CN113987682A - Method for predicting probability fatigue life of gap structure of weighted coupling weakest chain model - Google Patents

Method for predicting probability fatigue life of gap structure of weighted coupling weakest chain model Download PDF

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CN113987682A
CN113987682A CN202111287109.4A CN202111287109A CN113987682A CN 113987682 A CN113987682 A CN 113987682A CN 202111287109 A CN202111287109 A CN 202111287109A CN 113987682 A CN113987682 A CN 113987682A
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fatigue
fatigue life
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朱顺鹏
吴炎来
伊枭剑
张宏伟
王喆
何金超
牛晓鹏
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University of Electronic Science and Technology of China
Beijing Institute of Technology BIT
Inner Mongolia First Machinery Group Corp
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Beijing Institute of Technology BIT
Inner Mongolia First Machinery Group Corp
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Abstract

The invention discloses a method for predicting the probability fatigue life of a notch structure of a weighted coupling weakest chain model, which is applied to the field of the structural integrity and reliability evaluation of armored vehicles and aims at solving the problem that the prior art cannot predict the fatigue life when a plastic metal structural part bears cyclic fatigue load and the notch effect and the size effect act together; the method can comprehensively represent the functions of the notch effect and the size effect at the same time, and has high service life prediction accuracy.

Description

Method for predicting probability fatigue life of gap structure of weighted coupling weakest chain model
Technical Field
The invention belongs to the field of evaluation of structural integrity and reliability of special vehicles, and particularly relates to a service life prediction technology for probability fatigue of a notch structure.
Background
The progress of science and technology injects a large amount of fresh blood into the modern weaponry industry, stimulates the rapid development of military industry manufacturing industry, and special vehicles have irreplaceable functions in the past and future battlefields as basic elements and important forces in combined operation. During research and development and manufacturing of special vehicles, the operation system is required to be convenient to operate, stable in work, safe and reliable, and can adapt to remote, all-weather and all-terrain battle environments. Under the severe working environment and high working strength, the structural integrity and reliability evaluation of the core components is necessary. Titanium alloy is applied to various weaponry because of its excellent properties such as high strength, high toughness, and titanium alloy weight is lighter than steel, has always been regarded as perfect special vehicle armor material. The titanium alloy is used as an armor material, and good effects of enhancing the protection force and reducing the weight can be achieved. In recent years, with the use of new technology and new technology, the price of the titanium alloy armor is greatly reduced, the manufacturing cost is continuously reduced, and the structural frame and part of the armor of a novel domestic and foreign special vehicle are gradually manufactured by using the titanium alloy so as to meet the development requirement of a more modern special vehicle. With the rapid development of the weapon equipment group in China in the aspects of titanium alloy large-scale part manufacturing, welding, machining and the like, a large amount of titanium alloy can be widely applied to the manufacturing of basic structures of special vehicles in the future.
With the rapid development and progress of modern military science and technology, the core components of modern various weaponry, such as special vehicles, are designed and manufactured more and more complicated, the use environment is worse, and the use requirements are continuously improved, so that higher requirements are generated on the structural integrity and the reliability. Taking a special type vehicle core component engine as an example, in the structural design thereof, in order to meet the requirements including cooling, assembly, weight reduction and the like, the section of the component in the newly proposed design scheme becomes increasingly complex, thereby causing stress concentration inevitably occurring at some positions under the action of external load. Stress concentration can promote crack initiation, and further lead to fatigue damage and crack propagation, so that the stress concentration becomes a hotspot problem in the current research field of structural integrity and fatigue life. The complex shapes of various core components lead to the occurrence of a multi-axial stress-strain state under the action of cyclic loads, so that a model established based on a laboratory sample cannot meet the requirements of fatigue analysis of the components at present, and the research on the notch effect is not complete enough and needs to be further discussed deeply. In addition, dimensional effects are also a critical factor in the design of the mechanical integrity of the structure. The development of probabilistic fatigue life prediction models and methods that take into account size and notch effects is expected to ensure the structural integrity of armored vehicle core components based on the ever more stringent requirements for structural strength and fatigue analysis.
