An indentation inversion extraction method based on the constitutive relationship between the surface and subsurface layers of high-alloy steel

Abstract

An indentation inversion extraction method based on the constitutive relationship of the surface and sub-surface of high-alloy steel belongs to the field of characterization of mechanical properties of materials. The present invention solves the problems of low efficiency and large errors in existing constitutive relationship extraction methods. The present invention completely extracts the constitutive relationship of the surface and sub-surface of the material by combining the nanoindentation experiment of the tip of the spherical indenter and the Vickers indentation experiment, overcomes the problem that the change of material properties of heterogeneous gradient materials due to the change of microscopic composition is difficult to predict, and ensures the accuracy of constitutive relationship extraction. At the same time, relying on hardness measurement and simple finite element analysis, the calculation of a large number of material parameters is avoided, and the efficiency of gradient constitutive relationship extraction is improved. The method of the present invention can be used for high-efficiency and high-precision characterization of the mechanical properties of gradient materials such as high-alloy steel and carburized steel with a large carbide content. The method of the present invention can be applied to the field of characterization of mechanical properties of materials.

Description

Technical Field

[0001] The present invention belongs to the field of material mechanical property characterization, and specifically relates to an indentation inversion extraction method based on the constitutive relationship between the surface layer and sub-surface layer of high-alloy steel. Background Art

[0002] Spindle bearings are one of the important components of aircraft engines. As aircraft engine technology develops towards high thrust and high efficiency, the working environment of spindle bearings is becoming increasingly harsh. Currently, high-alloy steel is widely used in harsh bearing applications. It has a high surface hardness and a gradient hardened layer in which material properties (hardness, yield strength, etc.) vary with depth, which can effectively improve the fatigue performance and wear resistance of high-alloy steel. However, the influence of the gradient hardened layer on material fatigue damage is more complex, and its microstructure may have a negative impact on fatigue performance. Therefore, obtaining an effective constitutive relationship for gradient materials is an important prerequisite for analyzing the influence of materials on fatigue performance and predicting the fatigue life of high-alloy steel.

[0003] The Young's modulus, yield stress, work hardening rate, and engineering stress-strain relationship diagrams of existing metal materials are usually measured through macroscopic tensile tests. The experimental results of traditional tensile specimens are all relative to the entire large-volume specimen material, which is not applicable to materials whose mechanical properties change with changes in microscopic composition, especially high-alloy steels whose material properties are affected at the surface and subsurface layers at a depth of microns. For materials whose mechanical properties change with changes in microscopic composition, various basic mechanical property parameters, such as elastic modulus and fracture toughness, can be obtained based on the loading and unloading curves of nanoindentation. However, due to the continuous gradual change of microstructure or composition, it is still extremely difficult to obtain an accurate depth function based on the plastic response of the material. The Berkovich indenter, which is currently widely used in nanoindentation, has a self-similar geometric relationship. The deformation relationship of its indentation is often a specific value that changes with the indenter angle, but does not change with the depth. Information on stress-strain behavior can only be detected by changing the tip opening angle to detect stress within a certain range. For spherical indenters, due to their geometric non-self-similarity, the deformation relationship of their indentation changes with the indentation depth. Based on this feature, the elastic-plastic behavior of the tested material can be deduced by using a spherical tip to detect the surface and combining various data analysis programs to extract the constitutive relationship of the material. However, this method is often based on finite element analysis, computer algorithms, etc., and requires a lot of calculations. Therefore, the efficiency of extracting the material constitutive relationship is low. During the experiment, some test system problems related to the performance of the indentation test equipment and the sample size effect have a great influence on the results. At the same time, high-alloy steel is non-uniform at the microscopic level, and the error of extracting the gradient constitutive relationship of the material using nanoindentation is large.

[0004] In summary, since the existing constitutive relationship extraction methods have low efficiency and large errors, it is urgent to propose a method for extracting the constitutive relationship of the surface and subsurface layers of high-alloy steel. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems of low efficiency and large error of existing constitutive relationship extraction methods, and to propose an indentation inversion extraction method based on the constitutive relationship of the surface and subsurface layers of high alloy steel.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: an indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high-alloy steel, the method specifically comprising the following steps:

[0007] Step 1: Conduct a nanoindentation experiment using a spherical indenter tip on the surface of the high-alloy steel, and continuously measure the elastic modulus, contact stiffness, and contact load-indentation depth data of the surface area of ​​the material during the experiment;

[0008] Step 2: Calculate the geometric contact radius and Hertz contact radius based on the elastic modulus, contact stiffness data, contact load-indentation depth data, and spherical indenter tip radius measured in step 1;

[0009] Then, according to the geometric contact radius and the Hertz contact radius, data on four different indentation stress-strain curves are obtained;

[0010] Step 3: Based on the data on the various indentation stress-strain curves obtained in step 2, each indentation stress-strain curve is processed and calibrated to obtain a plastic constitutive equation;

[0011] Step 4: Perform a spherical indenter tip nanoindentation experiment at a depth position in the heat treatment direction of the subsurface region of the high-alloy steel, i.e., use the methods of Steps 1 to 3 to extract the plastic constitutive equation at the current depth position, and determine the strain hardening exponent range at the current depth position based on the strain hardening exponent in the plastic constitutive equation;

