Method for obtaining material mechanics parameters and constitutive curve based on spherical multi-stage compression unloading method

Abstract

The application provides a method for obtaining material mechanics parameters and constitutive curve based on spherical multistage indentation unloading method, comprising the following steps: aligning a hard spherical indenter with a to-be-tested indentation area of a metal sample; performing multistage indentation unloading test on the to-be-tested indentation area using the hard spherical indenter, and recording the relationship curve between indentation load and indentation depth; extracting the maximum indentation load F mi , the maximum indentation depth h mi , the loading slope S li , and the initial unloading slope S ui corresponding to each stage of indentation unloading test on the relationship curve between indentation load and indentation depth; and further calculating tensile mechanics parameters including unloading elastic modulus E, plastic extension strength R px , and tensile strength R m , and obtaining the constitutive curve reflecting the stress and strain relationship by power function fitting, so as to solve the technical problems that the deviation between the strength prediction value and the real value obtained by the existing indentation test method is large, and the finite element simulation equation is too complicated to be applied in engineering.

Description

TECHNICAL FIELD

[0001] The application relates to the field of material testing, and in particular to a method for obtaining material mechanical parameters and a constitutive curve based on a spherical multistage indentation unloading method. BACKGROUND

[0002] A tensile strength and stress-strain relationship curve is a basic mechanical characterization of a metal material, and a traditional mechanical test method needs to cut a tensile sample from a raw material or a structure to obtain material mechanical properties by performing a tensile test on a testing machine. However, for in-service equipment, welded parts, small structural parts and surface treatment such as coating, a sample cannot be processed to perform a traditional tensile test, and a large number of scholars hope to obtain the mechanical properties of the material through an indentation test. The indentation test does not need sampling, and the relationship curve between the indentation load and the indentation depth is obtained by simply applying an indentation load to a surface micro area, and the mechanical properties of the material are obtained by a calculation formula.

[0003] At present, the indentation method can be roughly divided into an empirical physical method and a finite element simulation numerical analysis method. The empirical physical method mainly defines a representative stress and a representative strain, which are approximately the stress and strain of the material, so as to realize the conversion of the relationship curve between the indentation load and the indentation depth into the constitutive curve of the stress and strain relationship. Most of the empirical physical models are based on the assumption of pure elastic material and ideal linear deformation, and the processing state of the material surface, the bulging or sinking phenomenon of the indentation edge and the nonlinear plastic deformation are not fully considered and corrected, resulting in a large deviation of the result from the true value and poor applicability. Some calculation methods are based on the power law fitting of the indentation curve as the basis of the mechanical empirical calculation formula, which is not applicable to the materials with a straight line or convex shape of the indentation curve.

[0004] The numerical analysis method based on finite element simulation considers the influence of the work hardening behavior of the material on the representative stress and the representative strain, and establishes a correlation equation of the uniaxial mechanical properties and the indentation properties of the material for different constitutive equations. Such expression completely depends on finite element calculation, and there are a large number of coefficients that need to be calibrated by finite element results in the simulation equation, and the equation is long and complicated, and for materials with different plastic characteristics, the coefficients need to be recalibrated. The numerical analysis method does not theoretically describe the mechanical behavior of the material, lacks clear physical meaning, and the selection and iteration process of the parameters are complex, which is difficult to apply in engineering.

[0005] Therefore, a method for obtaining material mechanical parameters and a constitutive curve based on a spherical multistage indentation unloading method is needed, which is used in a test environment where a sample cannot be processed to perform a traditional tensile test to obtain material mechanical parameters, and solves the technical problems that the deviation between the strength prediction value and the true value obtained by the existing indentation test method is large and the finite element simulation equation is too complicated to be applied in engineering. SUMMARY

[0006] In view of the shortcomings of the prior art described above, the purpose of this invention is to provide a method for obtaining material mechanical parameters and constitutive curves based on the spherical multi-stage indentation and unloading method, so as to solve the technical problems that the strength prediction values ​​obtained by the existing indentation test method have large deviations from the actual values ​​and that the finite element simulation equations are too cumbersome and difficult to apply in engineering.

[0007] To achieve the above and other related objectives, this invention provides a method for obtaining material mechanical parameters and constitutive curves based on a spherical multi-stage indentation and unloading method, comprising the following steps:

[0008] Align the hard spherical indenter with the test indentation area of ​​the metal sample;

[0009] A multi-stage indentation and unloading test was performed in the indentation area to be tested using a hard spherical indenter, and the relationship curve between the indentation load and the indentation depth was recorded.