So far, the research on the fatigue life prediction of the notch component has been deeply accumulated, researchers expect to find a method capable of reasonably characterizing the fatigue failure of a complex structure under the action of cyclic load, the current model is mainly established based on four ideas of stress, strain, energy, a critical plane, coupling energy, a critical plane and the like, wherein the stress-based method is actually established based on the relation between the fatigue life and the stress level in a fatigue test, the fatigue life is simply and conveniently operated in the actual prediction, and the method is considered to be the most direct method for the notch fatigue analysis. For the notch effect, due to the stress concentration effect, the local stress level at the surface position of the notch is usually higher, but the stress rapidly decreases along with the depth of the notch, and the unyielding part still plays a supporting role for the yielding part of the dangerous part, so that the stress strain at the dangerous point is unreasonable as the criterion of overall fatigue and failure, and for the problem, researchers provide methods such as a nominal stress method, a local stress strain method, a stress field intensity method, a critical distance theory and the like; but the nominal stress method and the local stress strain method do not consider the stress concentration at the notch, and the error of the prediction result is large; the parameters needed by a stress field intensity method and a critical distance theory are difficult to obtain.
Disclosure of Invention
In order to solve the technical problems, based on the requirement of comprehensively considering the notch effect and the size effect, the invention provides a fatigue life prediction method which is simple in calculation and can simultaneously consider the size effect and the notch effect by coupling a stress field strength normal weight function to represent the influence of the notch support effect on the basis of a weakest chain model method.
The technical scheme adopted by the invention is as follows: a probability fatigue life prediction method of a notch structure of a weighted coupling weakest chain model is characterized in that a material fatigue failure probability at different positions is corrected by adopting a weight function based on a stress field intensity method, a probability fatigue life prediction model is obtained on the basis of the weakest chain model, and the probability fatigue life prediction of the notch structure is carried out on the basis of the probability fatigue life prediction model.
The process of obtaining the probability fatigue life prediction model comprises the following steps:
s1, performing elastic-plastic finite element analysis on the component to be analyzed, and determining danger points and danger areas, wherein each danger area comprises a plurality of danger boundary units;
s2, acquiring von Mises equivalent stress peak values of all dangerous boundary units corresponding to the dangerous area in a certain stable cycle, and respectively calculating the relative stress gradients in the dangerous boundary units;
s3, marking the root of the gap as a starting point as a point A; along the direction of the maximum relative stress gradient in S2, the position of a point with the von Mises equivalent stress value of 50% of the stress value of the danger point is obtained and is marked as a point B; taking the point A as a sphere center, taking the distance between the point A and the point B as a radius of an incomplete sphere as a fatigue damage area, and extracting coordinates of all tetrahedral mesh units and von Mises equivalent stress values in the fatigue damage area;
s4, respectively calculating a weight function of each tetrahedral grid unit according to the coordinates of all the tetrahedral grid units in the fatigue damage area obtained in the step S3 and the von Mises equivalent stress values;
s5, respectively obtaining fatigue dispersion indexes K of the materials by utilizing a statistical methodNAnd characteristic fatigue life N*Respectively substituting the shape parameter and the position parameter which are two parameters of Weibull distribution;
and S6, substituting the weight function obtained in the step S4 and the Weibull distribution parameters obtained in the step S5 into the weakest chain model to obtain a probabilistic fatigue life prediction model.
The dangerous region includes all regions where local stress concentration occurs in step S1.
Step S5 of obtaining fatigue dispersion index K of materialNAnd characteristic fatigue life N*The process comprises the following steps: firstly, the non-use fatigue lives under the same stress level are arranged according to the numerical value sequence, the failure probability under the corresponding fatigue life is respectively calculated, and the fatigue life and the failure rate are subjected to linear fitting to obtain K under the stress levelNAnd N*(ii) a Solving distribution parameter K under different stress levelsNAnd N*Ultimate KNTaking the mean of the fatigue life indexes at all stress levels, and fitting the fatigue characteristic life N*And stress level σmaxThe Basquin formula: sigmamax＝a(N*)b；
Wherein a and b are material constants.
The a and the b are in fitting fatigue characteristic life N*And simultaneously obtaining.
