A method for calculating residual stress based on nanoindentation technology

Abstract

The application relates to a method for calculating residual stress based on a nanoindentation technology, belongs to the technical field of residual stress detection, and modifies an existing nanoindentation residual stress detection model to obtain a more accurate nanoindentation residual stress calculation model. The solution comprises the following steps: S1, establishing a residual stress calculation model; S2, setting physical parameters of each engineering material respectively to obtain corresponding nanoindentation P-h curves; S3, adopting finite element simulation to determine load-depth curves of each engineering material under different residual stress conditions; S4, inversely calculating the size of residual stress through the load-depth curve and the residual stress calculation model; S5, comparing the set residual stress and the calculated residual stress to obtain a model correction value corresponding to each engineering material; and S6, fitting the correction values of different materials to obtain a correction value formula, and obtaining a residual stress calculation model suitable for each engineering material.

Description

Technical Field

[0001] This invention belongs to the field of residual stress detection technology, specifically relating to a method for calculating residual stress based on nanoindentation technology. Background Technology

[0002] Residual stress, as spontaneously generated internal stress during material processing, profoundly affects the mechanical properties of products. In high-end manufacturing fields such as aerospace, microelectronics packaging, and nuclear energy equipment, the distribution of residual stress directly determines the fatigue strength, corrosion resistance, and dimensional stability of materials. Therefore, accurate measurement of residual stress has become a key aspect of modern materials design.

[0003] Traditional residual stress detection methods face technical bottlenecks: X-ray diffraction, while non-destructive, is limited by crystal structure requirements and insufficient penetration depth; drilling is a destructive operation and difficult to apply to micro-components; synchrotron radiation neutron diffraction, while capable of deep stress analysis, has high equipment costs and long testing cycles.

[0004] Nanoindentation technology, with its unique micromechanical detection characteristics, has opened up a new dimension for residual stress measurement. This technique records the load-displacement curves of a nanoscale indenter penetrating a material, simultaneously acquiring mechanical parameters such as hardness and elastic modulus. Existing research reveals that residual stress significantly affects the load-displacement curve; based on this, various models for measuring residual stress using nanoindentation have been proposed. To address the low measurement accuracy and limited applicability of traditional models, proposing a more accurate and widely applicable model is of significant importance. Summary of the Invention

[0005] The main objective of this invention is to overcome the shortcomings of the prior art and to modify the existing nanoindentation residual stress measurement model to obtain a more accurate nanoindentation residual stress calculation model.

[0006] This invention is achieved through the following technical solution: a method for calculating residual stress based on nanoindentation technology, which combines the traditional nanoindentation model for measuring residual stress with finite element simulation to obtain a more accurate residual stress calculation model, including the following steps:

[0007] S1. Establish a residual stress calculation model:

[0008]

[0009] Equation (1) is calculated using load-depth curves with and without residual stress; Equations (2) and (3) distinguish between residual stress in compression and tension states and are calculated using the integration method.

[0010] In equation (1), U is the work done by the residual stress on the indenter during the nanoindentation unloading process, P0 and P1 are the loads on the indenter at the maximum depth with and without residual stress, respectively, and h0 is the maximum depth of the indenter penetrating the material. f0 and h f1 The final depth of the indentation is given by m0 and m1 by power-law exponents.

[0011] In equations (2) and (3), equation (2) represents the compressive stress state, and equation (3) represents the tensile stress state; ΔS=2πrdh, r=htanα, α=70.3°, σ r This is residual stress;

[0012] S2. Set the physical parameters of each engineering material respectively, and on this basis, set several different sets of residual stresses. Then, use finite element simulation software to obtain the corresponding nanoindentation Ph curve.

[0013] S3. Using finite element simulation, determine the load-depth curves of various engineering materials under different residual stress conditions; the finite element simulation includes simulation without residual stress, tensile stress, and compressive stress simulation, and the stress-strain setting of the material during the simulation follows a power-law strengthening, defined as:

[0014]

[0015] In equation (3), E is the elastic modulus, σ y Where n is the yield strength and n is the strain hardening exponent;

[0016] S4. Using the load-depth curve determined in step S3 and the residual stress calculation model established in step S1, the magnitude of the residual stress is calculated in reverse.

[0017] S5. Compare the set residual stress with the calculated residual stress to obtain the model correction value corresponding to each engineering material. In this step S5, the calculation results of various traditional models are compared, and the overall accuracy of the corrected model is higher.

[0018] S6. Fit the correction values ​​for different materials to obtain the correction value formula, and then obtain the residual stress calculation model applicable to various engineering materials. The correction value formula is:

[0019]

[0020] In equation (5), a, b, c, d, and f are all parameters.

[0021] Furthermore, in step S2, the physical parameters of the engineering material include: elastic modulus E, yield strength σ. y And the strain hardening index n.

