A new beremin calibration method

Abstract

This invention belongs to the field of pressure vessel technology, and in particular, a novel Beremin calibration method. This invention obtains the volume dV and maximum principal stress σ1 of each element corresponding to each fracture toughness integral value J based on finite element simulation analysis data; then defines the initial value of the Weibull slope as m0, and calculates the Weibull stress σ corresponding to each fracture toughness integral value J based on the volume dV and maximum principal stress σ1 of each element obtained in step S2. ωc Take the maximum fracture toughness integral value J under different displacement loads. max And transform into fracture toughness k Jc ; the obtained σ ωc and k Jc Substituting into the formula, we obtain the parameter m. This invention's novel Beremin calibration method combines the principal curve method, which can directly establish σ. w and K Jc This method is simpler and faster than the traditional one.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of pressure vessels, and particularly relates to a novel beremin calibration method. BACKGROUND

[0002] In recent years, with the rapid development of modern industrial technology, pressure vessels are not only gradually developing towards large-scale, but also are increasingly applied to many key fields, such as nuclear power, chemical industry, aviation and the like. In a nuclear reactor, a pressure vessel is always in a high-temperature and high-pressure and nuclear radiation environment, and the harsh environment causes the pressure vessel material to deteriorate. In order to ensure the safe operation and service life of the nuclear reactor, it is necessary to detect the shift of the ductile-brittle transition zone of the pressure vessel material.

[0003] However, the fracture toughness test is complex to operate, and a large number of large-size standard samples are required; at the same time, a fatigue pre-crack also needs to be machined on the sample, which also makes the fracture toughness test need to spend a large amount of funds and time. Based on the above reasons, the fracture toughness test is difficult to be widely applied to actual engineering. Therefore, how to detect the ductile-brittle transition zone of the material based on the small-size sample test, utilize the beremin model and the master curve method to obtain the actual fracture toughness of the material is also a key to ensure the safety of the pressure vessel. However, the traditional beremin utilizes the relationship between the stress intensity factor and the weibull stress, and then iterates the relationship between the failure probability and the weibull, and the calibration process is complex, which is not conducive to the determination of the weibull slope m value in the beremin. SUMMARY

[0004] In order to overcome the defects in the prior art, the application provides a novel beremin calibration method. The application simplifies the calibration process.

[0005] To achieve the above purpose, the application adopts the following technical solutions:

[0006] A novel beremin calibration method, and the specific steps are as follows:

[0007] S1, through a finite element simulation software, setting a temperature T, performing finite element simulation analysis on a PCV sample under different displacement loads to obtain a reference temperature T0 of the PCV sample and fracture toughness integral values J under different displacement loads;

[0008] S2, according to the finite element simulation analysis data, defining a unit region corresponding to each fracture toughness integral value J as a fracture process zone when σ1≥λσ ys , and obtaining the volume dV and the maximum principal stress σ1 of each unit corresponding to each fracture toughness integral value J;

[0009] S3. Define the initial value of the Weibull slope as m0, and calculate the Weibull stress σ corresponding to each fracture toughness integral value J based on the volume dV and maximum principal stress σ1 of each element obtained in step S2. wc ;

[0010] S4. Take the maximum fracture toughness integral value J under different displacement loads and convert it into fracture toughness k. Jc ;

[0011] S5. The σ obtained in step S3 wc And obtain k in step S4 Jc Substituting the parameters into the following linear fitting equation, we obtain the parameter m. The linear fitting equation is shown below:

[0012] ln(k JC )=mln(σ w )-mln(σ u )+ln(1+77exp(0.019(T-T0)-20)) ①

[0013] In the formula σ u σ represents the Weibull stress corresponding to a failure probability of 63.2%. w It is the calculated value of the Weibull stress corresponding to the fracture toughness integral value J, σ wc Let σ be the calculated value of the Weibull stress corresponding to the fracture toughness integral value J under a specific experiment; conduct n experiments, and obtain σ from each group. wc Sort the values ​​in ascending order: σ w 1,σ w 2,...,σ wn .

