CN112149242A - Fatigue reliability assessment method for in-pile component compression spring considering stress relaxation and irradiation influence - Google Patents

Fatigue reliability assessment method for in-pile component compression spring considering stress relaxation and irradiation influence Download PDF

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CN112149242A
CN112149242A CN202010874322.4A CN202010874322A CN112149242A CN 112149242 A CN112149242 A CN 112149242A CN 202010874322 A CN202010874322 A CN 202010874322A CN 112149242 A CN112149242 A CN 112149242A
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fatigue
compression spring
model
stress relaxation
irradiation
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孙博
潘俊林
杨西
任羿
冯强
杨德真
王自力
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Beihang University
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    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
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Abstract

The invention provides a fatigue reliability evaluation method for a compression spring of an in-pile member, which considers stress relaxation and irradiation influence. Firstly, a fatigue life model and a stress relaxation model are combined, the influence of irradiation on fatigue parameters is considered, and a compression spring fatigue life model is constructed; on the basis of a compression spring fatigue life model, considering uncertainty of working condition parameters and material parameters, and calculating and acquiring fatigue life distribution by adopting a Monte Carlo method; and defining the reliability of the compression spring according to the generalized stress-intensity interference model, carrying out sensitivity analysis, and carrying out reliability evaluation on the compression spring. The method establishes the fatigue model of the compression spring of the reactor internals in consideration of stress relaxation and irradiation influence, provides the fatigue reliability evaluation flow of the compression spring, and can provide a theoretical basis for the design optimization of the compression spring.