[0012] Step 5: Use a micro Vickers hardness tester to perform N Vickers hardness measurements on the current depth position of step 4, and use the average value of the N Vickers hardness measurement results as the basic Vickers hardness of the current depth position;

[0013] Step 6: Based on the strain hardening index range obtained in step 4 and the relationship between the representative plastic strain and the strain hardening index, obtain the representative plastic strain corresponding to each strain hardening index;

[0014] Based on the expansion cavity model and basic Vickers hardness, the flow curves corresponding to each strain hardening index within the strain hardening index range are obtained, and the constraint factor of each flow curve is calculated based on the representative plastic strain;

[0015] Step 7: Perform a macroscopic Vickers indentation test at the current depth position in Step 4, then slice the high-alloy steel and gradually polish it until it is polished to the indentation diagonal line, showing a gradient plastic strain zone below the maximum surface indentation;

[0016] Step 8: Perform a micro-Vickers indentation test in the gradient plastic strain region, i.e., select various indentation positions at a fixed interval within the gradient plastic strain region, and measure the Vickers hardness of each selected indentation position respectively, until the measured Vickers hardness is the same as the basic Vickers hardness in step 5, and the measurement is terminated to obtain all measurement positions;

[0017] Step 9: Establish a two-dimensional axisymmetric finite element analysis model based on any flow curve obtained in step 6, and then use the established two-dimensional axisymmetric finite element analysis model to restore the macroscopic Vickers indentation experiment in step 7 to obtain the equivalent plastic strain experimental value corresponding to each measurement position in step 8;

[0018] Substitute the equivalent plastic strain experimental value of each measurement position into the flow curve, and calculate the indentation projected area hardness corresponding to each measurement position; then calculate the indentation projected area hardness deviation corresponding to the flow curve based on the calculated indentation projected area hardness value of each measurement position and the Vickers hardness of each measurement position in step eight;

[0019] Similarly, calculate the hardness deviation of the indentation projection area corresponding to each flow curve in step 6, and use the flow curve corresponding to the minimum hardness deviation as a plastic constitutive relation at the current depth position in step 4;

[0020] Step 10: Change the depth position of the high alloy steel subsurface region in the heat treatment direction, and then return to step 4 to step 9 for the new depth position;

[0021] Step 11: Obtain the indentation inversion result using the plastic constitutive relation of the high alloy steel surface layer obtained in step 3 and the plastic constitutive relation of each depth position of the subsurface layer obtained in steps 4 and 9.

[0022] Furthermore, the calculation method of the geometric contact radius is:

[0023]

[0024] Among them, a g is the geometric contact radius, R is the radius of the spherical indenter tip, h cis the contact depth, h is the indentation depth of the spherical indenter, ε is the indenter geometric constant, p is the contact load, and s is the contact stiffness.

[0025] Furthermore, the Hertz contact radius is calculated as follows:

[0026]

[0027] Among them, a H is the Hertz contact radius, E r is the reduced modulus, v is the Poisson's ratio of the indenter, E is the elastic modulus of the indenter, v1 is the Poisson's ratio of the material, and E1 is the elastic modulus of the material.

[0028] Furthermore, according to the geometric contact radius and the Hertz contact radius, data on four different indentation stress-strain curves are obtained, specifically:

[0029] 1. The first indentation stress-strain curve:

[0030]

[0031] Among them, A g is based on the geometric contact radius a g Calculated contact area, σ g is based on the geometric contact radius a g Calculated contact stresses;

[0032]

[0033] Among them, τ T，g is based on the geometric contact radius a g Calculated Tabor strain;

[0034] σ g and τ T，g As a set of data on the first indentation stress-strain curve;

[0035] 2. The second indentation stress-strain curve:

[0036]

[0037] Among them, A g is based on the geometric contact radius a g Calculated contact area, σ g is based on the geometric contact radius a g Calculated contact stresses;

[0038]

[0039] Among them, τ H，g is based on the geometric contact radius ag Calculated Pathak strain;

[0040] σ g and τ H，g As a set of data on the second indentation stress-strain curve;

[0041] 3. The third indentation stress-strain curve:

[0042]

[0043] Among them, A H is based on the Hertz contact radius a H Calculated contact area, σ H is based on the Hertz contact radius a H Calculated contact stresses;

[0044]

[0045] Among them, τ T，H is based on the Hertz contact radius a H Calculated Tabor strain;

[0046] σ H and τ T，H As a set of data on the third indentation stress-strain curve;

[0047] 4. The fourth indentation stress-strain curve:

[0048]

[0049] Among them, A H is based on the Hertz contact radius a H Calculated contact area, σ H is based on the Hertz contact radius a H Calculated contact stresses;

[0050]

[0051] Among them, τ H，H is the Pathak strain calculated based on the Hertz contact radius;

[0052] σ H and τ H，H As a set of data on the fourth indentation stress-strain curve.

[0053] Furthermore, the plastic constitutive equation is:

[0054] σ=A+B∈ n

[0055] Where A is the yield stress, B is the hardening coefficient, n is the strain hardening exponent, σ is the stress, and z is the strain.

