A method for obtaining the parameters of the JC damage model of materials

Abstract

The present invention discloses a method for obtaining the JC damage model parameters of a material. By establishing a high-speed orthogonal cutting simulation model and combining it with high-speed orthogonal cutting experiments, the Johnson-Cook damage model parameters of the material are determined. It includes the following steps: First, orthogonal cutting experiments are carried out on the material at five cutting speeds with gradient changes, and the serration degree of the formed serrated chips is measured; Second, a simulation scheme for the Johnson-Cook damage model parameters with gradient changes is designed, and a series of high-speed orthogonal cutting simulations are carried out through ABAQUS to measure the serration degree parameters; Then, a regression equation of the serration degree parameters with respect to the Johnson-Cook damage model parameters is established; Finally, substituting the experimental values, the Johnson-Cook damage model parameters of the material are obtained by solving. This method can solve the problems of long experimental period, high experimental cost, and difficulty in obtaining dynamic damage performance existing in the existing damage parameter calibration methods.

Description

Technical Field

[0001] The present invention relates to a method for obtaining the JC damage model parameters of materials, belonging to the field of metal processing. Background Art

[0002] Metal materials are widely used in the fields of aerospace, marine vessels, petrochemical industry, energy, electronics, medical treatment, etc., and will be more precisely used in future technologies, national defense, and various vertical and horizontal fields. As the main process of the current mechanical manufacturing industry, metal cutting is widely used in the processing of metal parts. In the process of studying problems related to material removal and finite element cutting simulation in cutting processing, damage models are widely used. Among various failure models, the Johnson-Cook damage model is the most widely applied failure criterion in dynamic mechanical simulation, which comprehensively considers the effects of stress triaxiality, strain rate, and temperature on material failure. At present, the calibration method for the Johnson-Cook damage model parameters fits the stress triaxiality term, strain rate term, and temperature term respectively. The stress triaxiality terms D1-D3 are fitted through quasi-static tensile, dynamic tensile, in-plane shear tensile, double-notch tensile, and center-hole tensile test data. The strain rate term D4 is fitted through room-temperature tensile test data under different strain rate conditions. The temperature term D5 is fitted through quasi-static tensile test data at different temperatures. Determining the Johnson-Cook damage model parameters by the current method has a long experimental period, high cost, and extremely high difficulty in obtaining the damage performance during the dynamic cutting process.

[0003] Wang Bing, Liu Zhanqiang et al. found through research that there is a linear relationship between the serration degree of the serrated chips generated by high-speed cutting and the Johnson-Cook damage model parameters. As the Johnson-Cook damage parameters decrease, the serration degree of the chips increases (Wang Bing. Research on the Influence Mechanism of the Deformation and Fracture Behavior of High-Speed Cutting Materials on Chip Formation [D]. Shandong: Shandong University, 2016).

[0004] According to this variation law, the present application combines simulation calculation and experiment to calculate the relationship expression between the chip serration degree parameter and the Johnson-Cook damage model parameters, and realizes obtaining the Johnson-Cook damage model parameters required for simulation through simple cutting experiments. Summary of the Invention

[0005] In view of the problems of high measurement difficulty, high cost, long period, and difficult acquisition of dynamic damage performance of Johnson-Cook damage parameters in high-speed cutting finite element simulation proposed above, a method for obtaining the JC damage model parameters of materials is studied and designed. The technical means adopted by the present invention are as follows:

[0006] A method for obtaining the JC damage model parameters of materials, comprising the following steps:

[0007] S1. Consider the Johnson-Cook damage model parameter D i For the influence relationship on the serration degree of the chip, obtain the relationship model between the serration degree parameter and the Johnson-Cook damage model parameter;

[0008] Through subsequent simulation fitting, the equation of the serration degree with respect to the serration degree parameter should be obtained, expressed as follows:

[0009]

[0010] where G s represents the serration degree parameter, i represents the i-th Johnson-Cook damage model parameter, j represents the j-th group of experiments, A ij is the correlation coefficient obtained by fitting, and ε j is the constant term.

