A detection method for spherical indenter penetration of uniaxial mechanical properties under adaptive working conditions

Abstract

The present invention provides a spherical indenter penetration detection method for uniaxial mechanical properties under adaptive working conditions, including: Step 10) determining a spherical indenter penetration scheme according to the test working conditions to obtain penetration data; Step 20) allowing the calculation of uniaxial stress-strain during measurement for the plastic zone radius r p ; Step 30) not allowing the calculation of uniaxial stress-strain during measurement for the plastic zone radius r p ; Step 40) determining the yield strength and tensile strength of the material to be tested. The present invention provides a spherical indenter penetration detection method for uniaxial mechanical properties applicable to different measurement working conditions, providing guidance for the structural integrity assessment and remaining life analysis of in-service equipment such as pressure vessels and pressure pipelines.

Description

Technical Field

[0001] The present invention relates to the technical field of uniaxial mechanical property testing of materials, and particularly to a spherical indenter penetration testing method for uniaxial mechanical properties under adaptive working conditions. Background Art

[0002] Conventional uniaxial mechanical property testing methods (such as uniaxial tensile testing, uniaxial compressive testing, and uniaxial shear testing) all require large-volume destructive sampling and cannot be applied to in-service equipment and occasions where the volume of the test material is limited (such as welded joints). As a mechanical property testing method that requires no sampling and is almost non-destructive, spherical indenter penetration testing can be used as an alternative to conventional uniaxial mechanical property testing.

[0003] In 1997, T. Byun et al. published a paper titled "Measurement of through-the-thickness variations of mechanical properties in SA508Gr.3 pressure vessel steels using ball indentation test technique" in the 3rd issue of the journal International Journal of Pressure Vessels and Piping, proposing a uniaxial stress-uniaxial strain indentation prediction method based on empirical formulas.

[0004] In 2010, J. Lee et al. published a paper titled "A study on robust indentation techniques to evaluate elastic–plastic properties of metals" in the 47th issue of the journal International Journal of Solids and Structures, proposing to conduct a systematic finite element analysis for power-law hardening materials, thereby establishing a phenomenological correlation between indentation load-indentation displacement and uniaxial stress-uniaxial strain.

[0005] In 2019, H. Chen et al. published a paper titled "Equivalent-energy indentation method to predict the tensile properties of light alloys" in Volume 162 of the journal Materials and Design, proposing a method that combines the analytical derivation based on the dilatant cavity model with finite element calibration to establish the relationship between the indentation load-indentation displacement and the power hardening material parameters.

[0006] In the prior art, usually a single indentation characteristic parameter (such as the indentation load-displacement curve, the radius of the indentation plastic zone, etc.) and test methods (such as monotonic loading method, multiple loading-unloading method) are adopted in an attempt to establish a correlation with the mechanical property parameters of the material to be tested, which cannot cope with the changing actual test conditions. The key to accurately inversing the uniaxial mechanical properties of the material to be tested through spherical indenter indentation testing lies in obtaining a sufficient number of indentation characteristic parameters. Usually, adopting the multiple loading-unloading method and obtaining as many indentation characteristic parameters as possible helps to improve the inversion accuracy of the uniaxial mechanical properties. However, when the flexibility of the indentation detection system increases due to the change of the clamping method, or when the surface strain distribution of the indentation specimen cannot be measured due to test condition limitations, the existing indentation detection methods cannot meet the relatively complex and changeable on-site indentation detection requirements.

[0007] Therefore, it is necessary to design a spherical indenter indentation detection method for uniaxial mechanical properties that can be applied to different working conditions. Summary of the Invention

[0008] The purpose of the present invention is to provide a spherical indenter indentation detection method for uniaxial mechanical properties under adaptive working conditions in view of the defects of the existing spherical indenter indentation test method for uniaxial mechanical properties being restricted by the acquisition of indentation characteristic parameters and test methods.

[0009] To solve the above technical problems, the present invention provides the following technical solutions:

[0010] A spherical indenter indentation detection method for uniaxial mechanical properties under adaptive working conditions, characterized by comprising:

[0011] S1: Using a spherical indenter with a radius R, slowly press it into the smooth surface of the material to be tested in a way that includes N times of equally spaced loading-unloading, and respectively obtain continuous indentation load P and indentation displacement h curves through the load sensor and displacement sensor integrated in the indentation testing machine;

[0012] S2: Judge whether the condition for optical measurement on the surface of the specimen to be tested is available. If the optical measurement condition is available, measure the radius r of the plastic zone around the residual indentation pit p , and execute S3, otherwise skip rp Measurement is directly performed in S3;

[0013] S3: Using the depth h of the residual indentation pit on the surface of the material under test in the i-th indentation cycle as the abscissa, and the effective Young's modulus E of the material under test in the i-th indentation cycle as the ordinate, where 1 ≤ i ≤ N, plot a scatter diagram and use a linear function to fit the scatter points in the diagram, so as to estimate the Young's modulus E0 of the material under test. The linear function is p E eff (i) = -Ch

[0014] E eff + E0 (1) p where C is the fitting coefficient and E0 is the estimated Young's modulus of the material under test;

[0015]

[0016] S4: Calculate the relative error ΔError between the estimated Young's modulus E0 of the material under test and the preset Young's modulus E of the material under test using the following formula: pre

[0017]

[0018] where E0 is the estimated Young's modulus of the material under test and E pre is the preset Young's modulus of the material under test;

