A simulation method for corroded steel based on random surface roughness

Abstract

The invention discloses a numerical method for simulating corroded steel based on random surface roughness. Specifically, the corroded steel surface is regarded as a two-dimensional / three-dimensional random rough surface, the corrosion rate of the steel is obtained according to actual measurement or empirical formula, the arithmetic mean height, root mean square height and maximum height of the corroded steel surface corresponding to the corrosion rate are obtained by morphology scanning or formula calculation, a Monte Carlo method is used to simulate and generate a one-dimensional / two-dimensional random rough surface, and finally the distance from the lowest point of the corroded surface to other surfaces is calculated according to the corrosion rate, the obtained rough surface is combined with other planes, and a steel corrosion model under different corrosion degrees is generated.

Description

Technical Field

[0001] The present invention relates to a method for simulating corroded steel based on random surface roughness, and more specifically, to a method for generating a corroded surface corresponding to a corrosion rate, which can be used to analyze stress concentration caused by local damage to corroded metal and study the influence of surface morphology on mechanical properties and fatigue properties of corroded metal. Background Art

[0002] The stress concentration caused by the uneven surface morphology of steel is the main reason for the reduction of plasticity, fracture toughness and fatigue performance of corroded steel structures. At present, the research methods on pitting and uneven corrosion of steel are mainly divided into two categories: reverse modeling methods based on actual measurements and hole-digging modeling methods. The reverse modeling methods based on actual measurements are only suitable for simulating scanned objects or areas, and their application range is limited; the hole-digging modeling methods often simplify the rust holes into regular circles or ellipses, ignoring the overall corrosion characteristics of the corroded surface. Therefore, it is necessary to propose a modeling method for corroded steel based on surface morphology to simulate and analyze corroded steel more quickly and accurately, and improve the efficiency and accuracy of the research. Summary of the invention

[0003] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for simulating corroded steel based on surface random roughness. The method can generate corresponding corroded surfaces according to different degrees of corrosion and can consider the influence of corrosion morphology on the mechanical properties of steel.

[0004] The present invention provides a method for simulating corroded steel based on surface random roughness, comprising:

[0005] (a) The corroded steel surface is regarded as a one-dimensional / two-dimensional random rough surface, and the corrosion rate w of the steel is obtained based on actual measurements or empirical formulas;

[0006] (b) The root mean square height of the corroded steel surface corresponding to the corrosion rate is obtained by topographic scanning or formula calculation; for a one-dimensional rough surface, the arithmetic mean height is recorded as R a , the root mean square height is R q , the maximum depth is R z For a two-dimensional rough surface, the arithmetic mean height is S a , the root mean square height is S q , the maximum depth is S z ;

[0007] (c) According to the roughness parameter, the Monte Carlo method is used to simulate and generate a one-dimensional / two-dimensional random rough surface, that is, the power spectrum is used to filter it in the frequency domain, and then the inverse fast Fourier transform is performed to obtain a highly undulating rough surface;

[0008] (d) Calculate the distance from the lowest point of the rusted surface to other surfaces based on the rust rate w;

[0009] (e) The generated rough surface is combined with other planes to generate a two-dimensional / three-dimensional steel corrosion model with different corrosion degrees.

[0010] Furthermore, in step (b), for the common structural steel Q355B steel after being subjected to atmospheric corrosion, the root mean square height and maximum depth of the rusted surface can be calculated according to the following formula.

[0011] For the rusted 2D model:

[0012] R a =0.0077·w+0.0031 (1)

[0013] R q =0.0096·w+0.0015 (2)

[0014] R z =0.0592·w-0.0544 (3)

[0015] For the 3D model after corrosion:

[0016] S a =26.19·w 0.555 (4)

[0017] S q =32.37·w 0.552 (5)

[0018] S z =179.22·w 0.567 (6)

[0019] Further, in step (c), in the process of generating a one-dimensional rough surface, a two-dimensional rough surface sample with a length of L and N data points is generated by the following function, namely:

[0020]

[0021] Where: x n =nΔx represents the nth sampling point on the rough surface, F(k j ) and f(x n ) is called the Fourier transform pair and is defined as: s(k j ) is the power spectral density of the rough surface, N(0,1) represents a normally distributed random number with a mean of 0 and a variance of 1, δ1 is the root mean square height, and l is the correlation length.

[0022] The power spectrum corresponding to the one-dimensional Gaussian rough surface is:

[0023]

[0024] In the process of generating a two-dimensional rough surface, the lengths in the x and y directions are L x and L y , the number of equally spaced discrete points is M and N, the distances between two adjacent points are △x and △y respectively, and L x =M·△x,L y =N·△y, then every point (x m =m△x,y n =n△y), (m=-M / 2+1,···,M / 2;n=-N / 2+1,···,N / 2) the height at can be expressed as:

[0025]

[0026] Where:

[0027]

[0028] S(k x ,k y ) is the power spectrum density of the two-dimensional random rough surface, δ2 is the root mean square height, l x With l y is the relevant length.