[0014] S6. If |m-m0|≤0.01, the parameter calibration of the Beremin model is completed, and m is the parameter of the finally calibrated Beremin model, i.e., the Weibull parameter m.

[0015] If |m-m0|>0.01, return to step S3, redefine an initial value m0 for the Weibull slope, and continue executing steps S3~S6 until |m-m0|≤0.01, thus completing the parameter calibration of the Beremin model.

[0016] Preferably, in step S3, λ takes the value of 1 or 2.

[0017] Preferably, in step S3, the calculated Weibull stress σ corresponding to each fracture toughness integral value J is... ωc The specific calculation method is as follows:

[0018]

[0019] wherein, l represents the total number of each unit in the fracture process zone corresponding to the fracture toughness integral value J; i represents the serial number of each unit in the fracture process zone corresponding to the fracture toughness integral value J, i.e. represents the i-th unit in the fracture process zone corresponding to the fracture toughness integral value J, i = 1, 2, 3, …, l; V0 is a reference volume; V i represents the volume of the i-th unit in the fracture process zone corresponding to the fracture toughness integral value J; Vp1 represents the volume of the fracture process zone corresponding to the fracture toughness integral value J, i.e. the total volume of all units in the fracture process zone; σ 1,i represents the maximum principal stress σ1 of the i-th unit in the fracture process zone corresponding to the fracture toughness integral value J.

[0020] Preferably, in step S4, the fracture toughness value k Jc is calculated as follows:

[0021]

[0022] wherein, J C is the obtained fracture toughness integral value J, E is the Young's modulus, and v is the Poisson's ratio.

[0023] Preferably, in step S1, finite element simulation analysis is performed by using the finite element simulation analysis software ABAQUS.

[0024] Preferably, in step S1, the value of the reference temperature T0 is determined according to the ASTM E1820 standard by using the single-temperature method or the multi-temperature method.

[0025] Preferably, in step S5, formula ① is fitted by the following formula:

[0026]

[0027]

[0028] K0 = 31 + 77exp[0.019(T-T0)];

[0029] K Jc (P f ) = 20 + [-ln(1-P f )] 1 / 4 {11 + 77exp[0.019(T-T0)]};

[0030]

[0031] wherein, J Cwhere J is the fracture toughness integral value, E is the Young's modulus, v is the Poisson's ratio, K0 is the scale parameter of Weibull distribution, and K min is the threshold fracture toughness of Weibull distribution; P f is the failure probability.

[0032] Preferably, K0 is the K f value under the failure probability P JC = 63.2%.

[0033] Preferably, K min is equal to

[0034] Preferably, in step S2, σ ys is the yield strength of the material at the set temperature.

[0035] The present application has the following advantages:

[0036] (1) The present application simplifies the calibration process and provides a reference for accurate calibration of the Beremin model by directly establishing the relationship between the fracture toughness K JC and the Weibull stress.

[0037] (2) The calibration of the traditional Beremin model requires determining the linear relationship between the stress intensity factor K J and the Weibull stress first, then obtaining n fracture toughnesses K Jc from the fracture toughness test, and using the linear interpolation method and the obtained relationship curve between σ w and K J to obtain the corresponding σ w of each K Jc , but the research on the problem of the dispersion of fracture toughness in the ductile-brittle transition zone of the material with temperature change is not mature, and the new Beremin calibration method of the present application combines the master curve method and can directly establish the relationship between σ w and K Jc , which is more convenient and faster than the traditional method. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 is a graph of the relationship between the fracture toughness integral value J and time of the present application.

[0039] Figure 2 is a fitting effect graph between K JC and the Weibull stress of the present application, and the slope is the value of m0.

[0040] Figure 3 is a model diagram of a 0.3B PCV sample of the present application.

[0041] Figure 4 The model diagram for loading PCV sample by using indenter for the present application.

[0042] Figure 5 The experimental result diagram for the present application in the case of indenter displacement 1.0 mm in Example 1.

[0043] Figure 6 The flowchart for the present application. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and examples, and all other examples obtained by those skilled in the art without making creative labor on the basis of the examples in the present application belong to the protection scope of the present application.