Step S6, the probabilistic fatigue life prediction model expression is:
Figure BDA0003333298040000031
wherein N isfIs tiredFatigue life, V(i)Is the volume of the ith tetrahedral mesh cell, VΩVolume of fatigue damage region, N*And KNA weibull location parameter and a shape parameter respectively,
Figure BDA0003333298040000032
as a function of the weight of the ith tetrahedral mesh cell,
Figure BDA0003333298040000033
von Mises equivalent stress amplitude, r, of ith tetrahedral mesh unit(i)Distance of ith tetrahedral mesh unit to root of gap, theta(i)The deviation angle of the ith tetrahedral mesh unit from the direction of maximum stress gradient.
And (5) solving the failure probability of the component under different service lives according to the probability fatigue life prediction model in the step S6 to obtain a quantitative result of the service life dispersity of the component fatigue test, wherein the fatigue life of the component with the failure probability of 50% is used as a prediction result.
The weight function expression of the tetrahedral mesh unit in step S4 is:
Figure BDA0003333298040000034
wherein σa,maxThe maximum von Mises equivalent stress of the component, and R is the radius of the fatigue damage area.
The invention has the beneficial effects that: according to the method, on the basis of an initial formula of the weakest chain model for calculating the failure probability, a stress field strength normal weight function is introduced to correct the notch effect, and finally a new weakest chain model failure probability calculation formula is obtained; has the following advantages:
(1) by combining the weakest chain model suitable for the size effect and the stress field strength weight function used for representing the notch effect, the size effect and the notch effect are organically combined, the fact that the fatigue strength is usually reduced along with the increase of the size of a sample in a fatigue test can be reflected, the influence of the uneven stress distribution of the notch on the fatigue strength can be reflected, and the influence of the two on the fatigue life is comprehensively considered;
(2) the fatigue damage area definition is newly provided, the fatigue damage area under the definition can be increased along with the increase of the size of the sample, the influence of the size effect on the fatigue life can be better reflected, and the defined fatigue damage area can be directly determined through finite element analysis and does not need to be obtained through repeated tests;
(3) a weight function based on unit position and stress level is newly provided, the extraction and calculation operations are simple and convenient, and the material constant K isN,N*The fitting of a and b is simple and convenient, and the correction formula is simple; the weakest chain model corrected by the weight function has small dispersity of a prediction result and high accuracy, can be used for predicting the probability fatigue life of a notch component with any size, and has more universality.
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FIG. 1 shows the dimensions of a TC4 alloy fatigue test specimen provided by an embodiment of the invention;
wherein, FIG. 1(a) shows TC4 stress concentration coefficient KtThe stress concentration coefficient K of TC4 in fig. 1(b) is a notched specimen size of 3tA notched specimen size of 5;
FIG. 2 is a flow chart of a scheme provided by an embodiment of the present invention;
FIG. 3 is a graph showing the result of the method of the present invention applied to the quantification of the fatigue life dispersion of a titanium alloy TC4 notched part;
wherein, FIG. 3(a) shows TC4 as a stress concentration coefficient KtThe fatigue life distribution diagram of the notched test piece is 3, and fig. 3(b) shows TC4 stress concentration coefficient KtA fatigue life distribution diagram of a notch test piece which is 5;
FIG. 4 is a comparison of predicted life and test life for TC4 according to the method of the present invention.
Detailed Description
In order to facilitate the understanding of the technical contents of the present invention by those skilled in the art, the present invention will be further explained with reference to the accompanying drawings.
The fatigue test data of the TC4 material is used for verifying the model, and specifically comprises a theoretical stress concentration coefficient K t3, 5 TC4 test pieces, wherein the TC4 test piece was tested atAt room temperature, KtThe notch test piece sizes of 3 and 5 are shown in fig. 1(a) and (b), where D in fig. 1 is the sample grip diameter, D is the diameter of the sample gauge length, r is the notch radius, and θ is the notch opening angle. The TC4 material is only used as an example for illustration, and the material parameters and test data are detailed in tables 1 and 2. The danger point refers to the position with the maximum local stress, the area near the danger point is a danger area, and the danger area comprises a plurality of danger boundary units;
as shown in fig. 2, which is a flowchart of the present application, the technical solution of the present invention is: a method for predicting the probability fatigue life of a gap structure of a weighted coupling weakest chain model comprises the following steps:
s1, performing elastic-plastic finite element analysis on a component to be analyzed, and determining stress-strain distribution and a dangerous area which is possibly subjected to fatigue failure, wherein the dangerous area comprises a plurality of dangerous boundary units; as shown in table 1, the fatigue properties of the TC4 material were first determined; then adding TC4 material static parameters in finite element analysis software, and calculating and adding stress strain data points in a basic model of The nonlinear kinetic hardening (KINH) according to uniaxial fatigue parameters, wherein The stress strain data points can be obtained by a Ramberg-Osgood equation; finite element analysis is carried out on a TC4 metal test piece or member, a dangerous area is determined through stress-strain distribution, because the influence of notch effect exists, and only the position of the maximum stress or strain is unreasonable, so all areas with local stress concentration are included, and a plurality of dangerous boundary elements are determined according to the dangerous boundary elements.