[0019] S5: When ΔError is less than the maximum allowable error δ, the material under test is allowed to be tested by spherical indenter indentation in the N-time loading-unloading mode, and the indentation load P and indentation displacement h curve including N-time loading-unloading obtained in S1 are directly used for uniaxial mechanical property calculation. If r can be measured p then go to S6, if r cannot be measured p then go to S9; when ΔError exceeds the maximum allowable error δ, the material under test is only allowed to be tested by spherical indenter indentation in the monotonic loading mode. Remove the unloading part of the indentation load P and indentation displacement h curve including N-time loading-unloading obtained in S1 to obtain a monotonic loading curve for uniaxial mechanical property calculation. If r can be measured p then go to S7, if r cannot be measured p then go to S13;

[0020] S6: Calculate the von Mises equivalent stress σ eq (i) and von Mises equivalent strain ε eq (i) of the i-th indentation cycle of the material under test respectively according to the following formulas, and then go to S14, where 1 ≤ i ≤ N: ​​

[0021]

[0022]

[0023] wherein, E eff (i) is the effective Young's modulus of the i-th indentation cycle of the material to be tested, E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter respectively, R is the radius of the spherical indenter, R0 (i) is the radius of curvature of the residual indentation pit after complete unloading of the i-th indentation cycle, P max (i) is the maximum indentation load of the i-th indentation cycle, W E (i) and W P (i) are the elastic external work and plastic external work of the i-th indentation cycle respectively, h max (i) is the maximum indentation depth of the i-th indentation cycle, h r (i) is the elastic recovery depth of the i-th indentation cycle, σ0 is the stress proportional limit of the material to be tested, ε0 is the strain proportional limit of the material to be tested. When i = 1, W P (0) = 0, P max (0) = 0, σ eq (0) = σ0, ε eq (0) = ε0;

[0024] S7: Fit the indentation load P-indentation displacement h curve in the monotonic loading stage by the power function shown in the following formula:

[0025] P = Ch m (5)

[0026] wherein, C is the fitting coefficient of the indentation load P-indentation displacement h curve, and m is the fitting exponent of the indentation load P-indentation displacement h curve;

[0027] S8: The von Mises equivalent stress σ eq -von Mises equivalent strain ε eq relationship is obtained according to the following formula:

[0028]

[0029] In the formula, ε0 is the strain proportional limit of the material to be tested, E is the Young's modulus of the material to be tested, and n is the work hardening index of the material to be tested; then go to S14;

[0030] S9: Assume that the strain proportional limit ε0 of the material to be tested is 0.002, and calculate the von Mises equivalent stress σ of the i-th indentation cycle of the material to be tested according to formula (3) and formula (4) respectively eq (i) and the von Mises equivalent strain ε eq (i) , where 1 ≤ i ≤ N;

[0031] S10: Substitute the data points of the von Mises equivalent stress σ eq and the von Mises equivalent strain ε eq calculated in S9 into formula (6) to fit the work hardening index n;

[0032] S12: Refit the strain proportional limit ε0 of the material to be tested according to formula (7). If the relative error of the refitted strain proportional limit compared with the strain proportional limit used in S9 is less than the allowable value, it is considered that the von Mises equivalent stress σ eq (i) and the von Mises equivalent strain ε eq (i) of the i-th indentation cycle of the material to be tested calculated in S9 are the true values; otherwise, substitute the updated strain proportional limit ε0 into step S9 to recalculate the von Mises equivalent stress σ eq (i) and the von Mises equivalent strain ε eq (i) until the relative error requirement is met, then go to S14;

[0033]

[0034] In the formula, E is the Young's modulus of the material to be tested, here E0 is used to replace E, E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter respectively, R is the radius of the spherical indenter, R0 (i) is the radius of curvature of the residual indentation pit after complete unloading of the i-th indentation cycle, P max (i) is the maximum indentation load of the i-th indentation cycle, W T (i) is the total external work of the i-th indentation cycle, h max (i) is the maximum indentation depth of the i-th indentation cycle, hr (i) is the elastic recovery depth for the i-th indentation cycle, σ0 is the stress proportional limit of the material under test, and ε0 is the strain proportional limit of the material under test; when i = 1, W P (0) = 0, P max (0) = 0, σ eq (0) = σ0, ε eq (0) = ε0; ξ and ψ are regression equations regarding the strain proportional limit ε0 and the work hardening index n of the material under test;

[0035] S13: Assume that the relationship between the von Mises equivalent stress σ eq and the von Mises equivalent strain ε eq of the material under test conforms to formula (6), and use the following formula to fit the strain proportional limit ε0 and the work hardening index n of the material under test:

[0036]

[0037] where E is the Young's modulus of the material under test, and here the preset value E pre is used to replace E, W T is the total external work, P is the indentation load, ξ T and ψ T are regression equations regarding the strain proportional limit ε0 and the work hardening index n of the material under test; then go to S14;

[0038] S14: Calculate the von Mises equivalent plastic strain ε p of the material under test according to formula (9), and regard the von Mises equivalent stress σ p when ε eq = 0.2% as the yield strength R p0.2 of the material under test.