[0010] Extract the maximum indentation load F corresponding to each stage of the indentation and unloading test from the relationship curve between indentation load and indentation depth. mi Maximum indentation depth h mi Loading slope S li and initial unloading slope S ui Measure the diameter d of the surface indentation on the metal sample. f ;

[0011] Calculate the corrected residual depth h corresponding to the first stage of unloading. c1 and equivalent elastic modulus E1 * , thus obtaining the unloading elastic modulus E;

[0012] Calculate the corrected residual depth h corresponding to the i-th level unloading. ci To obtain the equivalent elastic modulus E i * ;

[0013] Calculate the maximum indentation load F before the i-th stage unloading. mi The corresponding stress σ mi ;

[0014] The stress σ corresponding to the i-th stage of unloading is... mi and equivalent elastic modulus E i * Calculate the total elastic strain ε of the i-th stage of unloading. tei ;

[0015] Calculate the loading slope S before and after unloading at level i. li and unloading slope S ui The ratio p i Characterizing the total elastic strain ε tei With total strain ε tiThe ratio of the two values ​​is used to decompose the plastic strain ε of the i-th stage of unloading. pi ;

[0016] The plastic strain ε pi and stress σ mi Power function fitting is performed to obtain the indentation strengthening coefficient K. I and indentation hardening index n I ; by the indentation strengthening coefficient K I and indentation hardening index n I Obtain the constitutive curve of the material used for the metallic sample;

[0017] Calculate the plastic tensile strength R of the material used for the metal specimen px and tensile strength R m .

[0018] Preferably, the acquisition method further includes: performing surface treatment on the test pressing area of ​​the metal sample, wherein the surface roughness of the test pressing area is less than 0.8 μm, thereby further improving the accuracy of the data obtained through the experiment.

[0019] Preferably, the diameter of the rigid spherical indenter is D; the maximum indentation load F corresponding to the final stage of the indentation and unloading test is applied. mi Let it be F mf The following conditions must be met: For ferrous metals, the maximum indentation load F mf Satisfy F mf =294D 2 For non-ferrous metals, the maximum indentation load F mf Satisfy F mf =98D 2 This ensures the accuracy of the obtained curve relating the indentation load to the indentation depth.

[0020] Preferably, the step of performing a multi-stage indentation and unloading test in the indentation area to be tested using a hard spherical indenter includes: always keeping the hard spherical indenter perpendicular to the indentation area to be tested of the metal specimen, ensuring that the resulting indentation depth and indentation diameter are the direct result of the load, rather than the decomposed load in its normal direction.

[0021] Preferably, the maximum indentation load F corresponding to the final stage indentation and unloading test is used. mi Let it be F mf ; in 0~F mf The number of indentation and unloading tests conducted within the load range should be at least 8; ensuring that the number of indentation and unloading tests conducted is greater than or equal to 8 can guarantee that the relationship curve between the indentation load and the indentation depth obtained through the test is more accurate and that the data obtained is sufficiently abundant.

[0022] Preferably, the corrected residual depth hci The calculation method is as follows:

[0023] According to the relation Calculate the theoretical residual depth h corresponding to the i-th stage of unloading. * ci , where α = 0.75;

[0024] Then according to the relation Calculate the plasticity coefficient β, where h * cf For relational expressions The theoretical residual depth after the last stage unloading is obtained by taking the value i = f; h cf F represents the true residual depth of the final stage of unloading, obtained from the relationship curve between the indentation load and the indentation depth. mf The maximum indentation load before the final stage of unloading is obtained from the relationship curve between indentation load and indentation depth.

[0025] Substituting the plasticity coefficient β into the relationship Calculate the corrected residual depth h corresponding to the i-th level unloading. ci This method uses parameters obtained from the relationship curve between the indentation load and the indentation depth to calculate the corrected residual depth h. ci This provides a foundation for subsequent calculations of other tensile mechanical parameters.

[0026] Preferably, the equivalent elastic modulus E i * The calculation method is as follows: First, according to the relation A ci =π(Dh) ci -h ci 2 The contact projected area A of the i-th stage unloading is calculated. ci Substitute the relational expression into the expression. Calculate the equivalent elastic modulus E i * This method uses the relationship curve between the indentation load and the indentation depth obtained from testing, along with the experimental data obtained from measurements, to calculate the equivalent elastic modulus E. i * It's convenient and quick.

[0027] Preferably, the calculation of the corrected residual depth h corresponding to the first-stage unloading... c1 and equivalent elastic modulus E1 * The steps to obtain the unloading elastic modulus E include: taking i=1, and obtaining the corrected residual depth h of the first-stage unloading. c1 The equivalent elastic modulus E1 corresponding to the first stage of unloading was calculated. * Substitute into the relation The unloading elastic modulus E of the metal specimen was calculated; where E 压头 v is the unloading elastic modulus of the hard spherical indenter. 压头 denoted by , where is the Poisson's ratio of the hard spherical indenter; v is the Poisson's ratio of the metallic sample material, and for general alloy materials, v = 0.3. This method calculates the unloading elastic modulus E based on the relationship curve between the indentation load and the indentation depth obtained from the test and the experimental data obtained from the measurement, which is convenient and quick.

