A material hardening curve fitting method for CAE simulation

Abstract

This invention relates to a material hardening curve fitting method for CAE simulation. The method includes calculating the tangent slopes from two points to multiple points at the end of the effective stress-strain curve, obtaining the maximum slope, determining the slope range of the upper and lower fitting curves, fitting multiple points at the end of the effective stress-strain curve using a hardening model to form an upper fitting curve with a gradually decreasing slope, connecting the effective stress-strain curve to the upper fitting curve to form an upper simulation curve, inserting a point at the end of the effective stress-strain curve with the same stress as the end point and a strain of 105%–120% of the strain at the end point, and fitting the lower fitting curve using the same method as the upper fitting curve. The slope range determines whether to output the upper or lower simulation curve. This invention solves the problems of complex curve calculation, long processing time, difficult algorithm editing, and expensive software. The method is simple, not limited by steel type, and effectively saves manpower and resources.

Description

Technical Field

[0001] This invention relates to the field of metal sheet forming technology, and in particular to a material hardening curve fitting method for CAE simulation. Background Technology

[0002] When performing CAE simulations, it is necessary to first determine the input curve and verify whether the input curve can achieve the best fit between the simulation output curve and the experimental curve. This requires continuous adjustment of parameters to form different input curves. The input curve is a curve fitted based on the experimental curve. The commonly used fitting hardening model is Swift-Hockett-Shery. Manually editing the algorithm of this hardening model is a relatively complex, time-consuming, and difficult task. Using professional processing software such as MATLAB is expensive, and due to the fixed parameters of the model, the fitting effect is relatively poor for some steel grades.

[0003] Chinese Patent Publication No. CN115292995A discloses a method for fitting the hardening curve of metallic materials, including the following steps: S1, performing a uniaxial tensile test on the material to obtain the test force-displacement curve and the engineering stress-strain curve; S2, calculating the material's true stress-plastic strain curve based on data points before the peak point of the engineering stress-strain curve and using it as the first part of the hardening curve; S3, fitting and extrapolating to obtain the second part of the hardening curve; S4, merging the first and second parts; S5, establishing a finite element model and performing simulation calculations to obtain the simulated force-displacement curve; S6, comparing the simulated force-displacement curve and the test force-displacement curve. If the error between the two is within a set threshold, the hardening curve obtained in S4 is used as the material's hardening curve; if the error is not within the set threshold, returning to S3 and optimizing the parameter values ​​until the error is within the set threshold is correct. This method improves both fitting accuracy and ease of use. However, this invention does not involve a specific hardening curve fitting method. Summary of the Invention

[0004] This invention provides a material hardening curve fitting method for CAE simulation, which solves the problems of complex calculations, long time consumption, and high difficulty in editing algorithms when using the hardening model Swift-Hockett-Shery for curve fitting, and the high cost of professional processing software such as MATLAB. This invention can be implemented using VBA or any free programmable software based on WPS or Office, and the implementation method is simpler, not limited by steel type, and can effectively save manpower and resources.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A method for fitting material hardening curves for CAE simulation includes the following steps:

[0007] S1. Calculate the slope of the tangent from the last two points to multiple points of the effective stress-strain curve, obtain the maximum slope, determine the slope range of the upper fitting curve, and at the same time determine the slope range of the lower fitting curve.

[0008] S2. The effective stress-strain curve is fitted using a hardening model at multiple points at the end of the curve to form an upper fitted curve with a gradually decreasing slope. The effective stress-strain curve is then connected to the upper fitted curve to form the upper simulation curve.

[0009] S3. Insert a point at the end of the effective stress-strain curve with the same stress as the end point, and the strain is 105% to 120% of the strain at the end point, to form a new effective stress-strain curve.

[0010] S4. For the two or more points at the end of the new effective stress-strain curve, a hardened model is used to fit them to form a lower fitting curve with a gradually increasing tangent slope. The original effective stress-strain curve is connected to the lower fitting curve to form the lower simulation curve.

