CN115329544A - Fatigue life prediction method under multi-axis variable amplitude load - Google Patents
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Abstract
The invention discloses a method for predicting fatigue life under multi-axial variable amplitude load, belonging to the technical field of multi-axial fatigue strength. The method comprises the following steps: step 1: counting all the counting times by using a Wang-Brown multi-axis circulation counting algorithm to obtain a total counting repetition number n; and 2, step: calculating an axial equivalent stress amplitude on the critical plane in each counting iteration; and 3, step 3: considering the additional strengthening effect of the non-proportional load path, calculating an equivalent energy damage parameter (EBDP) on a critical surface in each counting iteration; and 4, step 4: estimating fatigue damage per cycle or repetition; and 5: calculating the total accumulated fatigue damage D by using Miner linear fatigue damage accumulation theory total (ii) a And 6: determining the number of load blocks N required for fatigue failure block . The method can consider the additional strengthening effect of the non-proportional load path, and the fatigue life prediction precision is higher; and the method does not contain empirical constants, and is convenient for engineering application.
Description
Technical Field
The invention relates to the technical field of multi-axial fatigue strength, in particular to a fatigue life prediction method under a multi-axial variable amplitude load.
Background
Fatigue fracture is a major cause of failure in many mechanical structural and engineering components, and typical components of many engineering machines, such as trains, automobiles, aerospace vehicles, and the nuclear industry, are subjected to complex multi-axis variable amplitude loading or to complex single axis, multi-axis proportional, multi-axis non-proportional alternating cyclic loading. The classical uniaxial fatigue strength theory is far from meeting the design requirements of strength, service life and the like of actual engineering components. Therefore, in recent years, the fatigue community generally pays attention to the more practical multi-axial fatigue research.
The biggest reason why the multi-axial fatigue problem is complicated compared to the single-axial fatigue problem is the multi-axial non-proportional fatigue behavior of the material. The main strain/stress axis rotates in the multi-axis non-proportional loading process, which causes the microstructure and the slip system of the material to change, and shows the non-proportional additional cyclic strengthening phenomenon which does not exist in the single-axis or multi-axis proportional loading process. The non-proportional additional strengthening phenomenon complicates the cyclic constitutive relation of the materials and also makes the fatigue life estimation under multi-axis non-proportional loading difficult. Therefore, in order to ensure the safe and reliable operation of a mechanical structure and prevent the economic and property loss caused by sudden fatigue damage, the research on the fatigue life prediction method under the multi-axial amplitude load suitable for engineering application has important theoretical significance and engineering application value.
Disclosure of Invention
The invention aims to provide a method for predicting fatigue life under multi-axis variable amplitude load, which is characterized by comprising the following steps of:
step 1: counting all the repeated counting by using a Wang-Brown multi-axis circulation counting algorithm to obtain a total counting repetition number n;
and 2, step: calculating an axial equivalent stress amplitude on the critical plane in each counting iteration;
and step 3: considering the additional strengthening effect of the non-proportional load path, calculating an equivalent energy damage parameter (EBDP) on a critical surface in each counting iteration;
and 4, step 4: estimating fatigue damage per cycle or repetition;
and 5: calculating the total accumulated fatigue damage D by using Miner linear fatigue damage accumulation theory total ；
And 6: determining the number of load blocks N required for fatigue failure block 。
The calculation formula of the axial equivalent stress amplitude on the critical surface in the step 2 is as follows:
wherein, Δ τ max The/2 is the shear stress amplitude at the critical plane,
is the critical planeThe normal stress variation between the upper adjacent maximum shear stress folding points is calculated by the following expression:
wherein, t begin And t finish Respectively used for representing the starting point and the ending point corresponding to the adjacent maximum shear strain reentrant points,
and
respectively used to represent the time interval t begin ,t finish ]Maximum and minimum values of internal normal stress.
The calculation formula of the equivalent energy damage parameter EBDP on the critical plane in step 3 is as follows:
wherein, σ' f Is the fatigue strength coefficient; e is the modulus of elasticity; epsilon' f Is the fatigue ductility coefficient; b is the fatigue strength index; c is fatigue ductility index; n is a radical of f Fatigue life is considered;
is the axial equivalent strain amplitude on the critical surface, and the calculation formula is as follows:
wherein, delta gamma max /2 is the shear strain amplitude at the maximum shear plane,
is the adjacent maximum shear strain fracture on the critical planeA virtual positive strain course between return points.
