Method for obtaining intrinsic stress-strain relation of material under residual stress effect

Abstract

The invention relates to the technical field of material basic mechanical property testing, in particular to a method for obtaining an intrinsic stress-strain relation of a material under the action of residual stress, and the method comprises the following steps: step 1, obtaining the surface residual stress sigma R of a to-be-tested area of a test material; 2, two diamond conical pressure heads with different angles are adopted, half cone angles are set to be theta 1 and theta 2, quasi-static press-in tests are completed on the to-be-tested area on the surface of the sample respectively, and a continuous press-in force-depth (F-h) curve is obtained; 3, respectively fitting press-in force-depth curves of the two types of half-cone angle pressure heads to obtain test loading curvatures CE-theta1 and CE-theta2; and 4, according to the sigma R obtained in the step 1 and the CE-theta1 and CE-theta2 obtained in the step 3, sequentially carrying out iterative calculation to obtain intrinsic indentation responses CN-theta1 and CN-theta2 of the material, a strain hardening index np, a nominal yield stress sigma y-p and a nominal yield strain epsilon y-p, and obtaining a stress-strain relationship of the material.

Description

Technical Field

[0001] The present invention relates to the technical field of testing the basic mechanical properties of materials, and particularly to a method for obtaining the intrinsic stress-strain relationship of materials under the action of residual stress. Background Art

[0002] The stress-strain relationship of materials is the basic information from materials to engineering structures, and is usually measured by conducting a uniaxial tensile test on a standard specimen with a relatively large size cut from the tested raw material or component. With the increasing demand for detecting the mechanical properties of welded component materials and gradient structure materials constructed by processes such as heat treatment and shot peening, it is difficult to effectively carry out tests according to the traditional sampling method due to the limitations of component size and material cutting. The instrumented indentation technology has the characteristics of micro-damage and micro-region detection. Combining with a portable indenter, it can realize the in-situ detection of the mechanical properties of structural materials and has good application prospects. By loading the material surface with an indenter of regular shape, the force-depth curve during the deformation process of the specimen and the indentation information after the test are obtained, and then the stress-strain curve of the material is analyzed. For welded structural materials and gradient structure materials constructed by processes such as heat treatment and shot peening, residual stresses are generated inside the structure due to uneven temperature distribution, plastic deformation, etc. Compared with the intrinsic indentation force-depth curve of the material under the condition of no residual stress, residual tensile / compressive stress will cause the force-depth curve to decrease / increase, resulting in the distortion of the mechanical properties of the material predicted by the indentation theory and test method based on the direct indentation test results. Therefore, peeling off the influence of residual stress on the force-depth curve and proposing an indentation test method for obtaining the intrinsic stress-strain curve of materials have important theoretical value and engineering significance for the safety evaluation of welded structures and the quality evaluation of gradient structure materials.

[0003] Currently, the existing indentation test technical routes cannot peel off the influence of residual stress on the test results, as follows:

[0004] The invention patent of "Method for Determining Uniaxial Constitutive Relationship of Materials by Dual-Cone Indentation" (Application No.: 201610024076.7) applied by Cai Lixun et al. uses dual-cone indentation with different cone angles to obtain the uniaxial constitutive relationship of materials. Based on the principle of equivalent energy density, a theoretical model between the loading curvature C of any combination of cone angles θ1 and θ2 and the material stress-strain relationship parameters (E, σ y and n) is established, that is

[0005]

[0006] where v * is the characteristic energy density, E is the elastic modulus of the tested material, σ yσ and n are the nominal yield strength and the strain hardening index respectively. This method requires two conical indenters with different cone angles to perform two indentation loadings on the material to be tested to obtain the test force - depth and then regress to obtain the loading curvature C θ1 and C θ2 , and then use the formula to solve and obtain the material constitutive relation parameters.