[0056] Furthermore, the flow curve corresponding to each strain hardening index within the strain hardening index range is obtained based on the expansion cavity model and the basic Vickers hardness, specifically:

[0057] For any strain hardening exponent:

[0058]

[0059] Where H is the indentation projected area hardness calculated based on the basic Vickers hardness, n is the strain hardening exponent, σ y is the yield strength of the material, α is the semi-included angle of the conical indenter;

[0060] Then the elastic part of the flow curve is σ=Eε, and the plastic part of the flow curve is σ=Kε n , where K is the strength coefficient;

[0061] K=E n σ y 1-n .

[0062] Furthermore, the calculation method for calculating the indentation projected area hardness based on the basic Vickers hardness is:

[0063]

[0064] Among them, H v is the basic Vickers hardness.

[0065] Furthermore, the constraint factor of each flow curve is calculated based on the representative plastic strain, and the specific process is as follows:

[0066] For any strain hardening exponent:

[0067] H=Cσ|ε p

[0068] Among them, ε p is the representative plastic strain corresponding to the strain hardening exponent, σ|ε p is the representative plastic strain ε on the flow curve p The stress at , C is the constraint factor of the strain hardening exponent.

[0069] Furthermore, in step nine, the hardness of the indentation projected area corresponding to each measurement position is calculated; specifically:

[0070] H i =Cσ|ε r，i +ε p

[0071] Among them, ε r，i is the equivalent plastic strain at the i-th measurement position, σ|ε r，i +ε p is the equivalent plastic strain ε r，i and the representative plastic strain ε p The sum of the stresses corresponding to the flow curve, C is the constraint factor of the strain hardening exponent, H i is the hardness of the indentation projection area corresponding to the i-th measurement position.

[0072] Furthermore, the indentation projected area hardness deviation corresponding to the flow curve is calculated based on the calculated indentation projected area hardness value at each measurement position and the Vickers hardness at each measurement position in step eight. The specific process is:

[0073]

[0074] Where H′ is the hardness deviation of the indentation projection area corresponding to the flow curve, |·| represents the calculated absolute value, I is the total number of measurement positions, and H′ i is the Vickers hardness of the i-th measurement position in step 8.

[0075] The beneficial effects of the present invention are:

[0076] The present invention completely extracts the constitutive relationship between the surface layer and the subsurface layer of the material by combining the nanoindentation experiment and the Vickers indentation experiment using the tip of a spherical indenter. This overcomes the problem of unpredictable changes in material properties of heterogeneous gradient materials due to changes in microscopic composition, ensures the accuracy of constitutive relationship extraction, gets rid of some shortcomings of the instrumental indentation method, and presses deeper into the measurement area, avoiding the influence of size effect on the experimental results.

[0077] At the same time, relying on hardness measurement and simple finite element analysis, the calculation of a large number of material parameters is avoided, and the efficiency of gradient constitutive relationship extraction is improved; the present invention is aimed at gradient materials such as high-alloy steel and carburized steel with a large carbide content, overcoming the poor homogeneity of such materials, and can be directly used for high-efficiency and high-precision characterization of the mechanical properties of gradient materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 This is a flow chart of an indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high alloy steel according to the present invention;

[0079] Figure 2 This is the relationship between contact load and indentation depth in the nanoindentation experiment with a spherical tip indenter;

[0080] In the figure, DEPTH represents the indentation depth and LOAD represents the contact load;

[0081] Figure 3 The relationship between the average representative plastic strain and hardening index of the 70.3-degree rigid conical indenter is shown in Figure 2.

[0082] Figure 4 The flow curves for different yield strengths and strain hardening exponents with the same original hardness and elastic modulus are shown below.

[0083] In the figure, Stress represents stress and Strain represents strain. DETAILED DESCRIPTION

[0084] Specific implementation method 1: Combination Figure 1 This embodiment describes an indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high alloy steel, and the method specifically includes the following steps:

[0085] Step 1: Conduct a nanoindentation experiment using a spherical indenter tip on the surface of the high-alloy steel, and continuously measure the elastic modulus, contact stiffness, and contact load-indentation depth data of the surface area of ​​the material during the experiment;

[0086] Step 2: Calculate the geometric contact radius and Hertz contact radius based on the elastic modulus, contact stiffness data, contact load-indentation depth data, and spherical indenter tip radius measured in step 1;

[0087] Then, according to the geometric contact radius and the Hertz contact radius, data on four different indentation stress-strain curves are obtained;

[0088] Step 3: Based on the data on the various indentation stress-strain curves obtained in step 2, each indentation stress-strain curve is processed and calibrated by data processing software to obtain a plastic constitutive equation;

[0089] Step 4: Perform a spherical indenter tip nanoindentation experiment at a depth position in the heat treatment direction of the subsurface region of the high-alloy steel, i.e., extract the plastic constitutive equation at the current depth position using the method of steps 1 to 3, and determine the strain hardening exponent range at the current depth position based on the strain hardening exponent in the plastic constitutive equation (based on the method of steps 1 to 3, four strain hardening exponents corresponding to the plastic constitutive equation can be obtained, with the smallest strain hardening exponent value as the lower limit of the range and the largest strain hardening exponent value as the upper limit of the range);

[0090] Step 5: Use a micro Vickers hardness tester to perform N Vickers hardness measurements on the current depth position of step 4, and use the average value of the N Vickers hardness measurement results as the basic Vickers hardness of the current depth position;