[0045] As shown in Figures 1-5 :

[0046] One: J-integral method is a kind of fracture mechanics theory with rigorous theory, clear definition, applicable to linear elasticity and elastoplasticity, which can be used to calculate the stress and strain field intensity of crack tip under various force conditions and various shaped structures, and is widely used in pressure vessel integrity assessment. J-integral and the relationship between the potential energy and deformation work of the sample in the loading process are used to calculate the J-integral value (i.e. fracture toughness integral value J).

[0047] Through Abaqus finite element simulation software, under a certain set temperature T, a certain displacement is applied to the sample in the same direction to obtain the J-integral of the object, and then through ASTM E1820 standard, the reference temperature T0 can be determined by single temperature method or multi-temperature method.

[0048] Through the obtained J-integral, the formula is used to obtain k JC ;

[0049]

[0050] When the stress and strain field intensity of crack tip reaches the critical state of crack propagation, the equivalent fracture toughness of 1B thickness sample (25.4 mm) under a certain cumulative failure probability;

[0051] In the formula, J C is the obtained J-integral, i.e. maximum J-integral; E is Young's modulus, which is 207 GPa, and v is Poisson's ratio, which is 0.3.

[0052] Two: the relationship between P f -k JC is established by using master curve method:

[0053]

[0054] where P f is the failure probability; k Jc is obtained from equation (1) ;

[0055] K0, scale parameter of Weibull distribution, whose value is equal to P f k at P Jc = 63.2%,

[0056] K min , threshold fracture toughness of Weibull distribution, for ferritic steels K min can be taken as a constant independent of temperature and specimen size, and generally taken as K This step adopts the master curve method.

[0057] Three: for ferritic steels

[0058] K0= 31 + 77exp[0.019(T - T0)] (3)

[0059] Substituting equation (3) into equation (2) gives:

[0060] K Jc (P f ) = 20 + [-ln(1 - P f )] 1 / 4 {11 + 77exp[0.019(T - T0)]} (4)

[0061] Since T and T0 have been determined in step one, equation (4) is still a function relationship of K JC and P f .

[0062] Four: through the beremin probability model of fracture toughness:

[0063]

[0064] where σ u and m can be considered as constants;

[0065] Based on different structures σ w are equal, the failure probabilities of the two are equal, so at this time their fracture toughnesses are also equivalent. That is, σ w are equal, P f in equation (4) and equation (5) are equal, according to the relationship of P f — k JC in equation (4), and P f — σ w in equation (5), KJC and σ w The relationship (the formula contains the constant σ) u and m).

[0066] 5: After transformation K JC and σ w The relationship is:

[0067] ln(k JC )=mln(σ w )-mln(σ u )+ln(1+77exp(0.019(T-T0)-20)).

[0068] Specifically, different k are obtained under different displacements. JC Its corresponding σ w Then, after fitting ln(k) JC ) and ln(σ w The slope of the obtained straight line is m, such as... Figure 2 As shown.

[0069] like Figure 6 As shown, a novel beremin calibration method is described, specifically:

[0070] S1. Using finite element simulation software, set the temperature T, and perform finite element simulation analysis on the PCV sample under different displacement loads to obtain the reference temperature T0 and the fracture toughness integral value J of the PCV sample under different displacement loads.

[0071] S2. Based on the finite element simulation analysis data, the σ1≥λσ corresponding to each fracture toughness integral value J is... ys The element region is defined as the fracture process region, and the volume dV and maximum principal stress σ1 of each element corresponding to each fracture toughness integral value J are obtained.

