Method for calibrating softening model parameters of material at high temperature

Abstract

The invention relates to the technical field of high-temperature instrument testing and material performance prediction, in particular to a method for calibrating softening model parameters of a material at a high temperature, which comprises the following steps: performing finite element analogue simulation on a hypothetical material to obtain simulated indentation responses under different hypothetical material parameters, and fitting the obtained indentation response data; performing nanoindentation test on different areas after welding at high temperature to obtain a high-temperature nanoindentation test indentation response curve; and solving the obtained nanoindentation response curve of the tested material at the high temperature according to the fitting parameters to finally obtain constitutive parameters. According to the method, high-temperature nanoindentation inversion is used for calibrating the softening model parameters of the material at the high temperature, prediction of a stress-strain curve is provided for a non-uniform structure at the high temperature, damage factors are introduced on the basis of a Ludwick constitutive model, and the high-temperature softening model parameters of the material at the high temperature are obtained. The problem that after the temperature rises, the stress value is reduced along with the increase of the strain value, and the model cannot simulate and predict is solved.

Description

Technical Field

[0001] The invention relates to the technical field of high-temperature instrument testing and prediction of material properties, and in particular to a method for calibrating material softening model parameters at high temperatures. Background Art

[0002] With the introduction of high-performance manufacturing technology, new challenges have been raised for the study of mechanical properties of high-temperature structural materials under high-temperature service. For inhomogeneous joints with gradient microstructures, the performance prediction and characterization of different gradient regions at high temperatures are the key to accurate and efficient prediction of high-temperature structural parts. The inhomogeneity of the joint can easily lead to fracture of the serving structure in harsh environments such as high temperature and complex stress states. However, the traditional high-temperature mechanical single-pull test method can only evaluate the overall performance of the inhomogeneous structure, and cannot fully characterize the partitioned microstructure performance of each region of the inhomogeneous structure. At the same time, due to the size limitations of inhomogeneous joints (such as: welded joints are only 2mm, heat-affected zones are 0.3mm), it further affects the in-depth understanding and development of inhomogeneous structure-performance.

[0003] Indentation hardness test is a widely used characterization technique that can be used to characterize the properties of materials at different scales and is widely used in the study of mechanical properties of materials. Nanoindentation test is a very mature high-throughput testing technology. Based on the Oliver-Pharr analysis of the displacement and load curves, the elastic modulus and hardness values ​​can be calculated according to the unloading process. The power hardening model is usually used to describe the relationship between stress and strain. However, for stress-strain curves at high temperatures, as the strain increases, the stress will decrease, that is, the material properties will soften. This situation cannot be simulated using the power hardening model at room temperature.

[0004] The application and development of finite element technology has achieved accurate simulation of nanoindentation technology. Literature shows that the constitutive parameters of materials can be inverted by combining finite element technology with nanoindentation technology. There are generally two types of inversion methods. The first type is to invert the material constitutive parameters based on the indentation response curve of indentation measurement through optimization algorithms, deep learning methods and finite element simulation, but the calculation process is complicated and the algorithm model is huge. The second type is to use the dimensionless method to predict the material constitutive parameters based on the indentation response curve. These methods are all based on the prediction of constitutive parameters of stress-strain curves where stress increases with increasing strain. However, there are very few studies on material constitutive prediction methods for the phenomenon of softening material properties. Summary of the invention

[0005] In order to solve the above problems, the present invention provides a method for calibrating the parameters of the softening model of materials at high temperatures. The method provides a method for calibrating the parameters of the softening model of materials at high temperatures by inversion of high-temperature nanoindentation, and provides a prediction of the stress-strain curve for non-uniform tissues at high temperatures. The Ludwick constitutive model evolved from the Hollomon constitutive model, which can more accurately describe the stress-strain curves of more materials. Its form is shown in the following formula:

[0006]

[0007] On the basis of Ludwick constitutive model, damage factor is introduced to solve the problem that the stress value decreases with the increase of strain value after the temperature rises and the model cannot simulate and predict.