[0091] Step 6: Based on the strain hardening index range obtained in step 4 and the relationship between the representative plastic strain and the strain hardening index, obtain the representative plastic strain corresponding to each strain hardening index;

[0092] Based on the expansion cavity model and basic Vickers hardness, the flow curves corresponding to each strain hardening index within the strain hardening index range are obtained, and the constraint factor of each flow curve is calculated based on the representative plastic strain;

[0093] Step 7: Perform a macroscopic Vickers indentation test at the current depth position in step 4, then slice the high-alloy steel and gradually polish it until it is polished to the diagonal line of the indentation, revealing a gradient plastic strain zone below the maximum surface indentation (i.e., slice the material, then grind and polish until the largest surface at the center of the indentation is exposed);

[0094] Step 8: Perform a micro-Vickers indentation test in the gradient plastic strain region, i.e., select various indentation positions at a fixed interval within the gradient plastic strain region, and measure the Vickers hardness of each selected indentation position respectively, until the measured Vickers hardness is the same as the basic Vickers hardness in step 5, and the measurement is terminated to obtain all measurement positions;

[0095] Step 9: Establish a two-dimensional axisymmetric finite element analysis model based on any flow curve obtained in step 6, and then use the established two-dimensional axisymmetric finite element analysis model to restore the macroscopic Vickers indentation experiment in step 7 to obtain the equivalent plastic strain experimental value corresponding to each measurement position in step 8;

[0096] Substitute the equivalent plastic strain experimental value of each measurement position into the flow curve, and calculate the indentation projected area hardness corresponding to each measurement position; then calculate the indentation projected area hardness deviation corresponding to the flow curve based on the calculated indentation projected area hardness value of each measurement position and the Vickers hardness of each measurement position in step eight;

[0097] Similarly, calculate the hardness deviation of the indentation projection area corresponding to each flow curve in step 6, and use the flow curve corresponding to the minimum hardness deviation as a plastic constitutive relation at the current depth position in step 4;

[0098] Step 10: Change the depth position of the high alloy steel subsurface region in the heat treatment direction, and then return to step 4 to step 9 for the new depth position;

[0099] Step 11: Obtain the indentation inversion result using the plastic constitutive relation of the high alloy steel surface layer obtained in step 3 and the plastic constitutive relation of each depth position of the subsurface layer obtained in steps 4 and 9.

[0100] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the calculation method of the geometric contact radius is:

[0101]

[0102]

[0103] Among them, a g is the geometric contact radius, R is the radius of the spherical indenter tip, h c is the contact depth, h is the indentation depth of the spherical indenter, ε is the geometric constant of the indenter, which is usually taken as 0.75 for spherical indenters, p is the contact load, and s is the contact stiffness.

[0104] Other steps and parameters are the same as those in the first embodiment.

[0105] Specific embodiment three: This embodiment differs from specific embodiments one or two in that the Hertz contact radius is calculated as follows:

[0106]

[0107] Among them, a H is the Hertz contact radius, E r is the reduced modulus, v is the Poisson's ratio of the indenter, E is the elastic modulus of the indenter, v1 is the Poisson's ratio of the material (high alloy steel), and E1 is the elastic modulus of the material.

[0108] Other steps and parameters are the same as those in the first or second embodiment.

[0109] Specific embodiment 4: This embodiment differs from one of specific embodiments 1 to 3 in that, according to the geometric contact radius and the Hertz contact radius, four different data on the indentation stress-strain curves are obtained, specifically:

[0110] 1. The first indentation stress-strain curve:

[0111]

[0112] Among them, A g is based on the geometric contact radius a g Calculated contact area σ g is based on the geometric contact radius a g Calculated contact stresses;

[0113]

[0114] Among them, τ T，g is based on the geometric contact radius a g Calculated Tabor strain;

[0115] σ g and τT，g As a set of data on the first indentation stress-strain curve;

[0116] 2. The second indentation stress-strain curve:

[0117]

[0118] Among them, A g is based on the geometric contact radius a g Calculated contact area, σ g is based on the geometric contact radius a g Calculated contact stresses;

[0119]

[0120] Among them, τ H，g is based on the geometric contact radius a g Calculated Pathak strain;

[0121] σ g and τ H，g As a set of data on the second indentation stress-strain curve;

[0122] 3. The third indentation stress-strain curve:

[0123]

[0124] Among them, A H is based on the Hertz contact radius a H Calculated contact area σ H is based on the Hertz contact radius a H Calculated contact stresses;

[0125]

[0126] Among them, τ T，H is based on the Hertz contact radius a H Calculated Tabor strain;

[0127] σ H and τ T，H As a set of data on the third indentation stress-strain curve;

[0128] 4. The fourth indentation stress-strain curve:

[0129]

[0130] Among them, A H is based on the Hertz contact radius a H Calculated contact area, σ His based on the Hertz contact radius a H Calculated contact stresses;

[0131]

[0132] Among them, τ H，H is the Pathak strain calculated based on the Hertz contact radius;

[0133] σ H and τ H，H As a set of data on the fourth indentation stress-strain curve.

[0134] The other steps and parameters are the same as those in the first to third embodiments.