[0028] Preferably, the calculation of the maximum indentation load F before the i-th stage unloading... mi The corresponding stress σ mi The steps include: based on relation A smi =πDh mi Calculate the indentation surface area A corresponding to the maximum indentation depth before the i-th stage of unloading. smi Then substitute into the relational expression Calculate the maximum indentation load F before the i-th stage unloading. mi The corresponding stress σ mi Where M is a material constant, and for metallic materials, the value of M ranges from 2.8 to 3. This method calculates the maximum indentation load F based on the relationship curve between the indentation load and the indentation depth obtained from testing and the experimental data obtained from measurements. mi The corresponding stress σ mi This provides data support for obtaining constitutive curves that reflect the relationship between stress and strain.

[0029] Preferably, the characterization of total elastic strain ε tei The calculation steps include: based on the relational formula Calculate the total elastic strain ε corresponding to the i-th stage of unloading. tei This method calculates the total elastic strain ε of the i-th stage of unloading based on the relationship curve between the indentation load and the indentation depth obtained from the test and the experimental data obtained from the measurement. tei This provides data support for obtaining constitutive curves that reflect the relationship between stress and strain.

[0030] Preferably, the calculation of the loading slope S before and after the i-th stage unloading... li and unloading slope S ui The ratio p i Characterizing the total elastic strain ε tei With total strain ε ti The ratio of the two values ​​is used to decompose the plastic strain ε of the i-th stage of unloading. pi The steps include: based on the relation Calculate the loading slope S before and after unloading at level i. li and unloading slope S ui The ratio p ii.e. total elastic strain ε tei The ratio of the total strain ε ti The ratio p li of the loading slope S ui and the unloading slope S i is obtained by calculation based on the relationship curve between the indentation load and the indentation depth obtained by testing and the test data obtained by measurement, thereby providing data support for obtaining the constitutive curve reflecting the stress and strain relationship subsequently.

[0031] Preferably, the step of decomposing to obtain the plastic strain amount ε pi of the i-th stage unloading comprises: calculating the plastic strain amount ε pi of the i-th stage unloading of the metal sample according to the relationship The plastic strain amount ε pi of the i-th stage unloading is obtained by calculation based on the relationship curve between the indentation load and the indentation depth obtained by testing and the test data obtained by measurement, thereby providing data support for obtaining the constitutive curve reflecting the stress and strain relationship subsequently.

[0032] Preferably, the step of performing power function fitting on the plastic strain amount ε pi and the stress σ mi to obtain the indentation strengthening coefficient K I and the indentation hardening index n I comprises: performing power function fitting on the plastic strain amount ε pi and the stress σ mi corresponding to each stage unloading according to the formula to obtain the indentation strengthening coefficient K I and the indentation hardening index n I The indentation strengthening coefficient K I and the indentation hardening index n I are obtained by power function fitting on the obtained test data based on the relationship curve between the indentation load and the indentation depth obtained by testing and the test data obtained by measurement, thereby providing data support for obtaining the constitutive curve reflecting the stress and strain relationship subsequently.

[0033] Preferably, the step of obtaining the constitutive curve reflecting the stress and strain relationship from the indentation strengthening coefficient K I and the indentation hardening index n I comprises: substituting the indentation strengthening coefficient K I , the indentation hardening index n I and the unloading elastic modulus E into the relationship The method obtains the constitutive curve reflecting the stress and strain relationship; the method obtains the constitutive curve reflecting the stress and strain relationship through power function fitting and calculation according to the relationship curve between the indentation load and the indentation depth obtained by the test and the test data obtained by the measurement.

[0034] Preferably, the calculation step of the plastic extension strength R px includes: substituting the indentation strengthening coefficient K I , the indentation hardening index n I and the percentage of the plastic extension amount x into the relationship formula to calculate the plastic extension strength R px ; the method obtains the plastic extension strength R px through calculation according to the relationship curve between the indentation load and the indentation depth obtained by the test and the test data obtained by the measurement, which is convenient and fast.

[0035] Preferably, the calculation step of the tensile strength R m includes:

[0036] According to the relationship formula A smi = πDh mi , the maximum indentation depth h m before the unloading of the last stage is obtained, and the corresponding indentation surface area A sm is obtained.

[0037] Then, according to the relationship formula , the indentation diameter d f is obtained, and the corresponding indentation surface area A sf is obtained.

[0038] Substituting A sm and A sf into the relationship formula obtains the proportional coefficient γ.

[0039] According to the relationship formula , the maximum stress σ mf before the unloading of the last stage is obtained.

[0040] Substituting the proportional coefficient γ and the maximum stress σ mf before the unloading of the last stage into the relationship formula R m = γσ mf obtains the tensile strength R m ; the method obtains the tensile strength R m through calculation according to the test data obtained by the measurement, which is convenient and fast.