[0039]

[0040] where E is the Young's modulus of the material under test. For the spherical indenter indentation test with monotonic loading, the preset value E pre is used to replace E; for the spherical indenter indentation test including N loading-unloading cycles, the Young's modulus E0 of the material under test obtained in S3 is used to replace E, σ eq and ε eq are the von Mises equivalent stress and the von Mises equivalent strain of the material under test respectively;

[0041] S15: Calculate the engineering stress σ of the material under test according to formula (10)ENG The maximum value of the engineering stress is regarded as the tensile strength R of the material under test m :

[0042]

[0043] In the formula, σ eq and ε eq are the von Mises equivalent stress and von Mises equivalent strain of the material under test, respectively

[0044] Furthermore, the effective Young's modulus E corresponding to the i-th indentation cycle is calculated according to formula (11) eff (i) :

[0045]

[0046] In the formula, v is the Poisson's ratio of the material under test, E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter material, R is the radius of the spherical indenter, is the maximum displacement before unloading in the i-th indentation cycle collected by the displacement sensor, S (i) and h p (i) are the unloading slope and the depth of the residual indentation pit in the i-th indentation cycle, respectively, 1 ≤ i ≤ N

[0047] Furthermore, in S5, when ΔError exceeds the maximum allowable error δ, when the material under test only allows spherical indenter indentation test with monotonic loading, directly perform spherical indenter indentation test with monotonic loading, and obtain the corresponding indentation load P and indentation displacement h curves

[0048] Furthermore, in S6, the stress proportional limit σ0 of the material under test is calculated according to the following formula

[0049]

[0050] In the formula, P max is the maximum indentation load in the spherical indenter indentation test. For the spherical indenter indentation test with N loading-unloading cycles, P max is the maximum load in the N-th indentation cycle, that is, P max (N) .

[0051] Furthermore, the strain proportional limit ε0 of the material under test is calculated according to formula (13)

[0052]

[0053] Wherein, σ0 is the stress proportional limit of the material to be tested, and E is the Young's modulus of the material to be tested. For the spherical indenter penetration test under monotonic loading, the preset value E is used pre to replace E; for the spherical indenter penetration test including N loading-unloading cycles, the Young's modulus E0 of the material to be tested obtained in S3 is used to replace E.

[0054] Furthermore, in S8, the work hardening index n of the material to be tested is determined according to formula (14):

[0055]

[0056] Wherein, ε0 is the strain proportional limit of the material to be tested, and E is the Young's modulus of the material to be tested. Here, the preset value E is used pre to replace E, n is the work hardening index of the material to be tested, C and m are the fitting coefficients and fitting exponents of the indentation load P-indentation displacement h curve respectively, and σ eq-M is the von Mises equivalent stress of the material to be tested corresponding to the maximum indentation load.

[0057] Furthermore, σ eq-M is calculated according to formula (15):

[0058]

[0059] Wherein, E is the Young's modulus of the material to be tested. Here, the preset value E is used pre to replace E, E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter respectively, R is the radius of the spherical indenter, R0 is the radius of curvature of the residual indentation pit after complete unloading, P max is the maximum indentation load, W E is the elastic external work, h max is the maximum indentation depth, h r is the elastic recovery depth, σ0 is the stress proportional limit of the material to be tested, and ε0 is the strain proportional limit of the material to be tested.

[0060] Furthermore, the material to be tested is SA508 steel plate, and the spherical indenter is tungsten carbide spherical indenter.

[0061] Compared with the prior art, the beneficial effects of the present invention are: the present invention overcomes the deficiencies of the existing uniaxial mechanical property spherical indenter penetration test method restricted by the acquisition and test methods of indentation characteristic parameters, and allows the plastic zone radius r pBased on the spherical indenter penetration test with N loading-unloading cycles, a uniaxial mechanical property penetration test method applicable to general test conditions is proposed. It is particularly suitable for on-site applications with variable test conditions such as pressure-bearing equipment, rail transit, and bridges, as well as applications with highly localized and significantly heterogeneous material properties such as welded joints. It provides guidance for the structural integrity assessment and remaining life analysis of in-service equipment such as pressure vessels and pipelines. Description of the Drawings

[0062] Figure 1 Schematic diagram of the spherical indenter penetrating into the SA508 steel plate in the embodiment of the present invention;

[0063] Figure 2 Penetration load P - penetration displacement h curve of SA508 steel in the embodiment of the present invention;

[0064] Figure 3 Effective Young's modulus E of SA508 steel in the embodiment of the present invention eff with the depth h of the residual indentation pit p Scatter plot of variation;

[0065] Figure 4 von Mises equivalent stress - von Mises equivalent strain inversion result diagram of SA508 steel in the embodiment of the present invention.

[0066] Where: 1 - Penetration load, 2 - Tungsten carbide spherical indenter, 3 - SA508 steel plate. Detailed Description of the Invention

[0067] To deepen the understanding of the present invention, the following will further elaborate on the present invention in conjunction with the drawings. This embodiment is only used to explain the present invention and does not constitute a limitation on the protection scope of the present invention.

[0068] A spherical indenter penetration detection method for uniaxial mechanical properties under adaptive working conditions according to the present invention includes:

[0069] S1: Using a spherical indenter with a radius R, slowly penetrate the smooth surface of the test material in a loading-unloading manner with N equal-spacing cycles, and obtain continuous penetration load P and penetration displacement h curves through the load sensor and displacement sensor integrated in the penetration testing machine respectively;

[0070] S2: Determine whether the condition for optical measurement on the surface of the test specimen is available. If the optical measurement condition is available, measure the plastic zone radius r around the residual indentation pit p , and execute S3. Otherwise, skip the r p measurement and directly execute S3;

[0071] S3: Taking the depth h of the residual indentation pit on the surface of the test material in the i-th penetration cyclep Using the [abscissa], and the effective Young's modulus E of the material under test in the i-th indentation cycle eff (i) as the ordinate, where 1 ≤ i ≤ N, plot a scatter diagram and fit the scatter points in the diagram using a linear function to estimate the Young's modulus E0 of the material under test. The linear function is

[0072] E eff = -Ch p + E0 (1)

[0073] In the formula, C is the fitting coefficient, and E0 is the Young's modulus of the material under test estimated.