[0135] In the present invention, a set of data on each indentation stress-strain curve can be obtained according to the elastic modulus, contact stiffness data, and contact load-indentation depth data at each test point.

[0136] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the plastic constitutive equation is:

[0137] σ=A+B∈ n

[0138] Where A is the yield stress, B is the hardening coefficient, n is the strain hardening exponent, σ is the stress, and ∈ is the strain.

[0139] The other steps and parameters are the same as those in the first to fourth embodiments.

[0140] By fitting each indentation stress-strain curve according to the constitutive model, the parameters of each indentation stress-strain curve can be calibrated, and the four fitted indentation stress-strain curves are the obtained plastic constitutive equations.

[0141] Specific embodiment 6: This embodiment differs from any one of specific embodiments 1 to 5 in that the flow curve corresponding to each strain hardening index within the strain hardening index range is obtained based on the expansion cavity model and the basic Vickers hardness, specifically:

[0142] For any strain hardening exponent:

[0143]

[0144] Where H is the indentation projected area hardness calculated based on the basic Vickers hardness, n is the strain hardening exponent, σy is the material yield strength, and α is the semi-indenter angle of the cone;

[0145] Then the elastic part of the flow curve is σ=Eε, and the plastic part of the flow curve is σ=Kε n, where K is the strength coefficient;

[0146] K=E n σ y 1-n

[0147] The other steps and parameters are the same as those in the first to fifth embodiments.

[0148] Specific embodiment seven: This embodiment differs from any one of specific embodiments one to six in that the calculation method for calculating the hardness of the indentation projected area based on the basic Vickers hardness is:

[0149]

[0150] Among them, H v is the basic Vickers hardness.

[0151] The other steps and parameters are the same as those in the first to sixth embodiments.

[0152] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the constraint factor of each flow curve is calculated based on the representative plastic strain. The specific process is as follows:

[0153] For any strain hardening exponent:

[0154] H=Cσ|ε p

[0155] Among them, ε p is the representative plastic strain corresponding to the strain hardening exponent, σ|ε p is the representative plastic strain ε on the flow curve p The stress at , C is the constraint factor of the strain hardening exponent.

[0156] The other steps and parameters are the same as those in the first to seventh embodiments.

[0157] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 in that, in step 9, the hardness of the indentation projected area corresponding to each measurement position is calculated; specifically:

[0158] H i =Cσ|ε r，i +ε p

[0159] Among them, ε r，i is the equivalent plastic strain at the i-th measurement position, σ|ε r，i +ε p is the equivalent plastic strain ε r，i and the representative plastic strain ε pThe sum of the stresses corresponding to the flow curve, C is the constraint factor of the strain hardening exponent, H i is the hardness of the indentation projection area corresponding to the i-th measurement position.

[0160] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0161] Specific embodiment ten: This embodiment differs from any one of specific embodiments one to nine in that the indentation projected area hardness deviation corresponding to the flow curve is calculated based on the calculated indentation projected area hardness value at each measurement position and the Vickers hardness at each measurement position in step eight. The specific process is as follows:

[0162]

[0163] Where H′ is the hardness deviation of the indentation projection area corresponding to the flow curve, |·| represents the calculated absolute value, I is the total number of measurement positions, and H' i is the Vickers hardness of the i-th measurement position in step 8.

[0164] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0165] Example

[0166] The following is a detailed description of an indentation inversion extraction method based on the constitutive relationship between the surface layer and the sub-surface layer of heterogeneous cemented carbide according to the present invention, with reference to the accompanying drawings. The specific process of the method is as follows:

[0167] Step 1: Perform a nanoindentation experiment with a spherical indenter tip on the surface of a high-alloy steel (the high-alloy steel material in this embodiment is a non-homogeneous cemented carbide). At each measurement point during the experiment, the elastic modulus, contact stiffness data, and contact load-indentation depth data of the surface area of ​​the material are measured. The contact load-indentation depth data at all measurement points constitute the load-depth curve data (e.g., Figure 2 shown);

[0168] Step 2: Calculate the geometric contact radius and Hertz contact radius based on the elastic modulus, contact stiffness data, contact load-indentation depth data, and spherical indenter tip radius measured in step 1;

[0169] The calculation method of the geometric contact radius is:

[0170]

[0171] Among them, a g is the geometric contact radius, R is the radius of the spherical indenter tip, h cis the contact depth, h is the indentation depth of the spherical indenter, ε is the geometric constant of the indenter, which is usually taken as 0.75 for spherical indenters, p is the contact load, and s is the contact stiffness.

