycle frequency, external environment and the like, and the high dispersity of the fatigue performance of the metal material makes the fatigue life prediction of the metal material more difficult. In the existing fatigue life prediction methods, the energy method considers the common influence of stress and strain on the fatigue life and becomes the mainstream method for establishing the fatigue life prediction model, but the fatigue life prediction model established by the energy method is too complex, and a simple and effective low-cycle fatigue life prediction model is still lacked at present.
Disclosure of Invention
The invention aims to provide a low cycle fatigue life prediction method based on unloading energy, and can provide a low cycle fatigue life prediction model with simple structure and high accuracy.
In order to achieve the above object, the present invention provides a method for predicting a low cycle fatigue life based on unload energy, the method comprising the steps of:
the low cycle fatigue life prediction model of the pre-established metal material to be tested is as follows:
in the formula, N f For cycle times, ε is the amplitude of strain, A SU 、B SU 、A TU And B TU Are all coefficients, obtained by fitting.
The invention has the beneficial effects that: the low cycle fatigue life prediction model is simple in structure, high in accuracy and suitable for low cycle fatigue life prediction.
Further, in the above method, the low cycle fatigue life prediction model of the metal material to be measured is established by the following steps:
carrying out a plurality of low-cycle fatigue experiments under equal strain amplitude on the metal material to be tested, and recording the cycle number and the stable hysteresis curve of each low-cycle fatigue experiment; calculating single stable unloading energy and total unloading energy of each low-cycle fatigue experiment, wherein the single stable unloading energy is a load-displacement integral result of a stable hysteresis curve of each low-cycle fatigue experiment in an unloading stage, and the total unloading energy is equal to the single stable unloading energy of each low-cycle fatigue experiment multiplied by cycle times;
carrying out linear fitting on single stable unloading energy and strain amplitude of all low-cycle fatigue experiments of the metal material to be tested, and establishing a relational expression between the single stable unloading energy and the strain amplitude;
carrying out linear fitting on the total unloading energy and the cycle number of all low-cycle fatigue experiments of the metal material to be tested, and establishing a relational expression between the total unloading energy and the cycle number;
and obtaining a low cycle fatigue life prediction model of the metal material to be measured by a relational expression between the single stable unloading energy and the strain amplitude, a relational expression between the total unloading energy and the cycle number and a relational expression between the total unloading energy, the single stable unloading energy and the cycle number.
The beneficial effects of doing so are: the low-cycle fatigue life prediction model of the metal material to be detected can be established based on unloading energy, the operation is simple, and the low-cycle fatigue life prediction model of the material can be obtained by utilizing less fatigue performance data of the metal material to be detected.
Further, in the above method, the fitted relation between the single stable unloading energy and the strain amplitude is as follows: q SU ＝A SU +B SU ε, wherein Q SU Representing the single stable unload energy, epsilon being the strain amplitude, A SU Representing the intercept of a line fitting the single stable unload energy and the strain amplitude, B SU Representing the slope of a line fitting the single stable unload energy to the strain amplitude.
Further, in the above method, the fitted relation between the total unloading energy and the number of cycles is: q TU ＝A TU +B TU N f In the formula, Q TU To total unload energy, N f For the number of cycles, A TU Representing the intercept of a line fitting the total unload energy and the number of cycles, B TU Representing the slope of a line fitting the total unload energy to the number of cycles.
Further, in the above method, a least square method is adopted when linear fitting is performed on the one-time stable unloading energy and the strain amplitude.
Further, in the above method, a least square method is employed in linearly fitting the total unload energy to the number of cycles.
Further, in the above method, the stable hysteresis curve is represented by a load-displacement curve, wherein the load-displacement curve is obtained by recording load and displacement data of a low cycle fatigue test, or by converting a stress-strain curve of the low cycle fatigue test.
Drawings
FIG. 1 is a flow chart of a method for unloading energy based low cycle fatigue life prediction in an embodiment of the method of the present invention;
FIG. 2 is a schematic diagram of unloading energy under a stable hysteresis curve in an embodiment of the method of the present invention;
FIG. 3 shows Mo-1.2vol% ZrO in the example of the method of the present invention 2 A comparison graph of the actual fatigue life and the predicted fatigue life of the alloy;
FIG. 4 shows Mo-1.2vol% of Al in the example of the method of the present invention 2 O 3 Actual fatigue life and predicted fatigue life of the alloy are compared.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments.