[0011] S2. Determine the cutting speed range and divide the speed gradient according to the formation law of serrated chips, conduct cutting experiments, and after the machining is completed, measure the serration degree of the serrated chips obtained during the machining process; specifically, use a vertical milling machine for milling, and use a scanning electron microscope to measure the serration degree of the serrated chips obtained by machining;

[0012] For difficult-to-machine metals such as titanium alloys, the critical cutting speed for forming serrated chips is approximately around 30 m / min. Since a total of five Johnson-Cook damage model parameters need to be obtained, set up five groups of high-speed orthogonal cutting experiments, conduct experiments at the cutting speeds divided into five gradients, and measure the serration degree parameters of the chips obtained from the five groups of experiments.

[0013] S3. Estimate the approximate range of the Johnson-Cook damage model parameters of the material to be measured through the Johnson-Cook damage model parameters of metal materials similar to the relevant materials;

[0014] S4. Let the parameter range be expanded by x%; specifically, let x take 50 to expand the parameter range;

[0015] On the basis of determining the range of the Johnson-Cook damage model parameters of the material to be measured through the category of the material to be measured, expand the range of each damage parameter to [50% D i , 150% D i , i = 1, 2, 3, 4, 5.

[0016] S5. Gradient division of Johnson-Cook damage model parameters, design simulation schemes under different gradients, combine cutting parameters, material properties and other factors, and establish simulation models through finite element analysis software.

[0017] Specifically: The Johnson-Cook constitutive model is used to describe the mechanical characteristics of the material, and the stress part is expressed as:

[0018]

[0019] in is the equivalent flow stress, is the equivalent plastic strain, is the equivalent plastic strain rate, is the equivalent reference strain rate, T is the current temperature, T m is the melting point of the workpiece material, T r is room temperature, A, B, C, n, m are material parameters.

[0020] The material damage process uses the Johnson-Cook damage model to describe the relationship between stress and strain. The Johnson-Cook damage model expression of equivalent damage strain is:

[0021]

[0022] Where P is the hydrostatic pressure, is stress triaxiality, Johnson-Cook damage model parameter D i (i=1,2,3,4,5) represents the initial failure strain, exponential factor, stress triaxiality factor, strain rate factor and temperature factor respectively.

[0023] The parameters of the Johnson-Cook damage model are divided into gradients, and simulation schemes under different gradients are designed. The simulation model is established through ABAQUS / Explicit in combination with factors such as cutting parameters and material properties.

[0024] In the simulation experiment at each cutting speed, the control variable is set to 1, and n = 2 gradients are taken to make the Johnson-Cook damage model parameter D i (i=1, 2, 3, 4, 5) are set as five groups, and simulation experiments are carried out separately under each group of parameters.

[0025] S6. The simulation results under different gradient Johnson-Cook damage model parameters are measured to obtain the jagged degree parameters, and the regression equations are fitted one by one. The experimental data are substituted and the Johnson-Cook damage model parameters are obtained by solving the simultaneous equations.

[0026] The serration degree of the chips obtained from each set of simulation experiments was measured as follows:

[0027] Mark the top of the sawtooth, the valley of the sawtooth and the bottom of the chip, make circles C1, C2 and C3, and record the distances from the center of the circle to the three marked points as r1, r2 and r3 respectively. The calculation formula of the sawtooth degree parameter is expressed as:

[0028]

[0029] Where r2-r1 represents the height of the discontinuous part of the serrated chip, and r3-r1 represents the overall height of the serrated chip.

[0030] The jaggedness parameter G obtained by simulation s Linear fitting is performed with five sets of Johnson-Cook damage model parameters, and the correlation coefficient A is solved using the regress() function in MATLAB ij With the constant term ε j , we get the non-homogeneous linear equations:

[0031]

[0032] Among them, G s represents the jaggedness parameter, i represents the number of Johnson-Cook damage model parameters, j represents the number of experiments, A ij is the correlation coefficient obtained by fitting, ε j is a constant term.