Description

Fatigue reliability assessment method for in-pile component compression spring considering stress relaxation and irradiation influence
The technical field is as follows:
the invention provides a method for evaluating fatigue reliability of a hold-down spring of an in-reactor component in consideration of stress relaxation and irradiation influence, which is a method suitable for evaluating the reliability of the hold-down spring of the in-reactor component of a reactor and belongs to the technical field of reliability engineering.
(II) background of the invention
The compression spring is one of the components of the reactor internals, and has the function of compressing and positioning the reactor internals and maintaining vertical stability, and the reliability of the compression spring is related to the operation safety of the whole reactor. Due to the special environment of the reactor, the compression spring is in a certain irradiation working condition. In addition, unlike other parts of the reactor, the internals compression spring has a stress relaxation phenomenon during operation. The average stress of the compression spring cannot be regarded as a constant value. Fatigue life is often greatly underestimated if fatigue life assessment is made without consideration of stress relaxation. In order to make the fatigue life evaluation result more accurate, the influence of both the irradiation and the stress relaxation should be considered at the same time.
Aiming at the problems of fatigue failure and reliability of the compression spring of the in-pile member, the fatigue reliability evaluation method of the compression spring of the in-pile member considering stress relaxation and irradiation influence is provided. The method establishes the fatigue model of the compression spring of the reactor internals in consideration of stress relaxation and irradiation influence, provides the fatigue reliability evaluation flow of the compression spring, and can provide a theoretical basis for the design optimization of the compression spring.
Disclosure of the invention
The invention relates to a method for evaluating fatigue reliability of a compression spring of an in-pile component by considering stress relaxation and irradiation influence, which comprises the steps of firstly obtaining constraint data of a compression spring material, a structure and a load; decomposing the variable amplitude temperature load into a constant amplitude load by using a rain flow counting method; a fatigue life SWT model and a stress relaxation Landgraf model are combined, the influence of irradiation on fatigue parameters is considered, and a compression spring fatigue life model is constructed; on the basis of a compression spring fatigue life model, considering uncertainty of working condition parameters and material parameters, and calculating and acquiring fatigue life distribution by adopting a Monte Carlo method; and defining the reliability of the compression spring according to the generalized stress-intensity interference model, carrying out sensitivity analysis, and carrying out reliability evaluation on the compression spring.
The method comprises the following specific steps:
(1) and acquiring the constraint data of the material, the structure and the load of the compression spring of the reactor internals according to literature investigation, engineering experience and test fitting.
(2) And decomposing the actual amplitude variation temperature load into a constant amplitude load according to a rain flow counting method.
(3) And combining the fatigue life SWT model and the stress relaxation Landgraf model, considering the influence of irradiation on fatigue parameters, and constructing a compression spring fatigue life model considering the influence of stress relaxation and irradiation.
(4) And generating a random parameter simulation input data set according to simulation, engineering experience and literature investigation.
(5) And (4) sampling according to a Monte Carlo method to generate n groups of data, and calculating the fatigue life corresponding to each group of parameters.
(6) Calculating the fatigue total damage D according to the fatigue accumulated damage criterionfAnd total fatigue life Nf。
(7) And calculating the reliability R of the compression spring according to a failure criterion.
(8) Calculating reliability sensitivity S (x) of uncertainty parameteri)。
And (3) decomposing the variable amplitude load into a constant amplitude load in the step (2), wherein the pressing force load of the pressing spring is basically constant and unchanged, but bears the variable amplitude temperature load under the normal working condition. The SWT model is used for solving the corresponding fatigue life according to stress-strain response under the action of constant amplitude cyclic load, and the actually measured amplitude-variable load needs to be decomposed into two constant amplitude loads with two parameters (variable range and mean value) reserved by a rain flow counting method.
Constructing a compression spring fatigue life model considering stress relaxation and irradiation influence in the step (3), wherein the step specifically comprises the following steps:
the SWT model can comprehensively consider the influence of strain, stress amplitude and average stress on the fatigue life, and the form is as follows:
Figure BDA0002650667850000021
in the formula, σaIs a stress amplitude; sigmamIs the average stress; deltatIs the strain range; sigma'fThe fatigue strength coefficient; 'fThe fatigue elongation coefficient; b is fatigue strength index; c is the fatigue elongation index; n is a radical offThe fatigue life is considered.
For the decomposed load, the ith constant amplitude fatigue load corresponds to the fatigue life Nf,iCorresponding fatigue damage Df,iComprises the following steps:
Figure BDA0002650667850000022
according to Miner fatigue damage accumulation criterion, total fatigue damage DfComprises the following steps:
Figure BDA0002650667850000023
in the formula, niThe load number of the ith constant amplitude fatigue load.
Total fatigue life NfComprises the following steps:
Figure BDA0002650667850000024
total fatigue life T in time unitsfComprises the following steps:
Tf＝Nf×TD (5)
in the formula, TDCorresponding time for one cycle period.
For the compression spring, the average stress in the SWT model is not constant but gradually decreases due to the stress relaxation phenomenon, and for the average stress relaxation phenomenon, the landgraff model can be well characterized and has the following form:
σmj＝σm1·Nj r (6)
the relationship between the number of load cycles and the fatigue life is:
Nj＝ni×Nf，i (7)
the relationship between relaxation index and strain amplitude is:
Figure BDA0002650667850000031
transforming the above equation yields:
Figure BDA0002650667850000032
the fatigue life model considering stress relaxation can be obtained by combining the above formula as follows:
Figure BDA0002650667850000033
in the formula, σmj、σm1The average stress after j cycles and the average stress after the first cycle are respectively; n is a radical ofjIs the number of load cycles; r is the relaxation index;a、threspectively, strain amplitude and critical strain amplitude; A. b is a stress relaxation parameter and a coefficient respectively, and can be obtained by fitting a stress relaxation curve in a fatigue test through a least square method.
The compaction spring of the reactor internals can be influenced by irradiation under normal working conditions, and after the irradiation of the material, the performance parameter P of the material can change along with the injection amount of neutrons, and the material can be fitted by the following formula:
P＝A0+A1[1-exp(-d/d0)] (11)
in the formula, d is neutron injection amount; a. the0Is the initial value of the performance; a. the1A performance value variation amplitude coefficient; p is the post-irradiation performance parameter.
For theFatigue life model for compression spring, irradiation results in a fatigue strength coefficient σ'fAnd reduction of area psi:
Figure BDA0002650667850000034
ψ＝ψ0+ψ1[1-exp(-d/dψ)] (13)
fatigue elongation coefficient of Material'fThe relationship with the reduction of area ψ is:
Figure BDA0002650667850000035
