CN113191525A - High cycle fatigue life prediction method based on defect form - Google Patents

High cycle fatigue life prediction method based on defect form Download PDF

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CN113191525A
CN113191525A CN202110266636.0A CN202110266636A CN113191525A CN 113191525 A CN113191525 A CN 113191525A CN 202110266636 A CN202110266636 A CN 202110266636A CN 113191525 A CN113191525 A CN 113191525A
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defect
fatigue life
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靳凯
刘新田
刘淼
葛海燕
陈铁
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Shanghai University of Engineering Science
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Abstract

The invention belongs to the technical field of fatigue life, and discloses a high cycle fatigue life prediction method based on defect morphologyfThe prediction is carried out in such a way that,
Figure DDA0002972246820000011
wherein, areaincIndicating the area of the defect, d indicating the depth of the defect, C, P being parameters relating to the fatigue defect propagation characteristics of the component to be tested,d represents a coefficient related to the position of the defect on the member to be measured, D being 1.56 when the defect is intrinsic and 1.43 when the defect is on the surface. The invention can simply, conveniently and effectively estimate the high cycle fatigue life of the component to be measured, provides guidance for the use and research and development design of mechanical components, reduces the research and development cost, ensures the quality of products and improves the reliability of the products.

Description

High cycle fatigue life prediction method based on defect form
Technical Field
The invention belongs to the technical field of fatigue life, and particularly relates to a high cycle fatigue life prediction method based on defect morphology.
Background
With the increasing demands on light weight, high performance and safety of mechanical equipment design, many mechanical parts are required to withstand ultra-high cyclic loads. In the fields of aerospace, biomedicine, mechanical engineering and the like, the actual bearing cycle of mechanical parts is far more than 107Load cycles, even up to 109～1010And (5) loading circulation. Therefore, elucidating the failure mechanism of the ultra-long life fatigue, and providing a suitable ultra-long life prediction method has become a hotspot in the field of fatigue research, and a great deal of experimental research shows that internal defects play a key role in very-high frequency cyclic fatigue, and fracture caused by the internal defects of the surface hardening metal material in a long-life region has become a key problem in engineering design. In recent years, researchers have studied internal defects of high cycle and ultrahigh cycle fatigue, and the influence of defect depth on high cycle fatigue life in the existing research is obtained by summarizing experimental rules, and no specific mathematical model is used for reflecting the influence.
Disclosure of Invention
The invention provides a high cycle fatigue life prediction method based on defect morphology, which solves the problems that the influence of defect depth on the high cycle fatigue life in the existing research is obtained by summarizing an experimental rule, no specific mathematical model is used for reflecting the influence, and the like.
The invention can be realized by the following technical scheme:
a high cycle fatigue life prediction method based on defect forms comprises the steps of firstly measuring the size and the depth of a defect on a component to be measured, and then utilizing the following formula to predict the high cycle fatigue life N of the component to be measuredfThe prediction is carried out in such a way that,
Figure BDA0002972246800000011
wherein, areaincThe area of the defect is indicated, D is the depth of the defect, C, P are parameters relating to the fatigue defect propagation characteristics of the member under test, D is a coefficient relating to the position of the defect on the member under test, D is 1.56 when the defect is intrinsic, and D is 1.43 when the defect is on the surface, respectively.
Further, a group of area data samples of the defects are obtained by using measuring equipment, the area data samples are processed by a bootstrap method, the mean value and 95% confidence interval of the area data samples within an error allowable range are obtained, and accordingly accurate and reasonable area data are obtained.
Further, processing the area data sample by using a Bootstrap error circle method of sample value BEMSV (BeMSV) gamma method, wherein a Weibull function or a gamma function is used as a distribution function for describing the defect area, an error circle model is established, and the probability density function expressions of the corresponding Weibull distribution and the gamma distribution are as follows:
Figure BDA0002972246800000021
Figure BDA0002972246800000022
where k and λ are the shape and position parameters of the weibull distribution, and α and β are the shape and position parameters of the gamma distribution.
Further, Δ K was obtained by measurement using the following formulaintAnd
Figure BDA0002972246800000023
the parameters P-11.31 and C-2.02-10 are calculated by combining the data fitting method-18
Figure BDA0002972246800000024
Wherein, Delta KintRepresenting a range of stress intensity factors.