[0172] The Hertz contact radius is calculated as follows:

[0173]

[0174] Among them, a H is the Hertz contact radius, E r is the reduced modulus, v is the Poisson's ratio of the indenter, E is the elastic modulus of the indenter, v1 is the Poisson's ratio of the material, and E1 is the elastic modulus of the material;

[0175] Then, according to the geometric contact radius and the Hertz contact radius, the data on four different indentation stress-strain curves are obtained; the specific process is as follows:

[0176] 1. The first indentation stress-strain curve:

[0177]

[0178] Among them, A g is based on the geometric contact radius a g Calculated contact area, σ g is based on the geometric contact radius a g Calculated contact stresses;

[0179]

[0180] Among them, τ T，g is based on the geometric contact radius a g Calculated Tabor strain;

[0181] σ g and τ T，g As a set of data on the first indentation stress-strain curve;

[0182] 2. The second indentation stress-strain curve:

[0183]

[0184] Among them, A g is based on the geometric contact radius a g Calculated contact area, σ g is based on the geometric contact radius a g Calculated contact stresses;

[0185]

[0186] Among them, τ H，gis based on the geometric contact radius a g Calculated Pathak strain;

[0187] σ g and τ H，g As a set of data on the second indentation stress-strain curve;

[0188] 3. The third indentation stress-strain curve:

[0189]

[0190] Among them, A H is based on the Hertz contact radius a H Calculated contact area, σ H is based on the Hertz contact radius a H Calculated contact stresses;

[0191]

[0192] Among them, τ T，H is based on the Hertz contact radius a H Calculated Tabor strain;

[0193] σ H and τ T，H As a set of data on the third indentation stress-strain curve;

[0194] 4. The fourth indentation stress-strain curve:

[0195]

[0196] Among them, A H is based on the Hertz contact radius a H Calculated contact area, σ H is based on the Hertz contact radius a H Calculated contact stresses;

[0197]

[0198] Among them, T H，H is the Pathak strain calculated based on the Hertz contact radius;

[0199] σ H and τ H，H As a set of data on the fourth indentation stress-strain curve.

[0200] Step 3: Based on the data on the various indentation stress-strain curves obtained in step 2, each indentation stress-strain curve obtained in step 2 is processed and calibrated by data processing software to obtain a simplified plastic constitutive equation based on the Johnson-Cook constitutive model;

[0201] σ=A+B∈ n

[0202] Where A is the yield stress, B is the hardening coefficient, n is the strain hardening exponent, σ is the stress, and ∈ is the strain.

[0203] Step 4: Perform a spherical indenter tip nanoindentation experiment at a depth position in the heat treatment direction of the subsurface region of the high-alloy steel, i.e., use the methods of Steps 1 to 3 to extract the plastic constitutive equation at the current depth position, and determine the strain hardening exponent range at the current depth position based on the strain hardening exponent in the plastic constitutive equation;

[0204] Step 5: Use a micro Vickers hardness tester to perform N Vickers hardness measurements on the current depth position of step 4, and use the average value of the N Vickers hardness measurement results as the basic Vickers hardness of the current depth position;

[0205] Step 6: Based on the strain hardening index range obtained in step 4 and the relationship between the representative plastic strain and the strain hardening index, obtain the representative plastic strain corresponding to each strain hardening index (the specific value of each strain hardening index can be randomly selected within the strain hardening index range, for example, some data points can be selected at equal intervals);

[0206] It should be noted that: for a Vickers indenter with a self-similar indenter geometry, the representative plastic strain is constant regardless of the indentation size and depth. Figure 3 The relationship between the average representative plastic strain and the strain hardening exponent of the 70.3-degree rigid conical indenter is shown;

[0207] Then, based on the expansion cavity model (ECM) and basic Vickers hardness, the flow curves corresponding to each strain hardening index within the strain hardening index range are obtained:

[0208] For any strain hardening exponent, the extended cavity model (ECM) that relates the indentation hardness to the stress-strain behavior of elastic-plastic power-law hardening is given by:

[0209]

[0210] Where H is the indentation projected area hardness calculated based on the basic Vickers hardness, n is the strain hardening exponent, σ y is the yield strength of the material, α is the semi-included angle of the conical indenter (70.3°);

[0211] The elastic part of the flow curve is σ = Eε, and the plastic part of the flow curve is defined by the power law model as σ = Kε n , where K is the strength coefficient;

[0212] The strength coefficient K is calculated from the intersection of the elastic and plastic parts of the flow curve:

[0213] K=E n σ y 1-n

[0214] This embodiment establishes a series of Figure 4 Shown are stress-strain curves for materials with the same original hardness and elastic modulus, but different yield strengths and strain hardening exponents.

[0215] The constraint factor for each flow curve is calculated based on the representative plastic strain: For any strain hardening exponent:

[0216] H=Cσ|ε p

[0217] Among them, ε p is the representative plastic strain corresponding to the strain hardening exponent, σ|ε p is the representative plastic strain ε on the flow curve p The stress at , C is the constraint factor of the strain hardening exponent (C is the constraint factor corresponding to the hardness and stress. When the hardening exponent is different, the representative strain is different, and the stress is different, so C is different).

[0218] Step 7: Perform a macroscopic Vickers indentation test at the current depth position in Step 4, then slice the high-alloy steel and gradually polish it until it is polished to the indentation diagonal line, showing a gradient plastic strain zone below the maximum surface indentation;

[0219] Step 8: Perform a micro-Vickers indentation test in the gradient plastic strain region, i.e., select various indentation positions at a fixed interval within the gradient plastic strain region, and measure the Vickers hardness of each selected indentation position respectively, until the measured Vickers hardness is the same as the basic Vickers hardness in step 5, and the measurement is terminated to obtain all measurement positions;

[0220] Step 9: Based on any flow curve obtained in step 6, a two-dimensional axisymmetric finite element analysis model is established using mechanical simulation software. The established two-dimensional axisymmetric finite element analysis model is then used to restore the macroscopic Vickers indentation experiment in step 7 to obtain the equivalent plastic strain experimental value corresponding to each measurement position in step 8;

[0221] It should be noted that the indenter part of the two-dimensional axisymmetric finite element analysis model uses a rigid conical indenter with a half-angle of 70.3 degrees. The indentation produced by this geometric indenter matches the indentation produced by the standard Vickers diamond indenter.

