CN115329546A - Fatigue life prediction method based on critical plane equivalent energy damage parameter - Google Patents

Fatigue life prediction method based on critical plane equivalent energy damage parameter Download PDF

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CN115329546A
CN115329546A CN202210872695.7A CN202210872695A CN115329546A CN 115329546 A CN115329546 A CN 115329546A CN 202210872695 A CN202210872695 A CN 202210872695A CN 115329546 A CN115329546 A CN 115329546A
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fatigue
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equivalent energy
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陶志强
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Beijing Union University
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Abstract

The invention discloses a fatigue life prediction method based on critical plane equivalent energy damage parameters, belonging to the technical field of multi-axial fatigue strength. Step 1: obtaining a total count inverse number; step 2: calculating an axial stress correction coefficient and a shear stress correction coefficient; and 3, step 3: calculating an axial equivalent stress correction coefficient; and 4, step 4: calculating normal stress, maximum normal stress and maximum shear stress on a critical surface; and 5: obtaining a relational expression between an axial equivalent stress correction coefficient and the fatigue failure cycle number; and 6: calculating equivalent energy damage parameters based on the critical surface; and 7: sorting equivalent energy damage parameters based on the critical surface; and 8: estimating fatigue damage per cycle or iteration; and step 9: calculating total accumulated fatigue damage; step 10: the number of load blocks required for fatigue failure is determined. The method has higher fatigue life prediction precision, does not contain empirical constants, and is convenient for engineering application.

Description

Fatigue life prediction method based on critical plane equivalent energy damage parameter
Technical Field
The invention relates to the technical field of multi-axial fatigue strength, in particular to a fatigue life prediction method based on critical plane equivalent energy damage parameters.
Background
In-service mechanical components or parts can fail due to a variety of factors, fatigue, wear and fracture are common, however, more than 80% of the failure modes are fatigue-induced. For example, in various industries and fields such as aircraft engines, gas turbines, hypersonic aircrafts, pressure vessels, nuclear power plants, metallurgical machinery, power machinery, hoisting and transportation machinery, petroleum drilling equipment, railroad bridges and the like, key parts of the parts usually bear complex single-shaft, multi-shaft-proportion, multi-shaft-non-proportion and multi-shaft-amplitude-variable interaction cyclic load effects. The classical uniaxial fatigue strength theory can not meet the design requirements of fatigue strength, service life and the like of actual engineering components, so that the fatigue boundary generally pays attention to the multiaxial fatigue research which is more practical in recent years.
The multiaxial non-proportional fatigue behavior of a material is the biggest reason why the multiaxial fatigue problem is more complex than the uniaxial fatigue problem. The principal strain/stress axis rotates during multi-axis non-proportional loading, which results in changes in the material slip system and microstructure, exhibiting a non-proportional additive cycle hardening phenomenon that is not present during either single-axis or multi-axis proportional loading. The non-proportional additive hardening phenomenon complicates the material cyclic deformation behavior and fatigue damage mechanism, and also makes fatigue life estimation under non-proportional multi-axial loading difficult. Therefore, in order to ensure the safe and reliable operation of a mechanical structure and prevent property and economic losses caused by sudden fatigue damage, the research on the fatigue life prediction method based on the critical plane equivalent energy damage parameter, which is suitable for engineering application, has important engineering application value and theoretical significance.