[0011] S5. When a simulation curve with a specific slope needs to be output, determine whether to use the upper simulation curve or the lower simulation curve for output based on the slope range obtained in the above steps, and output the simulation curve using step S2 or step S4.

[0012] Furthermore, step S1, determining the slope range of the upper fitted curve, includes: fitting multiple points at the end of the effective stress-strain curve using a hardening model, calculating the slope of the first two points of the fitted curve, and determining the slope range of the upper fitted curve if the slope of the upper fitted curve is less than or equal to the maximum slope of the effective stress-strain curve, less than the slope calculated previously, or the minimum slope.

[0013] Furthermore, the formula for the hardening model is as follows:

[0014] y = C·x n (1)

[0015] Where y is stress, x is strain, C is a coefficient, and n is a coefficient.

[0016] Furthermore, step S4, which forms a lower fitting curve with a gradually increasing tangent slope, includes: fitting two or more points at the end of the new effective stress-strain curve using a hardening model, calculating the slope of the first two points of the fitting curve, and determining the maximum slope as the slope of the lower fitting curve if it is greater than or equal to 0, less than or equal to the minimum slope of the upper fitting curve, and greater than the slope calculated previously. Then, the loop calculation is exited, forming a lower fitting curve with a gradually increasing tangent slope.

[0017] Compared with the prior art, the present invention has the following beneficial effects:

[0018] 1) This method is based on curve fitting of the effective stress-strain curve to form two curve slope ranges. The simulation curve with a specific slope can be output by selecting the upper simulation curve or the lower simulation curve through the slope range.

[0019] 2) This method can replace the hardened model Swift-Hockett-Shery curve fitting, solving the problems of Swift-Hockett-Shery's complex calculation, long time consumption, high difficulty in editing the algorithm, and high cost of using professional processing software such as MATLAB.

[0020] 3) The present invention can implement the above functions based on WPS or Office using VBA or any free programmable software. The implementation method is simpler and is not limited by the type of steel, which can effectively save manpower and material resources. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the fitting curve of the present invention. Detailed Implementation

[0022] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0023] This invention discloses a method for fitting material hardening curves in CAE simulation. The simulation curve consists of an effective stress-strain curve and a fitted curve. The fitted curve can be divided into an upper fitted curve and a lower fitted curve. First, the tangent slopes at multiple points at the end of the effective stress-strain curve are calculated to obtain the maximum slope. Then, a hardening model is used to fit two or more points at the end of the effective stress-strain curve to form an upper fitted curve with a gradually decreasing tangent slope. The tangent slope of the upper fitted curve is calculated using the first two points of the upper fitted curve. The tangent slope of the upper fitted curve should not exceed the maximum slope of the effective stress-strain curve to ensure a smooth transition between the effective stress-strain curve and the upper fitted curve. This step can determine the slope range of the upper fitted curve and also the lower fitted curve. The slope range of the curve; secondly, insert a point with the same stress as the end point at the end of the effective stress-strain curve, with a strain of 105% to 120% of the strain at the end point. By fitting two or more points at the end of the effective stress-strain curve using a hardening model, a lower fitting curve with a gradually increasing tangent slope can be formed. The tangent slope is calculated using the first two points of the lower fitting curve. The minimum slope of the lower fitting curve is 0, and the maximum slope is the minimum slope of the upper fitting curve. Connecting the effective stress-strain curve with the upper or lower fitting curve can form a set of simulation curves with gradually increasing slopes. For simulation curves with specific slopes, the slope range can be used to determine whether to use the upper or lower simulation curve for output. This method specifically includes the following steps:

[0024] S1. Calculate the tangent slopes from the two points at the end of the effective stress-strain curve to multiple points, obtain the maximum slope, and fit the multiple points at the end of the effective stress-strain curve using a hardening model. Calculate the slope of the first two points of the fitted curve, and determine whether the slope of the upper fitted curve is less than or equal to the maximum slope of the effective stress-strain curve, whether it is less than the slope calculated in the previous step, and whether it is already the minimum slope. If it is the minimum slope, exit the loop calculation. This step can determine the slope range of the upper fitted curve. The lower range of the curve is 0 to the slope of the lowest curve of the upper curve. Therefore, the slope range of the lower fitted curve is determined at the same time as the upper curve range.