In the step S1, the elastic-plastic finite element analysis of the component to be analyzed is performed according to the actual loading of the component to be analyzed, so as to determine a dangerous point and a dangerous area.
S2, acquiring equivalent stress peak values of von Mises of all dangerous boundary units corresponding to each dangerous area in a certain stable cycle, and calculating normalized relative stress gradient chi in the dangerous boundary units according to distribution of effect forces such as von Mises and the like in the dangerous boundary units near the dangerous pointselemThe specific operation of the normalization processing is as follows: make dangerous boundary unit inner phase oppositionStress gradient chielemDivided by the peak value σ of the equivalent stress of von Mises at the risk pointa，maxObtaining normalized relative stress gradient chi of each unitnor；
S3, with the notch root as a starting point, defining a path passing through the danger point along the direction of the maximum relative stress gradient obtained in the step S2 to obtain the distribution of the effect forces such as von Mises and the like in the danger boundary unit near the danger point, and further obtaining the position of the point with the equivalent stress value of the von Mises being 50% of the danger point (notch root); taking a dangerous point as a sphere center, taking the distance between the two points as a radius, taking an incomplete sphere as a fatigue damage area, extracting coordinates of all tetrahedral mesh units in the fatigue damage area and von Mises equivalent stress peak values, and respectively recording the coordinates as x(i),y(i),z(i)，σa (i)I is a unit number; regarding the sample size shown in fig. 1, the size of the tetrahedral mesh unit in the fatigue damage area is 0.025mm, in this embodiment, there are ten nodes in one tetrahedral mesh unit, and the coordinates of the ten nodes and the von Mises stress value are averaged to obtain the coordinates and the von Mises stress value of the tetrahedral mesh unit.
In practical application, the size of the grid can be valued according to practical conditions, the larger the sample size is, the larger the value of the grid sub-grid size is, and different sub-grid sizes are required to ensure that the error of the final fatigue life calculation result obtained by each sub-grid is kept within 3%.
S4, respectively calculating weight functions of all units according to the coordinates and von Mises equivalent stress values of all units in the fatigue damage area obtained in the step S3, and substituting the weight functions into the weakest chain model;
and S5, respectively obtaining the fatigue dispersion index and the fatigue distribution index of the material by using a statistical method, and respectively substituting the fatigue dispersion index and the fatigue distribution index into a shape parameter and a position parameter which are used as two parameters of Weibull distribution. The material fatigue distribution index KNAnd characteristic fatigue life N*The determination process of (2) is: firstly, the non-use fatigue lives under the same stress level are arranged according to the numerical value sequence, the failure probability under the corresponding fatigue life is respectively calculated, and the fatigue life and the failure rate are subjected to linear fitting to obtain K under the stress levelNAnd N*(ii) a Solving distribution parameter K under different stress levelsNAnd N*Ultimate KNTaking the mean of the fatigue life indexes at all stress levels, and fitting the fatigue characteristic life N*And stress level σmaxThe formula is shown in the specification, wherein a and b are material constants and can fit the fatigue characteristic life N*Simultaneously obtaining:
σmax＝a(N*)b
and S6, solving the failure probability of the component under different service lives according to the weight function and the Weibull distribution parameters obtained in the steps S4 and S5 to obtain a quantitative result of the service life dispersity of the component fatigue test, and taking the fatigue life of the component with the failure probability of 50% as a prediction result.
