CN113919079A - Probability fatigue life prediction method for coupling notch and size effect - Google Patents

Probability fatigue life prediction method for coupling notch and size effect Download PDF

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CN113919079A
CN113919079A CN202111287209.7A CN202111287209A CN113919079A CN 113919079 A CN113919079 A CN 113919079A CN 202111287209 A CN202111287209 A CN 202111287209A CN 113919079 A CN113919079 A CN 113919079A
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fatigue life
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notch
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朱顺鹏
何金超
伊枭剑
刘勇
王喆
廖鼎
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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Abstract

The invention discloses a probability fatigue life prediction method for coupling notch and size effect, which is applied to the field of structure strength check and reliability evaluation of armored vehicles. In order to solve the problem of fatigue life prediction of a metal structural part under the combined action of a notch, a size effect and uncertainty, the invention establishes a metal structural part probability fatigue life prediction method comprehensively considering the notch and the size effect by coupling a high stress volume (area) method and Weibull distribution; the method is based on a high stress volume (area) method and is matched with a fatigue failure mechanism; the fatigue life dispersity is quantified based on Weibull distribution, so that the uncertainty of the material can be effectively covered, and the design requirement of fatigue reliability is met; the combination of the volume method and the area method ensures that the method provided by the invention has universality to any failure mode, is simple and convenient to operate and has wide application range.

Description

Probability fatigue life prediction method for coupling notch and size effect
Technical Field
The invention belongs to the field of structural strength checking and reliability evaluation of armored vehicles, and particularly relates to a technology for predicting the probability fatigue life of a notch piece.
Background
As a basic element and important strength of combined operation, the role of armored vehicles on the battlefield cannot be replaced. With the future battlefield becoming more complex and variable, higher requirements are put forward on the comprehensive performance of armored vehicles, and the improvement of the comprehensive performance means stricter requirements on reliability indexes. The reasonable material selection is the key for guaranteeing the service reliability of the vehicle, and the titanium alloy material has the properties of high strength, high toughness, portability and the like and is considered as a perfect armor material. In recent years, with the popularization and application of new technology and new technology, the manufacturing cost of the titanium alloy armored vehicle is continuously reduced, and a structural frame and part of armors of the novel armored vehicle at home and abroad are gradually manufactured by using the titanium alloy so as to meet the modern development requirement of the armored vehicle. With the gradual success of the weapon equipment group in the technical attack and customs achievements of the fields of titanium alloy large-scale part manufacturing, welding, machining and the like, a large amount of titanium alloy can be widely applied to armored vehicles in the future.
Fatigue fracture is one of the major failure modes of critical components of armored vehicles, and once it occurs, will directly affect the arming efforts. As the functional requirements of armored vehicles become more complex, critical components thereof inevitably contain different types of notches and geometric discontinuities (e.g., holes, keys, grooves, etc.) and often exhibit complex stress/strain conditions in service, with fatigue failure readily beginning from such characteristics. Accurate analysis of the impact of notch effects on fatigue strength is critical to the structural strength analysis and integrity assessment of armored vehicles. Due to the limitation of test cost and conditions, the full-scale test of key parts of the armored vehicle is difficult, so that the derivation of the fatigue performance of the actual parts based on the fatigue test data of small-size samples is important. In addition, structural fatigue failure processes tend to exhibit strong uncertainty due to the objective presence of material uncertainty. Therefore, the method for predicting the fatigue life of the notch structure is deeply explored based on the small-size test piece, a set of fatigue life prediction method and analysis flow considering the notch, the size effect and the uncertainty are provided and popularized to engineering application, and the method has important theoretical significance and engineering value.
So far, there has been a deep accumulation in studies on the prediction of fatigue life of notched parts. The existing model is mainly established based on the ideas of stress, strain, energy, critical plane, coupling energy, critical plane and the like, wherein the stress-based method is simple and convenient to operate in practical application and is considered to be the most direct and simple method for analyzing the notch fatigue. For the notch effect, the local stress level on the notch surface is often higher due to the stress concentration. However, from the outside to the inside, the stress drops rapidly. In this case, the unyielding part still supports the yielding part, so that it is not reasonable to use only the stress at the risk point as the criterion for the overall fatigue strength. In response to this, researchers have proposed methods such as a nominal stress method, a stress field intensity method, and a critical distance theory. However, the nominal stress method is too conservative, and the stress field intensity method and the critical distance theory have the problem that the required parameters are difficult to obtain.
