A correction method for reducing the influence of surface roughness on the elastic modulus identified by spherical indentation

Abstract

The application discloses a correction method for reducing the influence of surface roughness on the identification of elastic modulus of spherical indentation, and numerical simulation finds that when the instrumented spherical indentation test is performed on the rough surface, the projection area of the contact area between the indenter and the sample will change according to the indentation position and the surface roughness value, and is generally smaller than the contact projection area calculated by the Oliver-Pharr method. Therefore, by correcting the contact projection area calculated by the Oliver-Pharr method, the error of the surface roughness on the identification of the elastic modulus can be effectively reduced, and the measurement accuracy of the elastic modulus is improved.

Description

Technical Field

[0001] This invention relates to the field of structural mechanics testing technology in engineering service, and specifically to a correction method for reducing the influence of surface roughness on the elastic modulus of spherical indentation identification. Background Technology

[0002] During their service life, engineering structures are subject to varying degrees of mechanical property degradation due to environmental factors, temperature, and complex stresses. To promptly identify potential safety hazards and prevent accidents, regular mechanical property testing of vulnerable areas is necessary. Compared to traditional testing methods, portable indenters offer advantages such as high resolution, lightweight design, and the ability to detect micro-areas and minimal damage. They enable in-situ instrumented spherical indentation tests on in-service structures like oil and gas pipelines and high-speed railway tracks, thus possessing broad and promising engineering application prospects. Theoretically, portable indenters require a smooth test surface. However, due to limitations in manufacturing processes and production costs, engineering structures often exhibit varying degrees of surface roughness. Surface roughness interferes with the instrumented indenter's identification of the elastic modulus, reducing the accuracy of test results.

[0003] Currently, the impact of surface roughness on the identification of elastic modulus using instrumented indentation techniques can be reduced through three main methods: 1. Correcting the contact depth, which requires accurately obtaining the height of the indentation or protrusion during the indentation process, making it difficult to achieve in engineering settings; 2. Shifting the load-depth curve, where the shift distance depends on material properties and the geometry of the indenter tip; 3. Reducing local surface roughness in the test area using a flat indenter, which requires loads of several thousand Newtons in practical operation. None of these methods are suitable for instrumented spherical indentation testing on the surface of metal service structures using portable indenters. Therefore, for in-situ instrumented spherical indentation testing in engineering settings, a correction method that effectively reduces the impact of surface roughness on the identification of elastic modulus using spherical indentation is needed. Summary of the Invention

[0004] In view of the problems existing in the prior art, the purpose of the present invention is to provide a correction method for reducing the influence of surface roughness on the elastic modulus of spherical indentation identification. By correcting the contact projection area calculated by the Oliver-Pharr method, the correction method can reduce the influence of surface roughness on the test elastic modulus, effectively improve the accuracy of the elastic modulus calculated by the Oliver-Pharr method, and enable testers to obtain more accurate and reliable test data.

[0005] The technical solution of the present invention is as follows:

[0006] A method for reducing the influence of surface roughness on the elastic modulus of spherical indentation identification includes the following steps:

[0007] 1) First, use sandpaper to polish the test area of ​​the metal material, divide the test area into sections, and measure the surface roughness of the local test area. The roughness category measured is the root mean square deviation S. q ;

[0008] 2) Perform instrumented spherical indentation test on the test area of ​​the metallic material to obtain the load-depth curve. Calculate the contact stiffness S and contact projected area A from the obtained load-depth curve using the Oliver-Pharr method.

[0009] 3) Substitute the contact stiffness S and the contact projected area A from step 2) into the formula for calculating the elastic modulus using the Oliver-Pharr method, as shown in Formula 1, and combine it with Formula 2 to calculate the elastic modulus.

[0010]

[0011] Among them, E r It is the reduced modulus;

[0012]

[0013] Where E is the elastic modulus, ν is the Poisson's ratio of the tested sample, and E i and ν i These are the elastic modulus and Poisson's ratio of the spherical indenter, respectively.