Disclosure of Invention
The invention aims to provide a fatigue life prediction method based on critical plane equivalent energy damage parameters, which is characterized by comprising the following steps of:
step 1: counting all the repetitions by using a Wang-Brown multi-axis circulation counting algorithm to obtain a total counting repetition number n;
and 2, step: calculating an axial stress correction coefficient and a shear stress correction coefficient;
and 3, step 3: calculating the axial equivalent stress correction coefficient
Figure BDA0003757206470000011
And 4, step 4: under the working condition of uniaxial tension and compression load, calculating normal stress on a critical surface, and calculating the maximum normal stress and the maximum shear stress on the critical surface under symmetrical cyclic loading based on a Basquin-coffee-Manson equation;
and 5: obtaining an axial equivalent stress correction coefficient from the maximum normal stress and the maximum shear stress in the step 4
Figure BDA0003757206470000021
Relation between fatigue failure cycle number；
And 6: considering the additional strengthening effect of the non-proportional load path, and calculating an equivalent energy damage parameter AESA based on a critical surface;
and 7: correction coefficient of axial equivalent stress in step 5
Figure BDA0003757206470000022
Sorting the equivalent energy damage parameter AESA based on the critical surface in the step 6 by a relational expression between the fatigue failure cycle number and the fatigue failure cycle number to obtain a sorted equivalent energy damage parameter AESA';
and 8: estimating fatigue damage of each cycle or repetition by using the equivalent energy damage parameter AESA' finished in the step 7;
and step 9: calculating the total accumulated fatigue damage D by using Miner linear fatigue damage accumulation theory total ；
Step 10: determining the number of load blocks N required for fatigue failure block 。
The calculation formula of the axial stress correction coefficient in the step 2 is as follows:
Figure BDA0003757206470000023
wherein σ f ' is the axial fatigue strength coefficient, σ n,max Is the maximum normal stress on the critical plane;
the calculation formula of the shear stress correction coefficient is as follows:
Figure BDA0003757206470000024
wherein, tau f ' is the shear fatigue Strength coefficient, Δ τ max And/2 is the maximum shear stress amplitude at the critical plane.
The axial equivalent stress correction coefficient in the step 3
Figure BDA0003757206470000025
The calculation formula of (2) is as follows:
Figure BDA0003757206470000026
the normal stress calculation formula on the critical surface in the step 4 is as follows:
Figure BDA0003757206470000027
wherein σ x Is a stress tensor component;
the maximum normal stress is calculated by the formula:
Figure BDA0003757206470000028
wherein, σ' f And b is the fatigue strength coefficient and fatigue strength index, N f Is the fatigue life;
the maximum shear stress is calculated by the formula:
Figure BDA0003757206470000031
the critical plane is located at an oblique cross section of 45 °.
The equivalent energy damage parameter calculation formula in the step 6 is as follows:
Figure BDA0003757206470000032
wherein the content of the first and second substances,
Figure BDA0003757206470000033
is the axial equivalent strain amplitude on the critical surface, and the calculation formula is as follows:
Figure BDA0003757206470000034
wherein, delta gamma max /2 is the shear strain amplitude at the maximum shear plane,
Figure BDA0003757206470000035
is the virtual positive strain course between the adjacent maximum shear strain inflection points on the critical plane, and E is the modulus of elasticity.
The calculation formula of the equivalent energy damage parameter after finishing in the step 7 is as follows:
Figure BDA0003757206470000036
the calculation formula of the fatigue damage in each cycle or repetition in the step 8 is as follows:
Figure BDA0003757206470000037
wherein, N fi The ith repeated fatigue life.
Total cumulative fatigue damage D in said step 9 total The calculation formula is as follows:
Figure BDA0003757206470000038
where n is the total number of cycles or iterations.
The number of load blocks N in the step 10 block The calculation formula is as follows:
Figure BDA0003757206470000039
wherein D is fatigue damage.
The invention has the beneficial effects that:
1. the critical surface-based equivalent energy damage parameter provided by the invention can be degraded into a form of a classic Smith-Watson-Topper equation;
2. the method can consider the additional strengthening effect of the non-proportional load path, and the fatigue life prediction precision is higher;
3. the method does not contain empirical constants, and is convenient for engineering application.
Drawings
FIG. 1 is a flowchart of a fatigue life prediction method based on critical plane equivalent energy damage parameters according to the present invention;
FIG. 2 (a) shows the fatigue life and test results of 7050-T7451 aluminum alloy determined by a fatigue life prediction method based on critical plane equivalent energy damage parameters under a multi-axial amplitude load;
fig. 2 (b) shows the fatigue life and the test result of the En15R steel test piece determined by the fatigue life prediction method based on the critical plane equivalent energy damage parameter under the multi-axial amplitude load.
Detailed Description
The invention provides a fatigue life prediction method based on critical plane equivalent energy damage parameters, and the invention is further explained by combining the drawings and specific embodiments.