[0008] The technical solution of the present invention is as follows:

[0009] A method for calibrating parameters of a material softening model at high temperature comprises the following steps:

[0010] S1: Perform finite element simulation on the hypothetical material to obtain simulated indentation responses under different hypothetical material parameters, and fit the obtained indentation response data;

[0011] S2: Perform high temperature nanoindentation test on different areas after welding to obtain the indentation response curve of high temperature nanoindentation test;

[0012] S3: Solve the nanoindentation response curve of the material under test to obtain the constitutive parameters.

[0013] In step S1, the following steps are included:

[0014] S11: Use orthogonal test method to establish hypothetical material model;

[0015] S12: Perform finite element indentation simulation analysis to obtain an indentation response curve of an imaginary material;

[0016] S13: The following relationship is obtained through the indentation response curve of the hypothetical material obtained in S12: y = W t / (E r h m 3 ), x=σ r *(1-ω) / E r ,

[0017] Where: W t is the total work;

[0018] E r is the reduced modulus;

[0019] hm is the maximum depth of indentation;

[0020] σ r * is characteristic stress;

[0021] ω is the damage factor;

[0022] Fitting to obtain the relationship between y=f(x);

[0023] S14: According to In the formula, σ y is the yield stress, n is the hardening index, and K is the hardening strength. is the characteristic strain;

[0024] The fitting equations are y=f1(x1,x2),x2=f2(K,n),x3=f2(K,η);

[0025] S15: Fit the following equation:

[0026] x=x1+x2;

[0027] y=A×exp(Bx1)×exp(Cx2)+D;

[0028]

[0029] x2=q1×exp(q2x3)×exp(q3n)+q4;

[0030] x3=p1×exp(p2K)×exp(p3η)+p4;

[0031] Among them, A, B, C, D, q i ,p i is the fitting parameter;

[0032] S16: Fit the equation in step S15 and find the parameters A, B, C, D, q i ,p i .

[0033] In step S3, the following steps are included:

[0034] S31: obtaining the nanoindentation response curve of the non-uniform high-temperature alloy after welding at high temperature by a high-temperature nanoindenter, calculating the y value, and then obtaining the x value according to the relationship y=f(x);

[0035] S32: Through the relationship x=x1+x2; y=A×exp(Bx1)×exp(Cx2)+D, we can obtain x1 and x2; and then Obtain the yield strength;

[0036] S33: By x2=f2(x3,n) and Find K,n;

[0037] S34: Passed and x3=p1×exp(p2K)×exp(p3η)+p4; find η,

[0038] S35: Conclusion

[0039] The beneficial effects of the present invention are:

[0040] 1. The present invention discloses a method for calibrating parameters of a material softening model at high temperatures. The method can provide accurate and efficient stress-strain prediction for different regions of non-uniform joints under high-temperature service, guide the structural design of high-temperature service parts, and provide strong support for structural design.

[0041] 2. The present invention discloses a method for calibrating the parameters of a material's softening model at high temperatures. The method for calibrating the parameters of a material's softening model at high temperatures is a key technology for accurately and efficiently predicting micro-area performance, and is used to solve the problem of unknown mechanical properties of joints with uneven gradient tissue properties.

[0042] 3. The present invention discloses a method for calibrating model parameters of a material softening at high temperature. The method for calibrating model parameters of a material softening at high temperature efficiently predicts the constitutive model parameters of the material softening phenomenon at high temperature and solves the mechanical constitutive model equation of the material softening phenomenon at high temperature. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] By reading the detailed description of the preferred embodiment below, the scheme and advantages of the present application will become clear to those skilled in the art. The accompanying drawings are only for the purpose of illustrating the preferred embodiment and are not to be considered as limiting the present invention.