[0007] "A method for identifying anisotropic plastic parameters of sheet metal based on single - cone indentation" (Application No.: 201710811281.2) applied by Wu Jianjun et al. established a dimensionless function between the above - mentioned indentation response quantity and the anisotropic plastic parameters of the sheet metal material according to the indentation force - depth curve and the contact depths in the orthogonal directions of the transverse and longitudinal stripes of the residual indentation morphology after unloading. It contains 60 fitting parameters, namely

[0008]

[0009] In the formula, ξ = σ YT / E r , δ = n, η = R 22 , and a i , b i , and c i (i = 1 - 20) are polynomial fitting parameters.

[0010] For structural materials with residual stress such as welded components and modified layers, the indentation force - depth curve is increased or decreased by the influence of residual stress. There is a deviation between the material stress - strain relationship predicted based on the existing technology and the actual intrinsic curve, that is, the prediction result is distorted. Summary of the Invention

[0011] The purpose of the present invention is to provide a method for obtaining the intrinsic stress - strain relationship of materials under the action of residual stress, and to solve the technical problem that for structural materials with residual stress such as metal welded components and modified layers, the indentation force - depth curve is increased or decreased by the influence of residual stress, and there is a deviation between the material stress - strain relationship measured based on the existing technology and the actual intrinsic curve, resulting in distorted prediction results.

[0012] The present invention discloses a method for obtaining the intrinsic stress - strain relationship of materials under the action of residual stress, including the following steps,

[0013] Step 1: Obtain the surface residual stress σ R ;

[0014] Step 2: Use two diamond conical indenters with different angles, and set the semi - cone angles as θ1 and θ2. Respectively complete the quasi - static indentation test on the surface area to be tested of the specimen, and obtain the continuous indentation force F - depth h curve;

[0015] Step 3: Fit the indentation force F - depth h curves of the two types of semi - cone angle indenters respectively to obtain the test loading curvature C E-θ1 and C E-θ2 ;

[0016] Step 4: According to σ obtained in Step 1 R and C obtained in Step 3 E-θ1 and C E-θ2 , iteratively calculate to obtain the material's intrinsic indentation response C N-θ1 and C N-θ2 , as well as the strain - hardening index n p , the nominal yield stress σ y-p and the nominal yield strain ε y-p , and obtain the material stress - strain relationship.

[0017] Furthermore, the surface residual stress σ of the area to be measured of the test material obtained in Step 1 R can be obtained by non - destructive testing methods.

[0018] Furthermore, the non - destructive testing method is the X - ray method or the ultrasonic testing method.

[0019] Furthermore, in Step 3, the relationship between the material's cone indentation force F and depth h satisfies the Kick law, that is

[0020] According to Equation (1), regress the F - h curve in the cone indentation stage to obtain C E-θ1 and C E-θ2 .

[0021] Furthermore, preset the material's yield strain ε y-s and hardening index n s , input the results obtained in Step 1 and Step 3 into Equation (2) to calculate the intrinsic indentation responses C N-θ1 and C N-θ2 ;

[0022]

[0023] In the formula, a 2i , a 1i , a 0i , b 2i , b 1i , b 0i , k i , g 1i , g 0i are model constants.

[0024] Furthermore, substitute the intrinsic indentation responses C N-θ1 and C N-θ2 into Equation (3) to predict the intrinsic stress and strain data corresponding to the indentation with two cone angles (εeq-θ1 , σ eq-θ1 ), and (ε eq-θ2 , σ eq-θ2 );

[0025]

[0026] Wherein, c 1i , c 0i , d 1i and d 0i are model constants.

[0027] Furthermore, substitute the result obtained from Equation (3) into Equation (4) to obtain the plastic parameters σ y-p , ε y-p and n p ;

[0028]

[0029] Wherein, E is the elastic modulus of the material; σ y-p , ε y-p and n p are the nominal yield stress, nominal yield strain, and strain hardening index obtained by indentation prediction, respectively.

