A strip steel defect simulation method based on anisotropic thermal expansion equivalent intrinsic strain

Abstract

The application discloses a strip steel defect simulation method based on anisotropic thermal expansion equivalent intrinsic strain, and belongs to the technical field of strip steel defect simulation. The method comprises the following steps: collecting geometric parameters, material physical characteristic parameters and plate shape defect characteristic parameters of a defective strip steel; establishing a strip steel finite element model based on the geometric parameters and the material physical characteristic parameters; setting a plastic intrinsic strain field of the strip steel in a rolling direction; applying anisotropic thermal expansion data to the strip steel in the finite element model; building an analysis step framework; submitting a program, and performing quality control and result output. The method can solve the problems of preset defect shape, complicated intrinsic strain application and constraint reaction force influence on residual stress field, and realizes spontaneous generation of a defect form and self-balanced solution of a residual stress field.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of metal plastic forming and sheet quality control, specifically involving a method for simulating defects in strip steel based on the equivalent intrinsic strain of anisotropic thermal expansion. Background Technology

[0002] The shape defects in strip steel originate from uneven plastic elongation along the width direction. Fiber strips with excessive elongation are under compression, while those with insufficient elongation are under tension, creating a self-balancing residual stress field. When the local compressive stress exceeds the critical buckling value, the compressed zone transforms the in-plane elastic strain energy into visible waviness through buckling and post-buckling, manifesting as edge waviness, center waviness, and other defects. The measurable deflection morphology and the unmeasurable internal residual stress are two sides of the same physical process.

[0003] Existing finite element simulations of strip defects generally suffer from the following shortcomings: First, they often rely on external loads or pre-specified cosine or Gaussian deflections before calculating amplitudes, essentially pre-setting the defect shape and failing to realistically reproduce the physical process of "the formation of corresponding defect morphologies from internal plastic incompatibility," nor can they handle the segmented distribution and overlap of multiple defect regions along the rolling direction. Second, applying intrinsic strain by imposing plastic pre-strain element by element and integration point by integration point is cumbersome in modeling and makes it difficult to ensure point-by-point consistency between the finite element input and the analytical model or measured data in space. Third, improper constraint application can introduce external constraint reaction forces, contaminating the residual stress field and causing the simulated residual stress to fail to meet the self-equilibrium condition of zero integral in the width direction, thus losing physical credibility. Therefore, there is an urgent need for a strip defect simulation method that does not require pre-setting the defect shape, can guarantee the self-equilibrium of residual stress, is simple to model, and can be consistent point-by-point with analytical or measured inputs. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art, such as the pre-setting of defect shape, the cumbersome application of intrinsic strain, and the influence of constraint reaction force on the residual stress field. It provides a method for simulating strip defects based on the equivalent intrinsic strain of anisotropic thermal expansion, so as to realize the spontaneous generation of defect morphology and the self-equilibrium solution of residual stress field.

[0005] This invention provides a method for simulating defects in strip steel based on the equivalent intrinsic strain of anisotropic thermal expansion, comprising:

[0006] Step 1: Collect the geometric parameters, material physical property parameters, and plate shape defect characteristic parameters of the defective strip steel;

[0007] Step 2: Establish a finite element model of the strip steel based on the geometric parameters and material physical property parameters from Step 1;

[0008] Step 3: Set up the plastic intrinsic strain field in the strip rolling direction;

[0009] Step 4: Apply anisotropic thermal expansion data to the strip in the finite element model;

[0010] Step 5: Build the analysis framework;

[0011] Step 6: Submit the program and perform quality control and output the results.

[0012] The present invention provides a method for simulating defects in strip steel based on equivalent intrinsic strain of anisotropic thermal expansion, which has the following beneficial effects:

[0013] (1) The defect shape is not used as input, but is spontaneously generated by the residual stress field through buckling / post-buckling. It can truly reproduce the formation process of edge waves, middle waves and their spatial separation, spatial overlap, multi-wavelength superposition and other composite defects, and change "defect shape description" to "plastic source drive".

[0014] (2) By combining the anisotropic thermal expansion coefficient with the spatial temperature field, the intrinsic strain is applied equivalently, so that the finite element input is consistent with the analytical model or the measured plastic strain point by point. The modeling is simple, physically transparent, and easy to cross-validate.

[0015] (3) It ensures that only the incompatible part of the intrinsic strain generates residual stress, the self-balancing residual can be controlled at an extremely low level, avoids external reaction force contamination, and the simulation results meet the physical requirements of residual stress self-balancing. Attached Figure Description

[0016] Figure 1 This is a flowchart of a method for simulating defects in strip steel based on equivalent intrinsic strain of anisotropic thermal expansion according to the present invention.