[0074] Where the E eff (i) is calculated according to formula (11):

[0075]

[0076] In the formula, v is the Poisson's ratio of the material under test, E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter material, R is the radius of the spherical indenter, is the maximum displacement before unloading in the i-th indentation cycle collected by the displacement sensor, S (i) and h p (i) are the unloading slope and the residual indentation depth of the i-th indentation cycle respectively, where 1 ≤ i ≤ N.

[0077] S4: Calculate the relative error ΔError between the estimated Young's modulus E0 of the material under test and the preset Young's modulus E of the material under test using the following formula: pre The relative error ΔError:

[0078]

[0079] In the formula, E0 is the estimated Young's modulus of the material under test, and E pre is the preset Young's modulus of the material under test;

[0080] S5: When ΔError is less than the maximum allowable error δ, the material under test is allowed to be tested by spherical indenter indentation in the N-time loading-unloading mode, and the indentation load P and indentation displacement h curves containing N-time loading-unloading obtained in S1 are directly used for uniaxial mechanical property calculation. If r can be measured p then go to S6, if r cannot be measured pThen go to S9; when ΔError exceeds the maximum allowable error δ, the material under test is only allowed to be tested by spherical indenter indentation in a monotonic loading manner. Remove the unloading part of the indentation load P and indentation displacement h curve obtained in S1 that contains N loading-unloading cycles to obtain a monotonic loading curve for uniaxial mechanical property calculation, or directly perform spherical indenter indentation test under monotonic loading and obtain the corresponding indentation load P and indentation displacement h curve. If r can be measured p Then go to S7. If r cannot be measured p Then go to S13;

[0081] S6: Calculate the von Mises equivalent stress σ of the i-th indentation cycle of the material under test according to the following formulas respectively eq (i) and von Mises equivalent strain ε eq (i) , and then go to S14, where 1 ≤ i ≤ N:

[0082]

[0083]

[0084] In the formula, E eff (i) is the effective Young's modulus of the i-th indentation cycle of the material under test, E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter respectively, R is the radius of the spherical indenter, R0 (i) is the radius of curvature of the residual indentation pit after complete unloading of the i-th indentation cycle, P max (i) is the maximum indentation load of the i-th indentation cycle, W E (i) and W P (i) are the elastic external work and plastic external work of the i-th indentation cycle respectively, h max (i) is the maximum indentation depth of the i-th indentation cycle, h r (i) is the elastic recovery depth of the i-th indentation cycle, σ0 is the stress proportional limit of the material under test, ε0 is the strain proportional limit of the material under test. When i = 1, W P (0) = 0, P max (0) = 0, σ eq (0) = σ0, ε eq (0) = ε0.

[0085] Wherein, the stress proportional limit σ0 of the material to be tested is calculated according to the following formula:

[0086]

[0087] In the formula, P max is the maximum indentation load in the spherical indenter penetration test. For the spherical indenter penetration test using the N - time loading - unloading method, P max is the maximum load of the N - th indentation cycle, that is, P max (N) .

[0088] The strain proportional limit ε0 of the material to be tested is calculated according to formula (13):

[0089]

[0090] In the formula, σ0 is the stress proportional limit of the material to be tested, and E is the Young's modulus of the material to be tested. For the monotonic loading spherical indenter penetration test, the preset value E pre is used to replace E; for the spherical indenter penetration test including N - time loading - unloading, the Young's modulus E0 of the material to be tested obtained in S3 is used to replace E.

[0091] S7: Fit the indentation load P - indentation displacement h curve in the monotonic loading stage by the power function shown in the following formula:

[0092] P = Ch m (5)

[0093] In the formula, C is the fitting coefficient of the indentation load P - indentation displacement h curve, and m is the fitting exponent of the indentation load P - indentation displacement h curve;

[0094] S8: The relationship between the von Mises equivalent stress σ eq - von Mises equivalent strain ε eq is obtained according to the following formula:

[0095]

[0096] In the formula, ε0 is the strain proportional limit of the material to be tested, E is the Young's modulus of the material to be tested, and n is the work - hardening index of the material to be tested; then go to S14.

[0097] Wherein: The work - hardening index n of the material to be tested is determined according to formula (14):

[0098]

[0099] In the formula, ε0 is the strain proportional limit of the material to be tested, E is the Young's modulus of the material to be tested, and here the preset value E is usedpre Instead of E, n is the work hardening index of the material to be tested, C and m are the fitting coefficients and fitting exponents of the indentation load P - indentation displacement h curve respectively, and σ eq-M is the von Mises equivalent stress corresponding to the maximum indentation load of the material to be tested. σ eq-M is calculated according to formula (15):

[0100]

[0101] where E is the Young's modulus of the material to be tested, and here the preset value E pre is used instead of E, E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter respectively, R is the radius of the spherical indenter, R0 is the curvature radius of the residual indentation pit after complete unloading, P max is the maximum indentation load, W E is the elastic external work, h max is the maximum indentation depth, h r is the elastic recovery depth, σ0 is the stress proportional limit of the material to be tested, and ε0 is the strain proportional limit of the material to be tested.