[0030] Furthermore, the elastic modulus of the material is measured by classical test methods such as the indentation unloading method or the ultrasonic method.

[0031] Furthermore, calculate the relative errors between the preset parameters (ε y-s and n s ) and the indentation prediction parameters (ε y-p and n p ). If the errors are all < 0.5%, then output the material intrinsic plastic parameters ε y-p and n p ; if the errors are all ≥ 0.5%, then assign ε y-p and n p to ε y-s and n s , and substitute them back into Equations (2) - (4) to calculate the relative errors between the preset parameters (ε y-s and n s ) and the indentation prediction parameters (ε y-p and n p ).

[0032] Furthermore, substitute the material intrinsic plastic parameters ε y-p and n p into the material power law hardening model Equation (5) to obtain the material stress-strain curve,

[0033]

[0034] In the formula, σ and ε are stress and strain respectively.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] 1. The present invention uses X-ray method or ultrasonic detection method to detect the surface residual stress σ of the area to be tested of the test material. R Quasi-static indentation tests are respectively carried out on the material surface by using two conical indenters with different angles to obtain continuous force-depth curves. The loading curvatures C E-θ1 and C E-θ2 are obtained by regression of the force-depth curves during the indentation stages of the two conical indenters with different angles, and then the stress-strain relationship of the material is predicted through simple post-processing.

[0037] 2. The present invention overcomes the problem that there is a deviation between the stress-strain curve of the metal material under the action of the residual stress predicted by the prior art and the actual intrinsic curve, resulting in distorted results. On the basis of finding out the residual stress, the intrinsic stress-strain relationship of the metal material with residual stress can be obtained by indenting a local area with two conical indenters with different angles. This method is efficient, universal, accurate, and convenient for popularization and application.

[0038] 3. It is of great significance for obtaining the intrinsic stress-strain of welded components and gradient structure materials with residual stress widely existing in engineering fields such as aerospace, nuclear power, and oil and gas transportation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required to be used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention, and thus should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can also be obtained based on these drawings without creative efforts.

[0040] Figure 1 FIG. is a schematic diagram of the indenting method of the conical indenter adopted by the present invention.

[0041] Figure 2 FIG. is a typical force-depth curve diagram of the indentation of two conical indenters with different angles of the present invention.

[0042] Figure 3 FIG. is a force-depth curve diagram of the indentation of two cone angles under the action of a residual stress of 200 MPa of the present invention.

[0043] Figure 4 FIG. is a force-depth curve diagram of the indentation of two cone angles under the action of a residual stress of -200 MPa of the present invention.

[0044] Figure 5This is a diagram showing the comparison and prediction results of the stress-strain curve and the tensile curve obtained by the method under the action of a residual stress of 200 MPa.

[0045] Figure 6 This is a diagram showing the comparison and prediction results of the stress-strain curve and the tensile curve obtained by the method under the action of the residual stress of -200MPa. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0047] Example 1

[0048] The method for obtaining the intrinsic stress-strain relationship of the material under the action of residual stress by the above-mentioned device adopted in this embodiment comprises the following steps:

[0049] Step 1: Use X-ray method to detect the surface residual stress σ of the test material in the test area R ;

[0050] Step 2: Use two diamond cone indenters with different angles (the half cone angle is set as θ1 and θ2) to complete the quasi-static indentation test on the surface of the sample to be tested. The schematic diagram of the cone indenter indentation is shown in Figure 1 As shown, a continuous indentation force-depth (Fh) curve is obtained, such as Figure 2 As shown;

[0051] Step 3: The force-depth curve of cone indentation satisfies the Kick law. The Kick law function shown in formula (6) is used to regress the force-depth curves of cone indentation at two different angles to obtain the loading curvature C E-θ1 and C E-θ2 ;

[0052]

[0053] Step 4: Based on the σ obtained in step 1 R and C obtained in step 3 E-θ1 and C E-θ2 , iteratively calculate the material intrinsic indentation response C N-θ1 and C N-θ2 , and the strain hardening exponent n p , nominal yield stress σ y-p and the nominal yield strain ε y-p , and obtain the material stress-strain relationship.