[0022] Further, in step S6, when the material is under compressive stress, in equation (5), a = 0.09243, b = -0.7555, c = 0.00365, d = 1.121, f = -1.67393e-6; when the material is under tensile stress, in equation (5), a = 0.51771, b = 0.872, c = 0.00359, d = -3.82, f = 2.15953e-6. Therefore, it can be seen that for the same material, the correction values ​​for tensile residual stress and compressive residual stress need to be distinguished, and the correction value formula is the correction value multiplied by E / σ. y The function of n.

[0023] The beneficial effects of this invention are as follows:

[0024] This invention proposes a novel model for measuring residual stress using nanoindentation, which offers higher overall calculation accuracy compared to traditional models. Furthermore, addressing the limitation of traditional models being applicable only to specific materials, a model modification method is proposed, making the new model applicable to a wide range of materials. Using the model proposed in this invention to calculate residual stress offers advantages such as high reliability and broad applicability. Attached Figure Description

[0025] Figure 1 The flowchart for fitting the modified form;

[0026] Figure 2 E / σ is the residual stress under compressive conditions. y A three-dimensional relationship diagram of n and the correction value k;

[0027] Figure 3 E / σ is the residual stress when it is under tension. y A three-dimensional relationship diagram of n and the correction value k. Detailed Implementation

[0028] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0029] Example 1

[0030] like Figure 1 The method for calculating residual stress based on nanoindentation technology, as shown, includes the following steps:

[0031] S1. Establish a residual stress calculation model:

[0032]

[0033] In equation (1), U is the work done by the residual stress on the indenter during the nanoindentation unloading process, P0 and P1 are the loads on the indenter at the maximum depth with and without residual stress, respectively, and h0 is the maximum depth of the indenter penetrating the material. f0 and hf1 The final depth of the indentation is given by m0 and m1 by power-law exponents.

[0034] Equation (2) represents the compressive stress state, ΔS = 2πrdh, r = htanα, α = 70.3°, σ r This is residual stress;

[0035] Equation (1) is obtained by calculating the load-depth curves with and without residual stress; Equation (2) is obtained by calculating the residual stress under compression conditions using the integral method; by solving the equations of Equation (1) and Equation (2) simultaneously, the following can be obtained:

[0036]

[0037] S2. Set the physical parameters of each engineering material, and on this basis, arbitrarily set several different sets of residual stresses. Then, use finite element simulation software to obtain the corresponding nanoindentation Ph curves. In this embodiment 1, E / σ is set. y The values ​​are 80, 100, 125, 150, 200, 250, 300, 400, 450, and 500, respectively, and n is 0.1, 0.2, and 0.3, respectively. Five sets of residual stress σ are taken. r / σ y The values ​​are 0, -0.2, -0.4, -0.6, and -0.8, representing different E / σ values. y , n and σ r / σ y The data are input into the finite element model for simulation.

[0038] S3. Using finite element simulation, different materials (i.e., different E / σ ratios) are obtained. y The load-depth curves of n) under five sets of residual stresses are obtained, and the stress-strain setting of the material during the simulation follows a power-law strengthening, defined as:

[0039]

[0040] In equation (4), E is the elastic modulus, σ y Where n is the yield strength and n is the strain hardening exponent;

[0041] S4. Using the load-depth curve determined in step S3 and the residual stress calculation model established in step S1, the magnitude of residual stress of different materials under each group of residual stress is calculated in reverse.

[0042] S5. By comparing the set residual stress with the calculated residual stress, the model correction values ​​corresponding to each engineering material are shown in the table below.

[0043]

[0044] S6. Fit the correction values ​​for different materials, such as Figure 2 To fit the 3D relationship graph, the formula for the compression correction value is obtained:

[0045]

[0046] In the formula, a = 0.09243, b = -0.7555, c = 0.00365, d = 1.121, f = -1.67393e-6;

[0047] Finally, we obtain a calculation model for compressive residual stress applicable to different materials:

[0048]

[0049] Based on existing literature data, the accuracy of the compressive residual stress calculation model obtained in Example 1 was verified. Compared with existing models, the results obtained by the residual stress calculation model established in Example 1 are similar to the actual residual stress values, and are on the same order of magnitude.

[0050] Example 2

[0051] like Figure 1 The method for calculating residual stress based on nanoindentation technology, as shown, is characterized by comprising the following steps:

[0052] S1. Establish a residual stress calculation model:

[0053]

[0054] Equation (1) is calculated using load-depth curves with and without residual stress; Equation (3) is calculated using the integral method for residual stress under tensile conditions.

[0055] In equation (1), U is the work done by the residual stress on the indenter during the nanoindentation unloading process, P0 and P1 are the loads on the indenter at the maximum depth with and without residual stress, respectively, and h0 is the maximum depth of the indenter penetrating the material. f0 and h f1 The final depth of the indentation is given by m0 and m1 by power-law exponents.