combining the formula, the fatigue life model considering the stress relaxation and the irradiation influence simultaneously is obtained as follows:
Figure BDA0002650667850000041
in the step (4), the uncertainty parameters mainly consider working condition parameters and material parameters, wherein the working condition parameters select a strain range and a stress amplitude; the material parameters are selected from elastic modulus, fatigue strength coefficient, fatigue elongation coefficient, fatigue strength index, fatigue elongation index, stress relaxation parameter, stress relaxation coefficient and the like.
The working condition parameters can be subjected to distribution fitting by utilizing a plurality of groups of output results of the simulation input data set to obtain corresponding parameter distribution characteristics (mean and variance). The material parameters can be generally characterized by normal distribution, the typical value is taken as the sample mean value, and the coefficient of variation is taken as 0.01-0.05.
In step (7), the load-corresponding fatigue life distribution is:
Figure BDA00026506678500000410
corresponding to total fatigue life TfThe distribution is as follows:
Figure BDA00026506678500000411
for the internals hold down springs, given the allowable lifetime, the reliability is defined as:
Figure BDA0002650667850000042
if allowable lifetime tdFollowing the corresponding distribution, the reliability can be calculated using a generalized stress intensity interference model:
Figure BDA0002650667850000043
in the formula (I), the compound is shown in the specification,
Figure BDA0002650667850000048
cumulative probability distribution function for total fatigue life; t is tdFor the allowable lifetime;
Figure BDA0002650667850000049
is a function of the probability density of allowable lifetime.
In step (8), the reliability sensitivity of each design variable is calculated by the finite difference method. Design variable xiHas a mean value of
Figure BDA00026506678500000412
Standard deviation of
Figure BDA0002650667850000044
By using
Figure BDA0002650667850000045
Replacing x in all datasetsiThe design variables in the other data sets are kept unchanged, and the reliability R is obtained by sampling calculation by using a Monte Carlo method1. In the same way, use
Figure BDA0002650667850000046
Replacing x in all datasetsiThe design variables in the other data sets are kept unchanged, and the reliability R is obtained by sampling calculation by using a Monte Carlo method2Then design the variable xiSensitivity S (x) ofi) Comprises the following steps:
Figure BDA0002650667850000051
the invention relates to a method for evaluating fatigue reliability of a compression spring of an in-pile member by considering stress relaxation and irradiation influence, which has the advantages and effects that: a fatigue life model of the reactor internals is constructed in consideration of stress relaxation and irradiation influence, a fatigue reliability evaluation flow of the compression spring is given, and a theoretical basis can be provided for design optimization of the compression spring.
(IV) description of the drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a graph of the total fatigue life probability density distribution of the hold-down spring;
FIG. 3 is a graph of hold-down spring reliability results;
FIG. 4 is a graph of the reliability and sensitivity analysis results of design parameters of a hold-down spring;
the reference numbers and symbols in the figures are as follows:
Nfrepresents the total fatigue life;
Dfrepresents total fatigue damage;
tdindicating an allowable lifetime;
r represents reliability;
S(xi) Indicating a reliability sensitivity;
e represents an elastic modulus;
Δtrepresenting a strain range;
σarepresenting the stress amplitude;
σ'frepresenting the fatigue strength coefficient;
'frepresents a fatigue elongation coefficient;
b represents a fatigue strength index;
c represents a fatigue elongation index;
a represents a stress relaxation parameter;
b represents a stress relaxation coefficient
(V) detailed description of the preferred embodiments
The invention will be further described in detail with reference to fig. 1 and an evaluation case of fatigue reliability of a compression spring of an AP1000 pressurized water reactor, and the specific process is as follows:
the compression spring material is SA-182F6a martensitic stainless steel, and relevant performance parameters are shown in Table 1 at 350 ℃:
TABLE 1 compression spring Material Performance parameters
Figure BDA0002650667850000061
The pressure spring is influenced by circulating water temperature change in the operation process, bears constant mechanical load and variable amplitude temperature load in a period, retains two parameters (variable range and mean value) by a rain flow counting method, counts to obtain two unit constant amplitude loads with large temperature circulation (the number of load circulation is 3) and small temperature circulation (the number of load circulation is 2) in a circulation period, and provides input for next-step simulation analysis.
According to the structural characteristics and the size information of the compression spring, a compression spring CAD model is established, a circle of concentrated force load with the size of 3153kN is applied to the highest position of an upper surface arc, a circle of fixed constraint is applied to the highest position of a lower surface arc, stress-strain response required by a fatigue life model is output through a thermodynamic simulation method, and the deterministic fatigue life of the compression spring is calculated and obtained for 4154566 times according to the fatigue life model.
Further considering parameter uncertainty, the engineering parameter distribution is obtained by fitting according to the simulation result, the material parameters adopt normal distribution, and the distribution characteristics of the selected random variables are shown in table 2:
TABLE 2 random variable distribution characteristics
Figure BDA0002650667850000062
Figure BDA0002650667850000071
And substituting the probability density distribution of the total fatigue life into the model for simulation calculation for 5000 times, wherein the probability density distribution of the total fatigue life is obtained and is shown in figure 2, the allowable life is taken as a failure criterion, and a curve of the reliability changing along with the allowable life is obtained and is shown in figure 3.
The total fatigue life was calculated at 95% and 50% reliability and compared with the deterministic calculation and the results without considering the stress relaxation, the related results are shown in table 3:
TABLE 3 fatigue Life calculation results
Figure BDA0002650667850000072
According to the calculation result, under the condition of considering stress relaxation, the certainty calculation result is closer to the median life, the certainty fatigue life is 158 years when the safety coefficient is 3, the design life requirement of the reactor for 60 years is met, and if the stress relaxation is not considered, the fatigue life is reduced by 88.3%.
For the selected design variables: the strain range, the stress amplitude, the material parameters, the elastic modulus, the fatigue strength coefficient, the fatigue elongation coefficient, the fatigue strength index, the fatigue elongation index, the stress relaxation parameter, and the stress relaxation coefficient are selected to perform reliability sensitivity analysis, and the result is shown in fig. 4.
From the sensitivity analysis result, the fatigue strength coefficient, the fatigue elongation coefficient and the stress relaxation coefficient are in positive correlation with the reliability, and the other design variables are in negative correlation with the reliability. The elastic modulus and the fatigue strength index have great influence on the reliability, and the reliability can be greatly improved by reducing the elastic modulus and the fatigue strength index of the material from the design aspect. The sensitivity of the large temperature cycle strain range is 3 times of that of the small temperature cycle strain range, and the influence on the reliability is more obvious.