[0102] S9: Assume that the strain proportional limit ε0 of the material to be tested is 0.002, and calculate the von Mises equivalent stress σ eq (i) and von Mises equivalent strain ε eq (i) of the i-th indentation cycle of the material to be tested according to formula (3) and formula (4) respectively, where 1 ≤ i ≤ N;

[0103] S10: Substitute the data points of the von Mises equivalent stress σ eq and von Mises equivalent strain ε eq calculated in S9 into formula (6) to fit the work hardening index n;

[0104] S12: Re - fit the strain proportional limit ε0 of the material to be tested according to formula (7). If the relative error of the re - fitted strain proportional limit compared with the strain proportional limit used in S9 is less than the allowable value, then the von Mises equivalent stress σ eq (i) and von Mises equivalent strain ε eq (i) of the i-th indentation cycle of the material to be tested calculated in S9 are considered as the true values; otherwise, substitute the updated strain proportional limit ε0 into step S9 to recalculate the von Mises equivalent stress σ eq (i)and von Mises equivalent strain ε eq (i) Until the relative error requirement is met, then go to S14;

[0105]

[0106] where E is the Young's modulus of the material to be tested, and here E0 is used to replace E, E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter respectively, R is the radius of the spherical indenter, R0 (i) is the radius of curvature of the residual indentation pit after complete unloading in the i-th indentation cycle, P max (i) is the maximum indentation load in the i-th indentation cycle, W T (i) is the total external work in the i-th indentation cycle, h max (i) is the maximum indentation depth in the i-th indentation cycle, h r (i) is the elastic recovery depth in the i-th indentation cycle, σ0 is the stress proportional limit of the material to be tested, ε0 is the strain proportional limit of the material to be tested; when i = 1, W P (0) = 0, P max (0) = 0, σ eq (0) = σ0, ε eq (0) = ε0; ξ and ψ are regression equations regarding the strain proportional limit ε0 and work hardening index n of the material to be tested;

[0107] S13: Assume that the relationship between the von Mises equivalent stress σ eq and von Mises equivalent strain ε eq of the material to be tested conforms to formula (6), and use the following formula to fit the strain proportional limit ε0 and work hardening index n of the material to be tested:

[0108]

[0109] where E is the Young's modulus of the material to be tested, and here the preset value E pre is used to replace E, W T is the total external work, P is the indentation load, ξ T and ψ T are regression equations regarding the strain proportional limit ε0 and work hardening index n of the material to be tested; then go to S14;

[0110] S14: Calculate the von Mises equivalent plastic strain ε of the material under test according to formula (9). p , and regard the von Mises equivalent stress σ p when ε eq = 0.2% as the yield strength R p0.2 of the material under test.

[0111]

[0112] Wherein, E is the Young's modulus of the material under test. For the spherical indenter penetration test under monotonic loading, use the preset value E pre to replace E; for the spherical indenter penetration test including N loading-unloading cycles, use the Young's modulus E0 of the material under test obtained in S3 to replace E, σ eq and ε eq are respectively the von Mises equivalent stress and von Mises equivalent strain of the material under test;

[0113] S15: Calculate the engineering stress σ ENG of the material under test according to formula (10), and regard the maximum value of the engineering stress as the tensile strength R m of the material under test:

[0114]

[0115] Wherein, σ eq and ε eq are respectively the von Mises equivalent stress and von Mises equivalent strain of the material under test.

[0116] The following takes specific embodiments and combines with the attached Figures 1-4 drawings to further illustrate the technical solution of the present application.

[0117] Applying the method of the present invention to determine the uniaxial mechanical properties of SA508 steel includes the following steps:

[0118] Use the SA508 steel plate 3 as shown in Figure 1 as the test specimen to be tested, and polish its surface to be tested successively with 180-400-600-800 mesh sandpaper. Use a tungsten carbide spherical indenter 2 with a tip radius of 0.78 mm for the indentation test. The elastic modulus E ind and Poisson's ratio v ind of the spherical indenter are 640 GPa and 0.21 respectively.

[0119] Since the digital speckle production conditions for measuring the indentation plastic zone radius r p are not available, it is therefore chosen not to perform the measurement of r p .

[0120] In a loading-unloading mode with 12 equally spaced intervals, under the action of an indentation load 1, a spherical indenter was slowly pressed into the surface of SA508 steel. The continuous indentation load P and indentation displacement h curves as shown in Figure 2 were obtained respectively through the load sensor and displacement sensor integrated in the indentation testing machine. The curves include two stages of loading and unloading.

[0121] Calculate the effective Young's modulus E corresponding to the i-th indentation cycle according to formula (11) eff (i) , (1 ≤ i ≤ 12)

[0122]

[0123] where v is the known Poisson's ratio of the tested material (v = 0.3), E ind and v ind are the Young's modulus and Poisson's ratio of the known spherical indenter material (E ind = 640 GPa, v ind = 0.21), R is the known radius of the spherical indenter (R = 0.78 mm), is the maximum displacement before unloading in the i-th indentation cycle collected by the displacement sensor, S (i) and h p (i) are the unloading slope and the residual indentation pit depth in the i-th indentation cycle respectively.

[0124] The effective Young's modulus E of SA508 steel calculated according to formula (11) eff varies with the residual indentation pit depth h p The data scatter points are as shown in Figure 3 According to formula (1), plot the data scatter points in Figure 3 to obtain the Young's modulus E0 = 211.89 GPa of SA508 steel.

[0125] E eff = -Ch p + E0 (1)

[0126] where C is the fitting coefficient (C = -609.86).