The beneficial technical effects of the invention are as follows:
the high cycle fatigue life prediction model based on the size and the depth of the defect quantitatively reflects the influence of the defect details on the material performance, effectively predicts the high/ultra high cycle fatigue life of the material, and estimates the high/ultra high cycle fatigue life based on the size and the depth of the defect to be closer to the actual state of the material. The high cycle fatigue life data obtained by the experiment have large discreteness, the minimum defect size is taken, the high cycle/ultrahigh cycle fatigue life estimated by the defect size and the depth is considered to be more dangerous, and the high cycle/ultrahigh cycle fatigue life estimated by the estimation of the defect size by introducing the error circle is more conservative and accurate than that estimated by the experiment, so that guidance suggestions are provided for the use, research and development cost and design of mechanical components, the quality of products is ensured, and the reliability of the products is improved.
Drawings
FIG. 1 is a schematic overview of the process of the present invention;
FIG. 2 is a goodness of fit of three alternative distributions of the invention to defect size data;
FIG. 3 is a schematic diagram of sampling points of an error circle sample of the present invention;
fig. 4 is a frequency histogram of the mean value of 100,000 cycles obtained by the error round method bemsv (w) of the present invention;
fig. 5 is a frequency histogram of the mean value of 100,000 cycles obtained by the error round method bemsv (g) of the present invention;
FIG. 6 is a graph of high cycle fatigue life obtained with HCFD-BEMSV of the present invention compared to experimental data;
FIG. 7 is a graph comparing the high cycle fatigue life of the present invention obtained from the HCFD-BEMSV model, the HCFD model and experimental data.
Detailed Description
The following detailed description of the preferred embodiments will be made with reference to the accompanying drawings.
In experimental studies, due to various measurement errors, the measured defect size inside the material may not be a true value, and the defect size may obey a certain distribution. The improved bootstrap method can effectively evaluate small sample parameters, considers the influence of various error factors on small sample data, obtains a sample mean value and a confidence interval through uncertainty analysis, improves the accuracy and reliability of small sample estimation, and effectively estimates the high cycle/ultra-high cycle fatigue life of the defect size. The method defines the distance between the defect and the surface of the component to be measured as the defect depth d, establishes a model, introduces an error circle to evaluate the defect size, introduces the defect size and the depth parameter into a Tanaka model, predicts the high cycle fatigue life of the carburizing steel, and discusses the influence of the defect depth and the defect size on the high cycle fatigue life of the carburizing steel. The method comprises the following specific steps:
step one, establishing a model
Tanaka et al believe that the Paris equation can be used to describe the propagation rate of internal defects of a component under test
Figure BDA0002972246800000041
Wherein C, P is a parameter related to the fatigue defect propagation characteristics of the material, and Δ K is the variation range of the stress intensity factor.
The distance between the defect and the surface of the component to be measured is defined as the defect depth and is represented by d, the defect size and the depth parameter are introduced into a Tanaka model to estimate the high cycle fatigue life of the carburizing steel, and the influence of the defect depth on the high cycle fatigue life of the carburizing steel is discussed.
Figure BDA0002972246800000042
Wherein Δ σ represents a stress range, Δ KintRepresenting the range of stress intensity factors, areaintRepresenting Bootstrap samples. When the stress ratio is-1, the stress intensity factor range calculated according to the formula (2) may replace the stress range with the stress magnitude.
Figure BDA0002972246800000043
Wherein, Delta sigmaaExpressing the stress amplitude, integrating equation (1), and combining equations (2) and (3) to obtain equation (4)
Figure BDA0002972246800000044
Since the size of FGA (a fine particle layer having a rough surface around inclusions is collectively referred to as FGA) is larger than that of the inclusions, the formula (4) can be simplified as
Figure BDA0002972246800000045
The relationship between the defect formation life and the size of inclusions is as follows:
Figure BDA0002972246800000046
the formula (3) is brought into the formula (6)
Figure BDA0002972246800000047
Murakami first considers the effects of material hardness and defect geometry and establishes a relationship between non-metallic characteristic defect size and fatigue strength.