[0041] As described above, the method for obtaining material mechanics parameters and constitutive curve based on spherical multi-stage indentation unloading method has the following beneficial effects: the method performs multi-stage indentation unloading test on a metal sample to be tested by using a hard spherical indenter, and obtains the unloading elastic modulus E, plastic extension strength R px , tensile strength R m , and other tensile mechanics parameters by calculation based on the relationship curve between the indentation load and the indentation depth obtained by the test and the test data obtained by measurement, and obtains the constitutive curve reflecting the stress and strain relationship by power function fitting; and further solves the technical problems of large deviation between the strength prediction value and the true value obtained by the existing indentation test method and the over-complicated finite element simulation equation which is difficult to apply in engineering. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 shows a schematic diagram of the method for obtaining material mechanics parameters and constitutive curve based on spherical multi-stage indentation unloading method of the present application;

[0043] Figure 2 shows a schematic diagram of the relationship curve between the indentation load and the indentation depth obtained by the method for obtaining material mechanics parameters and constitutive curve based on spherical multi-stage indentation unloading method of the present application;

[0044] Figure 3 shows a comparison diagram of the constitutive curve reflecting the stress and strain relationship obtained by the method for obtaining material mechanics parameters and constitutive curve based on spherical multi-stage indentation unloading method of the present application and the constitutive curve reflecting the stress and strain relationship obtained by tensile test.

[0045] ELEMENT NUMBER EXPLANATION

[0046] 1 hard spherical indenter

[0047] 2 metal sample DETAILED DESCRIPTION

[0048] The embodiments of the present application are described below by specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the content disclosed in the specification.

[0049] It is to be understood that the structures, proportions, sizes, etc. shown in the drawings accompanying the present specification are merely intended to assist in the understanding of the present disclosure and are not intended to limit the scope of the present disclosure, and therefore, any modification, change in proportion relationship, or adjustment in size, which does not affect the effects and purposes of the present disclosure, should still fall within the scope of the present disclosure. Meanwhile, the terms such as "upper", "lower", "left", "right", "middle", and "one" in the present specification are merely intended to facilitate the understanding of the present disclosure, and are not intended to limit the scope of the present disclosure, and any change in relative relationship or adjustment without substantial change in technical content should also be considered as the scope of the present disclosure.

[0050] As shown in Figure 1 , the present disclosure provides a method for obtaining material mechanics parameters and constitutive curves based on spherical multi-stage indentation unloading method, which comprises the following steps:

[0051] aligning a hard spherical indenter 1 with a to-be-tested indentation area of a metal sample 2;

[0052] performing a multi-stage indentation unloading test on the to-be-tested indentation area using the hard spherical indenter 1, and recording a relationship curve between indentation load and indentation depth;

[0053] extracting the maximum indentation load F mi , the maximum indentation depth h mi , the loading slope S li , and the initial unloading slope S ui corresponding to each stage of indentation unloading test on the relationship curve between indentation load and indentation depth, and measuring the surface indentation diameter d f of the metal sample 2;

[0054] calculating the modified residual depth h c1 and the equivalent elastic modulus E1 * corresponding to the first stage of unloading, and obtaining the unloading elastic modulus E;

[0055] calculating the modified residual depth h ci corresponding to the i-th stage of unloading, and obtaining the equivalent elastic modulus E i * ;

[0056] calculating the stress σ mi corresponding to the maximum indentation load F mi before the i-th stage of unloading;

[0057] obtaining the stress σ mi and the equivalent elastic modulus E i *Calculate the total elastic strain ε of the i-th stage of unloading. tei ;

[0058] Calculate the loading slope S before and after unloading at level i. li and unloading slope S ui The ratio p i Characterizing the total elastic strain ε tei With total strain ε ti The ratio of the two values ​​is used to decompose the plastic strain ε of the i-th stage of unloading. pi ;

[0059] The plastic strain ε pi and stress σ mi Power function fitting is performed to obtain the indentation strengthening coefficient K. I and indentation hardening index n I ; by the indentation strengthening coefficient K I and indentation hardening index n I Obtain the constitutive curve of the material used for metal sample 2;

[0060] Calculate the plastic tensile strength R of the material used for metal specimen 2 px and tensile strength R m .

[0061] In this embodiment, the above-mentioned acquisition method further includes:

[0062] The surface of the test pressing area of ​​metal sample 2 was treated to reduce the surface roughness to less than 0.8 μm, which further improved the accuracy of the data obtained by the experiment.

[0063] In this embodiment, as Figure 1 As shown, the diameter of the hard spherical indenter 1 is D; the maximum indentation load F corresponding to the final stage of the unloading test is applied. mi Let it be F mf The following conditions must be met: For ferrous metals, the maximum indentation load F mf Satisfy F mf =294D 2 For non-ferrous metals, the maximum indentation load F mf Satisfy F mf =98D 2 This ensures the accuracy of the obtained curve relating the indentation load to the indentation depth.