[0017] Figure 2 This is a diagram showing the three-dimensional post-buckling deflection field results of spatially overlapping composite defects simulated by the method of this invention. Detailed Implementation

[0018] like Figure 1 As shown, the present invention provides a method for simulating defects in strip steel based on equivalent intrinsic strain of anisotropic thermal expansion, comprising:

[0019] Step 1: Collect the geometric parameters, material physical property parameters, and plate shape defect characteristic parameters of the defective strip steel, specifically:

[0020] Step 1.1: Measure the strip length and width using an online dimensioning instrument, and measure the strip thickness using a thickness gauge.

[0021] The strip length L is the dimension along the rolling direction x, and in this example, L = 6000 mm. The strip width W is the dimension along the direction y, and in this example, W = 1200 mm. The center line y = 0, and the two side edges y = ±600 mm; the strip thickness t is the dimension along the thickness direction z, and in this example, t = 1.0 mm.

[0022] Step 1.2: Collect material physical property parameters, including elastic modulus, Poisson's ratio, and plastic Poisson's ratio.

[0023] The elastic modulus in this example Poisson's ratio Plastic Poisson's ratio Its parameters can be obtained by consulting material standards or by tensile testing.

[0024] Step 1.3: Collect plate shape defect characteristic parameters, including the number of defect areas, defect type, length of defect area along the rolling direction, and whether defect areas overlap; defect types include center wave defects and edge wave defects.

[0025] Its parameters can be obtained directly through existing analytical plate shape theory models, or by inverting the equivalent intrinsic strain distribution from the relative elongation distribution in the width direction of the actual strip measured by the plate shaper or the deflection morphology obtained by laser measurement.

[0026] Step 2: Based on the geometric parameters and material physical property parameters obtained in Step 1, construct a finite element model of the strip that can realistically reflect the buckling behavior of the strip in the finite element software.

[0027] Abaqus / Standard was used for the study. Modeling was completed sequentially across the Part, Property, Assembly, Step, Load, Mesh, and Job modules. Specifically:

[0028] Step 2.1: Create the geometric model (Part module).

[0029] Create a 3D, deformable, shell-type part in the Abaqus / Standard platform; draw a rectangular surface with a length L = 6000 mm and a width W = 1200 mm using the Planar / Shell sketch, and input the acquired geometric dimensions. Place the origin of the coordinate system at the center of the plate: x along the rolling direction (0~6000 mm), y along the width direction (−600~+600 mm).

[0030] Step 2.2: Define material properties (Property module 1).

[0031] Create a material by inputting the collected material physical property parameters, including: elastic modulus, Poisson's ratio, and plastic Poisson's ratio, and set thermal expansion to orthotropic.

[0032] Step 2.3: Set section properties and thickness integration points (Property module 2).

[0033] Create a shell section (Shell / Homogeneous), assign the material created in step 2.2 to it, and set the thickness; thickness direction integration points: use Simpson integration, with no less than 5 integration points to ensure buckling solution accuracy; then assign the section properties to the entire surface created in step 2.1.

[0034] Step 2.4: Assembly and Coordinate System (Assembly module).

[0035] Instantiating components into the assembly environment is mainly used to unify the global coordinate system and ensure that subsequent temperature field T(x,y), constraints, and disturbance forces are all based on the same x (rolling direction) and y (width) coordinate definitions.

[0036] Step 2.5: Mesh Generation (Mesh Module).

[0037] S4R, i.e., four-node, reduced-integral shell elements, is selected; the mesh size is determined based on the requirement that the mesh must be dense enough to distinguish the shortest wave shape. Let the shortest wavelength in the target defect be... This requires the grid size to be no larger than [the specified value]. Only in this way can the buckling waveform be smoothly described without distortion; and the mesh quality is checked to ensure that there are no warped or distorted elements after generation, to ensure the mesh is regular, and to avoid the introduction of pseudo-stress due to mesh problems.

[0038] Step 3: Set up the plastic intrinsic strain field in the strip rolling direction, specifically as follows:

[0039] The plate shape defect characteristic parameters collected in step 1 are written into mathematical expressions that can be calculated point by point, serving as the basis for defining the subsequent temperature field. Specifically, for any independent defect region n, the intrinsic plastic strain field in the rolling direction is parameterized using the method of separation of variables, and its expression is as follows:

[0040]

[0041] in: For peak dependent variable, The width distribution function, For the rolling direction spatial window function; edge wave defects Take a symmetrical Gaussian shape on both sides of the strip, with a mid-wave defect. Take the center of the strip as a Gaussian shape; A hyperbolic tangent smooth window function is used to avoid stress singularities; when there are multiple defect regions, the total intrinsic strain is the direct superposition of each region.