The fatigue damage calculation formula in the step 4 is as follows:
wherein, N fi The ith repeated fatigue life.
The calculation formula of the total accumulated fatigue damage in the step 5 is as follows:
where n is the total number of cycles or iterations.
The calculation formula of the number of the load blocks in the step 6 is as follows:
wherein D is fatigue damage.
The invention has the beneficial effects that:
1. the critical surface-based equivalent energy damage parameter in the invention can be degenerated into the 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 flow chart of a method for fatigue life prediction under multi-axial variable amplitude loading in accordance with the present invention;
FIG. 2 is a graph showing the normal stress variation course between adjacent maximum shear stress inflection points on the critical plane of the present invention
A schematic view;
FIG. 3 (a) is a graph of fatigue life and test results for 7050-T7451 aluminum alloy determined by the method of the present invention;
FIG. 3 (b) shows the fatigue life of En15R steel test piece determined by the method of the present invention and the test results.
Detailed Description
The invention provides a method for predicting fatigue life under multi-axis variable amplitude load, which is further explained by combining the attached drawings and specific embodiments.
FIG. 1 is a flow chart of a fatigue life prediction method under multi-axial variable amplitude load according to the present invention; the method comprises the following specific steps:
step 1): all iterations were counted using the Wang-Brown multi-axis cycle counting algorithm to obtain the 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:
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 The shear strain of the coordinate axis at time t is shown.
time t relative to t r Relative equivalent strain at time
The calculation formula of (2) is as follows:
wherein, the corresponding variation epsilon in the formula (2) r x (t)，ε r y (t)，ε r z (t)，
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 )，
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:
tensor σ of visible stress ij Containing 6 components, each being σ x ，σ y ，σ z ，τ xy ，τ yz ，τ xz 。
Stress tensor epsilon ij The expression of (a) is as follows:
visible stress tensor epsilon ij Containing 6 components, each of ε x ，ε y ，ε z ，γ xy ，γ yz ，γ xz 。
Step 2): in each counting iteration, the axial equivalent stress amplitude on the critical plane can be calculated by the formula provided herein, and the calculation formula of the axial equivalent stress amplitude on the critical plane is as follows:
wherein, Δ τ max The/2 is the shear stress amplitude on the critical plane,
is the normal stress variation between the adjacent maximum shear stress folding points on the critical plane, and fig. 2 is a schematic diagram of the normal stress variation between the adjacent maximum shear stress folding points on the critical plane;
this can be calculated by the following expression:
wherein, t begin And t finish Respectively used for representing the starting point and the ending point corresponding to the adjacent maximum shear strain reentrant points,
and
respectively used to represent the time interval t begin ,t finish ]Maximum and minimum values of internal normal stress.
Step 3): in each counting iteration, the equivalent energy damage on the critical plane can be determined by the damage parameter set forth herein, and the calculation formula of the equivalent energy damage parameter EBDP on the critical plane is as follows:
wherein, σ' f Is the fatigue strength coefficient; epsilon' f Is the fatigue ductility coefficient; b is the fatigue strength index; c is the fatigue ductility index;
is the axial equivalent strain amplitude on the critical surface, and adopts a stretching type Shang-Wang multiaxial fatigue damage parameter
The expression of the stretching type Shang-Wang multiaxial fatigue damage parameter is as follows:
wherein, delta gamma max /2 is the shear strain amplitude at the maximum shear plane,
is the virtual positive strain course between adjacent maximum shear strain inflection points on the critical plane.
Step 4) estimating fatigue damage of each cycle (or repetition) by using multi-axial amplitude fatigue life prediction method based on equivalent energy critical surface damage parameters
N fi Is the ith repeated fatigue life calculated by the formula (8);
step 5) calculating the total accumulated fatigue damage D by using Miner linear fatigue damage accumulation theory total ：
Wherein n is the total number of cycles (or iterations);
step 6) determining the number N of load blocks required by fatigue failure block ：
Under proportional multi-axis cyclic load, the tensile type Shang-Wang multi-axis fatigue damage parameter can be degraded into an equivalent strain amplitude
And, under uniaxial tension and compression loads, the tensile type Shang-Wang multiaxial fatigue damage parameter can be degraded into an axial strain amplitude
Under the condition of the symmetrical cyclic load, the load is balanced,
and Δ τ max The/2 can be expressed as:
then proposed axial equivalent stress correction factor
This can be calculated by the following formula:
thus, the critical plane-based equivalent energy damage parameter EBDP can be expressed as follows:
therefore, the critical plane-based equivalent energy damage parameter proposed by the present invention can be degenerated into the form of the classical Smith-Watson-Topper equation.