The method comprises the following steps:
the method for predicting the low cycle fatigue life based on the unloading energy of the embodiment is shown in fig. 1, and comprises the following steps:
and 2, substituting the strain amplitude under the given condition into a pre-established low-cycle fatigue life prediction model of the metal material to be tested, and predicting to obtain the low-cycle fatigue life of the metal material to be tested.
The low cycle fatigue life prediction model of the metal material to be tested, which is established in advance, is as follows:
in the formula, N f For cycle times, ε is the amplitude of strain, A SU 、B SU 、A TU And B TU Are all coefficients, obtained by fitting.
The establishment process of the low cycle fatigue life prediction model of the metal material to be measured is described in detail as follows:
step 1): carrying out a plurality of low-cycle fatigue experiments under equal strain amplitude on the metal material to be tested, and recording the cycle number and the stable hysteresis curve of each low-cycle fatigue experiment;
the stable hysteresis curve is expressed by a load-displacement curve mode, and two obtaining methods are available, wherein one method is to directly obtain a load-displacement curve by recording load and displacement data of a low-cycle fatigue test, the other method is to record a stress-strain curve of the low-cycle fatigue test, convert the stress-strain curve into the load-displacement curve, and select one method in practical application.
Step 2): calculating single stable unloading energy and total unloading energy of each low-cycle fatigue test;
the single stable unloading energy of each low-cycle fatigue test is the load-displacement integral result of the stable hysteresis curve of each low-cycle fatigue test in the unloading stage, and assuming that the stable hysteresis curve of a certain low-cycle fatigue test is shown in fig. 2, the single stable unloading energy of the low-cycle fatigue test is equal to the load-displacement integral result of the stable hysteresis curve in the unloading stage, namely equal to the area sum of two approximate small triangles shown by the shadow in fig. 2.
According to the Miner linear accumulated damage criterion, the relationship between the total unloading energy, the single stable unloading energy and the cycle number is shown in formula (1):
Q TU ＝Q SU N f (1)
in the formula, Q TU To total discharge energy, Q SU For a single stable unloading of energy, N f Is the number of cycles.
Therefore, the total unloading energy can be estimated according to the single stable unloading energy and the cycle number of each low-cycle fatigue test by using the formula (1), and the calculation amount is reduced.
Step 3): carrying out linear fitting on single stable unloading energy and strain amplitude of all low-cycle fatigue experiments of the metal material to be tested, and establishing a relational expression between the single stable unloading energy and the strain amplitude;
in this embodiment, data analysis shows that a good linear relationship is present between the single stable unloading energy and the strain amplitude, so that the least square method is used to perform linear fitting on the single stable unloading energy and the strain amplitude of all low cycle fatigue experiments of the metal material to be measured, and a relational expression between the single stable unloading energy and the strain amplitude is obtained, as shown in formula (2):
Q SU ＝A SU +B SU ε (2)
in the formula, Q SU Representing the one-time stable unloading energy, epsilon is the strain amplitude, A SU Represents the intercept of a straight line fitting the single stable unloading energy and the strain amplitude, B SU Representing the slope of a line fitting the single stable unload energy to the strain amplitude.
As another embodiment, the least square method may be replaced with another existing linear fitting method.
And step 4): carrying out linear fitting on the total unloading energy and the cycle number of all low-cycle fatigue experiments of the metal material to be detected, and establishing a relational expression between the total unloading energy and the cycle number;
in this embodiment, data analysis shows that a good linear relationship is present between the total unloading energy and the cycle number, so that the total unloading energy and the cycle number of all low-cycle fatigue experiments on the metal material to be tested are linearly fitted by using a least square method to obtain a relational expression between the total unloading energy and the cycle number, as shown in formula (3):
Q TU ＝A TU +B TU N f (3)
in the formula, A TU Representing the intercept of a line fitting the total unload energy and the number of cycles, B TU Representing the slope of a line fitting the total unload energy to the number of cycles.
As another embodiment, the least square method may be replaced with another existing linear fitting method.
Step 5): the low cycle fatigue life prediction model can be obtained by substituting the formula (2) and the formula (3) into the formula (1), as shown in the formula (4):
after a low-cycle fatigue life prediction model of the metal material to be measured is established, the low-cycle fatigue life of the metal material to be measured under the corresponding strain amplitude can be predicted and obtained by substituting the given strain amplitude into the model.
Hereinafter, mo-1.2vol% of ZrO 2 Alloy and Mo-1.2vol% Al 2 O 3 The alloy is used as a metal material to be tested, and the effectiveness of the method is verified.
