Indentation inversion extraction method based on constitutive relation between surface layer and subsurface layer of high alloy steel

Abstract

The invention discloses an indentation inversion extraction method based on a constitutive relation between a high alloy steel surface layer and a high alloy steel subsurface layer, and belongs to the field of material mechanical property characterization. The method solves the problems that an existing constitutive relation extraction method is low in efficiency and large in error. According to the method, the nanoindentation experiment and the Vickers indentation experiment of the tip end of the spherical indenter are combined, the constitutive relation between the surface layer and the subsurface layer of the material is completely extracted, the problem that the material performance change of a heterogeneous gradient material is difficult to predict due to the change of microcosmic components is solved, and the extraction precision of the constitutive relation is ensured. Meanwhile, by means of hardness measurement and simple finite element analysis, calculation of a large number of material parameters is avoided, and the gradient constitutive relation extraction efficiency is improved. The method can be used for high-efficiency and high-precision characterization of mechanical properties of gradient materials such as high alloy steel and carburizing steel with high carbide content. The method can be applied to the field of characterization of mechanical properties of materials.

Description

Technical Field

[0001] The 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. At present, 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 effect of the gradient hardened layer on material fatigue damage is more complicated, and its microstructure may have a negative impact on fatigue performance. Therefore, obtaining an effective constitutive relationship for determining 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 of the 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 sub-surface layers at a micron depth. 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, but 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 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. The information about the stress-strain behavior can only be detected by changing the tip opening angle to detect the stress within a certain range; for the spherical indenter, due to its geometric non-self-similarity, the deformation relationship of its indentation changes with the change of the indentation depth. According to this feature, the elastic-plastic behavior of the material under test 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 constitutive relationship of the material 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 greater impact 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 an urgent problem to propose a method for extracting the constitutive relationship of the surface and sub-surface 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 sub-surface 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 the sub-surface layer of high-alloy steel, the method specifically comprising the following steps:

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

[0008] Step 2, calculating the geometric contact radius and the Hertz contact radius respectively according to the elastic modulus, contact stiffness data, contact load-indentation depth data and the tip radius of the spherical indenter 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: According to the data on 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 on a depth position in the heat treatment direction of the subsurface region of the high alloy steel, that is, use the methods of steps 1 to 3 to extract the plastic constitutive equation of the current depth position, and determine the strain hardening index range of 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: According to the strain hardening exponent range obtained in step 4 and the relationship between the representative plastic strain and the strain hardening exponent, the representative plastic strain corresponding to each strain hardening exponent is obtained;

[0014] 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, 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 microscopic Vickers indentation experiment in the gradient plastic strain region, that is, select each indentation position at a fixed interval in 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 according to 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, and 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 measuring position into the flow curve, and calculate the hardness of the indentation projection area corresponding to each measuring position; then calculate the hardness deviation of the indentation projection area corresponding to the flow curve according to the calculated hardness value of the indentation projection area at each measuring position and the Vickers hardness of each measuring position in step eight;

[0019] Similarly, the hardness deviation of the indentation projection area corresponding to each flow curve in step six is ​​calculated respectively, and the flow curve corresponding to the minimum hardness deviation is used as a plastic constitutive relation at the current depth position in step four;

[0020] Step 10, changing the depth position of the sub-surface region of the high alloy steel in the heat treatment direction, and then returning to execute steps 4 to 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 type of 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 It 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] Among them, A is the yield stress, B is the hardening strengthening coefficient, n is the strain hardening exponent, σ is the stress, and z is the strain.

[0056] Furthermore, 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:

[0057] For any strain hardening exponent:

[0058]

[0059] Where H is the indentation projection 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 projection area hardness according to 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 projection 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 ith 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 projection area hardness deviation corresponding to the flow curve is calculated based on the calculated value of the indentation projection area hardness at each measuring position and the Vickers hardness at each measuring 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 eight.

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

[0076] The present invention completely extracts the constitutive relationship of the surface layer and sub-surface layer of the material by combining the nanoindentation experiment of the tip of the spherical indenter with the Vickers indentation experiment, overcomes the problem that the change of material properties of the inhomogeneous gradient material due to the change of microscopic composition is difficult to predict, ensures the accuracy of constitutive relationship extraction, gets rid of some shortcomings of the instrument indentation method, presses deeper into the measurement area, and avoids the influence of size effect on the experimental results.