[0014] 4) Establish a correction coefficient λ related to the surface roughness of the test area of ​​the metallic material through finite element simulation software. P As shown in Formula 3.

[0015]

[0016] By adjusting the coefficient λ P Introducing it into Formula 1 of the Oliver-Pharr method for calculating the elastic modulus can effectively reduce the influence of surface roughness on the identification of the elastic modulus. The form after introduction is shown in Formula 4.

[0017]

[0018] The root mean square deviation S obtained in step 1) q Substituting into Formula 3, the correction coefficient λ is calculated. P The specific values ​​are obtained by substituting the contact stiffness S and the contact projected area A obtained in step 2) into formula 4 and combining them with formula 5, the corrected elastic modulus can be calculated.

[0019]

[0020] Among them, E PP-C It is the corrected elastic modulus.

[0021] Furthermore, in step 1), the root mean square deviation of surface roughness S q Calculated using a commercial portable surface roughness measuring instrument and empirical formulas; the root mean square deviation S q The ratio of the roughness to that of the spherical indenter is denoted as the normalized roughness, where the normalized roughness ranges from 1.34 × 10⁻⁶. -3 ≤S q / R≤2.6×10 -3 .

[0022] Further, in step 2), the contact stiffness S is obtained by fitting the first 50% to 95% of the data of the unloading curve; the ratio of the indentation depth to the spherical indenter is recorded as the normalized indentation depth of the instrumented spherical indentation test, wherein the correction method requires the normalized indentation depth to be no more than 5%.

[0023] Furthermore, in step 4), the correction coefficient λ P The setup process is as follows:

[0024] a. Obtain the three-dimensional morphological information of the rough surface of the sample by scanning with a laser confocal microscope. In the finite element software COMSOL, the above morphological information is reconstructed into a rough surface by interpolation. A three-dimensional part with a real rough surface is constructed by Boolean operation. The part is imported into the commercial finite element software ABAQUS to construct a finite element model for simulating spherical indentation.

[0025] b. Simulate the metallic material using the finite element model, taking the input value of the elastic modulus in the finite element model as the agreed true value, and performing numerical simulations at nine locations on the same rough surface of the model under the same normalized indentation depth. Process the simulation results using the Oliver-Pharr method and calculate the mean value of the elastic modulus. Repeat the above steps in simulation results with different normalized indentation depths and normalized roughness.

[0026] c. Calculate the ratio of the mean elastic modulus to the conventional true value, and use this ratio as a correction coefficient for surface roughness. Based on the numerical simulation results, this correction coefficient can be expressed using normalized indentation depth and normalized roughness, as shown in Formula 6:

[0027]

[0028] Where λ is a correction factor for surface roughness, h / R is the normalized indentation depth, and S q / R is the normalized roughness;

[0029] d. Some engineering materials exhibit indentation protrusions during the indentation process. When the normalized indentation depth does not exceed 5%, the relationship between the error in identifying the elastic modulus caused by the indentation protrusions and the normalized indentation depth is shown in Formula 7:

[0030]

[0031] Among them, e E This is the error caused by the indentation protrusion in identifying the elastic modulus; to simultaneously eliminate the effects of surface roughness and indentation protrusion, the expression for the correction coefficient can be rewritten as shown in Formula 8:

[0032]

[0033] Where λ P It is a correction factor that can simultaneously reduce the effects of surface roughness and indentation protrusion.

[0034] Furthermore, in step a, AA 7075 and AA 2014 were selected as simulation materials, and the normalized indentation depths for simulation were selected as 1%, 3%, 5%, 7%, and 10%.

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

[0036] 1) The correction method of the present invention can effectively correct the contact projection area calculated by the Oliver-Pharr method when performing instrumented spherical indentation test on a rough surface, making it closer to the true value in terms of value, which is beneficial to improving the accuracy of mechanical parameters identified based on the contact projection area.