Fig. 1 is a flowchart of a fatigue life prediction method based on critical plane equivalent energy damage parameters, which includes the steps of:
step 1): all iterations are counted using the Wang-Brown multi-axis cycle counting algorithm to obtain a total count iteration number n.
In the multi-axis cycle counting method of Wang-Brown, the load spectrum is rearranged by first defining the maximum von Mises equivalent strain of the entire load history as the initial reference point. Then, the equivalent relative strain of the subsequent point with respect to the reference point is calculated. Once the equivalent relative strain no longer monotonically increases, a drop occurs, and the load between the reference point and the point at which the equivalent relative strain drops is counted as a half cycle (or iteration). And defining the descending point as a new relative reference point, repeating the previous process to continue counting the latter half cycle, and finally determining all counting iterations of the whole load process. The calculation formula of von Mises equivalent strain in the Wang-Brown multiaxial cycle counting method is as follows:
Figure BDA0003757206470000041
wherein, v eff Is the effective Poisson's ratio, epsilon x (t)、ε y (t)、ε z (t) is the normal stress of the coordinate axis corresponding to the moment t respectively; gamma ray xy 、γ yz 、γ xz Respectively, the shear strain of the coordinate axis corresponding to the time t.
time t relative to t r Relative equivalent strain at time of day
Figure BDA0003757206470000042
The calculation formula of (2) is as follows:
Figure BDA0003757206470000043
Figure BDA0003757206470000051
wherein the corresponding strain ε in formula (2) r x (t)，ε r y (t)，ε r z (t)，
Figure BDA0003757206470000052
The calculation expressions of (a) are respectively: epsilon r x (t)＝ε x (t)-ε x (t r )，ε r y (t)＝ε y (t)-ε y (t r )，ε r z (t)＝ε z (t)-ε z (t r )，
Figure BDA0003757206470000053
ε ij (t r ) Is t r The strain tensor of the time point.
Stress tensor σ ij The expression of (a) is as follows:
Figure BDA0003757206470000054
tensor σ of visible stress ij Contains 6 components, each of which is σ x ，σ y ，σ z ，τ xy ，τ yz ，τ xz 。
Stress tensor epsilon ij The expression of (c) is as follows:
Figure BDA0003757206470000055
visible stress tensor epsilon ij Comprising 6 components, each being ε x ，ε y ，ε z ，γ xy ，γ yz ，γ xz 。
Step 2): the axial stress correction factor and the shear stress correction factor can be calculated for each counting iteration by the following equations:
Figure BDA0003757206470000056
Figure BDA0003757206470000057
wherein, σ' f And τ' f Respectively axial fatigue strength coefficient and shear fatigue strength coefficient, sigma n,max And Δ τ max And/2 is the maximum normal stress and maximum shear stress amplitude on the critical plane.
Step 3): proposed axial equivalent stress correction factor
Figure BDA0003757206470000058
This can be calculated by the following formula:
Figure BDA0003757206470000059
step 4): under the working condition of uniaxial tension and compression load, the critical plane is positioned at an oblique section of 45 degrees, and the normal stress on the critical plane can be expressed as the following formula:
Figure BDA00037572064700000510
based on the Basquin-coffee-Manson equation, the maximum normal stress on the critical surface under the symmetrical cyclic loading can be expressed as the following formula:
Figure BDA0003757206470000061
wherein, σ' f And b is the fatigue strength coefficient and fatigue strength index, N f Is the fatigue life;
similarly, the maximum shear stress at the critical plane under symmetric cyclic loading can be expressed as:
Figure BDA0003757206470000062
and step 5): substituting equations (9) and (10) into equation (7) can obtain the axial equivalent stress correction coefficient
Figure BDA0003757206470000063
Relation (11) with fatigue failure cycle number:
Figure BDA0003757206470000064
step 6): the equivalent energy damage parameter based on the critical surface is provided as follows:
Figure BDA0003757206470000065
wherein the content of the first and second substances,
Figure BDA0003757206470000066
is the axial equivalent strain amplitude on the critical plane, and adopts a stretching type Shang-Wang multiaxialFatigue damage parameter
Figure BDA0003757206470000067
The expression of the stretching type Shang-Wang multiaxial fatigue damage parameter is as follows:
Figure BDA0003757206470000068
wherein, delta gamma max /2 is the shear strain amplitude at the maximum shear plane,
Figure BDA0003757206470000069
is the virtual positive strain course between adjacent maximum shear strain inflection points on the critical plane, and E is the modulus of elasticity.