[0072] S3. Define the initial value of the Weibull slope as m0, and calculate the Weibull stress σ corresponding to each fracture toughness integral value J based on the volume dV and maximum principal stress σ1 of each element obtained in step S2. wc The specific calculation method is as follows:

[0073]

[0074] In the formula, l represents the total number of elements in the fracture process region corresponding to the fracture toughness integral value J; i represents the sequence number of each element in the fracture process region corresponding to the fracture toughness integral value J, i.e., the i-th element in the fracture process region corresponding to the fracture toughness integral value J, i = 1, 2, 3, ..., l; V0 is the reference volume; V iVpi represents the volume of the i-th element in the fracture process zone corresponding to the fracture toughness integral value J; Vp1 represents the volume of the fracture process zone corresponding to the fracture toughness integral value J, that is, the total volume of all elements in the fracture process zone; σ 1,i represents the maximum principal stress σ1 of the i-th element in the fracture process zone corresponding to the fracture toughness integral value J;

[0075] S4, take the maximum fracture toughness integral value J under different displacement loads, and convert it into fracture toughness k Jc , the fracture toughness value k Jc is calculated as follows:

[0076]

[0077] In the formula, J C is the obtained fracture toughness integral value J, E is the Young's modulus, and v is the Poisson's ratio;

[0078] S5, substituting σ wc obtained in step S3 and k Jc obtained in step S4 into the following formula to obtain the parameter m, and the linear fitting relationship is as follows:

[0079] ln(k JC )=mln(σ w )-mln(σ u )+ln(1+77exp(0.019(T-T0)-20))

[0080] In the formula, σ u is the Weibull stress corresponding to the failure probability of 63.2%, which is 4.9425*10^3 MPa in the embodiment of the present application; σ wc is the calculated value of the Weibull stress corresponding to the fracture toughness integral value J under a certain specific experiment; n experiments are performed, and the obtained σ wc values of each group are sorted from small to large: σ w1 , σ w2 ,..., σ wn ;

[0081] S6, if |m-m0|≤0.01, the parameter calibration of the beremin model is completed, and m is the final calibrated parameter of the beremin model, that is, the Weibull parameter m;

[0082] If |m-m0|>0.01, return to step S3, redefine an initial value m0 of the Weibull slope, and continue to execute steps S3-S6 until |m-m0|≤0.01, and the parameter calibration of the beremin model is completed.

[0083] Embodiment 1

[0084] The PCV sample of 0.3B thickness (1B=25.4mm) was calibrated as follows:

[0085] (1) The PCV sample model of 0.3T, and the results are shown in Figure 3

[0086] (2) The load of different displacements of the PCV sample was obtained by using the indenter, and the corresponding fracture toughness integral value J and fracture toughness value k JC , as shown in Table 1 below:

[0087] Table 1

[0088] Penetration head displacement (mm) J (MJ / m 2 )]]> k jc ]]> 0.1 14.8148 58.05135657 0.2 39.2341 94.47052392 0.3 75.2284 130.8143505 0.4 128.832 171.1891955 0.5 177.788 201.10168 0.6 223.791 225.6242549 0.7 277.088 251.0575784 0.8 333.025 275.2345154 0.9 385.891 296.2762243 1.0 458.694 323.0174663 1.1 525.255 345.660357 1.2 578.131 362.6415858 1.3 627.644 377.8515145 1.4 675.546 392.005301

[0089] The relationship diagram between the fracture toughness integral value J and time can be obtained by the finite element software, as shown in Figure 1 ; Figure 4 The experimental result diagram when the indenter displacement is 1.0mm, and the weibull stress σ w of this part is calculated by the following formula:

[0090]

[0091] Then a group of data can be obtained by the k jc and weibull stress σ w under the condition of the indenter displacement of 1.0mm, and the corresponding data can also be obtained when the indenter displacement is 0.1mm and 0.2mm, finally the fitting effect diagram between K JC and weibull stress σ w is obtained as shown in Figure 2 , and as shown in Figure 2 , it can be seen that K JC and weibull stress σ w are linear after fitting, and the linear relationship between them, and the slope is the value of m0, which is consistent with the formula derived by the present application:

[0092] ln(k JC )=mln(σ w )-mln(σ u )+ln(1+77exp(0.019(T-T0)-20)), which shows the effectiveness of the beremin model parameter calibration method of the present application.