[0222] Substitute the equivalent plastic strain experimental value of each measuring position into the flow curve and calculate the hardness of the indentation projected area corresponding to each measuring position;

[0223] H i =Cσ|ε r，i +ε p

[0224] Among them, ε r，i is the equivalent plastic strain at the i-th measurement position, σ|ε r，i +ε p is the equivalent plastic strain ε r，i and the representative plastic strain ε p The sum of the stresses corresponding to the flow curve, C is the constraint factor of the strain hardening exponent, H i is the hardness of the indentation projection area corresponding to the i-th measurement position.

[0225] Then, the indentation projected area hardness deviation corresponding to the flow curve is calculated based on the calculated indentation projected area hardness value at each measurement position and the Vickers hardness at each measurement position in step eight;

[0226]

[0227] Where H′ is the hardness deviation of the indentation projection area corresponding to the flow curve, |·| represents the calculated absolute value, I is the total number of measurement positions, and H′ i is the Vickers hardness of the i-th measurement position in step 8.

[0228] Similarly, calculate the hardness deviation of the indentation projection area corresponding to each flow curve in step 6, and use the flow curve corresponding to the minimum hardness deviation as a plastic constitutive relation at the current depth position in step 4;

[0229] Similarly, calculate the hardness deviation of the indentation projection area corresponding to each flow curve in step 6, and use the flow curve corresponding to the minimum hardness deviation as the plastic constitutive relation at the current depth position in step 4;

[0230] Step 10: Change the depth position of the high alloy steel subsurface region in the heat treatment direction, and then return to step 4 to step 9 for the new depth position;

[0231] Step 11: Obtain the indentation inversion result using the plastic constitutive relation of the high alloy steel surface layer obtained in step 3 and the plastic constitutive relation of each depth position of the subsurface layer obtained in steps 4 and 9.

[0232] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. An indentation inversion extraction method based on the constitutive relationship between the surface and subsurface layers of high alloy steel, characterized in that: The method specifically comprises the following steps: Step 1: Conduct a nanoindentation experiment using a spherical indenter tip on the surface of the high-alloy steel, and continuously measure the elastic modulus, contact stiffness, and contact load-indentation depth data of the surface area of ​​the material during the experiment; Step 2: Calculate the geometric contact radius and Hertz contact radius based on the elastic modulus, contact stiffness data, contact load-indentation depth data, and spherical indenter tip radius measured in step 1; Then, according to the geometric contact radius and the Hertz contact radius, data on four different indentation stress-strain curves are obtained; Step 3: Based on the data on the various indentation stress-strain curves obtained in step 2, each indentation stress-strain curve is processed and calibrated to obtain a plastic constitutive equation; Step 4: Perform a spherical indenter tip nanoindentation experiment at a depth position in the heat treatment direction of the subsurface region of the high-alloy steel, i.e., use the methods of Steps 1 to 3 to extract the plastic constitutive equation at the current depth position, and determine the strain hardening exponent range at the current depth position based on the strain hardening exponent in the plastic constitutive equation; Step 5: Use a micro Vickers hardness tester to perform N Vickers hardness measurements on the current depth position of step 4, and use the average value of the N Vickers hardness measurement results as the basic Vickers hardness of the current depth position; Step 6: Based on the strain hardening index range obtained in step 4 and the relationship between the representative plastic strain and the strain hardening index, obtain the representative plastic strain corresponding to each strain hardening index; Based on the expansion cavity model and basic Vickers hardness, the flow curves corresponding to each strain hardening index within the strain hardening index range are obtained, and the constraint factor of each flow curve is calculated based on the representative plastic strain; Step 7: Perform a macroscopic Vickers indentation test at the current depth position in Step 4, then slice the high-alloy steel and gradually polish it until it is polished to the indentation diagonal line, showing a gradient plastic strain zone below the maximum surface indentation; Step 8: Perform a micro-Vickers indentation test in the gradient plastic strain region, i.e., select various indentation positions at a fixed interval within the gradient plastic strain region, and measure the Vickers hardness of each selected indentation position respectively, until the measured Vickers hardness is the same as the basic Vickers hardness in step 5, and the measurement is terminated to obtain all measurement positions; Step 9: Establish a two-dimensional axisymmetric finite element analysis model based on any flow curve obtained in step 6, and then use the established two-dimensional axisymmetric finite element analysis model to restore the macroscopic Vickers indentation experiment in step 7 to obtain the equivalent plastic strain experimental value corresponding to each measurement position in step 8; Substitute the equivalent plastic strain experimental value of each measurement position into the flow curve, and calculate the indentation projected area hardness corresponding to each measurement position; then calculate the indentation projected area hardness deviation corresponding to the flow curve based on the calculated indentation projected area hardness value of each measurement position and the Vickers hardness of each measurement position in step eight; Similarly, calculate the hardness deviation of the indentation projection area corresponding to each flow curve in step 6, and use the flow curve corresponding to the minimum hardness deviation as a plastic constitutive relation at the current depth position in step 4; Step 10: Change the depth position of the high alloy steel subsurface region in the heat treatment direction, and then return to step 4 to step 9 for the new depth position; Step 11: Obtain the indentation inversion result using the plastic constitutive relation of the high alloy steel surface layer obtained in step 3 and the plastic constitutive relation of each depth position of the subsurface layer obtained in steps 4 and 9.