Step 7): substituting equations (11) and (13) into equation (12) may determine the following relationship:
Figure BDA00037572064700000610
multiplication of equal sign of equation (14) on both sides
Figure BDA00037572064700000611
After the arrangement, equation (15) can be obtained:
Figure BDA00037572064700000612
step 8) estimating fatigue damage of each cycle (or repetition) by adopting a notched part fatigue life prediction method based on a load control mode
Figure BDA0003757206470000071
N fi Is the i-th repeated fatigue life calculated by the formula (15);
step 9) calculating the total accumulated fatigue damage D by utilizing Miner linear fatigue damage accumulation theory total ：
Figure BDA0003757206470000072
Wherein n is the total number of cycles (or iterations);
step 10) determining the number N of load blocks required for fatigue failure block ：
Figure BDA0003757206470000073
Under the proportional multi-axis cyclic load, the stretching type Shang-Wang multi-axis fatigue damage parameter can be degraded into an equivalent strain amplitude
Figure BDA0003757206470000074
And, under uniaxial tension and compression load, the tensile type Shang-Wang multiaxial fatigue damage parameter can be degraded into an axial strain amplitude
Figure BDA0003757206470000075
And, under symmetrical cyclic loading, σ n,max /σ′ f And Δ τ max /(2·τ′ f ) Can be expressed as:
Figure BDA0003757206470000076
Figure BDA0003757206470000077
then proposed axial equivalent stress correction factor
Figure BDA0003757206470000078
This can be calculated by the following formula:
Figure BDA0003757206470000079
thus, the equivalent energy damage parameters based on the critical plane are as follows:
Figure BDA00037572064700000710
the equal sign of the pair (24) is divided by the equal sign
Figure BDA00037572064700000711
After work-up the following formula can be obtained:
Figure BDA00037572064700000712
therefore, the critical plane-based equivalent energy damage parameter can be degenerated into the form of the classical Smith-Watson-Topper equation.
In order to verify the fatigue life prediction method based on the critical plane equivalent energy damage parameter, the obtained prediction result is compared with the fatigue test results of the En15R steel and the 7050-T7451 aluminum alloy test piece, as shown in fig. 2 (a) and 2 (b).
The experimental data are derived from the following documents:
[1]Wang CH,Brown MW.Life prediction techniques for variable amplitude multiaxial fatigue–Part I:Theories.J.Eng.Mater.Technol.–Trans.ASME 1996；118(3):367–70.
[2]Chen H,Shang DG,Tian YJ,Liu JZ.Comparison of multiaxial fatigue damage models under variable amplitude loading.J Mech Sci Technol 2012；26(11):3439–46.
test verification results show that the fatigue life prediction results are mostly within a factor of 2 times (the prediction results are between 0.5 times and 2 times of the experimental results). Therefore, the fatigue life prediction method can better predict the fatigue life under the multi-axial variable amplitude load, does not contain empirical constants, and is convenient for engineering application.