[0042] This example sets up two overlapping defect regions with local intermediate waves and local edge waves: (1) Intermediate wave region: the rolling direction is in The region is enclosed, and the width direction adopts the central Gaussian distribution function. Distribution feature width Peak strain (2) Edge wave zone: the rolling direction is in The region adopts a two-sided symmetrical Gaussian distribution in the width direction, with a characteristic width of the distribution. Peak strain The rolling direction window function uses a hyperbolic tangent smoothing function, with the transition zone controlled within 30–50 mm. The two defect zones are located in… A spatial overlap zone of 1000 mm is formed.

[0043] Step 4: Apply anisotropic thermal expansion data to the strip in the finite element model, specifically:

[0044] Step 4.1: Assign the material an orthotropic coefficient of thermal expansion, and fill in the numerical rolling direction in the material thermal expansion property established in Step 2.2. Horizontal Cutting .

[0045] Step 4.2: In the Load module, apply a nodal temperature field that varies continuously with position to the entire strip surface. To satisfy the needs of the entire region point by point. Point-by-point equals target rolling eigenstrain .

[0046] The traditional approach involves directly applying plastic pre-strain element by element and integration point by integration point, which is cumbersome in modeling and makes it difficult to ensure point-by-point consistency with analytical or measured inputs. This method uses anisotropic thermal expansion and space temperature field to apply the pre-strain equivalently, which is both simple and can achieve accurate point-by-point matching.

[0047] Step 5: Build the analysis step framework.

[0048] In practice, before the actual loading in step 5, two consecutive analysis steps, Step-1 and Step-2, are planned, as follows:

[0049] In the analysis step Step-1, geometric nonlinearity is turned off, and a minimum constraint system is applied to constrain only the rigid body motion without applying any unnecessary external forces to the steel plate, thus not affecting the stress field. Specifically, the minimum constraint system is applied as follows: constrain the out-of-plane displacement of all nodes in the entire field (U3=0); constrain two in-plane translational degrees of freedom at a point in the center of the plate (U1=U2=0) to prevent the entire plate from drifting in the plane; and constrain another in-plane translational degree of freedom at the midpoint of one end of the strip to eliminate the rotation of the entire plate around the out-of-plane axis.

[0050] In Step-2 of the analysis, geometric nonlinearity is enabled, and the out-of-plane displacement constraints applied to all nodes in Step-1 are removed, retaining only the minimum in-plane constraint to eliminate rigid body motion, allowing the steel plate to deform freely out of plane. A small disturbance force of magnitude is applied at the center of the plate to trigger bifurcation. Because the post-buckling path is highly unstable and direct solution is prone to non-convergence, automatic stabilization (damping factor) is enabled. In this example, a damping factor of 2 × 10⁻⁶ is used. -4 A stable solution process.

[0051] Step 6: Submit the program and perform quality control and result output. Specifically, submit the program, control the ratio of stabilization energy to total strain energy to not exceed 5% to ensure that the stabilization has negligible impact on the solution's perturbation energy, and finally output the corresponding three-dimensional deflection field.

[0052] like Figure 2 As shown, the method of the present invention simulates the overlapping region of defects in strip steel. The plate exhibits a composite warping morphology with coupled mid-wave and edge-wave structures. Out-of-plane deformation occurs simultaneously at the plate center and edge, with a maximum deflection of 3.09 mm across the entire region. The peak deflection in the overlapping region is significantly higher than that of a single mid-wave or edge-wave, forming a typical coupled bulge characteristic. Furthermore, the stabilization energy ratio in this example is controlled to within 5%, and the simulation results deviate from the analytical theoretical model by only 4.6%, fully verifying the accuracy and reliability of the simulation method of this invention.

[0053] The above description is only a preferred embodiment of the present invention and is not intended to limit the ideas of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for simulating defects in strip steel based on equivalent intrinsic strain of anisotropic thermal expansion, characterized in that, include: Step 1: Collect the geometric parameters, material physical property parameters, and plate shape defect characteristic parameters of the defective strip steel; Step 2: Establish a finite element model of the strip steel based on the geometric parameters and material physical property parameters from Step 1; Step 3: Set up the plastic intrinsic strain field in the strip rolling direction; Step 4: Apply anisotropic thermal expansion data to the strip in the finite element model; Step 5: Build the analysis framework; Step 6: Submit the program and perform quality control and output the results.

2. The method for simulating strip defects based on equivalent intrinsic strain of anisotropic thermal expansion according to claim 1, characterized in that, Step 1 specifically involves: Step 1.1: Measure the strip length and width using an online dimension measuring instrument, and measure the strip thickness using a thickness gauge; Step 1.2: Collect material physical property parameters, including elastic modulus, Poisson's ratio, and plastic Poisson's ratio; Step 1.3: Collect plate shape defect characteristic parameters, including the number of defect areas, defect type, length of defect area along the rolling direction, and whether defect areas overlap; defect types include center wave defects and edge wave defects.