Figure BDA0002972246800000051
Wherein σwThe fatigue strength, Hv Vickers hardness,
Figure BDA0002972246800000052
the square root of the defect area, itThe inclusion size, D is a coefficient related to the defect location, D is 1.56 when the defect is intrinsic, and D is 1.43 when the defect is on the surface. The fatigue strength can replace the stress amplitude sigma in high cycle fatigue and ultrahigh cycle fatigueaTherefore, the high cycle fatigue life can be obtained from the equations (4) and (8):
Figure BDA0002972246800000053
where Hv is a function of the defect depth d,
Hv＝f(d) (10)
the relationship between the high cycle fatigue life and the depth of defect can be obtained by substituting formula (10) for formula (9):
Figure BDA0002972246800000054
from the formula (11), the high cycle fatigue life can be predicted from the inclusion size and the inclusion distance.
Sun researches the ultra-high cycle fatigue S-N characteristics and the failure mechanism of the carburized chromium-manganese gear steel, discusses the formation mechanism of FGA fine particle areas and defects, and obtains the relationship between the hardness and the carburization depth of the carburized chromium-manganese gear steel by fitting experimental data.
Hv＝2149d-0.217 (12)
Finally, the relationship between the size of the defect in the carburized chromium manganese gear steel and the high cycle fatigue life can be determined from the equations (8), (11) and (12).
Figure BDA0002972246800000055
Wherein, based on the numerical analysis method, the method is characterized by the following formula (5)
Figure BDA0002972246800000056
And Δ KintFitting to obtain
Figure BDA0002972246800000057
And Δ KintBased on the fitting result, the linear relationship between P and C can be solved to obtain P and C as 11.31 and 2.02 and 10-18。
Step two: case analysis
1. Defect size estimation
The method is characterized in that experimental research is carried out on a member composed of a batch of materials, the measured defect size in the member may not be a true value due to various measurement errors, the defect size may obey certain distribution, and the improved bootstrap method can effectively evaluate small sample parameters, wherein an error circle is the improved bootstrap method (BEMSV) provided by Wang, the method is irrelevant to the shape of the defect, the influence of various error factors on small sample data is considered, the mean value and the confidence interval of the sample are obtained through uncertainty analysis, a more accurate and reasonable sample is obtained, the error of the sample is reduced, and the accuracy and the reliability of small sample estimation are improved.
In actual calculation, the defect area of the inventionincParameters, not a measured value, but a group of sample values, and defect area is measured by using an improved Boostrap error circular method of sample value BEMSV (binary intensity vector) methodincThe parameters are estimated, the method is disclosed in the paper of Prediction of material failure parameters for low alloy formed step connected error circuit, the defect area of 95% confidence interval of the sample group is finally obtainedincAnd (4) parameters. The method comprises the following specific steps:
to determine more precisely which optimal distribution the defect sizes fit, a basis is established for the error circle. And calculating which optimal distribution is met by the statistic and the P value based on a numerical analysis method, so as to establish an error circle model.
In hypothesis testing, the distribution of the alternative test is usually selected from normal distribution, log-normal distribution, weibull distribution, gamma distribution, etc. The distribution of hardness sample data may follow some of the distributions described above. Hypothesis testing was performed on the distribution of known samples. Since it is known that samples may conform to different distributions simultaneously, it is necessary to select the best fit to improve the accuracy of the parameter estimation. There are many ways to determine the degree of data fit, such as the Anderson-Darling test, Cram er-von Mises test, and Kuiper test.
TABLE 1 goodness of fit of parameters under different distributions
Figure BDA0002972246800000061
Figure BDA0002972246800000071
As can be seen from the hypothesis testing results of Table 1 and FIG. 2, the degree of fit of the Anderson-Darling test, Cram er-von Mises test, and kuipeer test was different for the three different distributions, and the statistical and P values indicated that the log-normal goodness of fit was the worst. Therefore, a Weibull function and a gamma function are used as distribution functions of defect sizes to establish an error circle model, and the probability density function expressions of the Weibull distribution and the gamma distribution of the two parameters are as follows:
Figure BDA0002972246800000072
Figure BDA0002972246800000073
where k and λ are the shape and position parameters of the weibull distribution, and α and β are the parameters of the gamma distribution.