[0064] Furthermore, in this embodiment, the steps of performing a multi-stage indentation and unloading test in the indentation area to be tested using a hard spherical indenter 1 include: always keeping the hard spherical indenter 1 perpendicular to the indentation area to be tested of the metal sample 2, ensuring that the resulting indentation depth and indentation diameter are the result of the direct action of the load, rather than the decomposed load in its normal direction.

[0065] In this embodiment, the maximum indentation load F corresponding to the final stage indentation and unloading test is used. mi Let it be F mf ; in 0~F mf Within the load range, at least 8 stages of indentation and unloading tests should be conducted; ensure that the number of multi-stage indentation and unloading tests is greater than or equal to 8. By controlling the number of indentation and unloading test stages, it is possible to ensure that the relationship curve between the indentation load and the indentation depth obtained through the test is more accurate and that the data obtained is sufficiently rich.

[0066] Furthermore, in this embodiment, as Figure 1 As shown, a single-point, multi-stage indentation and unloading test was conducted on the surface of a 10Cr metal sample 2 using a 2.5mm diameter tungsten carbide alloy hard spherical indenter 1. The surface of the indentation area to be tested should be flat with a roughness of less than 0.8μm. The indentation test employed load control, with a loading rate of 30N / s and an unloading rate of 50N / s. Nine equally spaced load indentation and unloading operations were performed within the indentation load range of 0–1838N. The relationship curve between the indentation load and the indentation depth during the indentation and unloading process was recorded, as shown in the figure. Figure 2 As shown; the indentation diameter d on the surface of 10Cr material was measured using an optical microscope. f =0.90mm.

[0067] In this embodiment, the multi-stage indentation and unloading test adopts the single-point method. The single-point method involves performing multiple multi-stage indentation and unloading operations at a single indentation point with a preset indentation speed and a preset unloading speed. The single-point method is simple to implement, faster, and suitable for situations where the surface space of the material test is limited. Furthermore, the multi-stage indentation and unloading test can also adopt the multi-point method. The multi-point method involves applying different indentation loads at different indentation points with preset indentation speeds and preset unloading speeds to perform a single indentation and unloading operation. The effective number of tests is not less than 8, and the distance between each indentation point is greater than 10D. The multi-point method is suitable for indentation equipment where multi-stage indentation and unloading operations cannot be performed and for situations where the surface space of the material test is large.

[0068] Furthermore, in this embodiment, the corrected residual depth h ci The calculation method is as follows:

[0069] According to the relation Calculate the theoretical residual depth h corresponding to the i-th stage of unloading. * ci , where α = 0.75;

[0070] Then according to the relation Calculate the plasticity coefficient β, where h * cf For relational expressions The theoretical residual depth after the last stage unloading is obtained by taking the value i = f; h cf F represents the true residual depth of the final stage of unloading, obtained from the relationship curve between the indentation load and the indentation depth. mf The maximum indentation load before the final stage of unloading is obtained from the relationship curve between indentation load and indentation depth.

[0071] Substituting the plasticity coefficient β into the relationship Calculate the corrected residual depth h corresponding to the i-th level unloading. ci This embodiment is based on, for example, Figure 2 The parameters were obtained from the curve showing the relationship between the indentation load and the indentation depth, and the corrected residual depth h was calculated. ci This provides a foundation for subsequent calculations of other tensile mechanical parameters.

[0072] Furthermore, in this embodiment, the equivalent elastic modulus E i * The calculation method is as follows: First, according to the relation A ci =π(Dh) ci -h ci 2 The contact projected area A of the i-th stage unloading is calculated. ci Substitute the relational expression into the expression. Calculate the equivalent elastic modulus E i * This embodiment is based on the test results as follows: Figure 2 The relationship curve between the indentation load and the indentation depth, along with the experimental data obtained from measurements, are shown. The equivalent elastic modulus E is then calculated. i * It's convenient and quick.

[0073] In this embodiment, the corrected residual depth h corresponding to the first-stage unloading is calculated. c1 and equivalent elastic modulus E1 * The steps to obtain the unloading elastic modulus E include: taking i=1, and obtaining the corrected residual depth h of the first-stage unloading. c1 The equivalent elastic modulus E1 corresponding to the first stage of unloading was calculated. * Substitute into the relation The unloading elastic modulus E of metal sample 2 was calculated; where E 压头 v is the elastic modulus of the hard spherical indenter 1. 压头 The Poisson's ratio of the hardened spherical indenter 1 is given by E in this embodiment. 压头 =710Gpa, v 压头=0.21; v is the Poisson's ratio of the metal sample 2, taken as v = 0.3; further calculation yields the elastic modulus of the metal sample 2 as E = 219.91 GPa; this embodiment is based on the test results as follows Figure 2 The relationship curve between the indentation load and the indentation depth, along with the measured and obtained experimental data, allows for the convenient and quick calculation of the unloading elastic modulus E.