2. The indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high alloy steel according to claim 1 is characterized in that: The calculation method of the geometric contact radius is: Among them, a g is the geometric contact radius, R is the radius of the spherical indenter tip, h c is the contact depth, h is the indentation depth of the spherical indenter, ε is the indenter geometric constant, p is the contact load, and s is the contact stiffness.

3. The indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high alloy steel according to claim 2 is characterized in that: The Hertz contact radius is calculated as follows: Among them, a H is the Hertz contact radius, E r is the reduced modulus, v is the Poisson's ratio of the indenter, E is the elastic modulus of the indenter, v1 is the Poisson's ratio of the material, and E1 is the elastic modulus of the material.

4. The indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high alloy steel according to claim 3 is characterized in that: According to the geometric contact radius and the Hertz contact radius, data on four different indentation stress-strain curves are obtained, specifically:

1. The first indentation stress-strain curve: Among them, A g is based on the geometric contact radius a g Calculated contact area, σ g is based on the geometric contact radius a g Calculated contact stresses; Among them, τ T,g is based on the geometric contact radius a g Calculated Tabor strain; σ g and τ T,g As a set of data on the first indentation stress-strain curve; 2. The second indentation stress-strain curve: Among them, A g is based on the geometric contact radius a g Calculated contact area, σ g is based on the geometric contact radius a g Calculated contact stresses; Among them, τ H,g is based on the geometric contact radius a g Calculated Pathak strain; σ g and τ H,g As a set of data on the second indentation stress-strain curve; 3. The third indentation stress-strain curve: Among them, A H is based on the Hertz contact radius a H Calculated contact area, σ H is based on the Hertz contact radius a H Calculated contact stresses; Among them, τ T,H is based on the Hertz contact radius a H Calculated Tabor strain; σ H and τ T,H As a set of data on the third indentation stress-strain curve; 4. The fourth indentation stress-strain curve: Among them, A H is based on the Hertz contact radius a H Calculated contact area, σ H is based on the Hertz contact radius a H Calculated contact stresses; Among them, τ H,H is the Pathak strain calculated based on the Hertz contact radius; σ H and τ H,H As a set of data on the fourth indentation stress-strain curve.

5. The indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high alloy steel according to claim 4 is characterized in that: The plastic constitutive equation is: σ=A+B∈ n Where A is the yield stress, B is the hardening coefficient, n is the strain hardening exponent, σ is the stress, and ∈ is the strain.

6. The indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high alloy steel according to claim 5 is characterized in that: The flow curves corresponding to each strain hardening index within the strain hardening index range are obtained based on the expansion cavity model and the basic Vickers hardness, specifically: For any strain hardening exponent: Where H is the indentation projected area hardness calculated based on the basic Vickers hardness, n is the strain hardening exponent, σ y is the yield strength of the material, α is the semi-included angle of the conical indenter; Then the elastic part of the flow curve is σ=Eε, and the plastic part of the flow curve is σ=Kε n , where K is the strength coefficient; K=E n s y 1-n 。 7. The indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high alloy steel according to claim 6 is characterized in that: The calculation method for calculating the indentation projected area hardness based on the basic Vickers hardness is: Among them, H v is the basic Vickers hardness.

8. The indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high alloy steel according to claim 7 is characterized in that: The constraint factor of each flow curve is calculated based on the representative plastic strain. The specific process is as follows: For any strain hardening exponent: H=Cσ|ε p Among them, ε p is the representative plastic strain corresponding to the strain hardening exponent, σ|ε p is the representative plastic strain ε on the flow curve p The stress at , C is the constraint factor of the strain hardening exponent.

9. The indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high alloy steel according to claim 8, characterized in that: In step nine, the hardness of the indentation projection area corresponding to each measurement position is calculated; specifically: H i =Cσ|ε r,i +e p Among them, ε r,i is the equivalent plastic strain at the i-th measurement position, σ|ε r,i +ε p is the equivalent plastic strain ε r,i and the representative plastic strain ε p The sum of the stresses corresponding to the flow curve, C is the constraint factor of the strain hardening exponent, H i is the hardness of the indentation projection area corresponding to the i-th measurement position.

10. The indentation inversion extraction method based on the constitutive relationship between the surface layer and subsurface layer of high alloy steel according to claim 9, characterized in that: The indentation projected area hardness deviation corresponding to the flow curve is calculated based on the calculated hardness value of the indentation projected area at each measurement position and the Vickers hardness at each measurement position in step eight. The specific process is as follows: Where H' is the hardness deviation of the indentation projection area corresponding to the flow curve, |·| represents the calculated absolute value, I is the total number of measurement positions, and H' i is the Vickers hardness of the i-th measurement position in step 8.

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