The present invention is not limited to the above embodiments, and any modifications or alterations that can be easily conceived by those skilled in the art within the technical scope of the present invention are intended to be covered by the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (10)

1. The fatigue life prediction method based on the critical plane equivalent energy damage parameter is characterized by comprising the following steps:
step 1: counting all the iterations by using a Wang-Brown multi-axis circulation counting algorithm to obtain a total counting iteration number n;
step 2: calculating an axial stress correction coefficient and a shear stress correction coefficient;
and step 3: calculating the axial equivalent stress correction coefficient
Figure FDA0003757206460000011
And 4, step 4: under the working condition of uniaxial tension and compression load, calculating normal stress on a critical surface, and calculating the maximum normal stress and the maximum shear stress on the critical surface under symmetrical cyclic loading based on a Basquin-coffee-Manson equation;
and 5: obtaining an axial equivalent stress correction coefficient from the maximum normal stress and the maximum shear stress in the step 4
Figure FDA0003757206460000012
A relationship to the number of fatigue failure cycles;
and 6: considering the additional strengthening effect of the non-proportional load path, and calculating an equivalent energy damage parameter AESA based on the critical plane;
and 7: correction coefficient of axial equivalent stress in step 5
Figure FDA0003757206460000013
Sorting the equivalent energy damage parameter AESA based on the critical surface in the step 6 by a relational expression between the fatigue failure cycle number and the fatigue failure cycle number to obtain a sorted equivalent energy damage parameter AESA';
and 8: estimating fatigue damage of each cycle or repetition by using the equivalent energy damage parameter AESA' finished in the step 7;
and step 9: calculating the total accumulated fatigue damage D by using Miner linear fatigue damage accumulation theory total ；
Step 10: determining the number of load blocks N required for fatigue failure block 。
2. The fatigue life prediction method based on the critical plane equivalent energy damage parameter as claimed in claim 1, wherein the calculation formula of the axial stress correction coefficient in step 2 is:
Figure FDA0003757206460000014
wherein, σ' f Is the axial fatigue strength coefficient, σ n,max Is the maximum normal stress on the critical plane;
the calculation formula of the shear stress correction coefficient is as follows:
Figure FDA0003757206460000015
wherein, tau' f Is the shear fatigue strength coefficient, Δ τ max And/2 is the maximum shear stress amplitude at the critical plane.
3. The fatigue life prediction method based on critical plane equivalent energy damage parameters as claimed in claim 1, wherein the axial equivalent stress correction coefficient in step 3
Figure FDA0003757206460000021
The calculation formula of (2) is as follows:
Figure FDA0003757206460000022
4. the fatigue life prediction method based on the critical plane equivalent energy damage parameter as claimed in claim 1, wherein the normal stress calculation formula on the critical plane in step 4 is as follows:
Figure FDA0003757206460000023
wherein σ x Is a stress tensor component;
the maximum normal stress is calculated by the formula:
Figure FDA0003757206460000024
wherein, σ' f And b is the fatigue strength coefficient and fatigue strength index, N f Is the fatigue life;
the maximum shear stress is calculated by the formula:
Figure FDA0003757206460000025
5. the fatigue life prediction method based on the critical plane equivalent energy damage parameter according to claim 1 or 4, wherein the critical plane is located at a 45 ° oblique section.
6. The method for predicting fatigue life based on critical plane equivalent energy damage parameters according to claim 1, wherein the equivalent energy damage parameter calculation formula in the step 6 is as follows:
Figure FDA0003757206460000026
wherein the content of the first and second substances,
Figure FDA0003757206460000027
is the axial equivalent strain amplitude on the critical plane, and the calculation formula is as follows:
Figure FDA0003757206460000031
wherein, delta gamma max /2 is the shear strain amplitude at the maximum shear plane,
Figure FDA0003757206460000032
is the virtual positive strain course between adjacent maximum shear strain inflection points on the critical plane, and E is the modulus of elasticity.
7. The fatigue life prediction method based on the critical plane equivalent energy damage parameter as claimed in claim 1, wherein the equivalent energy damage parameter calculation formula after being sorted in step 7 is:
Figure FDA0003757206460000033
8. the method for predicting fatigue life based on critical plane equivalent energy damage parameters according to claim 1, wherein the calculation formula of fatigue damage in each cycle or iteration in the step 8 is as follows:
Figure FDA0003757206460000034
wherein, N fi The ith repeated fatigue life.
9. The method for predicting fatigue life based on critical plane equivalent energy damage parameter as claimed in claim 1, wherein the total accumulated fatigue damage D in step 9 total The calculation formula is as follows:
Figure FDA0003757206460000035
where n is the total number of cycles or iterations.
10. The method for predicting fatigue life based on critical plane equivalent energy damage parameter according to claim 1, wherein the number of load blocks N in step 10 is N block The calculation formula is as follows:
Figure FDA0003757206460000036
wherein D is fatigue damage.
CN202210872695.7A 2022-07-21 2022-07-21 Fatigue life prediction method based on critical plane equivalent energy damage parameter Pending CN115329546A (en)

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