[0127] Since the Young's modulus E0 = 211.89 GPa of SA508 steel has a deviation of less than 5% from the recommended value E pre = 205 GPa of the Young's modulus of steel materials, the tested SA508 steel allows the use of the loading-unloading method for spherical indenter indentation testing. The obtained indentation load P and indentation displacement h curves including 12 loadings-unloadings can be directly used for uniaxial mechanical property calculations.

[0128] Assume that the strain proportional limit ε0 of SA508 steel is 0.002.

[0129] Calculate the von Mises equivalent stress σ of the i-th indentation cycle of SA508 steel according to formula (3) and formula (4) respectively eq (i) and the von Mises equivalent strain ε eq (i) , where 1 ≤ i ≤ 12.

[0130]

[0131]

[0132] In the formula, E eff (i) is the effective Young's modulus of the i-th indentation cycle, E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter respectively, R is the radius of the spherical indenter, R0 (i) is the radius of curvature of the residual indentation pit after complete unloading of the i-th indentation cycle, P max (i) is the maximum indentation load of the i-th indentation cycle, W E (i) and W P (i) are the elastic external work and plastic external work of the i-th indentation cycle respectively, h max (i) is the maximum indentation depth of the i-th indentation cycle, h r (i) is the elastic recovery depth of the i-th indentation cycle, σ0 is the stress proportional limit of the tested material, and ε0 is the strain proportional limit of the tested material. Specifically, when i = 1, W P (0) = 0, P max (0) = 0, σ eq (0) = σ0, ε eq (0) = ε0.

[0133] Substitute the data points of the von Mises equivalent stress σ eq and the von Mises equivalent strain ε eq calculated by formula (3) and formula (4) into formula (6), and the work-hardening index n = 0.0971 is obtained by fitting. Among them, the Young's modulus E in formula (6) is replaced by the Young's modulus E0 = 211.89 GPa of SA508 steel calculated by formula (1).

[0134] According to formula (7), the strain proportional limit of SA508 steel is refitted as ε0 = 0.00231. The error compared with the strain proportional limit of 0.002 used in the above steps is greater than 5%. Therefore, the updated strain proportional limit ε0 = 0.0023 is re-substituted into formula (3) and formula (4) to calculate the von Mises equivalent stress σ of SA508 steel. eq and von Mises equivalent strain ε eq data points.

[0135]

[0136] In the formula, E0 is the Young's modulus of SA508 steel (E0 = 211.89 GPa), E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter respectively, R is the radius of the spherical indenter, R0 (i) is the radius of curvature of the residual indentation pit after complete unloading of the i-th indentation cycle, P max (i) is the maximum indentation load of the i-th indentation cycle, W T (i) is the total external work of the i-th indentation cycle, h max (i) is the maximum indentation depth of the i-th indentation cycle, h r (i) is the elastic recovery depth of the i-th indentation cycle, σ0 is the stress proportional limit of the tested material, and ε0 is the strain proportional limit of the tested material. In particular, when i = 1, W P (0) = 0, P max (0) = 0, σ eq (0) = σ0, ε eq (0) = ε0. ξ and ψ are regression equations regarding the strain proportional limit ε0 and work-hardening index n of the tested material.

[0137] The von Mises equivalent stress σ eq (i) and von Mises equivalent strain ε eq (i) of the i-th indentation cycle of SA508 steel recalculated are substituted into formula (6), and the work-hardening index n = 0.0968 is obtained by fitting. Among them, the Young's modulus E in formula (6) is replaced by the Young's modulus E0 = 211.89 GPa of SA508 steel calculated by formula (1).

[0138] According to formula (7), the strain proportional limit ε0 of SA508 steel is refitted as ε0 = 0.00229. The error compared with the strain proportional limit of 0.00231 used in the above steps is less than 5%. Therefore, the von Mises equivalent stress σ eq (i) and von Mises equivalent strain ε eq (i) of the i-th indentation cycle of SA508 steel calculated again are the true values.

[0139] Substitute the parameters n = 0.0968 and ε0 = 0.00229 of SA508 steel obtained by the method of this patent into formula (6) to obtain the relationship between the von Mises equivalent stress and von Mises equivalent strain of SA508 steel. The comparison with the results of the conventional uniaxial tensile test is as Figure 4 shown, and the consistency between the two is good. Among them, the Young's modulus E in formula (6) is replaced by the Young's modulus E0 = 211.89 GPa of SA508 steel calculated by formula (1).

[0140] Calculate the von Mises equivalent plastic strain ε p of the tested material according to formula (9). When ε p = 0.2%, regard the von Mises equivalent stress σ eq as the yield strength R p0.2 of SA508 steel. It is calculated that R p0.2 of SA508 steel is 526 MPa, and the error compared with the uniaxial tensile test result of 550 MPa is less than 5%.

[0141]

[0142] In the formula, E0 is the Young's modulus of SA508 steel (E0 = 211.89 GPa), and σ eq and ε eq are the von Mises equivalent stress and von Mises equivalent strain of SA508 steel respectively.

[0143] Calculate the engineering stress σ ENG of SA508 steel according to formula (10). Regard the maximum value of the engineering stress as the tensile strength R m of SA508 steel. It is calculated that R m of SA508 steel is 641 MPa, and the error compared with the uniaxial tensile test result of 700 MPa is less than 10%.

[0144]

[0145] In the formula, σ eq and ε eqThey are respectively the von Mises equivalent stress and von Mises equivalent strain of SA508 steel.