[0029] The power spectrum corresponding to the two-dimensional Gaussian rough surface is:

[0030]

[0031] Furthermore, in step (c), the Monte Carlo method is used to simulate the process of generating one-dimensional / two-dimensional random rough surfaces. Two parameters, root mean square height and correlation length, are required. The root mean square height can be obtained by topography scanning or empirical formula, and the correlation length is 0.5 times the maximum depth, that is, for a one-dimensional rough surface, δ1=R q , l=0.5R z For a two-dimensional rough surface, δ2=S q , l x = l y =0.5S z .

[0032] Further, in step (d), the distance from the lowest point of the rusted surface to the center line is calculated according to the rust rate w. For the two-dimensional model of steel corrosion, the calculation diagram is as follows: Figure 1 As shown. The area between the crest and trough of the corrosion surface is A1, that is:

[0033]

[0034] The distance from the lowest point of the rusted surface to the midline is recorded as b1, and the area included is recorded as A2, that is: A2 = L·b1. The distance from the midline of the two-dimensional model to the original surface is recorded as r, and the rust rate w can be expressed as:

[0035]

[0036] Then the calculation formula of b1 is:

[0037]

[0038] For the three-dimensional model of steel corrosion, the calculation diagram is as follows: Figure 2 As shown. The volume between the highest point and the lowest point of the rust surface is V1, that is:

[0039]

[0040] The distance from the deepest point of the rust surface to the bottom surface is recorded as b2, and the volume from the lowest point of the rust surface to the bottom surface is recorded as V2, that is: V2 = L x ·L y b2. Let the initial thickness of the three-dimensional model be d, and the corrosion rate w can be expressed as:

[0041]

[0042] Then the calculation formula of b2 is:

[0043] BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of a two-dimensional model;

[0045] Figure 2 It is a schematic diagram of the three-dimensional model;

[0046] Figure 3 The flowchart of the simulation method of corroded steel based on random surface roughness is shown in the figure.

[0047] Figure 4 is a one-dimensional random surface;

[0048] Figure 5 This is a schematic diagram of the two-dimensional model of steel after corrosion;

[0049] Figure 6 This is a finite element diagram of a two-dimensional model of steel after corrosion;

[0050] Figure 7 is a two-dimensional random surface;

[0051] Figure 8 This is a schematic diagram of the three-dimensional model of steel after corrosion;

[0052] Fig. 9 This is a finite element schematic diagram of the three-dimensional model of steel after corrosion.

[0053] Fig.10 These are steel tensile specimens under different degrees of corrosion.

[0054] Fig.11 It is a comparison diagram of the simulation result and the test result obtained by the method of the present invention when the corrosion rate is 6.88%.

[0055] Fig.12 It is a comparison diagram of the simulation result and the test result obtained by the method of the present invention when the corrosion rate is 13.83%.

[0056] Fig.13 It is a comparison diagram of the simulation result and the test result obtained by the method of the present invention when the corrosion rate is 20.58%.

[0057] Fig.14 It is a comparison diagram of the simulation result and the test result obtained by using the method of the present invention when the corrosion rate is 23.97%. DETAILED DESCRIPTION

[0058] The present invention will be further described below in conjunction with the accompanying drawings. Figure 3 The steps shown use the proposed method to generate a finite element model of Q355B steel subjected to atmospheric corrosion.

[0059] For the two-dimensional model, assume that the original length (L) is 100 mm, the height (2r) is 7 mm, and the corrosion rate w = 13.83%. According to formulas (1) to (3), the roughness parameter R of the two-dimensional model surface of the corroded steel corresponding to the corrosion rate w is calculated: a , R q With R z . Set δ1 = R q , l=0.5R z Substituting formula (7) and formula (8) into the equation, we can generate a one-dimensional random surface, as Figure 4 According to formula (13), the parameter b1 is calculated to determine the distance between the rusted surface and the center line, forming a two-dimensional model, as shown in Figure 5 The obtained model is imported into the finite element method to divide the mesh to obtain a two-dimensional numerical model of the corroded steel, as shown in Figure 6 shown.

[0060] For three-dimensional models, assume that the original length (L x ) is 30mm, width (L y ) is 20 mm, the thickness (d) is 8 mm, and the corrosion rate w = 13.83%. According to formulas (4) to (6), the roughness parameter S of the two-dimensional model surface of the corroded steel corresponding to the corrosion rate w is calculated: a, S q With S z . Set δ2 = S q , l x = l y =0.5S z Substituting into formulas (8) to (10), a two-dimensional random surface is generated, such as Figure 7 According to formula (16), the parameter b2 is calculated to determine the distance between the rusted surface and the bottom surface, forming a three-dimensional model, as shown in Figure 8 The obtained model is imported into the finite element method to divide the mesh and obtain a three-dimensional model of the corroded steel based on the random surface roughness, as shown in Fig. 9 shown.