[0074] In this embodiment, the maximum indentation load F before the i-th stage unloading is calculated. mi The corresponding stress σ mi The steps include: based on relation A smi =πDh mi Calculate the indentation surface area A corresponding to the maximum indentation depth before the i-th stage of unloading. smi Then substitute into the relational expression Calculate the maximum indentation load F before the i-th stage unloading. mi The corresponding stress σ mi Where M is a material constant, and for metallic materials, the value of M ranges from 2.8 to 3. In this embodiment, the value of M is 2.9. This embodiment is based on the test results as follows: Figure 2 The relationship curve between indentation load and indentation depth, along with the experimental data obtained from measurements, is shown. The maximum indentation load F is then calculated. mi The corresponding stress σ mi This provides data support for obtaining constitutive curves that reflect the relationship between stress and strain.

[0075] Furthermore, in this embodiment, the total elastic strain ε tei The calculation steps include:

[0076] According to the relation Calculate the total elastic strain ε corresponding to the i-th stage of unloading. tei This embodiment is based on the test results as follows: Figure 2 The relationship curve between the indentation load and the indentation depth, along with the measured and obtained experimental data, are shown. The total elastic strain ε at the i-th stage of unloading is then calculated. tei This provides data support for obtaining constitutive curves that reflect the relationship between stress and strain.

[0077] In this embodiment, the loading slope S before and after the i-th stage unloading is calculated. li and unloading slope S ui The ratio p i Characterizing the total elastic strain ε tei With total strain ε ti The ratio of the two values ​​is used to decompose the plastic strain ε of the i-th stage of unloading. pi The steps include:

[0078] According to the relation Calculate the loading slope S before and after unloading at level i. li and unloading slope S ui The ratio p i That is, the total elastic strain ε tei With total strain ε ti The ratio;

[0079] According to the relation The plastic strain ε of the i-th stage of unloading of metal specimen 2 was calculated. pi This embodiment calculates the plastic strain ε of the i-th stage of unloading based on the relationship curve between the indentation load and the indentation depth obtained from the test and the experimental data obtained from the measurement. pi This provides data support for obtaining constitutive curves that reflect the relationship between stress and strain.

[0080] In this embodiment, the aforementioned plastic strain ε pi and stress σ mi Power function fitting is performed to obtain the indentation strengthening coefficient K. I and indentation hardening index n I The steps include: unloading the corresponding plastic strain ε at each stage. pi and stress σ mi According to the formula Perform power function fitting to obtain the indentation strengthening coefficient K. I and indentation hardening index n I In this embodiment, the indentation strengthening coefficient K is obtained. I =1023.7MPa and indentation hardening index n I =0.0477, this embodiment is based on the test results as follows. Figure 2 The curve showing the relationship between indentation load and indentation depth, along with the experimental data obtained from measurements, is used to obtain the indentation strengthening coefficient K by performing power function fitting on the obtained experimental data. I and indentation hardening index n I This provides data support for obtaining constitutive curves that reflect the relationship between stress and strain.

[0081] In this embodiment, the above-mentioned indentation strengthening coefficient K I and indentation hardening index n I The steps to obtain a constitutive curve reflecting the stress-strain relationship include: indenting the indentation hardening factor K I Indentation hardening index n I And the unloading elastic modulus E, substitute into the relation To obtain constitutive curves reflecting the stress-strain relationship, this embodiment is based on test results such as... Figure 2The relationship curve between the indentation load and the indentation depth and the test data obtained by measurement, and then by power function fitting and calculation, the constitutive curve reflecting the stress and strain relationship is obtained.

[0082] The constitutive curve reflecting the stress and strain relationship obtained in the present embodiment is compared with the constitutive curve reflecting the stress and strain relationship obtained by the tensile test as shown in the following figure. Figure 3 As shown, the two curves basically coincide.

[0083] In the present embodiment, the plastic elongation strength R px The calculation steps of the plastic elongation strength R includes: substituting the percentage x of the plastic elongation into the relationship formula px In the present embodiment, x = 0.2 is adopted, and the numerical calculation by substitution obtains R p0.2 = 761 MPa. According to the relationship curve between the indentation load and the indentation depth and the test data obtained by measurement as shown in the following figure, the plastic elongation strength R px is obtained by calculation, which is convenient and fast.