The implementation process of step S6 is:
a1, fatigue life prediction initial formula based on the weakest chain model is:
Figure BDA0003333298040000061
wherein N isfFor fatigue life, V0For reference sample volume, N*And KNThe Weibull position parameter and the Weibull shape parameter have different values according to different materials;
A3. respectively calculating a weight function of each unit in the fatigue damage area, wherein the calculation formula is as follows:
Figure BDA0003333298040000062
wherein
Figure BDA0003333298040000063
As a function of the weight of the ith cell,
Figure BDA0003333298040000064
r(i),θ(i)the equivalent stress amplitude of von Mises of the ith unit, the distance from the root of the gap and the maximum stressOff angle, σ, in the direction of large stress gradienta,maxR is the radius of the fatigue damage region for the maximum von mises equivalent stress of the member, which can be obtained from step S3.
A3. Based on the formula in step a1, the influence of the weight function value of each cell of the fatigue damage area point obtained in combination with step a2 on the notch effect is corrected, and the obtained new formula of the probabilistic fatigue life prediction is as follows:
Figure BDA0003333298040000071
wherein, V(i)Is the volume of the ith tetrahedral mesh cell, VΩThe volume of the fatigue damage region.
In general, when the fatigue failure probability of the component is calculated based on the stress distribution and the weakest chain model, the influence of the position of each unit on the failure probability of the unit does not need to be considered, and the inventor finds that various fatigue test phenomena show that: the unit with the same stress level is closer to a dangerous point, the failure probability is higher, and in the method, the failure probability is weighted and corrected based on the position of each unit, so that the application range of the weight function based on the stress field intensity method can be widened, and the method has general applicability when structural integrity and reliability analysis is carried out on stress concentration/notch components with any geometric shapes.
FIG. 3 is a graph showing the result of quantifying the fatigue life dispersity of the titanium alloy TC4 notch piece by applying the method of the present invention, and it can be seen from FIG. 3 that the method of the present invention better characterizes the fatigue life dispersity, and the test result is substantially in the probability dispersion band of 10% and 90% survival rate; fig. 4 is a comparison graph of the predicted life of the TC4 and the test life by the method of the present invention, and it can be seen that most of the life prediction results are within two times of the error band, which proves that the life prediction model provided by the present application obtains a better prediction effect, and the material performance parameters and fatigue test data of the TC4 are shown in tables 1 and 2:
material Property parameters of Table 1 TC4
Figure BDA0003333298040000072
TABLE 2 fatigue test data for TC4 under symmetric loading
NO. Kt σmax(MPa) Nt(Cycles) NO. Kt σmax(MPa) Nt(Cycles)
1 3 495 1606 30 3 150 262218
2 3 495 1746 31 3 150 329789
3 3 495 1955 32 3 150 389268
4 3 495 2130 33 5 275 3451
5 3 495 2707 34 5 275 5481
6 3 395 4507 35 5 275 6042
7 3 395 5054 36 5 275 8975
8 3 395 5276 37 5 275 10014
9 3 395 5738 38 5 195 8462
10 3 395 6089 39 5 195 17566
11 3 260 23661 40 5 195 18859
12 3 260 25732 41 5 195 27899
13 3 260 29215 42 5 195 33968
14 3 260 30938 43 5 165 26039
15 3 260 34203 44 5 165 28703
16 3 260 40454 45 5 165 36914
17 3 180 107629 46 5 165 54057
18 3 180 149034 47 5 165 69521
19 3 180 189367 48 5 165 76632
20 3 180 209348 49 5 95 104315
21 3 180 230963 50 5 95 129083
22 3 180 258488 51 5 95 139996
23 3 170 269842 52 5 95 159084
24 3 160 88426 53 5 95 175357
25 3 160 218544 54 5 95 222340
26 3 160 315266 55 5 95 282484
27 3 160 390066 56 5 85 343926
28 3 150 134810 57 5 85 443210
29 3 150 200539
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (8)

1. A method for predicting the probability fatigue life of a notch structure of a weighted coupling weakest chain model is characterized in that the material fatigue failure probability at different positions is corrected by adopting a weight function based on a stress field intensity method, a probability fatigue life prediction model is obtained on the basis of the weakest chain model, and the probability fatigue life of the notch structure is predicted on the basis of the probability fatigue life prediction model.