[0077] At the same time, by 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 It is a flow chart of an indentation inversion extraction method based on the constitutive relationship between the surface layer and the sub-surface layer of high alloy steel of the present invention;

[0079] Figure 2 This is the relationship between the contact load and the 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 average representative plastic strain and hardening index relationship diagram of 70.3 degree rigid cone indenter;

[0082] Figure 4 The flow curves for the same original hardness and elastic modulus but different yield strengths and strain hardening exponents;

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

[0084] Specific implementation method 1: Combination Figure 1 The present embodiment is described as follows. The indentation inversion extraction method based on the constitutive relationship between the surface layer and the sub-surface layer of high alloy steel described in the present embodiment specifically comprises the following steps:

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

[0086] Step 2, calculating the geometric contact radius and the Hertz contact radius respectively according to the elastic modulus, contact stiffness data, contact load-indentation depth data and the tip radius of the spherical indenter 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 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 on a depth position in the heat treatment direction of the subsurface region of the high alloy steel, that is, use the method of steps 1 to 3 to extract the plastic constitutive equation of the current depth position, and determine the strain hardening index range of the current depth position based on the strain hardening exponent in the plastic constitutive equation (based on the method of steps 1 to 3, 4 strain hardening exponents corresponding to the plastic constitutive equation can be obtained, and the smallest strain hardening exponent value is used as the lower limit of the range, and the largest strain hardening exponent value is used 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: According to the strain hardening exponent range obtained in step 4 and the relationship between the representative plastic strain and the strain hardening exponent, the representative plastic strain corresponding to each strain hardening exponent is obtained;

[0092] 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, 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, showing the gradient plastic strain zone below the maximum surface indentation (i.e., slice the material, and then grind and polish it until the maximum surface at the center of the indentation is exposed);

[0094] Step 8: Perform a microscopic Vickers indentation experiment in the gradient plastic strain region, that is, select each indentation position at a fixed interval in 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 according to 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, and 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 measuring position into the flow curve, and calculate the hardness of the indentation projection area corresponding to each measuring position; then calculate the hardness deviation of the indentation projection area corresponding to the flow curve according to the calculated hardness value of the indentation projection area at each measuring position and the Vickers hardness of each measuring position in step eight;

[0097] Similarly, the hardness deviation of the indentation projection area corresponding to each flow curve in step six is ​​calculated respectively, and the flow curve corresponding to the minimum hardness deviation is used as a plastic constitutive relation at the current depth position in step four;

[0098] Step 10, changing the depth position of the sub-surface region of the high alloy steel in the heat treatment direction, and then returning to execute steps 4 to 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 implementation method 2: This implementation method is different from the specific implementation method 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] The other steps and parameters are the same as those in the first embodiment.

[0105] Specific implementation method three: This implementation method is different from specific implementation methods 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] The other steps and parameters are the same as those in the first or second embodiment.

[0109] Specific implementation method 4: This implementation method is different from the specific implementation methods 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 type of 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 It 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 Specific Embodiments 1 to 3.

[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 implementation method 5: This implementation method is different from any one of the specific implementation methods 1 to 4 in that the plastic constitutive equation is:

[0137] σ=A+B∈ n

[0138] Among them, A is the yield stress, B is the hardening strengthening 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 Specific Embodiments 1 to 4.

[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 implementation method 6: This implementation method is different from any one of specific implementation methods 1 to 5 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:

[0142] For any strain hardening exponent:

[0143]

[0144] Where H is the hardness of the indentation projection area calculated according to the basic Vickers hardness, n is the strain hardening exponent, σy is the yield strength of the material, and α is the semi-angle of the conical indenter;

[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 Specific Implementation Methods 1 to 5.

[0148] Specific implementation method 7: This implementation method is different from one of the specific implementation methods 1 to 6 in that the calculation method of the hardness of the indentation projection area according to 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 Specific Embodiments 1 to 6.

[0152] Specific implementation eight: This implementation differs from any one of specific implementations one to seven in that the constraint factor of each flow curve is calculated based on the representative plastic strain, and 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 Specific Embodiments 1 to 7.

[0157] Specific implementation method 9: This implementation method is different from any one of specific implementation methods 1 to 8 in that, in step 9, the hardness of the indentation projection 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 ith 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 implementation ten: This implementation differs from one of specific implementations one to nine in that the hardness deviation of the indentation projection area corresponding to the flow curve is calculated based on the calculated hardness value of the indentation projection area at each measuring position and the Vickers hardness at each measuring 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 eight.

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

[0165] Example

[0166] The following is a further detailed description of an indentation inversion extraction method based on the constitutive relationship of the surface layer and sub-surface layer of heterogeneous cemented carbide according to the present invention in conjunction with 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 area of ​​high alloy steel (the high alloy steel material in this embodiment is a non-homogeneous cemented carbide), and measure the elastic modulus, contact stiffness data and contact load-indentation depth data of the surface area of ​​the material at each measuring point during the experiment. The contact load-indentation depth data at all measuring points constitute the load-depth curve data (such as Figure 2 shown);

[0168] Step 2, calculating the geometric contact radius and the Hertz contact radius respectively according to the elastic modulus, contact stiffness data, contact load-indentation depth data and the tip radius of the spherical indenter 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 calculation method of the Hertz contact radius is:

[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 type of 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 It 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: According to the data on 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] Among them, A is the yield stress, B is the hardening strengthening 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 on a depth position in the heat treatment direction of the subsurface region of the high alloy steel, that is, use the methods of steps 1 to 3 to extract the plastic constitutive equation of the current depth position, and determine the strain hardening index range of 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: According to the strain hardening index range obtained in step 4 and the relationship between the representative plastic strain and the strain hardening index, the representative plastic strain corresponding to each strain hardening index is obtained (wherein 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 cone indenter is shown;

[0207] Then, based on the expansion cavity model (ECM) and the 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 projection 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 hardness and stress. When the hardening exponent is different, the representative strain is different, 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 microscopic Vickers indentation experiment in the gradient plastic strain region, that is, select each indentation position at a fixed interval in 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: According to any flow curve obtained in step 6, a two-dimensional axisymmetric finite element analysis model is established based on mechanical simulation software, and then the established two-dimensional axisymmetric finite element analysis model is used to restore the macroscopic Vickers indentation experiment in step 7, and the equivalent plastic strain experimental value corresponding to each measurement position in step 8 is obtained respectively;

[0221] It should be noted that the indenter part in 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 projection 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 ith 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 hardness deviation of the indentation projection area corresponding to the flow curve is calculated according to the calculated hardness value of the indentation projection area at each measuring position and the Vickers hardness at each measuring 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 eight.

[0228] Similarly, the hardness deviation of the indentation projection area corresponding to each flow curve in step six is ​​calculated respectively, and the flow curve corresponding to the minimum hardness deviation is used as a plastic constitutive relation at the current depth position in step four;

[0229] Similarly, the hardness deviation of the indentation projection area corresponding to each flow curve in step six is ​​calculated respectively, and the flow curve corresponding to the minimum hardness deviation is used as the plastic constitutive relation of the current depth position in step four;

[0230] Step 10, changing the depth position of the sub-surface region of the high alloy steel in the heat treatment direction, and then returning to execute steps 4 to 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 calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. An indentation inversion extraction method based on the constitutive relationship between the surface layer and the sub-surface layer of high alloy steel, characterized in that: The method specifically comprises the following steps: Step 1: Perform a nanoindentation experiment with a spherical indenter tip on the surface area of ​​the high alloy steel, and continuously measure the elastic modulus, contact stiffness data, and contact load-indentation depth data of the surface area of ​​the material during the experiment; Step 2, calculating the geometric contact radius and the Hertz contact radius respectively according to the elastic modulus, contact stiffness data, contact load-indentation depth data and the tip radius of the spherical indenter 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: According to the data on 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 on a depth position in the heat treatment direction of the subsurface region of the high alloy steel, that is, use the methods of steps 1 to 3 to extract the plastic constitutive equation of the current depth position, and determine the strain hardening index range of 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: According to the strain hardening exponent range obtained in step 4 and the relationship between the representative plastic strain and the strain hardening exponent, the representative plastic strain corresponding to each strain hardening exponent is obtained; 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, 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 microscopic Vickers indentation experiment in the gradient plastic strain region, that is, select each indentation position at a fixed interval in 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 according to 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, and obtain the equivalent plastic strain experimental value corresponding to each measurement position in step 8; Substitute the equivalent plastic strain experimental value of each measuring position into the flow curve, and calculate the hardness of the indentation projection area corresponding to each measuring position; then calculate the hardness deviation of the indentation projection area corresponding to the flow curve according to the calculated hardness value of the indentation projection area at each measuring position and the Vickers hardness of each measuring position in step eight; Similarly, the hardness deviation of the indentation projection area corresponding to each flow curve in step six is ​​calculated respectively, and the flow curve corresponding to the minimum hardness deviation is used as a plastic constitutive relation at the current depth position in step four; Step 10, changing the depth position of the sub-surface region of the high alloy steel in the heat treatment direction, and then returning to execute steps 4 to 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 the sub-surface 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 the sub-surface layer of high alloy steel according to claim 2 is characterized in that: The calculation method of the Hertz contact radius is: 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 the sub-surface 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 type of 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 It 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 the sub-surface layer of high alloy steel according to claim 4 is characterized in that: The plastic constitutive equation is: σ=A+B∈ n Among them, A is the yield stress, B is the hardening strengthening 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 the sub-surface 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 projection 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 the sub-surface layer of high alloy steel according to claim 6 is characterized in that: The calculation method for calculating the indentation projection 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 the sub-surface 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, and 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 the sub-surface 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 ith 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 the sub-surface layer of high alloy steel according to claim 9, characterized in that: The specific process of calculating the hardness deviation of the indentation projection area corresponding to the flow curve according to the calculated hardness value of the indentation projection area at each measuring position and the Vickers hardness at each measuring position in step eight 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 eight.

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