[0054] The elastic modulus E of the material under test can be simply obtained by the Oliver-Pharr method or ultrasonic measurement.

[0055] Obtain the intrinsic indentation response C of the material N-θ1 and C N-θ2 , and the strain hardening index n p , the nominal yield stress σ y-p and the nominal yield strain ε y-p , and the process of obtaining the stress-strain relationship of the material is as follows:

[0056] S1: Preset the material yield strain ε y-s and the hardening index n s , and input the results obtained in Step 1 and Step 3 into Equation (7) to calculate the intrinsic indentation responses C N-θ1 and C N-θ2 of the two-angle indentation tests of the material to be measured;

[0057]

[0058] where a 2i , a 1i , a 0i , b 2i , b 1i , b 0i , k i , g 1i , g 0i are model constants.

[0059] S2: Substitute the intrinsic indentation responses C N-θ1 and C N-θ2 into Equation (8) to predict the intrinsic stress and strain data (ε eq-θ1 , σ eq-θ1 ) and (ε eq-θ2 , σ eq-θ2 ) corresponding to the two cone angle indentations;

[0060]

[0061] where c 1i , c 0i , d 1i and d 0i are model constants.

[0062] S3: Substitute the results obtained in S2 into Equation (9) to obtain the plastic parameters σ y-p , ε y-p and n p of the material to be measured;

[0063]

[0064] where E is the elastic modulus of the material; σ y-p , ε y-p and n pThey are the nominal yield stress, nominal yield strain, and strain hardening exponent obtained from indentation prediction, respectively.

[0065] S4: Calculate the relative errors between the preset parameters (ε y-s and n s ) and the indentation prediction parameters (ε y-p and n p ). If the errors are all < 0.5%, output the material intrinsic plastic parameters ε y-p and n p . If the errors are all ≥ 0.5%, assign ε y-p and n p to ε y-s and n s respectively, and repeat steps S1 - S4.

[0066] S5: Substitute the results obtained in step S4 into the material power law hardening model formula (10) to obtain the material stress - strain curve.

[0067]

[0068] In the formula, σ and ε are stress and strain.

[0069] So far, the material intrinsic indentation responses C N-θ1 and C N-θ2 (S1), as well as the strain hardening exponent n p , nominal yield stress σ y-p and nominal yield strain ε y-p (S3) have been obtained, and the material stress - strain relationship (S4) has been obtained.

[0070] For conventional macroscopic indentation tests, the indentation depth is generally not less than 20 μm. When the indentation depth is relatively shallow, the surface of the material or welded component to be measured needs to be polished to make its roughness better than 0.32 μm to carry out the quasi - static conical indentation test. The loading method is as Figure 1 shown, and the obtained force - depth curve is as Figure 2 shown.

[0071] Model constant determination method:

[0072] Using commercial finite element analysis software, simulate the indentation processes of two different - angle conical indenters under the combined working conditions of different material plastic parameters (σ y and n) and residual stress (σ R ). For common engineering metal materials, the elastic modulus E is taken as 200 GPa, and the nominal yield strength σ yTake it as 200 MPa to 1800 MPa, with an interval of 400 MPa, the hardening index n is taken as 0.1 to 0.4, with an interval of 0.1, a total of 20 ideal materials, and the applied residual stresses are σ R / σ y =-3 / 4, -1 / 2, -1 / 4, 0, 1 / 4, 1 / 2, 3 / 4, a total of 7 levels, where "-" represents compressive residual stress. 140 working conditions with different material parameters and different residual stress combinations are simulated and analyzed to obtain the indentation force-depth simulation curve, and the regression force-depth curve is used to obtain C E-θ1 and C E-θ2 . According to the data sets {E, σ y , n, θ, C E-θ1} and {E, σ y , n, θ, C E-θ2} (σ R / σ y = 0, 20 groups of data for each of the 2 different angle conical indenters) and Equation (8), substitute them into the fitting software for regression to obtain c 1i , c 0i , d 1i and d 0i ; According to the data sets {E, σ y , n, θ, σ R , C E-θ1} and {E, σ y , n, θ, σ R , C E-θ2} (140 groups of data for each of the 2 different angle conical indenters) and Equation (7), substitute them into the fitting software for regression to obtain in the formula, and obtain the model constants a 2i , a 1i , a 0i , b 2i , b 1i , b 0i , k i , g 1i , g 0i . a 2i , a 1i , a 0i , b 2i , b 1i , b 0i and α i .