[0044] In the attached picture:

[0045] Figure 1 A flow chart of a method for calibrating parameters of a material softening model at high temperature according to an embodiment of the present invention;

[0046] Figure 2 is the nanoindentation load-displacement diagram;

[0047] Figure 3 This is the stress-strain diagram with softening phenomenon at high temperature;

[0048] Figure 4 It is the finite element simulation model and mesh model of the orthogonal test method in ABAQUS;

[0049] Figure 5 is the indentation response curve of the nanoindentation test;

[0050] Figure 6 Stress-strain curves in different regions. DETAILED DESCRIPTION

[0051] See also Figure 1 A method for calibrating parameters of a material softening model at high temperature comprises the following steps:

[0052] S1: Perform finite element simulation on the hypothetical material to obtain the simulated indentation response under different hypothetical material parameters, as shown in the attached figure. Figure 4 As shown, the obtained indentation response data are fitted;

[0053] S2: Perform nanoindentation tests on different areas after welding at high temperature. During the test, the sample to be tested is first polished and ground to a level with a difference of less than 1 degree between the upper and lower horizontal planes. Then the sample to be tested is placed in the nanoindenter and loaded using a fixed maximum load mode to 10mN. Then it is unloaded. Finally, the device can obtain the nanoindentation test indentation response curve, as shown in the attached figure. Figure 5 As shown;

[0054] S3: Solve the nanoindentation response curve of the material under test to obtain the constitutive parameters.

[0055] In step S1, the following steps are included:

[0056] S11: Use orthogonal test method to establish hypothetical material model;

[0057] The orthogonal test method (Table 1) was used, where E is the elastic modulus, n is the hardening index, and K is the hardening strength. y is the yield stress, η is the material constant. ) Establish a hypothetical material model. It can be seen from the table that it is a five-factor four-level test. According to the orthogonal test, 16 tests are required, as shown in Table 2.

[0058] Table 1 Hypothetical material parameters

[0059]

[0060] Table 2 Simulation analysis of 16 groups of hypothetical materials in orthogonal test

[0061]

[0062] S12: Perform finite element indentation simulation analysis to obtain an indentation response curve of an imaginary material;

[0063] The finite element simulation model is established as shown in the attached Figure 4As shown, it is divided into two parts, the indenter part and the sample part. The material properties of the sample are defined according to the imaginary material. The indenter is defined as diamond. The analysis step is set in two steps, one for the indenter to press down, and the other for unloading. The contact property is surface-to-surface contact. The boundary condition is set to fix the bottom surface of the sample. A reference point is established, which is the center point of the upper surface of the indenter. A force of 10mN is applied to the center point. When defining the field, a temperature of 800℃ is assigned to the material. The sample grid is subdivided on the surface. Submit the assignment. After completing the assignment, extract the force-displacement curve at the center of the indenter to obtain the indentation response curve of the imaginary material.

[0064] S13: The following relationship is obtained through the indentation response curve of the hypothetical material obtained in S12: y = W t / (E r h m 3 ), x=σ r *(1-ω) / E r ,

[0065] Where: W t is the total work;

[0066] E r is the reduced modulus;

[0067] h m is the maximum depth of indentation;

[0068] σ r * is characteristic stress;

[0069] ω is the damage factor;

[0070] According to the attached Figure 2 It can be clearly seen from the load-displacement diagram shown that W t is the product of the maximum displacement and the maximum load, E r is the reduced modulus, Where, β = 1.034, A c is the contact area, obtained from the indentation test, and S is obtained by taking the derivative of the equation of the displacement load curve in the loading stage after the maximum value is reached, that is,

[0071] The y value is obtained from the indentation curve, and the x value is obtained based on the parameters given by the hypothetical material. Figure 2 It can be clearly seen from the load-displacement diagram shown that W t is the product of the maximum displacement and the maximum load, E r is the reduced modulus, Where, β = 1.034, A c is the contact area, obtained from the indentation test, and S is obtained by taking the derivative of the equation of the displacement load curve in the loading stage after the maximum value is reached, that is, σ r * is the characteristic stress value at the characteristic strain of 0.033.