Disclosure of Invention
In order to solve the technical problems, the invention provides a probabilistic fatigue life prediction method for coupling notch and size effects, which couples a high stress volume (area) method and Weibull distribution to obtain a model with higher accuracy of prediction results.
The technical scheme adopted by the invention is as follows: a probabilistic fatigue life prediction method for coupling notch and size effects comprises the following steps:
s1, carrying out finite element analysis on notch samples with different sizes, and determining a potential fatigue failure dangerous area, wherein the potential fatigue failure dangerous area comprises a plurality of dangerous nodes;
s2, extracting the maximum main stress peak values of all danger nodes in the danger area, and calculating high stress volumes and high stress areas of the notch samples with different sizes according to the maximum main stress peak values;
s3, respectively establishing fatigue life conversion formulas among the notch samples with different sizes based on the high stress volume and the high stress area obtained in the step S2;
s4, acquiring a fatigue life dispersion index k and a characteristic fatigue life N of materials used by notch samples with different sizes based on a statistical method, and taking the fatigue life dispersion index k and the characteristic fatigue life N as shape and position parameters of two parameters of Weibull distribution;
and S5, predicting the fatigue life of the component based on the fatigue life conversion formula obtained in the step S3 and the Weibull distribution parameter obtained in the step S4.
The finite element analysis described in step S1 is a linear elastic analysis without considering plastic deformation.
The hazardous area of step S1 includes all nodes having stress values greater than or equal to 60% of the maximum primary stress value.
The high stress nodes of step S2 include all nodes having a stress value greater than or equal to 90% of the maximum primary stress value.
In step S2, the calculation formula of the high stress volume is:
Figure BDA0003333341620000021
wherein V is the high stress volume of a notch sample with a certain size, VrVolume of dangerous area of specimen with a certain size gap, Nh,vNumber of high stress nodes for a notch specimen of a certain size, Nr,vThe total number of nodes in the high stress area of the notch sample with a certain size is shown. In finite element simulation calculation Nh,vAnd Nr,vAnd meanwhile, the size of the whole grid of the research object is required to be ensured to be consistent.
In step S2, the calculation formula of the high stress area is:
Figure BDA0003333341620000022
wherein A is the high stress area of a notch sample with a certain size, and ArSurface area of dangerous area of specimen with certain size gap, Nh,sNumber of high stress nodes on surface of dangerous area of sample with certain size of notch, Nr,sThe total number of surface nodes in the dangerous area of the notch sample with a certain size is shown. In finite element simulation calculation Nh,sAnd N,sAnd meanwhile, the size of the whole grid of the research object is required to be ensured to be consistent.
Step S3 shows the fatigue life conversion formula as follows:
Figure BDA0003333341620000031
Figure BDA0003333341620000032
wherein N is1、N2For the fatigue life of two specimens with notches of different sizes, V1、V2For two differently dimensioned notched specimens with high stress volumes, A1、A2For two notch specimens of different dimensions, high stress area, beta1、β2Are fitting parameters.
The step S4 is specifically implemented as follows:
firstly, sequencing the fatigue lives under the same stress amplitude according to the magnitude of the numerical values, respectively calculating the failure probability corresponding to each fatigue life, and performing linear fitting on the fatigue lives and the failure probabilities to obtain k and N under the stress amplitude;
secondly, solving k and N under different stress amplitudes;
finally, k is the mean value of all stress amplitudes;
the fatigue characteristic life N is found based on the following formula:
σa＝a(N)b
wherein a and b are curve fitting parameters sigmaaIs the stress magnitude.