[0073] Taking the conical indenters with two angles of 60° and 70.3° as examples, according to the above model parameter determination method, the obtained model constants are listed in Table 1.

[0074] Table 1 Model Constants of 60° and 70.3° Conical Indenters

[0075]

[0076] Using the alloy steel of gear steel 18CrNiMo7-6 as the test material to verify the effectiveness of the double-cone indentation method for the intrinsic stress-strain relationship of metallic materials under the action of the residual stress.

[0077] First step, use the stress application device to apply working stress to the 18CrNiMo7-6 alloy steel specimen to simulate the residual stress; prepare a uniaxial tensile specimen from the 18CrNiMo7-6 alloy steel, and carry out a tensile test in accordance with GB / T 228.1-2021 "Metallic materials - Tensile testing - Part 1: Method of test at room temperature" to obtain the stress-strain relationship of the material for comparison with the stress-strain curve obtained by the double-cone indentation test method.

[0078] Second step, on the indentation instrument, use two types of conical indenters with different angles to perform quasi-static indentation on the 18CrNiMo7-6 alloy steel specimen with pre-applied residual stress to obtain the test force-depth curve. As Figure 3 and Figure 4 shown, the residual stress values in the indentation area are 200 MPa and -200 MPa respectively, the two indenter angles are 60° and 70.3° respectively, and the indentation depth is 50 μm.

[0079] Third step, fit the indentation force-depth curves of the two different angles of the cone according to the Kick's law to obtain the loading curvature C E-θ1 and C E-θ2 , which are listed in Table 2.

[0080] Table 2 Loading curvatures C E-θ1 and C E-θ2

[0081]

[0082]

[0083] Fourth step, according to σ R obtained in the first step and C E-θ1 and C E-θ2 obtained in the third step, calculate iteratively in turn to obtain the intrinsic indentation response C N-θ1 and C N-θ2 , as well as the strain hardening index n p , the nominal yield stress σ y-p and the nominal yield strain ε y-p , and obtain the stress-strain relationship of the material.

[0084] Figure 5 The comparison between the stress-strain curve of the material predicted by the solution of the present invention and the stress-strain curve obtained by the traditional uniaxial tensile test is shown. The goodness of fit between the two is better than 96.0%. From Figure 5and Figure 6 It can be seen that the solution of the present invention has good prediction accuracy for the intrinsic stress-strain relationship of metal materials under the action of residual stress.

[0085] The above are the implementation manners listed in this embodiment. However, this embodiment is not limited to the above optional implementation manners. Those skilled in the art can obtain many other implementation manners by arbitrarily combining the above manners. Anyone can obtain other various forms of implementation manners under the inspiration of this embodiment. The above specific implementation manners should not be construed as limiting the protection scope of this embodiment. The protection scope of this embodiment should be defined by the claims, and the specification can be used to interpret the claims.