2. The method for predicting the probabilistic fatigue life of the gap structure of the weighted coupling weakest chain model as claimed in claim 1, wherein the process of obtaining the probabilistic fatigue life prediction model is as follows:
s1, performing elastic-plastic finite element analysis on the component to be analyzed, and determining danger points and danger areas, wherein each danger area comprises a plurality of danger boundary units;
s2, acquiring von Mises equivalent stress peak values of all dangerous boundary units corresponding to the dangerous area in a certain stable cycle, and respectively calculating the relative stress gradients in the dangerous boundary units;
s3, marking the root of the notch as a starting point as a point A; along the direction of the maximum relative stress gradient in S2, the position of a point with the von Mises equivalent stress value of 50% of the stress value of the danger point is obtained and is marked as a point B; taking the point A as a sphere center, taking the distance between the point A and the point B as a radius of an incomplete sphere as a fatigue damage area, and extracting coordinates of all tetrahedral mesh units and von Mises equivalent stress values in the fatigue damage area;
s4, respectively calculating a weight function of each tetrahedral mesh unit according to the coordinates of all the tetrahedral mesh units in the fatigue damage region obtained in the step S3 and the von Mises equivalent stress values;
s5, respectively obtaining fatigue dispersion indexes K of the materials by using a statistical methodNAnd characteristic fatigue life N*Respectively substituting the shape parameter and the position parameter which are two parameters of Weibull distribution;
and S6, substituting the weight function obtained in the step S4 and the Weibull distribution parameters obtained in the step S5 into the weakest chain model to obtain a probabilistic fatigue life prediction model.
3. The method for predicting probabilistic fatigue life of a gap structure based on a weighted coupled weakest chain model as claimed in claim 2, wherein the risk region of step S1 comprises all regions where local stress concentration occurs.
4. The method for predicting the fatigue life of the notch structure of the weighted coupling weakest chain model as claimed in claim 2, wherein the step S5 is to obtain the fatigue dispersion index K of the materialNAnd characteristic fatigue life N*The process comprises the following steps: firstly, the non-use fatigue lives under the same stress level are arranged according to the numerical value sequence, the failure probability under the corresponding fatigue life is respectively calculated, and the fatigue life and the failure rate are subjected to linear fitting to obtain K under the stress levelNAnd N*(ii) a Solving distribution parameter K under different stress levelsNAnd N*Ultimate KNTaking the mean of the fatigue life indexes at all stress levels, and fitting the fatigue characteristic life N*And stress level σmaxThe Basquin formula: sigmamax＝a(N*)b；
Wherein a and b are material constants.
5. The method for predicting the probabilistic fatigue life of the gap structure of the weighted coupling weakest chain model as claimed in claim 4, wherein the a and b are in the fitting fatigue feature life N*And simultaneously obtaining.
6. The method for predicting probabilistic fatigue life of a gap structure based on a weighted coupling weakest link model as claimed in claim 2, wherein the probabilistic fatigue life prediction model expression in step S6 is:
Figure FDA0003333298030000021
wherein N isfFor fatigue life, V(i)Is the volume of the ith tetrahedral mesh cell, VΩVolume of fatigue damage region, N*And KNA weibull location parameter and a shape parameter respectively,
Figure FDA0003333298030000022
is the ith four faceThe weight function of the volume grid cell is,
Figure FDA0003333298030000023
von Mises equivalent stress amplitude, r, of ith tetrahedral mesh unit(i)Distance of ith tetrahedral mesh unit to root of gap, theta(i)The deviation angle of the ith tetrahedral mesh unit from the direction of maximum stress gradient.
7. The method of claim 6, wherein the probability fatigue life prediction method of the gap structure of the weighted coupling weakest chain model,
Figure FDA0003333298030000024
the expression is as follows:
Figure FDA0003333298030000025
wherein σa,maxThe maximum von Mises equivalent stress of the component, and R is the radius of the fatigue damage area.
8. The method for predicting the probabilistic fatigue life of the gap structure of the weighted coupling weakest chain model as claimed in claim 6, wherein the probability of failure of the component under different life spans is solved according to the probabilistic fatigue life prediction model of step S6 to obtain a quantitative result of the fatigue test life dispersity of the component, and the fatigue life of the component at 50% failure probability is taken as a prediction result.
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