Improved Minami parameter calibration method

Abstract

The invention relates to the technical field of material mechanical property research, in particular to an improved Minami parameter calibration method. According to the method, a complete calibration process is formed through systematic finite element modeling, fracture process zone analysis and parameter iteration fitting, the dependence of a traditional Minami method on test data is remarkably reduced, the parameter calibration efficiency and accuracy are improved, and the method is suitable for cleavage fracture analysis of various materials.

Description

Technical Field

[0001] The present invention relates to the technical field of the study of the mechanical properties of materials, and particularly to an improved method for calibrating Minami parameters. Background Art

[0002] In recent years, with the booming development of the materials industry, it has become an urgent need to conduct more accurate analyses of the integrity and applicability of engineering structures in order to formulate more precise maintenance strategies for engineering structures and extend their service life. However, traditional prediction methods based on a single macroscopic mechanical parameter (such as the stress intensity factor K or the J-integral) are insufficient in this regard. Such methods have obvious limitations in dealing with the influence of constraints on cleavage fracture behavior. More critically, they fail to accurately reveal the great influence of cleavage fracture toughness on material properties from the microscopic level.

[0003] Therefore, people have started to seek new solutions, that is, microscopic mechanical models based on the probabilistic interpretation of the cleavage fracture process. Currently, the research focus is mainly on probability models combined with the weakest link statistics. For example, the Beremin model combines the statistical characteristics of the local stress field at the crack tip with the discreteness of the material fracture toughness by introducing the Weibull stress, providing a more scientific basis for the maintenance and life extension of engineering structures. This model determines the range of the fracture process zone by finite element simulation of the stress distribution at the crack tip, combines the improved RKR criterion, and fits the fracture probability through the Weibull distribution, significantly simplifying the experimental dependence of the traditional method for calibrating Minami parameters. At the same time, it can quantify the influence of constraint effects (such as the t-stress or q-parameter) on the fracture behavior. However, the reliability of the traditional method for calibrating Minami parameters is closely related to its parameters m and σ u and the calibration process of the parameters has great complexity and instability of the calibration method; at the same time, the traditional method for calibrating Minami parameters relies on a large number of fracture toughness tests, which is less feasible for materials with scarce data, and does not fully consider the statistical distribution characteristics of the local stress field at the crack tip.

[0004] It can be seen that the traditional method for calibrating Minami parameters still needs to be further optimized. Summary of the Invention

[0005] In order to avoid and overcome the technical problems existing in the prior art, the present invention provides an improved method for calibrating Minami parameters. The present invention can effectively reduce the amount of data in the calibration process of the Minami parameter calibration method and significantly simplify the calibration process.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] An improved method for calibrating Minami parameters, comprising the following calibration steps:

[0008] S1. Establish a finite element model based on the material parameters of the material to be measured and the sample model of the fracture toughness test, and perform finite element analysis at each set fracture toughness limit value K J ;

[0009] S2. Obtain the volume dV of each element and the corresponding maximum principal stress σ1 in the fracture process zone corresponding to each fracture toughness limit value K J ;

[0010] S3. Define the region where the maximum principal stress σ1 is greater than or equal to λ times the material yield strength σ ys as the fracture process zone;

[0011] S4. Set the initial value m0 of the parameter m in the stress calculation formula, and use this stress calculation formula to calculate the Weibull stress limit value σ J corresponding to each fracture toughness limit value K ω in the fracture process zone through the volume dV and the maximum principal stress σ1 of each element;

[0012] S5. Construct a relationship curve between the fracture toughness limit value K J and the Weibull stress limit value σ ω , and input the fracture toughness measurement value K JC obtained through the fracture toughness test into this relationship curve by interpolation to obtain the Weibull stress estimated value σ JC corresponding to each fracture toughness measurement value K ωC ;

[0013] S6. Calculate the failure probability P ωC of each Weibull stress estimated value σ f (σ ωC ), and then perform linear fitting using the relationship between ln[ln 1 / (1 - P f )] and ln(σ ωC ) to calculate the calculated value m i of the parameter m and the calculated value σ ui of the Weibull stress;

[0014] S7. If |m0 - m i | is less than the fitting threshold t, the parameter calibration is completed; otherwise, repeat steps S4 - S6 until the parameter calibration is completed.

[0015] As a further solution of the present invention: The calculation formula of the Weibull stress limit value σ ω is expressed as follows:

[0016]

[0017] In the formula, V pl 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; V0 represents the reference volume; V i represents the volume of the i-th element in the fracture process zone corresponding to the fracture toughness integral value J; 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; n represents the total number of each element in the fracture process zone corresponding to the fracture toughness integral value J.