[0072] Fitting to obtain the relationship between y=f(x);

[0073] S14: According to In the formula, σ y is the yield stress, n is the hardening index, and K is the hardening strength. is the characteristic strain;

[0074] The fitting equations are y=f1(x1,x2),x2=f2(K,n),x3=f2(K,η);

[0075] S15: Fit the following equation:

[0076] x=x1+x2;

[0077] y=A×exp(Bx1)×exp(Cx2)+D;

[0078]

[0079] x2=q1×exp(q2x3)×exp(q3n)+q4;

[0080] x3=p1×exp(p2K)×exp(p3η)+p4;

[0081] Among them, A, B, C, D, q i ,p i is the fitting parameter;

[0082] S16: Fit the equation in step S15 and find the parameters A, B, C, D, q i ,p i .

[0083] In step S3, the following steps are included:

[0084] S31: Calculate the y value through the nanoindentation response curve at high temperature, and then obtain the x value according to the relationship y=f(x);

[0085] pass Figure 2 As you can see, y = W t / (E r h m 3 ), where W t is the total work, which is obtained by integrating the maximum load and the maximum position, E r is the reduced modulus, which can be obtained through the load-displacement relationship, h m is the maximum indentation depth. The y value is solved from this.

[0086] S32: Through the relationship x=x1+x2; y=A×exp(Bx1)×exp(Cx2)+D, we can obtain x1 and x2; and then Obtain the yield strength;

[0087] S33: By x2=f2(x3,n) and Find K,n;

[0088] S34: Passed and x3=p1×exp(p2K)×exp(p3η)+p4; find η,

[0089] S35: Conclusion The constitutive parameters are as follows: Figure 6 shown.

Claims

1. A method for calibrating material softening model parameters at high temperature, characterized in that: The following steps are involved: S1: Perform finite element simulation on the hypothetical material to obtain simulated indentation response curves under high temperature with different hypothetical material parameters, and fit the obtained indentation response data; S2: Perform nanoindentation tests on different areas after welding to obtain the indentation response curves of the nanoindentation test at high temperature; S3: Inversely solve the nanoindentation response curve of the material under test to obtain the constitutive parameters.

2. A method for calibrating material softening model parameters at high temperature according to claim 1, characterized in that: In step S1, the following steps are included: S11: Use orthogonal test method to establish hypothetical material model; S12: Perform finite element indentation simulation analysis to obtain an indentation response curve of an imaginary material; S13: The following relationship is obtained through the indentation response curve of the hypothetical material obtained in S12: y = W t / (E r h m 3 ), x=σ r *(1-ω) / E r , Where: W t is the total work; E r is the reduced modulus; h m is the maximum depth of indentation; σ r * is characteristic stress; ω is the damage factor; Fitting to obtain the relationship between y=f(x); S14: According to Where: y is the yield stress, n is the hardening index, and K is the hardening strength. is the characteristic strain; The fitting equations are y=f1(x1,x2),x2=f2(K,n),x3=f2(K,η); S15: Fit the following equation: x=x1+x2; y=A×exp(Bx1)×exp(Cx2)+D; x2=q1×exp(q2x3)×exp(q3n)+q4; x3=p1×exp(p2K)×exp(p3η)+p4; Where: A, B, C, D, q i ,p i is the fitting parameter; S16: Fit the equation in step S15 and find the parameters A, B, C, D, q i ,p i .

3. A method for calibrating material softening model parameters at high temperature according to claim 2, characterized in that: In step S3, the following steps are included: S31: The y value is calculated through the nanoindentation response curves of different areas of the weldment at high temperature, and then the y=f(x) relationship is obtained x value; S32: Through the relationship x=x1+x2; y=A×exp(Bx1)×exp(Cx2)+D, we can obtain x1 and x2; and then Obtain the yield strength; S33: By x2=f2(x3,n) and Find K,n; S34: Passed and x3=p1×exp(p2K)×exp(p3η)+p4; find η, S35: Conclusion Constitutive parameters.

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