In step S5, the calculation formula of the fatigue life of the member is:
Figure BDA0003333341620000033
wherein, V0And A0Respectively representing the high stress volume and the high stress area of the reference specimen, NfFor fatigue life, the formula can be further simplified as:
Figure BDA0003333341620000034
the invention has the beneficial effects that: based on a Weibull distribution initial formula, a correction factor based on a high stress volume and a high stress area is introduced to correct the gap and the size effect, so that a new service life prediction model is obtained; the method of the invention has the following advantages:
(1) uncertainty quantification and modeling of notch and size effects are organically combined by combining the weibull distribution for quantifying fatigue life dispersion with a high stress volume (area) method for characterizing notch and size effects. The method of the invention not only can embody the random characteristic of the fatigue life, but also can reflect the adverse effect of factors such as gaps, size effect and the like on the fatigue life;
(2) the area method is higher in applicability aiming at the surface failure mode, the volume method is more suitable for the internal failure mode, and the model is suitable for predicting the fatigue life of the notch under the complex failure mode by combining the high-stress volume method and the high-stress area method, so that the universality is higher;
(3) the probability fatigue life prediction model considering the notch and size effect is provided, wherein the solution of the high stress volume and area is simple and convenient, the fitting of Weibull distribution parameters is convenient, and the accuracy of the model prediction result is high.
Drawings
FIG. 1 shows the dimensions of a TC4 alloy fatigue test specimen provided by an embodiment of the invention;
wherein (a) is the stress concentration coefficient KtThe size of the smooth specimen (1) and (b) the stress concentration coefficient KtA notched specimen size of 3, and (c) is a stress concentration coefficient KtA 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 of the results of the method of the present invention applied to the quantification of fatigue life dispersion of TC4 titanium alloy notched parts;
FIG. 4 is a graph of fatigue test life dispersion for TC4 alloy notched specimens using 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 method provided by the invention is verified through TC4 material fatigue test data, and specifically comprises a theoretical stress concentration coefficient KtThe fatigue test pieces 1, 3 and 5 have the corresponding test piece dimensions shown in fig. 1, wherein (a) is the stress concentration coefficient KtThe size of the smooth specimen (1) and (b) the stress concentration coefficient KtA notched specimen size of 3, and (c) is a stress concentration coefficient KtNotched specimen size of 5. In fig. 1, D is the diameter of the sample clamping section, D is the diameter of the sample gauge length section, r is the notch radius, theta is the notch opening angle, phi is the arc radius of the smooth sample gauge length section, and the test is carried out at normal temperature. The invention is described only by taking the TC4 material as an example, and the material parameters and test data are detailed in tables 1 and 2. Table 1 is taken from the handbook of materials for aircraft Engine design, and can also be obtained by experiments in engineering applications; where the physical meaning of the parameters is referred to, those skilled in the art can refer to material data handbooks and the invention is not set forth herein in detail.
Static Material and fatigue parameters of Table 1 TC4
Alloy (I) E(GPa) ve K′(MPa) n′
TC4 109 0.34 1420 0.07
TABLE 2 fatigue test data for TC4 under symmetric loading
Figure BDA0003333341620000051
Figure BDA0003333341620000061
Fig. 2 is a flow chart of the technical scheme of the invention, and the technical scheme of the invention is as follows: a probabilistic fatigue life prediction method for coupling notch and size effects comprises the following steps:
s1, carrying out finite element analysis on notch samples with different sizes, and determining a potential fatigue failure dangerous area, wherein the potential fatigue failure dangerous area comprises a plurality of dangerous nodes; the parameter input process in the finite element analysis is as follows: as shown in table 1, the TC4 alloy static material parameters and fatigue parameters were first determined; then adding TC4 alloy static material parameters and a Chaboche follow-up hardening constitutive model into finite element software, wherein the parameters of the Chaboche model can be obtained by obtaining stress-strain points through Ramberg-Osgood and then fitting through numerical analysis software;
the finite element analysis of the step S1 is linear elastic analysis without considering plastic deformation; the hazardous area contains all nodes with stress values greater than or equal to 60% of the maximum principal stress value.
S2, extracting the maximum main stress peak values of all danger nodes in the danger area, and calculating high stress volumes and high stress areas of the notch samples with different sizes according to the maximum main stress peak values, wherein the high stress volumes and the high stress areas of the notch samples with different sizes are shown in a table 3.
Step S2 the high stress volume calculation process includes: firstly, acquiring the volume of a dangerous area and the number of nodes of the dangerous area; then counting the number of high stress nodes in the dangerous area, wherein the high stress nodes are defined as nodes with the stress values reaching and exceeding 90% of the maximum main stress value; finally, the high stress volume of the sample is solved based on the following formula:
Figure BDA0003333341620000062
wherein V is the high stress volume of the notch specimen, VrIs the volume of the dangerous area of the notched specimen, Nh,vNumber of high stress nodes for notched specimen, Nr,vThe total number of nodes in the high stress area of the notch test sample. In finite element simulation calculation Nh,vAnd Nr,vAnd meanwhile, the size of the whole grid of the research object is required to be ensured to be consistent.