[0061] By artificially accelerating the corrosion, Q355 material specimens with corrosion degrees of 6.88%, 13.83%, 20.58% and 23.97% were obtained and subjected to tensile tests. Fig.10 The numerical method of simulating corroded steel based on random surface roughness of the present invention is used to numerically model and simulate the steels at these four corrosion levels. The simulation results are consistent with the test results. The comparison of the results is shown in the figure below. Figure 11 to Figure 14 shown.

Claims

1. A method for simulating corroded steel based on random surface roughness, characterized in that: The following steps are involved: (a) The corroded steel surface is regarded as a one-dimensional / two-dimensional random rough surface, and the mass loss rate w of the steel is obtained based on actual measurements or empirical formulas; (b) The root mean square height and maximum depth of the roughness parameters of the corroded steel surface corresponding to the corrosion rate are obtained by topographic scanning or formula calculation; for a one-dimensional rough surface, the arithmetic mean height is recorded as R a , the root mean square height is R q , the maximum depth is R z For a two-dimensional rough surface, the arithmetic mean height is S a , the root mean square height is S q , the maximum depth is S z ; (c) According to the roughness parameter, the Monte Carlo method is used to simulate and generate a one-dimensional / two-dimensional random rough surface, that is, the power spectrum is used to filter it in the frequency domain, and then the inverse fast Fourier transform is performed to obtain a highly undulating rough surface; (d) Calculate the distance from the lowest point of the rusted surface to other surfaces based on the rust rate w; (e) The generated rough surface is combined with other surfaces to generate a two-dimensional / three-dimensional steel corrosion model with different corrosion degrees.

2. The simulation method according to claim 1, characterized in that: For generating a one-dimensional rough surface, a one-dimensional rough surface sample with a length of L and N data points is generated by the following function, namely: Where: x n =n.Δx represents the nth sampling point on the rough surface, F(k j ) and f(x n ) is called the Fourier transform pair and is defined as: s(k j ) is the power spectral density of the rough surface, N(0,1) represents a normally distributed random number with a mean of 0 and a variance of 1, δ1 is the root mean square height, and l is the correlation length; The power spectrum corresponding to the one-dimensional Gaussian rough surface is:

3. The simulation method according to claim 2, characterized in that: For a two-dimensional rough surface, the lengths in the x and y directions are L x and L y , the number of equally spaced discrete points is M and N, the distances between two adjacent points are △x and △y respectively, and L x =M·△x,L y =N·△y, then every point (x m =m△x,y n =n△y), (m=-M / 2+1,···,M / 2;n=-N / 2+1,···,N / 2) the height at can be expressed as: Where: S(k x ,k y ) is the power spectral density of the two-dimensional random rough surface, δ2 is the root mean square height, l x With l y is the correlation length; The power spectrum corresponding to the two-dimensional Gaussian rough surface is:

4. The simulation method according to claim 1, characterized in that: In the process of simulating the generation of one-dimensional / two-dimensional random rough surfaces using the Monte Carlo method, two parameters are required: the root mean square height and the correlation length. The root mean square height can be obtained through topography scanning or empirical formula, and the correlation length l is 0.5 times the maximum depth, that is, for a one-dimensional rough surface, δ1 = R q , l=0.5R z , for a two-dimensional rough surface, δ2=S q , l x = l y =0.5S z .

5. The simulation method according to claim 3, characterized in that: The distance from the lowest point of the rusted surface to other planes is calculated according to the rust rate w; for the two-dimensional model of steel corrosion, the area between the highest point and the lowest point of the rusted surface is recorded as A1, that is: The distance from the lowest point of the rust surface to the midline is recorded as b1, and the area included is recorded as A2, that is: A2=L·b1 The distance from the center line of the two-dimensional model to the original surface is recorded as r, and the corrosion rate w can be expressed as: Then the calculation formula of b1 is: For the three-dimensional model of steel corrosion, the volume between the highest point and the lowest point of the corrosion surface is V1, that is: The distance from the deepest point of the rust surface to the bottom is recorded as b2, and the volume from the lowest point of the rust surface to the bottom is recorded as V2, that is: <h2 style=";text-align:left;direction:ltr">V2=L<h2 style=";text-align:left;direction:ltr"> x <h2 style=";text-align:left;direction:ltr"> ·L<h2 style=";text-align:left;direction:ltr"> y <h2 style=";text-align:left;direction:ltr"> b2 The initial thickness of the three-dimensional model is recorded as d, and the corrosion rate w can be expressed as: Then the calculation formula of b2 is:

Images