1. ZrO 2% by Mo-1.2vol% 2 Alloy as metal material to be measured
Brief introduction of experimental conditions: selecting Mo-1.2vol ZrO% 2 The alloy is used as a metal material to be tested, the experimental environment is a room-temperature air medium, the strain ratio is-1, the waveform is loaded in a triangular waveform mode, and the constant speed is 4 multiplied by 10 -3 The room temperature fatigue test is carried out at the temperature/s, the strain amplitude is 0.3 percent, 0.4 percent and 0.5 percent, and the failure criterion is sample fracture.
First, the Mo-1.2vol% ZrO 2 The establishment process of the low cycle fatigue life prediction model of the alloy comprises the following specific steps:
(1) ZrO for Mo-1.2vol% 2 The alloy is subjected to low-cycle fatigue experiments under equal strain amplitude, the cycle number and the stable hysteresis curve of each low-cycle fatigue experiment are recorded, and the data acquisition and processing results are shown in table 1:
TABLE 1Mo-1.2vol% ZrO 2 Fatigue test data of alloy
In Table 1, the strain amplitude ε is an experimental set value and the number N of cycles f Is an experimental measurement value, and the single stable unloading energy Q SU Is calculated according to a stable hysteresis curve measured by each low cycle fatigue experiment, and the total unloading energy Q TU The method is calculated by utilizing single stable unloading energy and cycle times of each low-cycle fatigue experiment according to a Miner linear accumulated damage criterion.
(2) Using least square method to pairSingle stable unload energy Q in Table 1 SU Linear fitting is carried out on the strain amplitude epsilon to obtain single stable unloading energy Q SU The relationship with the strain amplitude ε is:
Q SU ＝0.25139+36.991ε
(3) Total unload energy Q in Table 1 using least squares TU And number of cycles N f Linear fitting is carried out to obtain the total unloading energy Q TU And the number of cycles N f The relationship between them is:
Q TU ＝39.962+0.34870N f
(4) Due to single stable unloading energy Q SU And total unload energy Q TU The relationship between them follows the formula: q TU ＝Q SU N f Then simultaneous formula Q SU ＝0.25139+36.991ε、Q TU ＝39.962+0.34870N f And Q TU ＝Q SU N f I.e. obtaining Mo-1.2vol% ZrO 2 The low cycle fatigue life prediction model of the alloy is as follows:
establishment of Mo-1.2vol% ZrO 2 After modeling the low cycle fatigue life of the alloy, the model can be used to predict Mo-1.2vol ZrO at different strain amplitudes 2 The low cycle fatigue life of the alloy is predicted.
The strain amplitudes ε in Table 1 were substituted into Mo-1.2vol% of ZrO 2 Low cycle fatigue life prediction model of alloy
The effectiveness of the model is verified, the prediction result is shown in figure 3, the fitted epsilon-N curve in the figure represents the predicted service life, the 2 curve and the 1/2 curve represent a double dispersion band, the black box represents the actual experimental service life, and the average error between the actual experimental service life and the predicted service life is about 15 percent, which shows that the model can better predict Mo-1.2vol ZrO 2 The alloy has low cycle fatigue life, simple model and convenient application.
2. Al content of Mo-1.2vol% 2 O 3 Alloy as metal material to be measured
Brief introduction of experimental conditions: selecting Mo-1.2vol% of Al 2 O 3 The alloy is used as a metal material to be tested, the experimental environment is a room-temperature air medium, the strain ratio is-1, the waveform is loaded in a triangular waveform mode, and the constant speed is 4 multiplied by 10 -3 The room temperature fatigue test is carried out at the temperature/s, the strain amplitude is 0.3 percent, 0.4 percent and 0.5 percent, and the failure criterion is sample fracture.
First, the Mo-1.2vol% ZrO 2 The process for establishing the low cycle fatigue life prediction model of the alloy comprises the following specific steps:
(1) For Mo-1.2vol% of Al 2 O 3 The alloy is subjected to low-cycle fatigue experiments under equal strain amplitude, the cycle number and the stable hysteresis curve of each low-cycle fatigue experiment are recorded, and the data acquisition and processing results are shown in table 2:
TABLE 2Mo-1.2vol% Al 2 O 3 Fatigue test data of alloy
(2) Single stable unload energy Q in Table 2 using least squares SU Linear fitting is carried out on the strain amplitude epsilon to obtain single stable unloading energy Q SU The relationship with the strain amplitude ε is:
Q SU ＝0.17791+46.448ε
(3) Total unload energy Q in Table 2 using least squares TU And number of cycles N f Linear fitting is carried out to obtain the total unloading energy Q TU And the number of cycles N f The relationship between them is:
Q TU ＝90.108+0.29468N f
(4) Due to single stable unloading energy Q SU And total unload energy Q TU The relationship between them follows the formula: q TU ＝Q SU N f Then the simultaneous formula Q SU ＝0.17791+46.448ε、Q TU ＝90.108+0.29468N f And Q TU ＝Q SU N f Thus obtaining Mo-1.2vol% of Al 2 O 3 The low cycle fatigue life prediction model of the alloy is as follows:
establishment of Mo-1.2vol% of Al 2 O 3 After the low cycle fatigue life of the alloy is predicted, mo-1.2vol% of Al can be calculated for different strain amplitudes by using the model 2 O 3 The low cycle fatigue life of the alloy is predicted.