[0146] The above specific embodiments are only used to illustrate the technical concept and structural features of the present invention, aiming to enable those skilled in the art to implement it accordingly. However, the above content does not limit the protection scope of the present invention. Any equivalent changes or modifications made according to the spirit and essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for detecting the indentation of a spherical indenter for the uniaxial mechanical properties under adaptive working conditions, characterized in that, Including: S1: A spherical indenter with a radius R is used to slowly press into the smooth surface of the material to be tested in a way that includes N equally spaced loading-unloading processes. The continuous indentation load P and indentation displacement h curves are obtained through the load sensor and displacement sensor integrated in the indentation testing machine respectively; S2: Determine whether the conditions for optical measurement on the surface of the test sample are met. If the optical measurement conditions are met, measure the plastic zone radius r around the residual indentation pit, and execute S3. Otherwise, skip r. p , and execute S3. Otherwise, skip r. p Measurement: Directly execute S3; S3: Using the depth h of the residual indentation pit on the surface of the material under test in the i-th indentation cycle as the abscissa, and using the effective Young's modulus E of the material under test in the i-th indentation cycle as the ordinate, where 1 ≤ i ≤ N, plot a scatter diagram and fit the scatter points in the diagram using a linear function to estimate the Young's modulus E0 of the material under test. The linear function is p as the abscissa, and the effective Young's modulus E of the material under test in the i-th indentation cycle eff (i) as the ordinate, 1 ≤ i ≤ N, plot a scatter diagram and fit the scatter points in the diagram using a linear function to estimate the Young's modulus E0 of the material under test. The linear function is E eff =-Ch p +E0(1) Where C is the fitting coefficient and E0 is the estimated Young's modulus of the material to be tested; S4: Calculate the Young's modulus E0 of the material under test estimated using the following formula and the Young's modulus E of the material under test preset pre Relative error ΔError: where E0 is the estimated Young's modulus of the material under test, and E pre is the preset Young's modulus of the material under test; S5: When ΔError is less than the maximum allowable error δ, the material under test is allowed to be tested by the spherical indenter with N loading-unloading cycles, and the indenter load P and indenter displacement h curves obtained in S1, which include N loading-unloading cycles, are directly used for uniaxial mechanical property calculation. If r can be measured p then go to S6; if r cannot be measured p then go to S9; When ΔError exceeds the maximum allowable error δ, the material under test is only allowed to be tested by spherical indenter indentation in a monotonic loading manner. The unloading part of the indentation load P and indentation displacement h curve containing N loading-unloading cycles obtained in S1 is removed to obtain a monotonic loading curve for uniaxial mechanical property calculation. If r can be measured p then go to S7. If r cannot be measured p then go to S13; S6: Calculate the von Mises equivalent stress σ of the i-th indentation cycle of the material under test according to the following formulas respectively eq (i) and the von Mises equivalent strain ε eq (i) , and then go to S14, where 1 ≤ i ≤ N: where E eff (i) is the effective Young's modulus of the i-th indentation cycle of the material to be tested, E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter respectively, R is the radius of the spherical indenter, R0 (i) is the radius of curvature of the residual indentation pit after complete unloading of the i-th indentation cycle, P max (i) is the maximum indentation load of the i-th indentation cycle, W E (i) and W P (i) are the elastic external work and plastic external work of the i-th indentation cycle respectively, h max (i) is the maximum indentation depth of the i-th indentation cycle, h r (i) is the elastic recovery depth of the i-th indentation cycle, σ0 is the stress proportional limit of the material to be tested, ε0 is the strain proportional limit of the material to be tested. When i = 1, W P (0) = 0, P max (0) = 0, σ eq (0) = σ0, ε eq (0) = ε0; S7: The indentation load P-indentation displacement h curve in the monotonic loading stage is fitted using the power function shown in the following formula: P = Ch m (5) Where C is the fitting coefficient of the indentation load P-indentation displacement h curve and m is the fitting exponent of the indentation load P-indentation displacement h curve; S8: von Mises equivalent stress σ of the material under test eq - von Mises equivalent strain ε eq The relationship is obtained according to the following formula: Where ε0 is the strain proportional limit of the material to be tested, E is the Young's modulus of the material to be tested, and n is the work hardening index of the material to be tested; then go to S14; S9: Assume that the strain proportional limit ε0 of the material under test is 0.002, and calculate the von Mises equivalent stress σ eq (i) and von Mises equivalent strain ε eq (i) of the i-th indentation cycle of the material under test according to formula (3) and formula (4) respectively, where 1 ≤ i ≤ N; S10: Substitute the von Mises equivalent stress σ eq and von Mises equivalent strain ε eq data points into Equation (6) to fit the work hardening index n; S12: Re-fit the strain proportional limit ε0 of the material under test according to formula (7). If the relative error of the re-fitted strain proportional limit compared with the strain proportional limit used in S9 is less than the allowable value, then the von Mises equivalent stress σ eq (i) and the von Mises equivalent strain ε eq (i) for the i-th indentation cycle of the material under test are considered to be the true values; otherwise, substitute the updated strain proportional limit ε0 into step S9 and recalculate the von Mises equivalent stress σ eq (i) and the von Mises equivalent strain ε eq (i) until the relative error requirement is met, and then go to S14; Where E is the Young's modulus of the material to be tested, and here E0 is used to replace E, E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter respectively, R is the radius of the spherical indenter, R0 (i) is the radius of curvature of the residual indentation pit after complete unloading in the i-th indentation cycle, P max (i) is the maximum indentation load in the i-th indentation cycle, W T (i) is the total external force work in the i-th indentation cycle, h max (i) is the maximum indentation depth in the i-th indentation cycle, h r (i) is the elastic recovery depth in the i-th indentation cycle, σ0 is the stress proportional limit of the material to be tested, and ε0 is the strain proportional limit of the material to be tested; When i = 1, W P (0) = 0, P max (0) = 0, σ eq (0) = σ0, ε eq (0) = ε0; ξ and ψ are regression equations for the strain proportional limit ε0 and the work hardening index n of the material under test; S13: Assume that the von Mises equivalent stress σ of the material under test eq and the von Mises equivalent strain ε eq are in accordance with formula (6). Use the following formula to fit the strain proportional limit ε0 and the work hardening index n of the material under test: Where E is the Young's modulus of the material to be tested, and here the preset value E pre is used to replace E, and W T is the total external work, P is the indentation load, and ξ T and ψ T are the regression equations for the strain proportional limit ε0 and the work hardening index n of the material to be tested; then go to S14; S14: Calculate the von Mises equivalent plastic strain ε of the material under test according to formula (9). p , and take the von Mises equivalent stress σ p when ε eq = 0.2% as the yield strength R p0.2 In the formula, E is the Young's modulus of the material under test. For the indentation test of a spherical indenter under monotonic loading, the preset value E pre is used to replace E; for the indentation test of a spherical indenter involving N loading-unloading cycles, the Young's modulus E0 of the material under test obtained in S3 is used to replace E, and σ eq and ε eq are the von Mises equivalent stress and von Mises equivalent strain of the material under test, respectively; S15: Calculate the engineering stress σ of the material under test according to formula (10), and regard the maximum value of the engineering stress as the tensile strength R of the material under test ENG , and regard the maximum value of the engineering stress as the tensile strength R of the material under test m : In the formula, σ eq and ε eq are respectively the von Mises equivalent stress and the von Mises equivalent strain of the material under test.