[0025] S2. The following formulas are used to fit multiple points at the end of the effective stress-strain curve:

[0026] Formula y = C·x n (2)

[0027] Where y is stress, x is strain, C is a coefficient, and n is a coefficient;

[0028] An upper fitting curve with a gradually decreasing slope is formed, and the effective stress-strain curve is connected to the upper fitting curve to form the upper simulation curve.

[0029] S3. Insert a point at the end of the effective stress-strain curve that is the same as the stress at the end point, with a strain of 105% to 120% of the strain at the end point, to form a new effective stress-strain curve.

[0030] S4. Apply the formula y = C·x to two or more points at the end of the new effective stress-strain curve. n The fitting process involves calculating the slope of the first two points of the fitted curve, determining whether the slope of the lower fitted curve is greater than or equal to 0, less than or equal to the minimum slope of the upper fitted curve, greater than the slope calculated previously, or the maximum slope. This step generates a lower fitted curve with a gradually increasing tangent slope. The original effective stress-strain curve can be connected to the lower fitted curve to form the lower simulation curve.

[0031] S5. When a simulation curve with a specific slope needs to be output, the upper simulation curve or the lower simulation curve should be output by determining the slope range, and the simulation curve should be calculated using step S2 or step S4.

[0032] The following embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments. Unless otherwise specified, the methods used in the following embodiments are conventional methods.

[0033]

Example

[0034] like Figure 1 The figure shown is a schematic diagram of the fitting curve of the present invention. This method is based on the effective stress-strain curve L. 有效 Perform curve fitting, L 有效 This data was obtained from experimental data processing; the first half of the fitting process was L. 有效 The latter half is the fitted curve L. 拟合 curve L 仿真i Fitted curve L 拟合 Divided into upper fitting curve L 拟合上i and the lower fitted curve L 拟合下i curve L 仿真i Divided into upper simulation curve L 仿真上i and the lower simulation curve L 仿真下i Effective stress-strain curve L 有效 The maximum tangent slope at multiple points at the end is k0, and the upper fitted curve L 拟合上i The slope of the two initial points is k1 i The lower fitted curve L 拟合下i The slope of the two initial points is k2 i k1 i The range is k1 min ≤k1 i The range of ≤k0,k2 is 0≤k2i ≤k1 min L 仿真上i The range is L 仿真上min ≤L 仿真上i ≤L 仿真上max L 仿真下 The range is L 仿真下min ≤L 仿真下i ≤L 仿真下max Specifically, it includes the following steps:

[0035] S1. Calculate the effective stress-strain curves L respectively. 有效 The slopes of the tangents from the last 2 points to the 10th point are used to obtain the maximum slope k0, and the effective stress-strain curve L is then analyzed. 有效 The multiple points at the end are respectively represented by the formula y = C·x n Perform fitting and calculate the fitted curve L. 拟合上i The slope k1 of the first two points i If k1 i If k ≤ k0, then determine k1. i Is it less than the slope k1 calculated in the previous calculation? i-1 If k1 i ≤k1 i-1 Then record k1 min =k1 i The maximum number of iterations is L. 有效 The points are counted until the entire loop ends, at which point k1 can be obtained. min The value of k1 was obtained at the same time. i The range, if the slope k1 i >k0 or k1 i >k1 i-1 If the result is negative, then abandon this calculation, adjust the number of points selected at the end, and use the formula y = C·x. n Refitting is performed; this step determines the upper fitted curve L. 拟合上i The slope range is k1 min ≤k1 i ≤k0, and at the same time, the lower fitted curve L can be determined. 拟合下i The slope range is 0 ≤ k2 i ≤k1 min .