[0056] In equation (3), equation (3) represents the tensile stress state, ΔS=2πrdh, r=htanα, α=70.3°, σ r This is residual stress;

[0057] S2. Set the physical parameters of each engineering material, and based on this, arbitrarily set several different sets of residual stresses. Then, use finite element simulation software to obtain the corresponding nanoindentation Ph curves. In this embodiment 2, E / σ is set. yThe values ​​are 80, 100, 125, 150, 200, 250, 300, 400, 450, and 500, respectively, and n is 0.1, 0.2, and 0.3, respectively. Five sets of residual stress σ are taken. r / σ y The values ​​are 0, 0.2, 0.4, 0.6, and 0.8, representing different E / σ values. y , n and σ r / σ y The data are input into the finite element model for simulation.

[0058] S3. Using finite element simulation, different materials (i.e., different E / σ ratios) are obtained. y The load-depth curves of n) under five sets of residual stresses are obtained, and the stress-strain setting of the material during the simulation follows a power-law strengthening, defined as:

[0059]

[0060] In equation (4), E is the elastic modulus, σ y Where n is the yield strength and n is the strain hardening exponent;

[0061] S4. Using the load-depth curve determined in step S3 and the residual stress calculation model established in step S1, calculate the magnitude of the residual stress of different materials under each set of residual stresses in reverse.

[0062] S5. By comparing the set residual stress with the calculated residual stress, the model correction values ​​corresponding to each engineering material are shown in the table below.

[0063]

[0064] S6. Fit the correction values ​​for different materials, such as Figure 3 To obtain the corrected value formula from the fitted 3D relationship graph:

[0065]

[0066] In the formula, a = 0.51771, b = 0.872, c = 0.00359, d = -3.82, f = 2.15953e-6;

[0067] Finally, we obtain a tensile residual stress calculation model applicable to different materials:

[0068]

[0069] Based on existing literature data, the accuracy of the tensile residual stress calculation model obtained in Example 2 was verified. Compared with the existing model, the result obtained by the residual stress calculation model established in Example 2 is similar to the actual residual stress value, and is within the same order of magnitude.

[0070] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method of calculating residual stress based on nanoindentation technique, characterized by, The method comprises the following steps: S1, establishing a residual stress calculation model: Wherein, formula (1) is calculated by the load-depth curve without residual stress and with residual stress; formula (2) and formula (3) distinguish the residual stress as compression state and tension state, and are calculated by integral method; In formula (1), U is the work done by the residual stress on the indenter during the unloading process of the nanoindentation, P0 and P1 are the load on the indenter at the maximum depth without residual stress and with residual stress, respectively, h0 is the maximum depth of the indenter into the material, h is the final depth of the indentation, m0 and m1 are the power law exponents. f0 and h f1 are the final depth of the indentation, m0 and m1 are the power law exponents. In formula (2) and formula (3), formula (2) is a compressive stress state, and formula (3) is a tensile stress state; ΔS = 2πrdh, r = htanα, α = 70.3°, σ r is a residual stress; S2, setting the physical parameters of each engineering material respectively, on this basis, setting several different residual stresses at will, then using finite element simulation software, obtaining the corresponding nanoindentation P-h curve; S3, using finite element simulation, determining the load-depth curve of each engineering material under different residual stress conditions; the finite element simulation includes residual stress-free simulation, tensile stress and compression stress simulation, and the stress-strain of the material in the simulation process is set to obey the power law strengthening, defined as: In formula (4), E is the modulus of elasticity, σ y is the yield strength, and n is the strain hardening exponent. S4, through the load-depth curve determined in step S3 and the residual stress calculation model established in step S1, the size of the residual stress is reversely calculated; S5, comparing the set residual stress and the calculated residual stress, obtaining the corresponding model correction value of each engineering material; in this step S5, the calculation results of various traditional models are compared, and the overall accuracy of the modified model is higher; S6, fitting the correction values of different materials to obtain a correction value formula, and then obtaining a residual stress calculation model suitable for each engineering material, the correction value formula is: In formula (5), a, b, c, d, f are parameters.

2. The method for calculating residual stress based on nanoindentation technique according to claim 1, characterized in that: In the step S2, the physical parameters of the engineering material include: the elastic modulus E, the yield strength σ y and the strain hardening index n.

3. The method for calculating residual stress based on nanoindentation technique according to claim 1, characterized in that: In the step S6, when the material is in compression stress state, in formula (5), a=0.09243, b=-0.7555, c=0.00365, d=1.121, f=-1.67393e-6; when the material is in tension stress state, in formula (5), a=0.51771, b=0.872, c=0.00359, d=-3.82, f=2.15953e-6.

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