2. The method for detecting the indentation of a spherical indenter for the uniaxial mechanical properties under an adaptive working condition according to claim 1, characterized in that: Calculate the effective Young's modulus E corresponding to the i-th indentation cycle according to Equation (11). eff (i) : where v is the Poisson's ratio of the material to be tested, and E ind and v ind are the Young's modulus and Poisson's ratio of the spherical indenter material, R is the radius of the spherical indenter, is the maximum displacement before unloading in the i-th indentation cycle collected by the displacement sensor, S (i) and h p (i) are the unloading slope and the residual indentation depth of the i-th indentation cycle respectively, where 1 ≤ i ≤ N.

3. The spherical indenter penetration detection method for uniaxial mechanical properties under an adaptive working condition according to claim 1, wherein: In the above S5, when ΔError exceeds the maximum allowable error δ, if the material to be tested only allows the spherical indenter indentation test to be carried out in the monotonic loading mode, directly carry out the spherical indenter indentation test in the monotonic loading mode and obtain the corresponding indentation load P and indentation displacement h curves.

4. The spherical indenter indentation detection method for uniaxial mechanical properties under adaptive working conditions according to claim 1, characterized in that: In the above S6, the stress proportional limit σ0 of the material to be tested is calculated according to the following formula: Wherein, P max is the maximum indentation load in the spherical indenter indentation test. For the spherical indenter indentation test using the N - time loading - unloading method, P max is the maximum load of the N - th indentation cycle, that is, P max (N) .

5. The spherical indenter penetration detection method for uniaxial mechanical properties under an adaptive working condition according to claim 4, wherein: The strain proportional limit ε0 of the material to be tested is calculated according to formula (13): In the formula, σ0 is the stress proportional limit of the material to be tested, and E is the Young's modulus of the material to be tested. For the spherical indenter penetration test under monotonic loading, the preset value E pre is used to replace E; for the spherical indenter penetration test involving N loading-unloading cycles, the Young's modulus E0 of the material to be tested obtained in S3 is used to replace E.

6. The spherical indenter indentation detection method for the uniaxial mechanical properties under adaptive working conditions according to claim 1, wherein: In the above S8, the work hardening index n of the material to be tested is determined according to formula (14): In the formula, ε0 is the strain proportional limit of the material to be tested, E is the Young's modulus of the material to be tested, and here the preset value E pre is used to replace E, n is the work hardening index of the material to be tested, C and m are the fitting coefficient and fitting index of the indentation load P-indentation displacement h curve respectively, and σ eq-M is the von Mises equivalent stress of the material to be tested corresponding to the maximum indentation load.

7. The method for detecting the indentation of a spherical indenter for the uniaxial mechanical properties under an adaptive working condition according to claim 6, wherein: σ eq-M Calculated according to formula (15): Where E is the Young's modulus of the material to be tested, and here the preset value E pre is used to replace E, E ind and v ind are respectively the Young's modulus and Poisson's ratio of the spherical indenter, R is the radius of the spherical indenter, R0 is the radius of curvature of the residual indentation pit after complete unloading, P max is the maximum indentation load, W E is the elastic external work, h max is the maximum indentation depth, h r is the elastic recovery depth, σ0 is the stress proportional limit of the material to be tested, and ε0 is the strain proportional limit of the material to be tested.

8. The method for detecting the indentation of a spherical indenter for the uniaxial mechanical properties under an adaptive working condition according to claim 1, wherein: The material to be tested is SA508 steel plate and the spherical indenter is tungsten carbide spherical indenter.

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