[0084] In the present embodiment, the calculation steps of the tensile strength R m includes:

[0085] According to the relationship formula A smi = πDh mi , the maximum indentation depth h m before the unloading of the last stage is obtained by calculation, and the corresponding indentation surface area A sm ;

[0086] According to the relationship formula , the indentation diameter d f corresponding to the indentation surface area A sf is obtained by calculation;

[0087] Substituting A sm and A sf into the relationship formula obtains the proportional coefficient γ;

[0088] According to the relationship formula , the maximum stress σ mf before the unloading of the last stage is obtained by calculation;

[0089] Substituting the proportional coefficient γ and the maximum stress σ mf before the unloading of the last stage into the relationship formula R m = γσ mf , the tensile strength R m is obtained by calculation; substituting the numerical value obtains R m = 933 MPa; according to the relationship curve between the indentation load and the indentation depth and the test data obtained by measurement as shown in the following figure, the tensile strength R m is obtained by calculation, which is convenient and fast.Figure 2 The relationship curve between the indentation load and the indentation depth and the test data obtained by measurement, and further the tensile strength R m , convenient and fast.

[0090] The mechanical parameters and the constitutive parameters obtained by the embodiment of the application are compared with the tensile test results in the following table, and it can be known that the material unloading elastic modulus E, the yield strength R p0.2 , the tensile strength R m , the strengthening coefficient K and the strengthening index n obtained by the embodiment of the application have very small deviation compared with the tensile test results, which proves the effectiveness and accuracy of the application technology.

[0091]

[0092] In summary, the method for obtaining the material mechanical parameters and the constitutive curve based on the spherical multi-stage indentation unloading method of the application, through the multi-stage indentation unloading test of the hard spherical indenter 1 and the metal sample 2 to be tested, and according to the relationship curve between the indentation load and the indentation depth and the test data obtained by measurement, and further through calculation, the material mechanical parameters are obtained and the constitutive curve reflecting the stress and strain relationship is obtained by power function fitting; solve the technical problems that the strength prediction value obtained by the existing indentation test method has large deviation from the true value and the finite element simulation equation is too complicated to be applied in engineering. Therefore, the application effectively overcomes the various shortcomings in the prior art and has high industrial utilization value.

[0093] The above embodiments only exemplarily illustrate the principles and effects of the application, and are not used to limit the application. Any person skilled in the art can modify or change the above embodiments without departing from the spirit and scope of the application. Therefore, all equivalent modifications or changes completed by those skilled in the art without departing from the spirit and technical thought disclosed by the application should be covered by the claims of the application.

Claims

1. A method for obtaining material mechanical parameters and constitutive curves based on spherical multistage indentation unloading method, characterized in that, The method comprises the following steps: aligning a hard spherical indenter (1) with a to-be-tested indentation area of a metal sample (2); implementing a multi-stage indentation unloading test on the to-be-tested indentation area using the hard spherical indenter (1), and recording a curve between indentation load and indentation depth; extracting the maximum indentation load F corresponding to each level of indentation unloading test on the relationship curve between the indentation load and the indentation depth mi , the maximum indentation depth h mi , the loading slope S li , and the initial unloading slope S ui , measuring the surface indentation diameter d f of the metal test sample (2) calculating a modified residual depth h corresponding to the first level of unloading c1 and an equivalent elastic modulus E1 * obtaining an unloading elastic modulus E; calculating the modified residual depth h corresponding to the i-th level of unloading ci obtaining the equivalent elastic modulus E i * ; Calculate the maximum penetration load F before the i-th stage of unloading mi Corresponding stress σ mi ; corresponding stress σ by the i-th level of unloading mi and the equivalent elastic modulus E i * the total elastic strain ε by the i-th level of unloading is calculated tei ; Calculate the loading slope S before and after unloading at level i. li and unloading slope S ui The ratio p i Characterizing the total elastic strain ε tei With total strain ε ti The ratio of the two values ​​is used to decompose the plastic strain ε of the i-th stage of unloading. pi ; The plastic strain ε pi and stress σ mi are subjected to power function fitting to obtain the indentation strengthening coefficient K I and the indentation hardening index n I ; The constitutive curve of the material of the metal test specimen (2) is obtained from the press-in strengthening coefficient K I and the press-in hardening index n I ​ The plastic elongation strength R of the material of the metal test specimen (2) is calculated px and the tensile strength R m .

2. The method for obtaining material mechanical parameters and a constitutive curve based on a spherical multi-stage indentation unloading method according to claim 1, characterized in that: The diameter of the hard spherical indenter (1) is D, and the maximum indentation load F mi corresponding to the last stage of the indentation unloading test is mf denoted as F mf The maximum indentation load F mf satisfies F 2 = 294D mf for ferrous metals, and F mf = 98D 2， for non-ferrous metals. The surface of the indentation area to be tested should be flat and have a roughness of less than 0.8 μm; the indenter (1) should always be kept perpendicular to the indentation area of the metal sample (2) to be tested, and the indentation unloading test should be carried out in at least 8 stages in the load range of 0 ~ F mf .