From the parameters obtained in table 1, the probability density functions of the weibull distribution and the gamma distribution of the defect sizes can be obtained as follows:
Figure BDA0002972246800000074
f(x)＝4.33206×10-6e-0.11468xx3.54228 (18)
2. determining error radius of defect size
The defect size is represented by RincDenotes, based on the measured data, Rinc＝{17.82,19.18,20.36,21.03,21.20,23.40,28.30,32.18,33.02,33.19,39.45,39.79,40.29,40.63,54.82,59.05,67.15,71.21,90.48}。
By introducing an error circle, the error circle radius of the defect size can be obtained as follows:
r＝Rinc×α (19)
Rincis the actual measured defect size and alpha is the sampling error range. To reduce the effect of these errors, the samples need to be extended based on sample size considerations.
3. Sample expansion and sampling
Fig. 3 is a schematic diagram of sampling points of an error circle sample. In order to establish a reasonable error circle model and enable extended samples randomly extracted from an error circle to have universality, the samples are prevented from being concentrated in a certain area of the error circle. The error circle is divided into A, B, C, D, E areas, the extended sample range of each area is A (X-r is not less than X is not less than X-0.95r), B (X-0.95r is not less than X is not less than X-0.85r), C (X-0.85r is not less than X +0.85r), D (X +0.85r is not less than X +0.95r), E (X +0.85r is not less than X is not less than X +0.95r)
The number of extended samples is extended by their probability. The error circle is divided into five regions based on the confidence intervals of 85% and 95%, and the probability of each region is calculated. The area of each region in the error circle is:
Figure BDA0002972246800000081
Figure BDA0002972246800000082
Figure BDA0002972246800000083
the probability for each region is:
Figure BDA0002972246800000084
Figure BDA0002972246800000085
Figure BDA0002972246800000086
each error circle is extended by 500 samples, and the samples taken from the above 5 regions can be calculated by equation (15):
mi＝500×P(i),i＝A,B,C,D,E (19)
wherein m isiIs the number of spread samples per region. An error circle is created with each sample point as the center, and if a number of data are expanded within each error circle, the total expanded sample data is 19 × 500 — 9500. Based on the bootstrap method, error circle samples are randomly extracted, and the bootstrap error circle samples are obtained through 10000 times of circulation.
Fig. 4 and 5 are frequency histograms of the mean values of the cycles N of 100,000 obtained by the error round method BEMSV (w) and BEMSV (g), and it can be seen that the fitting effect of the BEMSV method (weibull distribution) is good. The parameters of the three methods of estimation of the hardness data are shown in table 2.
TABLE 2. three methods of estimating defect size
Figure BDA0002972246800000091
As can be seen from table 2, compared with the maximum likelihood method MLE, the confidence interval based on the BEMSV (gamma) method and the BEMSV (weibull) method is shorter in length and smaller in variance, and the stability and accuracy of the evaluation result are improved. From the above three methods, it can be concluded that the length and variance of the confidence interval obtained by the BEMSV (gamma) method are minimal, the method is more accurate and stable, followed by the BEMSV (weibull) method.
In order to verify the feasibility of the high-cycle fatigue life prediction method, the size and the depth of the defect on the component to be measured are measured, and then the high-cycle fatigue life of the component to be measured is predicted by using the following formula, as shown in fig. 1, a high-cycle fatigue life model considering the size and the depth of the defect can be written into an HCFD model, and a high-cycle fatigue life model introducing an error circle considering the size and the depth of the defect can also be written into an HCFD-BEMSV model.
And (5) verifying the model. To verify the feasibility of the model, the data were obtained from stress high cycle life data for different defect depths, as shown in table 3.
Table 3 depth and high cycle fatigue test data under different stresses
Figure BDA0002972246800000092
Comparing the depth and high cycle fatigue data under different stresses with a high cycle fatigue life prediction model considering the depth of the defect and the size of the defect according to equation (11) and table 3 shows that:
FIG. 6 is a comparison of high cycle fatigue life obtained for HCFD-BEMSV with experimental data. HCFD-BEMSV model (U), HCFD-BEMSV model (L), and HCFD-BEMSV model (M) are the upper and lower confidence interval values and mean values, respectively, for a confidence interval of 95%. It can be seen that the experimental data of the ultra-high cycle fatigue life are few, the data dispersion is large, and the dispersion of the high cycle fatigue life data is smaller than that of the ultra-high cycle fatigue life data. As the depth of the defect increases, the high/ultra high cycle fatigue life increases. Low cycle fatigue is often caused by surface defects of the material, while high cycle fatigue failure is often caused by internal defects of the material.