[0018] As a further solution of the present invention: The calculation formula of the fracture toughness measured value K JC is as follows:

[0019]

[0020] In the formula, E represents the Young's modulus of the material to be measured, v represents the Poisson's ratio of the material to be measured; J c represents the obtained fracture toughness integral value J.

[0021] As a further solution of the present invention: The relationship between ln[ln 1 / (1 - P f )] and ln(σ ωC ) is derived by the following formula:

[0022]

[0023] In the formula, j represents the serial number after arranging the calculated Weibull stress limit values σ ω in ascending order; N represents the total number of the calculated Weibull stress limit values σ ω ; exp(·) represents the exponential function with the natural constant e as the base; σ u represents the Weibull stress value when the failure probability is equal to 63.2%.

[0024] As a further solution of the present invention: Use ABAQUS software to establish a finite element model. When defining the plastic properties of the material to be measured in ABAQUS software, the true stress and strain relationship of the material to be measured is required. Therefore, the material data of the material to be measured also needs to be transformed by the following formula to obtain the true stress and true strain relationship required by ABAQUS software;

[0025] A = (1 + ε)σ;

[0026] a = ln(1 + ε);

[0027] In the formula, σ represents the engineering stress obtained through the fracture toughness test; ε represents the engineering strain obtained through the fracture toughness test; A represents the true stress of the material to be measured; a represents the true strain of the material to be measured.

[0028] As a further solution of the present invention: the value of λ is 1 or 2.

[0029] As a further solution of the present invention: the value of t is 0.01.

[0030] As a further solution of the present invention: the fracture toughness tests are respectively carried out at -28°C and -7°C.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] 1. Through systematic finite element modeling, fracture process zone analysis and parameter iterative fitting, the present invention forms a complete calibration process, significantly reducing the dependence on test data of the traditional Minami method, improving the efficiency and accuracy of parameter calibration, and being applicable to cleavage fracture analysis of various materials.

[0033] 2. The clear calculation formula of Weibull stress quantitatively correlates parameters such as the volume of the fracture process zone and the element stress, providing a standardized method for microscopic stress calculation and ensuring the standardization and accuracy of stress calculation.

[0034] 3. By constructing a fracture toughness measurement formula through the Young's modulus and Poisson's ratio of the material, the present invention directly correlates the inherent properties of the material with the fracture toughness, improving the accuracy and reliability of the measured value and providing a scientific basis for subsequent analysis.

[0035] 4. By establishing a statistical model of the failure probability and Weibull stress, and quantitatively correlating the fracture probability with the local stress state through the linear fitting method, the present invention conforms to the statistical characteristics of material fracture and improves the scientificity of fracture probability analysis.

[0036] 5. By providing a conversion formula from engineering stress and strain to true stress and strain, the present invention ensures the accuracy of the definition of material plastic properties in the ABAQUS software, improving the reliability of finite element simulation and the credibility of the results.

[0037] 6. By limiting the value of λ to 1 or 2, the present invention simplifies the determination criterion of the fracture process zone, avoids the randomness of parameter values, and improves the practicability and engineering operability of the method.

[0038] 7. By setting the fitting threshold t = 0.01, while ensuring the parameter accuracy, the present invention effectively controls the number of iterations, balances the calculation efficiency and result accuracy, and makes the calibration process efficient and controllable.

[0039] 8. It is stipulated that the fracture toughness test is carried out at -28°C and -7°C, and the fracture property data of the material under low-temperature environment are obtained specifically, which improves the applicability of the method to low-temperature working conditions and its engineering guiding significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of the present invention.

[0041] Figure 2 It is the C(T) specimen configuration in the present invention.

[0042] Figure 3 It is the finite element model and mesh distribution of the specimen in the present invention.

[0043] Figure 4 It is a graph showing the relationship between true stress and true strain of A515-70 steel proposed by the present invention.

[0044] Figure 5 It is the linear fitting graph of the Weibull stress σ ω and the fracture toughness value K JC of A515-70 steel in the present invention at -28°C.

[0045] Figure 6 It is the curve of the failure probability P f and the fracture toughness value K JC of the improved Minami-type prediction of A515-70 steel at -28°C in the present invention.

[0046] Figure 7 It is the stress distribution nephogram of the specimen of A515-70 steel at -7°C proposed by the present invention.

[0047] Figure 8 It is the fracture toughness data distribution of A515-70 steel studied in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0048] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0049] Please refer to Figures 1 to 8 , the present invention includes the following contents:

[0050] I. Finite element analysis

[0051] A finite element model is established according to the material parameters of the material to be tested and the specimen model of the fracture toughness test, and at each set fracture toughness limit value KJ Perform finite element analysis below.