Step S2 the high stress area calculation process includes: firstly, acquiring the area of a dangerous area and the number of nodes of the area; then counting the number of high stress nodes in the dangerous area, wherein the high stress nodes are defined as nodes with the stress values reaching and exceeding 90% of the maximum main stress value; finally, solving the high stress area of the test sample based on the following formula:
Figure BDA0003333341620000071
wherein A is the high stress area of the notch sample, ArSurface area of dangerous area of notched specimen, Nh,sFor notched specimen dangerNumber of high stress nodes on the surface of the region, Nr,sThe total number of surface nodes in the dangerous area of the notch sample. In finite element simulation calculation Nh,sAnd Nr,sAnd meanwhile, the size of the whole grid of the research object is required to be ensured to be consistent.
TABLE 3 TC4 test specimens high stress volume and high stress area
TC4 Kt＝1 Kt＝3 Kt＝5
High stress volume/mm3 218.68 0.111 0.023
High stress area/mm2 128.8 4.71 2.23
S3, respectively establishing fatigue life conversion formulas among the notch samples with different sizes based on the high stress volumes and the high stress areas obtained in the step S2;
s4, acquiring a material fatigue life dispersion index k and a characteristic fatigue life N based on a statistical method, and taking the material fatigue life dispersion index k and the characteristic fatigue life N as shape and position parameters of two parameters of Weibull distribution;
step S4 of obtaining fatigue life of materialThe process of dispersion index k and characteristic fatigue life N is: firstly, sequencing the fatigue lives under the same stress amplitude according to the numerical values, respectively calculating the failure probability corresponding to each fatigue life, and performing linear fitting on the fatigue lives and the failure probabilities to obtain k and N under the stress amplitude; solving k and N under different stress amplitude values, and finally taking the average value of k under each stress amplitude value, the characteristic fatigue life N and the stress amplitude value sigmaaCan be described by the following equation: sigmaa＝a(N)bWherein a and b are curve fitting parameters.
Those skilled in the art will note that characteristic fatigue life is a distributed parameter of the weibull distribution, and is referred to as characteristic fatigue life because it is affected by fatigue life; in the present invention, N represents a characteristic fatigue life, NfIndicating fatigue life.
And S5, predicting the fatigue life of the component based on the fatigue life conversion formula obtained in the step S3 and the Weibull distribution parameters obtained in the step S4. And based on the probability fatigue life prediction model in the step S5, solving the fatigue life of the component under different failure probabilities, obtaining the quantitative result of the component fatigue test life dispersity, and drawing a P-S-N curve of the component fatigue test life dispersity.
Step S5 is implemented as:
a1 initial formula for fatigue life prediction based on Weibull distribution is:
Figure BDA0003333341620000081
wherein, PfTo the probability of failure, NfFor fatigue life, N and k are the weibull distribution parameters (i.e., position parameters and shape parameters) described in step S4, and are fitted to the smooth specimen fatigue life data.
The conversion formulas of the fatigue life based on the high stress volume and the high stress area are respectively as follows in step A2 and step S3:
Figure BDA0003333341620000082
Figure BDA0003333341620000083
wherein N is1、N2For fatigue life, V1、V2For high stress volume of the test specimen, A1、A2For high stress area of the specimen, beta1、β2Are fitting parameters.
A3, combining the volume formula and the area formula in A2 to obtain a size effect model considering both surface and internal failure modes, and further combining the size effect model with the formula in A1 to obtain a new probabilistic fatigue life prediction formula:
Figure BDA0003333341620000084
wherein, V0And A0For reference specimen high stress volume and high stress area, NfFor fatigue life, the formula can be further simplified as:
Figure BDA0003333341620000085
generally speaking, the notch and size effects of the component can be reasonably quantified only by high stress volume, and the inventor finds various fatigue test phenomena to show that: the area method is more effective in the case of surface failure mode, the volume method is more applicable to the internal failure mode, the fatigue life prediction in the composite failure mode is more effective by combining the volume method and the area method, and the newly proposed model is stronger in universality.