[0093] The above merely describes preferred embodiments of the present application, and is not used to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A novel method of beremin calibration, characterized by, The specific steps are as follows: S1, through finite element simulation software, set temperature T, under different displacement load, PCV sample is analyzed by finite element simulation, the reference temperature T0 and the fracture toughness integral value J under different displacement load of the PCV sample are obtained; S2, according to the finite element simulation analysis data, defining the unit area corresponding to each fracture toughness integral value J σ1≥λσ as the fracture process zone, obtaining the volume dV of each unit corresponding to each fracture toughness integral value J and the maximum principal stress σ1; ys S2, according to the finite element simulation analysis data, defining the unit area corresponding to each fracture toughness integral value J σ1≥λσ as the fracture process zone, obtaining the volume dV of each unit corresponding to each fracture toughness integral value J and the maximum principal stress σ1; S3, defining an initial value of the Weibull slope as m0, and calculating a calculated value of the Weibull stress σ corresponding to each fracture toughness integral value J based on the volume dV of each unit and the maximum principal stress σ1 obtained in step S2 wc ; S4, take the maximum fracture toughness integral value J under different displacement load, and convert it into fracture toughness k Jc ; S5, obtaining σ from step S3 wc and k from step S4 Jc Substituting the following linear fitting relationship, the parameter m is obtained, and the linear fitting relationship is as follows: ln(k JC )=mln(σ w )-mln(σ u )+ln(1+77exp(0.019(T-T0)-20)) ① where σ u is the Weibull stress corresponding to a failure probability of 63.2%. Formula ① is fitted from the following formula: ； ； ； ； ； wherein J C To obtain the fracture toughness integral value J, E is the Young's modulus, v is the Poisson's ratio, K 0 is the scale parameter of the Weibull distribution, unit: ; K min is the threshold fracture toughness of the Weibull distribution; P f is the failure probability; S6, if |m-m0|≤0.01, the parameter calibration of beremin model is completed, and m is the parameter of the final calibrated beremin model, that is, Weibull parameter m; If |m-m0|>0.01, return to step S3, redefine an initial value m0 of Weibull slope, continue to execute steps S3-S6 until |m-m0|≤0.01, complete the parameter calibration of beremin model.

2. The novel method of calibrating beremin according to claim 1, wherein: In step S3, λ takes 1 or 2.

3. The novel method of calibrating beremin according to claim 1, wherein, In step S3, the calculated value σ of the weibull stress corresponding to each fracture toughness integral value J ωc The specific calculation is as follows: In the formula, l represents the total number of each unit in the fracture process zone corresponding to the fracture toughness integral value J; i represents the serial number of each unit in the fracture process zone corresponding to the fracture toughness integral value J, that is, the i-th unit in the fracture process zone corresponding to the fracture toughness integral value J, i = 1, 2, 3, …, l; V0 is a reference volume; V i represents the volume of the i-th unit in the fracture process zone corresponding to the fracture toughness integral value J; Vp1 represents the volume of the fracture process zone corresponding to the fracture toughness integral value J, that is, the total volume of all units in the fracture process zone; σ 1,i represents the maximum principal stress σ1 of the i-th unit in the fracture process zone corresponding to the fracture toughness integral value J.

4. The novel method of calibrating beremin according to claim 1, wherein, In step S4, the fracture toughness value k Jc is calculated as shown below: wherein J C To obtain the fracture toughness integral value J, E is the Young's modulus and v is the Poisson's ratio.

5. The novel method of calibrating beremin according to claim 1, wherein: In step S1, finite element simulation analysis is carried out by using finite element simulation analysis software ABAQUS.

6. The novel method of beremin calibration according to claim 1, characterized in that: In step S1, the value of reference temperature T0 is determined according to ASTM E1820 standard by single temperature method or multiple temperature method.

7. The novel method of calibrating beremin according to claim 1, wherein: The K 0 Failure probability P f =63.2% under K JC value.

8. The novel method of beremin calibration according to claim 1, characterized in that: The K min 20 .

9. The novel method of beremin calibration according to claim 1, characterized in that: In step S2, σ ys is the yield strength of the material at the corresponding set temperature.

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