[0052] As Figure 2 shown, use ABAQUS software to establish a finite element model. When defining the plastic properties of the material to be tested in ABAQUS software, the true stress-strain relationship of the material to be tested is required. Therefore, the material data of the material to be tested needs to be transformed using the following formula to obtain the true stress-true strain relationship required by ABAQUS software;

[0053] A = (1 + ε)σ;

[0054] a = ln(1 + ε);

[0055] In the formula, σ represents the engineering stress obtained through the fracture toughness test; ε represents the engineering strain obtained through the fracture toughness test; A represents the true stress of the material to be tested; a represents the true strain of the material to be tested.

[0056] As Figure 2 shown, calibrate the C(T) specimen with a specimen thickness B = 25 mm and a specimen width W = 50 mm. As Figure 3 shown, by analyzing A515-70 steel in the finite element analysis software, the true stress-true strain relationship curve is obtained. It can be seen from Figure 3 that for A515-70 steel at -7°C and -28°C, its true stress and true strain show a positive correlation.

[0057] The measured fracture toughness value K of the A515-70 steel specimen JC data is shown in Table 1.

[0058] Table 1 Measured fracture toughness value K JC Data

[0059]

[0060] II. Fracture toughness limit value

[0061] Obtain the volume dV of each element and the corresponding maximum principal stress σ1 in each fracture process zone corresponding to each fracture toughness limit value K J . The calculation formula for the measured fracture toughness value K JC is as follows:

[0062]

[0063] In the formula, E represents the Young's modulus of the material to be tested, v represents the Poisson's ratio of the material to be tested; J c represents the obtained fracture toughness integral value J.

[0064] The minimum and maximum J-integral values of the C(T) specimen of A515-70 steel at -28 °C were determined to be 5.4914 KJ / m2 and 200 KJ / m2 respectively, and then a series of fracture toughness integral values J within this range obtained from finite element analysis were extracted. c And the fracture toughness measurement values are shown in Table 2:

[0065] Table 2 Calibration Results of A515-70 Steel at -28 °C

[0066]

[0067] III. Fracture Process Zone

[0068] The region where the maximum principal stress σ1 is greater than or equal to λ times the material yield strength σ ys is defined as the fracture process zone. Among them, the value of λ is usually 1 or 2.

[0069] IV. Weibull Stress Limit Value

[0070] Set the initial value m0 of the parameter m in the stress calculation formula, and use this stress calculation formula to calculate the fracture toughness limit values K in the fracture process zone through the volume dV of each element and the maximum principal stress σ1 J The corresponding Weibull stress limit value σ ω .

[0071] The calculation formula of the Weibull stress limit value σ ω is expressed as follows:

[0072]

[0073] In the formula, V pl 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; V0 represents the reference volume; V i represents the volume of the i-th element in the fracture process zone corresponding to the fracture toughness integral value J; 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; n represents the total number of elements in the fracture process zone corresponding to the fracture toughness integral value J.

[0074] The Weibull stress limit values of A515-70 steel at -28 °C are shown in Table 2.

[0075] Table 2 Weibull Stress Limit Values

[0076]

[0077]

[0078] V. Relationship curve

[0079] Construct the relationship curve between the fracture toughness limit value K J and the Weibull stress limit value σ ω , and input the fracture toughness measurement value K JC obtained through the fracture toughness test into this relationship curve by interpolation to obtain the corresponding Weibull stress estimated value σ JC for each fracture toughness measurement value K ωC .

[0080] The relationship formula of this relationship curve was obtained through linear fitting, as shown in Figure 5 . Subsequently, in order to verify the accuracy of the calibrated data, substitute this relationship formula into the following formula:

[0081]

[0082] In the formula, b0 represents the initial ligament size, mm; σ ys represents the yield stress of the material at the corresponding temperature, MPa; M represents the dimensionless deformation degree.

[0083] VI. Calculate specific values

[0084] Calculate the failure probability P ωC for each Weibull stress estimated value σ f (σ ωC ), and then perform linear fitting on the relationship between ln[ln 1 / (1 - P f )] and ln(σ ωC ) to calculate the calculated value m i of the parameter m and the calculated value σ ui of the Weibull stress.