3. The method for obtaining material mechanical parameters and constitutive curve based on spherical multi-stage indentation unloading method according to claim 1, characterized in that: said calculated equivalent elastic modulus E i * comprises: According to the relationship The theoretical residual depth h corresponding to the i-th level of unloading is calculated * ci where α = 0.75; wherein h the plasticity coefficient β is calculated from the relation * cf is the relation the theoretical residual depth after unloading of the last stage is obtained for i = f; h cf is the real residual depth after unloading of the last stage obtained from the curve of the relation between the indentation load and the indentation depth; F mf is the maximum indentation load before unloading of the last stage obtained from the curve of the relation between the indentation load and the indentation depth; Substitute the plasticity coefficient β into the relationship Calculate the modified residual depth h corresponding to the i-th level of unloading ci ; According to the relationship A ci = π(Dh ci -h ci 2 The contact projection area A ci of the i-th stage unloading is calculated The equivalent elastic modulus E i * of the i-th stage unloading is calculated 4. The method for obtaining material mechanical parameters and constitutive curve based on spherical multi-stage indentation unloading method according to claim 1, characterized in that: said calculating a first level of unloading corresponding modified residual depth h c1 and an equivalent elastic modulus E1 * said step of obtaining an unloading elastic modulus E comprises: Taking i = 1, the modified residual depth h of the first stage unloading is obtained c1 , the equivalent elastic modulus E1 corresponding to the first stage unloading is calculated * , and substituted into the relationship The unloading elastic modulus E of the metal sample (2) is calculated; wherein E 压头 is the unloading elastic modulus of the hard spherical indenter (1), v 压头 is the Poisson's ratio of the hard spherical indenter (1); v is the Poisson's ratio of the metal sample (2) material.

5. The method for obtaining material mechanical parameters and constitutive curve based on spherical multi-stage indentation unloading method according to claim 1, characterized in that: The calculation of the maximum indentation load F before the i-th level of unloading mi The corresponding stress σ mi The steps of the method comprise: According to the relationship A smi = πDh mi The indentation surface area A corresponding to the maximum indentation depth before the i-th level of unloading is calculated smi , and the relationship is substituted The maximum indentation load F before the i-th level of unloading is calculated mi The corresponding stress σ mi ; wherein M is a material constant, and for a metal material, the value range of M is 2.8-3.

6. The method for obtaining material mechanical parameters and constitutive curve based on spherical multi-stage indentation unloading method according to claim 1, characterized in that: the total elastic strain ε tei the calculation step comprises: According to the relationship The total elastic strain ε corresponding to the i-th level of unloading is calculated tei .

7. The method for obtaining material mechanical parameters and constitutive curve based on spherical multi-stage indentation unloading method according to claim 1, characterized in that: The calculation of the loading slope S before and after the i-th level unloading. li and unloading slope S ui The ratio p i The plastic strain ε of the i-th stage unloading is obtained from the decomposition. pi The steps include: According to the relationship The ratio p i of the loading slope S li and the unloading slope S ui before and after the i-th stage of unloading, i.e., the ratio of the total elastic strain ε tei and the total strain ε ti , According to the relationship The plastic strain amount ε of the i-th stage unloading of the metal sample (2) is calculated pi .

8. The method for obtaining material mechanical parameters and constitutive curve based on spherical multi-stage indentation unloading method according to claim 1, characterized in that: said plastic strain ε pi and stress σ mi power function fitting to obtain the indentation strengthening coefficient K I and the indentation hardening index n I and the steps of the constitutive curve include: Unloading the corresponding plastic strain ε of each level pi and stress σ mi According to the formula Power function fitting is performed to obtain the indentation strengthening coefficient K I and the indentation hardening index n I， The press-in reinforcement coefficient K I , the press-in hardening index n I , and the unloading elastic modulus E are substituted into the relational expression to obtain a constitutive curve for reflecting the stress and strain relationship.

9. The method for obtaining material mechanical parameters and constitutive curve based on spherical multi-stage indentation unloading method according to claim 1, characterized in that: the plastic elongation strength R px the calculation step comprises: The press-in reinforcement coefficient K I , the press-in hardening index n I and the percentage of plastic elongation x are substituted into the relational expression to calculate the plastic elongation strength R px .

10. The method for obtaining material mechanical parameters and constitutive curve based on spherical multi-stage indentation unloading method according to claim 1, characterized in that: said tensile strength R m the calculation step comprises: According to the relationship A smi = πDh mi The maximum indentation depth h before the last stage of unloading is calculated m The corresponding indentation surface area A sm ; According to the relationship The indentation diameter d is calculated f The corresponding indentation surface area A sf ; Substitute A sm and A sf into the relationship to obtain the proportionality coefficient γ; According to the relationship The maximum stress σ before unloading of the last stage is calculated mf ; The proportional coefficient γ and the maximum stress σ before unloading of the last stage are calculated mf The relationship R = γσ is substituted m mf The tensile strength R is calculated m .​

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