Claims (6)

1. A fatigue reliability assessment method for a compression spring of an in-pile component considering stress relaxation and irradiation influence is characterized by comprising the following steps: the method comprises the following steps:
(1) and acquiring the constraint data of the material, the structure and the load of the compression spring of the reactor internals according to literature investigation, engineering experience and test fitting.
(2) And decomposing the actual amplitude variation temperature load into a constant amplitude load according to a rain flow counting method.
(3) And combining the fatigue life SWT model and the stress relaxation Landgraf model, considering the influence of irradiation on fatigue parameters, and constructing a compression spring fatigue life model considering the influence of stress relaxation and irradiation.
(4) And generating a random parameter simulation input data set according to simulation, engineering experience and literature investigation.
(5) And (4) sampling according to a Monte Carlo method to generate n groups of data, and calculating the fatigue life corresponding to each group of parameters.
(6) Calculating the fatigue total damage D according to the fatigue accumulated damage criterionfAnd total fatigue life Nf。
(7) And calculating the reliability R of the compression spring according to a failure criterion.
(8) Calculating reliability sensitivity S (x) of uncertainty parameteri)。
2. The determination method according to claim 1, wherein the load decomposition method in the second step is a rain flow counting method, and the actually measured variable amplitude load is decomposed into a constant amplitude load with two parameters (variable range and mean value) reserved.
3. The determination method according to claim 1, wherein the compression spring fatigue life model considering stress relaxation and irradiation influence of the step three is a combination of a fatigue life SWT model and a stress relaxation landgraff model; calculating total damage according to Miner fatigue damage accumulation criterion; the influence of irradiation is taken into account by the reduction of the fatigue strength coefficient and the reduction of area due to irradiation.
4. The method of claim 1, wherein in the uncertainty parameters of step four, the operating condition parameters are fitted to the distribution using the multiple sets of output results from the simulation input data set, the material parameters are generally characterized by a normal distribution, the typical values are taken as the sample mean, and the coefficient of variation is taken to be 0.01-0.05.
5. The determination method according to claim 1, wherein the reliability calculation method of step seven is a generalized stress intensity interference model.
6. The method according to claim 1, wherein the reliability sensitivity calculation method of the step eight is a finite difference method.
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