The strain magnitudes ε in Table 2 are substituted into Mo-1.2vol% of Al 2 O 3 Low cycle fatigue life prediction model of alloy
The validity of the model was verified, and the prediction results are shown in FIG. 4, in which the fitted ε -N curve represents the predicted lifetime, the × 2 curve and the × 1/2 curve represent the double dispersion band, the black square represents the actual experimental lifetime, and the average error between the actual experimental lifetime and the predicted lifetime is about 7%, indicating that the model can better predict Mo-1.2vol Al content 2 O 3 The alloy has low cycle fatigue life, simple model and convenient application.
Claims (7)
1. A low cycle fatigue life prediction method based on unloading energy is characterized by comprising the following steps:
step 1, obtaining a strain amplitude under a given condition;
step 2, substituting the strain amplitude under the given condition into a pre-established low-cycle fatigue life prediction model of the metal material to be tested, and predicting to obtain the low-cycle fatigue life of the metal material to be tested;
the low cycle fatigue life prediction model of the pre-established metal material to be tested is as follows:
in the formula, N f For the number of cycles, ε isAmplitude of strain, A SU 、B SU 、A TU And B TU Are all coefficients, obtained by fitting.
2. The unloading energy-based low cycle fatigue life prediction method according to claim 1, wherein the low cycle fatigue life prediction model of the metal material to be tested is established by the following steps:
carrying out a plurality of low-cycle fatigue experiments under equal strain amplitude on the metal material to be tested, and recording the cycle number and the stable hysteresis curve of each low-cycle fatigue experiment; calculating single stable unloading energy and total unloading energy of each low-cycle fatigue experiment, wherein the single stable unloading energy is a load-displacement integral result of a stable hysteresis curve of each low-cycle fatigue experiment in an unloading stage, and the total unloading energy is equal to the single stable unloading energy multiplied by cycle times of each low-cycle fatigue experiment;
carrying out linear fitting on single stable unloading energy and strain amplitude of all low-cycle fatigue experiments of the metal material to be tested, and establishing a relational expression between the single stable unloading energy and the strain amplitude;
carrying out linear fitting on the total unloading energy and the cycle number of all low-cycle fatigue experiments of the metal material to be tested, and establishing a relational expression between the total unloading energy and the cycle number;
and obtaining a low cycle fatigue life prediction model of the metal material to be measured by a relational expression between the single stable unloading energy and the strain amplitude, a relational expression between the total unloading energy and the cycle number and a relational expression between the total unloading energy, the single stable unloading energy and the cycle number.
3. The method of claim 2, wherein the relationship between the single stable unload energy and the strain amplitude is obtained by fitting: q SU ＝A SU +B SU ε, wherein Q SU Representing the single stable unload energy, epsilon being the strain amplitude, A SU Representing the intercept of a line fitting the single stable unload energy and the strain amplitude, B SU Representing the slope of a line fitting the single stable unload energy to the strain amplitude.
4. The method of claim 2, wherein the fitted relation between total unload energy and cycle number is: q TU ＝A TU +B TU N f In the formula, Q TU To total unload energy, N f For the number of cycles, A TU Representing the intercept of a line fitting the total unload energy and the number of cycles, B TU Representing the slope of a line fitting the total unload energy to the number of cycles.
5. The method of any one of claims 2-4, wherein a least squares method is used to linearly fit the single stable unload energy to the strain amplitude.
6. The unloading energy-based low-cycle fatigue life prediction method according to any one of claims 2-4, wherein a least square method is adopted when linearly fitting the total unloading energy to the number of cycles.
7. The unloading energy-based low-cycle fatigue life prediction method according to any one of claims 2-4, wherein the stable hysteresis curve is expressed by a load-displacement curve, wherein the load-displacement curve is obtained by recording load and displacement data of a low-cycle fatigue experiment, or by converting a stress-strain curve of the low-cycle fatigue experiment.
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