[0037] 2) By adopting the technical solution of the present invention, when performing spherical indentation tests on the rough surfaces of service components in engineering sites, the influence of surface roughness on the test elastic modulus can be reduced by using this correction method, effectively improving the accuracy of the elastic modulus calculated by the Oliver-Pharr method, and enabling testers to obtain more accurate and reliable test data. Attached Figure Description

[0038] Figure 1 This invention presents the trend of elastic modulus with normalized roughness before and after T2 correction of copper, under different normalized indentation depths.

[0039] Figure 2 This invention presents the trend of elastic modulus with normalized roughness before and after modification of stainless steel 316L, under different normalized indentation depths.

[0040] Figure 3This invention shows the trend of elastic modulus with normalized roughness before and after AA 7075 modification, under different normalized indentation depths.

[0041] Figure 4 This invention shows the trend of elastic modulus with normalized roughness before and after AA 2014 modification, under different normalized indentation depths. Detailed Implementation

[0042] The present invention will be further described below with reference to embodiments and accompanying drawings, but the scope of protection of the present invention is not limited to the scope described.

[0043] Examples 1-4

[0044] Four typical metallic materials (AA 7075, AA 2014, stainless steel 316L and copper T2) were selected as experimental materials to verify the effectiveness of the correction method.

[0045] 1) The test surfaces of four metal materials—AA 7075, AA 2014, 316L stainless steel, and T2 copper—were polished using SiC sandpaper of different grits, and the rough surfaces of the samples were divided into sections. The root mean square deviation (RMS) of the indentation test area was measured using a laser confocal microscope. The range of the RMS deviation was 0.35 μm ≤ S q1 ≤1.45μm, 0.35μm≤S q2 ≤1.4μm, 0.25μm≤S q3 ≤0.8μm, 0.3μm≤S q4 ≤1.25μm;

[0046] 2) Instrumented spherical indentation tests were conducted on four metal materials—AA 7075, AA 2014, 316L stainless steel, and T2 copper—using a commercial instrumented indenter (ZHU2.5 / Z2.5, Zwick / Rowel Corporation, Ulm-Einsingen, Germany) to obtain load-depth curves. The contact stiffness S1, S2, S3, and S4, and the contact projected area A1, A2, A3, and A4 were calculated from the obtained load-depth curves using the Oliver-Pharr method. The normalized indentation depths were 1%, 3%, and 5%.

[0047] 3) Take S from step one q1 S q2 S q3 and S q4 Substituting into the formula for the correction factor, we obtain the correction factor λ. P1 , λ P2 , λ P3 and λ P4Using the original Oliver-Pharr method formula and introducing a correction coefficient λ P1 , λ P2 , λ P3 and λ P4 The Oliver-Pharr method was then used to process the experimental results, and the mean values ​​of the elastic modulus before and after the correction were calculated. The results are as follows: Figure 1-4 As shown.

[0048] 4) Calculate the relative errors between the mean and the conventional true value of the elastic modulus before and after correction. The conventional true value of the elastic modulus is obtained through uniaxial tensile testing. The absolute values ​​of the maximum relative errors of the elastic modulus before and after correction are shown in Table 1. The calculation results show that by using the correction method, the relative errors between the elastic modulus and the conventional true value are generally controlled within ±4%. Therefore, this correction method can effectively improve the accuracy of identifying the elastic modulus on rough surfaces.

[0049] Table 1

[0050]