The invention adopts the fatigue test data of the TC4 alloy test piece to carry out model verification, and the sizes of the test pieces are shown in figure 1. FIG. 3 is a graph showing P-S-N curves of a TC4 notch predicted based on the method of the present invention versus test life; as can be seen from FIG. 3, the test results are both within the probability distribution bands of 5% and 95% survival rate, demonstrating that the proposed method can simultaneously characterize the impact of notch, size effect and uncertainty on fatigue life.
It will be appreciated by those of ordinary skill in the art that the embodiments of the invention 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 (9)

1. A method for probabilistic fatigue life prediction coupling notch and size effects, comprising:
s1, carrying out finite element analysis on notch samples with different sizes, and determining a potential fatigue failure dangerous area, wherein the potential fatigue failure dangerous area comprises a plurality of dangerous nodes;
s2, extracting the maximum main stress peak values of all dangerous nodes in the potential fatigue failure dangerous area, and calculating high stress volumes and high stress areas of notch samples with different sizes according to the maximum main stress peak values;
s3, respectively establishing fatigue life conversion formulas among the notch samples with different sizes based on the high stress volume and the high stress area obtained in the step S2;
s4, acquiring a fatigue life dispersion index k and a characteristic fatigue life N of materials used by notch samples with different sizes based on a statistical method, and taking the fatigue life dispersion index k and the characteristic fatigue life N as shape and position parameters of two parameters of Weibull distribution;
s5, predicting the fatigue life of the component based on the fatigue life conversion formula obtained in the step S3 and the Weibull distribution parameter obtained in the step S4.
2. The method of claim 1, wherein the finite element analysis of step S1 is a linear elastic analysis.
3. The method of claim 1, wherein the potentially dangerous area of fatigue failure of step S1 comprises all nodes with stress values greater than or equal to 60% of the maximum principal stress value.
4. The method of claim 1, wherein the high stress nodes of step S2 include all nodes having a stress value greater than or equal to 90% of the maximum primary stress value.
5. The method of claim 1, wherein the calculation formula of the volume of the high stress in step S2 is:
Figure FDA0003333341610000011
wherein V is the high stress volume of a notch sample with a certain size, VrVolume of dangerous area of specimen with a certain size gap, Nh,vNumber of high stress nodes for a notch specimen of a certain size, Nr,vThe total number of nodes in the high stress area of the notch sample with a certain size is shown.
6. The method of claim 5, wherein the calculation formula of the area of high stress in step S2 is as follows:
Figure FDA0003333341610000012
wherein A is the high stress area of a notch sample with a certain size, and ArSurface area of dangerous area of specimen with certain size gap, Nh,sNumber of high stress nodes on surface of dangerous area of sample with certain size of notch, Nr,sThe number of nodes on the surface of the sample danger area with a certain size of notch.
7. The method of claim 6, wherein the fatigue life conversion formula of step S3 is:
Figure FDA0003333341610000021
Figure FDA0003333341610000022
wherein N is1、N2For the fatigue life of two specimens with notches of different sizes, V1、V2For two differently dimensioned notched specimens with high stress volumes, A1、A2For two notch specimens of different dimensions, high stress area, beta1、β2Are fitting parameters.
8. The method of claim 7, wherein the step S4 is implemented by the following steps:
firstly, sequencing the fatigue lives under the same stress amplitude according to the magnitude of the numerical values, respectively calculating the failure probability corresponding to each fatigue life, and performing linear fitting on the fatigue lives and the failure probabilities to obtain k and N under the stress amplitude;
secondly, solving k and N under different stress amplitudes;
finally, k is the mean value of all stress amplitudes;
the characteristic fatigue life N is obtained according to the following formula:
σa＝a(N)b
wherein a and b are curve fitting parameters sigmaaIs the stress magnitude.
9. The method of claim 8, wherein the calculation formula of the component fatigue life in step S5 is:
Figure FDA0003333341610000023
wherein, V0And A0High stress volume and high stress area of the reference specimen, NfThe fatigue life is considered.
CN202111287209.7A 2021-11-02 2021-11-02 Probability fatigue life prediction method for coupling notch and size effect Pending CN113919079A (en)

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