As can be seen from the experimental data of Table 3 and FIG. 7, 106～107The cycle life is close to the high cycle fatigue life, and the depth value of the defect is reduced. The smaller the depth value of the defect, the closer the defect is to the surface of the material, and the smaller the corresponding fatigue life. Introducing the error circle results in a high cycle fatigue life model (HCFD-BEMSV) that takes into account the defect size and depth. The moldThe type and the experimental result are consistent with the high cycle fatigue characteristics obtained by previous researches.
FIG. 7 shows a comparison of high cycle fatigue life derived from HCFD-BEMSV models, HCFD models, and experimental data. In the literature (Sun 2016), the maximum, minimum and average values of defect size are used to predict high cycle fatigue life. The HCFD model (Min) represents the high cycle fatigue life model with the smallest defect size, and the HCFD model (Max) represents the high cycle fatigue life model with the largest defect size. It can be seen that the high cycle fatigue life calculated from the maximum and minimum defect sizes increases with increasing defect depth. The high cycle fatigue life model, which takes into account the depth and size of the defect, is strongly affected by the size of the defect. And (3) introducing an error circle method to estimate the high cycle/ultrahigh cycle fatigue life ratio, wherein experimental data are conservative. In the high/ultra high cycle fatigue life estimation, the minimum depth of the defect size is considered to be closer to the experimental data. As can be seen from the high/ultra high cycle experimental data, these data are relatively discrete and therefore more dangerous in engineering applications to estimate fatigue life with minimum defect size. The HCFD-BEMSV model yields a 95% confidence interval for high cycle fatigue life. It can be seen from FIG. 2 that most of the experimental data, except for individual data, are evenly distributed over the lifetime obtained by the HCFD-BEMSV model. In order to prolong the service life of the material as far as possible within the safe life range, the HCFD-BEMSV model has important engineering application value.
Although specific embodiments of the present invention have been described above, it will be appreciated by those skilled in the art that these are merely examples and that many variations or modifications may be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is therefore defined by the appended claims.

Claims (4)

1. A high cycle fatigue life prediction method based on defect morphology is characterized by comprising the following steps: firstly, measuring the size and depth of the defect on the component to be measured, and then utilizing the following formula to measure the high cycle fatigue life N of the component to be measuredfThe prediction is carried out in such a way that,
Figure FDA0002972246790000011
wherein, areaincThe area of the defect is indicated, D is the depth of the defect, C, P are parameters relating to the fatigue defect propagation characteristics of the member under test, D is a coefficient relating to the position of the defect on the member under test, D is 1.56 when the defect is intrinsic, and D is 1.43 when the defect is on the surface, respectively.
2. The method of claim 1, wherein the high cycle fatigue life prediction based on defect morphology comprises: a group of area data samples of defects are obtained by using measuring equipment, the area data samples are processed by a bootstrap method, the mean value and 95% confidence interval of the area data samples within an error allowable range are obtained, and therefore accurate and reasonable area data are obtained.
3. The method of claim 2, wherein the high cycle fatigue life prediction based on defect morphology comprises: processing the area data sample by using a Bootstrap error circular method of sample value BEMSV for short, wherein a Weibull function or a gamma function is used as a distribution function for describing the defect area, an error circle model is established, and the probability density function expressions of corresponding Weibull distribution and gamma distribution are as follows:
Figure FDA0002972246790000012
Figure FDA0002972246790000013
where k and λ are the shape and position parameters of the weibull distribution, and α and β are the shape and position parameters of the gamma distribution.
4. According to claim 1The high cycle fatigue life prediction method based on the defect form is characterized by comprising the following steps: Δ K was obtained by measurement using the following formulaintAnd
Figure FDA0002972246790000014
the parameters P-11.31 and C-2.02-10 are calculated by combining the data fitting method-18
Figure FDA0002972246790000021
Wherein, Delta KintRepresenting a range of stress intensity factors.
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Application publication date: 20210730