Claims

1. A method for reducing the influence of surface roughness on the elastic modulus of spherical indentation identification, characterized in that... Includes the following steps: 1) First, use sandpaper to polish the area of ​​the metal material to be tested and measure its local surface roughness. The roughness category measured is the root mean square deviation S. q ; The root mean square deviation S q The ratio to the spherical indenter is denoted as the normalized roughness; 2) Perform instrumented spherical indentation test on the test area of ​​the metallic material to obtain the load-depth curve. Calculate the contact stiffness S and contact projected area A from the obtained load-depth curve using the Oliver-Pharr method. The ratio of indentation depth to spherical indenter is denoted as the normalized indentation depth of the instrumented spherical indentation test; 3) Substitute the contact stiffness S and the contact projected area A from step 2) into the formula for calculating the elastic modulus using the Oliver-Pharr method, as shown in Formula 1, and combine it with Formula 2 to calculate the elastic modulus. Among them, E r It is the reduced modulus; Where E is the elastic modulus. It is the Poisson ratio of the test sample, E i and These are the elastic modulus and Poisson's ratio of the spherical indenter, respectively. 4) Establish a correction coefficient λ related to the surface roughness of the test area of ​​the metallic material through finite element simulation software. P As shown in Formula 3. Where h / R is the normalized push-in depth, S q / R is the normalized roughness, λ P It is a correction factor that can simultaneously reduce surface roughness and the effects of indentation protrusions; By adjusting the coefficient λ P Introducing it into Formula 1 can effectively reduce the influence of surface roughness on the identification of elastic modulus. The form after introduction is shown in Formula 4. The root mean square deviation S obtained in step 1) q Substituting into Formula 3, the correction coefficient is calculated. The specific values ​​are obtained by substituting the contact stiffness S and the contact projected area A obtained in step 2) into formula 4 and combining them with formula 5, the corrected elastic modulus can be calculated. Among them, E PP-C It is the corrected elastic modulus.

2. The method for reducing the influence of surface roughness on the elastic modulus of spherical indentation identification according to claim 1, characterized in that... 1) Root mean square deviation of surface roughness S in the step q The roughness was calculated using a commercial portable roughness measuring instrument and empirical formulas; the normalized roughness ranged from 1.34 × 10⁻⁶. -3 ≤ S q / R ≤ 2.6×10 -3 .

3. The method for reducing the influence of surface roughness on the elastic modulus of spherical indentation identification according to claim 1, characterized in that... 2) The contact stiffness S in the step is obtained by fitting the first 50% to 95% of the data of the unloading curve; among which, the correction method requires the normalized indentation depth to be no more than 5%.

4. The method for reducing the influence of surface roughness on the elastic modulus of spherical indentation identification according to claim 1, characterized in that... 4) Correction coefficient λ in the step P The setup process is as follows: a. Obtain the three-dimensional morphological information of the rough surface by scanning with a laser confocal microscope. In the finite element software COMSOL, the above morphological information is reconstructed into a rough surface by interpolation. A three-dimensional part with a real rough surface is constructed by Boolean operations. The part is imported into the commercial finite element software ABAQUS to construct a finite element model for simulating spherical indentation. b. Select a metallic material for finite element simulation. Use the input value of the elastic modulus in the finite element model as the agreed true value. Under the same normalized indentation depth, select nine locations on the rough surface of the same model for numerical simulation. Use the Oliver-Pharr method to process the simulation results and calculate the mean value of the elastic modulus. Repeat the above steps in simulation results with different normalized indentation depths and normalized roughness. c. Calculate the ratio of the mean elastic modulus to the conventional true value, and use this ratio as a correction coefficient for surface roughness. Based on the numerical simulation results, this correction coefficient can be expressed using normalized indentation depth and normalized roughness, as shown in Formula 6: Where λ is a correction factor for surface roughness; d. Some materials exhibit indentation protrusions during the indentation process. When the normalized indentation depth does not exceed 5%, the relationship between the error in identifying the elastic modulus caused by the indentation protrusions and the normalized indentation depth is shown in Equation 7: Among them, e E This is the error caused by the indentation protrusion in identifying the elastic modulus; to simultaneously eliminate the effects of surface roughness and indentation protrusion, the expression for the correction coefficient can be rewritten as shown in Formula 8: 。 5. The method for reducing the influence of surface roughness on the elastic modulus of spherical indentation identification according to claim 1, characterized in that... In step a, AA 7075 and AA 2014 were selected as simulation materials, and the normalized indentation depths for simulation were 1%, 3%, 5%, 7% and 10%.

Images