The test of the embodiment is a multi-axial amplitude-variation fatigue test, and the verified materials are En15R steel and 7050-T7451 aluminum alloy. The experimental data are from the following two references:
[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.
and comparing the prediction result obtained by the method with the fatigue test results of En15R steel and 7050-T7451 aluminum alloy test pieces. As shown by the experimental verification results of fig. 3 (a) and fig. 3 (b), the fatigue life prediction results are mostly within a factor of 2 (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 amplitude variation load.
In the embodiment, the additional strengthening effect of the non-proportional load path is considered, so that the fatigue life prediction precision is higher; and the method does not contain empirical constants, and is convenient for engineering application.
The present invention is not limited to the above embodiments, and any changes or substitutions that can be easily made by those skilled in the art within the technical scope of the present invention are also within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (6)
1. A fatigue life prediction method under a multi-axis variable amplitude load is characterized by comprising the following steps:
step 1: counting all the counting times by using a Wang-Brown multi-axis circulation counting algorithm to obtain a total counting repetition number n;
and 2, step: calculating an axial equivalent stress amplitude on the critical plane in each counting iteration;
and 3, step 3: considering the additional strengthening effect of the non-proportional load path, calculating an equivalent energy damage parameter EBDP on the critical surface in each counting iteration;
and 4, step 4: estimating fatigue damage per cycle or iteration;
and 5: calculating the total accumulated fatigue damage D by using Miner linear fatigue damage accumulation theory total ；
Step 6: determining the number of load blocks N required for fatigue failure block 。
2. The method for predicting the fatigue life under the multi-axial variable amplitude load according to claim 1, wherein the calculation formula of the axial equivalent stress amplitude on the critical surface in the step 2 is as follows:
wherein, Δ τ max The/2 is the shear stress amplitude on the critical plane,
the normal stress variation range between the adjacent maximum shear stress folding points on the critical surface is calculated by the following expression:
wherein, t begin And t finish Respectively used for representing the starting point and the ending point corresponding to the adjacent maximum shear strain reentrant points,
and
respectively used to represent the time interval t begin ,t finish ]Maximum and minimum values of internal normal stress.
3. The method for predicting the fatigue life under the multi-axial variable amplitude load according to claim 1, wherein the calculation formula of the equivalent energy damage parameter EBDP on the critical surface in the step 3 is as follows:
wherein, σ' f Is the fatigue strength coefficient; e is the modulus of elasticity; epsilon' f Is the fatigue ductility coefficient; b is the fatigue strength index; c is the fatigue ductility index; n is a radical of hydrogen f Fatigue life is considered;
is the axial equivalent strain amplitude on the critical surface, and the calculation formula is as follows:
wherein, delta gamma max /2 is the shear strain amplitude at the maximum shear plane,
is the virtual positive strain course between the adjacent maximum shear strain inflection points on the critical plane.
4. The method for predicting the fatigue life under the multi-axial amplitude load according to claim 1, wherein the fatigue damage calculation formula in the step 4 is as follows:
wherein, N fi The ith repeated fatigue life.
5. The method for predicting fatigue life under multiaxial variable amplitude load as recited in claim 1, wherein the total cumulative fatigue damage calculation formula in the step 5 is as follows:
where n is the total number of cycles or iterations.
6. The method for predicting the fatigue life under the multi-axial amplitude load according to claim 1, wherein the calculation formula of the number of the load blocks in the step 6 is as follows:
wherein D is fatigue damage.
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| CN115828628A (en) * | 2022-12-27 | 2023-03-21 | 南京航空航天大学 | Method for calculating residual life of multistage amplitude-variable fatigue loading |
| CN116595654A (en) * | 2023-02-28 | 2023-08-15 | 南京航空航天大学 | Multi-axis fatigue test spectrum compiling method based on genetic algorithm |
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| CN111680436A (en) * | 2020-05-09 | 2020-09-18 | 清华大学 | Notch part fatigue life prediction method and prediction device based on main load mode |
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