3. The method for simulating strip defects based on equivalent intrinsic strain of anisotropic thermal expansion according to claim 2, characterized in that, Step 2 specifically involves: Step 2.1: Establish the geometric model; Create a 3D, deformable, shell-type part in the Abaqus / Standard platform; draw a rectangular face using Planar / Shell planar sketch and input the acquired geometric dimensions; Step 2.2: Define material properties; Create a material by inputting the collected material physical property parameters, including: elastic modulus, Poisson's ratio, and plastic Poisson's ratio, and set the thermal expansion to orthotropic. Step 2.3: Setting section properties and thickness integration points; Create a shell section, assign the material created in step 2.2 to it, and set the thickness; thickness direction integration points: use Simpson integration, with no less than 5 integration points to ensure buckling solution accuracy; then assign the section properties to the entire surface created in step 2.1; Step 2.4: Assembly and Coordinate System; Instantiate the component into the assembly environment. Assembly is mainly used to unify the global coordinate system and ensure that the subsequent temperature field T(x,y), constraints, and disturbance forces are all defined based on the same x and y coordinates. Step 2.5: Mesh generation; S4R, i.e., four-node, reduced-integral shell elements, is selected; the mesh size is determined based on the requirement that the mesh must be dense enough to distinguish the shortest wave shape. Let the shortest wavelength in the target defect be... This requires the grid size to be no larger than [the specified value]. Only in this way can the buckling waveform be smoothly described without distortion; and the mesh quality is checked to ensure that there are no warped or distorted elements after generation, to ensure the mesh is regular, and to avoid the introduction of pseudo-stress due to mesh problems.

4. The method for simulating strip defects based on equivalent intrinsic strain of anisotropic thermal expansion according to claim 3, characterized in that, Step 3 specifically involves: The plate shape defect characteristic parameters collected in step 1 are written into mathematical expressions that can be calculated point by point, serving as the basis for defining the subsequent temperature field. Specifically, for any independent defect region n, the intrinsic plastic strain field in the rolling direction is parameterized using the method of separation of variables, and its expression is as follows: in: For peak dependent variable, The width distribution function, For the rolling direction spatial window function; edge wave defects Take a symmetrical Gaussian shape on both sides of the strip, with a mid-wave defect. Take the center of the strip as a Gaussian shape; A hyperbolic tangent smooth window function is used to avoid stress singularities; when there are multiple defect regions, the total intrinsic strain is the direct superposition of each region.

5. The method for simulating strip defects based on equivalent intrinsic strain of anisotropic thermal expansion according to claim 4, characterized in that, Step 4 specifically involves: Step 4.1: Assign the material an orthotropic coefficient of thermal expansion, and fill in the numerical rolling direction in the material thermal expansion property established in Step 2.

2. Horizontal Cutting ; Step 4.2: In the Load module, apply a nodal temperature field that varies continuously with position to the entire strip surface. To satisfy the needs of the entire region point by point. Point-by-point equals target rolling eigenstrain .

6. The method for simulating strip defects based on equivalent intrinsic strain of anisotropic thermal expansion according to claim 3, characterized in that, In step 5, before the actual loading, two consecutive analysis steps, Step-1 and Step-2, are planned, as follows: In analysis step Step-1, geometric nonlinearity is turned off, and a minimum constraint system is applied to constrain only the rigid body motion without applying any unnecessary external forces to the steel plate, thus not affecting the stress field. Specifically, the minimum constraint system is applied as follows: constrain the out-of-plane displacement of all nodes in the entire field; constrain two in-plane translational degrees of freedom at the center point of the plate to prevent the entire plate from drifting in the plane; and constrain another in-plane translational degree of freedom at the midpoint of one end of the strip to eliminate the rotation of the entire plate around the out-of-plane axis. In the analysis step Step-2, enable geometric nonlinearity, remove the out-of-plane displacement constraints of all nodes in the entire field applied in Step-1, and retain only the minimum in-plane constraint to eliminate rigid body motion, allowing the steel plate to deform freely out of the plane; apply a small disturbance force at the center of the plate surface to trigger bifurcation; enable automatic stabilization to stabilize the solution process.

7. The method for simulating strip defects based on equivalent intrinsic strain of anisotropic thermal expansion according to claim 1, characterized in that, Step 6 specifically involves: submitting the program, controlling the ratio of stabilization energy to total strain energy to not exceed 5% to ensure that the stabilization effect on the solution's perturbation energy is negligible, and finally outputting the corresponding three-dimensional deflection field.

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