[0036] S2, regarding the effective stress-strain curve L 有效 The multiple points at the end are respectively represented by the formula y = C·x n Perform fitting to form the slope k1 i The upper fitted curve L gradually decreases 拟合上i Effective stress-strain curve L 有效 Connecting the upper fitted curve L 拟合上i Forming the upper simulation curve L 仿真上i .

[0037] S3, Effective stress-strain curve L 有效 The strain point is strain i The stress point is i , in strain i Then insert a strain i+1 L must be satisfied 有效 The strain interval, i.e., the strain i+1 -strain i =strain i -strain i-1 Then, in the effective stress-strain curve L 有效 end stress i Then insert a stress of the same size. i+1 That is, stress i+1 =stress i The effective stress-strain curve after the insertion point at this time is marked as L. 有效下 .

[0038] S4, for curve L 有效下 From two points to multiple points at the end, the formula y = C·x is used respectively. n Perform fitting and calculate the fitted curve L. 拟合下i The slope k2 of the first two points i If 0 < k2 i ≤k1 min Then the output slope k2 i The lower fitted curve L gradually increases 拟合下i Effective stress-strain curve L 有效 Connecting the lower fitted curve L 拟合下i Forming the lower simulation curve L 仿真下i .

[0039] S5. When it is necessary to output a simulation curve L with a specific slope ki 仿真i At that time, the slope range k1 generated by step S1 min ≤k1 i ≤k0 and 0≤k2 i ≤k1 min Determine whether to use step S2 or step S4 to output the simulation curve L. 仿真i .

Claims

1. A method for fitting material hardening curves in CAE simulation, characterized in that, Includes the following steps: S1. Calculate the slope of the tangent lines from the two points at the end of the effective stress-strain curve to multiple points, obtain the maximum slope, and fit the multiple points at the end of the effective stress-strain curve using a hardening model. Calculate the slope of the first two points of the fitted curve, and determine whether the slope of the upper fitted curve is less than or equal to the maximum slope of the effective stress-strain curve, whether it is less than the slope calculated in the previous step, and whether it is already the minimum slope. If it is the minimum slope, exit the loop calculation. This step determines the slope range of the upper fitted curve and also determines the slope range of the lower fitted curve. S2. The effective stress-strain curve is fitted using a hardening model at multiple points at the end of the curve to form an upper fitted curve with a gradually decreasing slope. The effective stress-strain curve is then connected to the upper fitted curve to form the upper simulation curve. S3. Insert a point at the end of the effective stress-strain curve with the same stress as the end point, and the strain is 105% to 120% of the strain at the end point, to form a new effective stress-strain curve. S4. For the two or more points at the end of the new effective stress-strain curve, a hardened model is used to fit them to form a lower fitting curve with a gradually increasing tangent slope. The original effective stress-strain curve is connected to the lower fitting curve to form the lower simulation curve. S5. When a simulation curve with a specific slope needs to be output, determine whether to use the upper simulation curve or the lower simulation curve for output based on the slope range obtained in the above steps, and output the simulation curve using step S2 or step S4.

2. The material hardening curve fitting method for CAE simulation according to claim 1, characterized in that, The formula for the hardening model is as follows: （1） Where y is stress, x is strain, C is a coefficient, and n is a coefficient.

3. The material hardening curve fitting method for CAE simulation according to claim 1, characterized in that, Step S4, forming a lower fitting curve with a gradually increasing tangent slope, includes: fitting two or more points at the end of the new effective stress-strain curve using a hardening model, calculating the slope of the first two points of the fitting curve, and determining the maximum slope as the slope of the lower fitting curve if the slope is greater than or equal to 0, less than or equal to the minimum slope of the upper fitting curve, and greater than the slope calculated previously. Then, the loop calculation is exited, forming a lower fitting curve with a gradually increasing tangent slope.

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