Claims

1. A method for obtaining the intrinsic stress-strain relationship of a material under the action of residual stress, characterized in that: including the following steps, Step 1: Obtain the residual stress σ on the surface of the test material in the area to be measured R ; Step 2: Use two diamond conical indenters with different angles, and set the semi-cone angles as θ1 and θ2. Perform quasi-static indentation tests on the area to be measured on the specimen surface respectively, and obtain continuous indentation force F-depth h curves; Step 3: Fit the indentation force F - depth curve h of the two types of semi - cone - angle indenters respectively to obtain the test loading curvature C E-θ1 and C E-θ2 ; Step 4: According to σ obtained in Step 1 R and C obtained in Step 3 E-θ1 and C E-θ2 , iteratively calculate the material's intrinsic indentation response C N-θ1 and C N-θ2 , as well as the strain hardening exponent n p , the nominal yield stress σ y-p and the nominal yield strain ε y-p , and obtain the material stress-strain relationship.

2. The method for obtaining the intrinsic stress-strain relationship of a material under the action of residual stress according to claim 1, wherein: The residual stress σ on the surface of the test material to be measured is obtained in the said step 1 R A non-destructive testing method is adopted.

3. The method for obtaining the intrinsic stress-strain relationship of a material under the action of residual stress according to claim 2, wherein: The non-destructive testing method is the X-ray method or the ultrasonic testing method.

4. The method for obtaining the intrinsic stress-strain relationship of a material under the action of residual stress according to any one of claims 1 to 3, characterized in that: In the said Step 3, the relationship between the material cone indentation force F and depth h satisfies Kick's law, that is According to Equation (1), C is obtained from the F-h curve during the regression cone penetration stage E-θ1 and C E-θ2 .

5. The method for obtaining the intrinsic stress-strain relationship of a material under the action of residual stress according to claim 4, characterized in that: Preset material yield strain ε y-s and hardening index n s , input the results obtained in Step 1 and Step 3 into Equation (2) to calculate the intrinsic indentation responses C N-θ1 and C N-θ2 ; where a 2i , a 1i , a 0i , b 2i , b 1i , b 0i , k i , g 1i , g 0i are model constants.

6. The method for obtaining the intrinsic stress-strain relationship of a material under the action of residual stress according to claim 5, characterized in that: Substitute the intrinsic indentation response C N-θ1 and C N-θ2 into Equation (3) to predict the intrinsic stress and strain data (ε eq-θ1 , σ eq-θ1 ) and (ε eq-θ2 , σ eq-θ2 ) corresponding to the indentation with two cone angles; where c 1i , c 0i , d 1i and d 0i are model constants.

7. The method for obtaining the intrinsic stress-strain relationship of a material under the action of residual stress according to claim 6, characterized in that: Substitute the result obtained from Equation (3) into Equation (4) to obtain the plastic parameters σ y-p , ε y-p and n p ; where E is the elastic modulus of the material; σ y-p , ε y-p and n p are the nominal yield stress, nominal yield strain, and strain hardening exponent obtained from the indentation prediction, respectively.

8. The method for obtaining the intrinsic stress-strain relationship of a material under the action of residual stress according to claim 7, characterized in that: The elastic modulus of the material is measured by the indentation unloading method or the ultrasonic method.

9. The method for obtaining the intrinsic stress-strain relationship of a material under the action of residual stress according to claim 7, characterized in that: Calculate the relative errors between the preset parameters (ε y-s and n s ) and the indentation prediction parameters (ε y-p and n p ). If the errors are all < 0.5%, output the material intrinsic plasticity parameters ε y-p and n p ; if the errors are all ≥ 0.5%, assign ε y-p and n p to ε y-s and n s , and substitute them back into Eqs. (2)-(4) to recalculate the relative errors between the preset parameters (ε y-s and n s ) and the indentation prediction parameters (ε y-p and n p ).

10. The method for obtaining the intrinsic stress-strain relationship of a material under the action of residual stress according to claim 9, wherein: Substitute the material's intrinsic plastic parameters ε y-p and n p into the material power-law hardening model formula (5) to obtain the material stress-strain curve. where σ and ε are stress and strain.

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