[0085] The relationship between ln[ln 1 / (1 - P f )] and ln(σ ωC ) is derived through the following formula:

[0086]

[0087] In the formula, j represents the serial number after arranging the calculated Weibull stress limit values σ ω in ascending order; N represents the total number of the calculated Weibull stress limit values σ ω ; exp(·) represents the exponential function with the natural constant e as the base; σ u represents the Weibull stress value when the failure probability is equal to 63.2%.

[0088] The failure probabilities corresponding to the calculated fracture toughness data are listed in Table 3. The obtained failure probability P f versus the fracture toughness value K JC is shown in the curve as Figure 6 follows.

[0089] Table 3 Failure Probabilities Corresponding to the Test Data of A515-70 Steel

[0090]

[0091] VII. Loop Processing

[0092] If |m0 - m i | is less than the fitting threshold t, where t is taken as 0.01, then the parameter calibration is completed; otherwise, steps four to six are repeated until the parameter calibration is completed.

[0093] As mentioned above, the above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, making equivalent replacements or changes, shall be covered by the protection scope of the present invention.

Claims

1. An improved method for calibrating Minami parameters, characterized in that, It includes the following calibration steps: S1. Establish a finite element model based on the material parameters of the material to be tested and the specimen model of the fracture toughness test, and conduct finite element analysis under each set fracture toughness limit value K J ; S2. Obtain the fracture toughness limit values K for each one J The volume dV of each unit in the corresponding fracture process zone and the corresponding maximum principal stress σ1; S3. Define the region where the maximum principal stress σ1 is greater than or equal to λ times the material yield strength σ ys as the fracture process zone; S4. Set the initial value m0 of the parameter m in the stress calculation formula, and use this stress calculation formula to calculate the respective fracture toughness limit values K in the fracture process zone through the volume dV and the maximum principal stress σ1 of each element. J The corresponding Weibull stress limit value σ ω ; S5. Construct the fracture toughness limit value K J and the relationship curve with the Weibull stress limit value σ ω . Then input the fracture toughness measured value K JC obtained through the fracture toughness test into this relationship curve to obtain the corresponding Weibull stress estimated value σ JC for each fracture toughness measured value K ωC ; S6. Calculate the Weibull stress estimate values σ ωC of the failure probability P f (σ ωC ), and then use the relationship between ln[ln1 / (1 - P f )] and ln(σ ωC ) for linear fitting to calculate the calculated value m i of the parameter m and the calculated value σ ui of the Weibull stress; S7. If |m0 - m i | is less than the fitting threshold t, then the parameter calibration is completed; Otherwise, steps S4 - S6 are repeatedly executed until the parameter calibration is completed.

2. An improved Minami parameter calibration method according to claim 1, characterized in that, Weibull stress limit value σ ω The calculation formula is expressed as follows: Wherein, V pl 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; V0 represents the reference volume; V i represents the volume of the i-th element in the fracture process zone corresponding to the fracture toughness integral value J; 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; n represents the total number of each element in the fracture process zone corresponding to the fracture toughness integral value J.

3. An improved Minami parameter calibration method according to claim 2, characterized in that, Measured value of fracture toughness K JC The calculation formula is as follows: where E represents the Young's modulus of the material to be measured, and ν represents the Poisson's ratio of the material to be measured; J c represents the obtained fracture toughness integral value J.

4. An improved Minami parameter calibration method according to claim 3, characterized in that, ln[ln(1 / (1 - P))] f )] and ln(σ ωC ) is derived by the following formula: In the formula, j represents the calculated Weibull stress limit value σ ω The serial number arranged in ascending order; N represents the calculated Weibull stress limit value σ ω The total quantity; exp(·) represents the exponential function with the natural constant e as the base; σ u Represents the Weibull stress value when the failure probability is equal to 63.2%.

5. An improved Minami parameter calibration method according to any one of claims 1-4, characterized in that, Use ABAQUS software to establish a finite element model. When defining the plastic properties of the material to be tested in ABAQUS software, the true stress - strain relationship of the material to be tested is required. Therefore, the following formula is also needed to transform the material data of the material to be tested to obtain the true stress - true strain relationship required by ABAQUS software; A = (1 + ε)σ; a = ln(1 + ε); In the formula, σ represents the engineering stress obtained through the fracture toughness test; ε represents the engineering strain obtained through the fracture toughness test; A represents the true stress of the material to be tested; a represents the true strain of the material to be tested.

6. An improved Minami parameter calibration method according to claim 5, characterized in that, The value of λ is 1 or 2.

7. An improved Minami parameter calibration method according to claim 6, characterized in that, t takes the value of 0.

01.

8. An improved Minami parameter calibration method according to claim 7, characterized in that, The fracture toughness tests are carried out at - 28°C and - 7°C respectively.

Images