[0033] Substitute the serration parameter G measured in the high-speed right-angle cutting experiment into s The actual value of the Johnson-Cook damage model parameter D is solved by the simultaneous equations. i (i=1,2,3,4,5).

[0034] The present invention proposes a method for obtaining the Johnson-Cook damage model parameters of metal materials through finite element simulation, and establishes equations between the sawtooth degree parameters and the Johnson-Cook damage model parameters. Only a few sets of cutting experiments are needed to solve the Johnson-Cook damage model parameters, which greatly reduces the experimental cost and improves efficiency. Due to the simulation of the dynamic cutting process, the Johnson-Cook damage parameters determined by the method proposed in this article can better reflect the damage performance in the dynamic cutting process. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0036] Figure 1 is a schematic flowchart of the method of the present invention;

[0037] Figure 2 is a schematic diagram of the serration degree measurement method;

[0038] Figure 3 is a two-dimensional orthogonal cutting finite element model diagram;

[0039] Figure 4 is an experimental data diagram in the citation. Specific embodiments

[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0041] The technical route of the present invention is as Figure 1 shown.

[0042] A method for obtaining the JC damage model parameters of a metal material based on finite element simulation, including the following steps: S1. Considering the relationship between the Johnson-Cook damage model parameters and the serration degree parameters, a theoretical guess of the relationship between the serration degree parameters and the Johnson-Cook damage model parameters is obtained, and an equation for the serration degree with respect to the serration degree parameters is to be obtained, which is expressed as follows:

[0043]

[0044] where G s represents the serration degree parameter, i represents the i-th Johnson-Cook damage model parameter, j represents the j-th group of experiments, A ij is the correlation coefficient obtained by fitting, and ε j is the constant term.

[0045] S2. The machine tool used in the experiment is the SMTCL VMC0540d vertical milling machine, with a rake angle of 0°, a clearance angle of 10°, and a cutting edge inclination angle of 0°. The material of the workpiece to be machined is Ti-6Al-4V, and the undeformed chip thickness is fixed at 0.1 mm. Orthogonal cutting experiments are carried out at speeds of 50 m / min, 500 m / min, 1000 m / min, 1500 m / min, and 2500 m / min. The obtained chips are made into metallographic specimens. After grinding and polishing their surfaces, the chip morphology is observed under a scanning electron microscope, and the experimental values of the serrated parameters are obtained (Wang Bing. Research on the Influence Mechanism of High-Speed Cutting Material Deformation and Fracture Behavior on Chip Formation [D]. Shandong: Shandong University, 2016, Figure 4 )

[0046] S3. Through the Johnson-Cook damage model parameters of materials similar to Ti-6Al-4V, the damage parameter range of Ti-6Al-4V is roughly estimated.

[0047] S4. Expand the parameter range by 50%. In this example, the damage parameter range of the material Ti-6Al-4V is as follows: D1 ∈ [-1.155, 0.093], D2 ∈ [-0.091, 0.390], D3 ∈ [-3.182, 1.503], D4 ∈ [-0.201, 0.033], D5 ∈ [-2.385, 5.971]. The values within the range are taken as the initial values in the simulation experiment.

[0048] S5. Establish the orthogonal cutting finite element simulation model as shown in Figure 3 through ABAQUS 2021. The specific steps are as follows:

[0049] Establish a deformable solid according to the experimental material size and tool geometric parameters, divide the grids for the undeformed chip and the workpiece matrix. The grid type is selected as Quad-dominated, and the free grid division technology is adopted. The workpiece matrix is evenly seeded along the feed direction, and from the direction close to the undeformed chip to the bottom of the workpiece matrix in the direction perpendicular to the feed direction, the seeding density decreases from dense to sparse. Assemble and set the tool reference point, establish a temperature-displacement coupling analysis step, and define the contact relationship. The tool feed direction is the -X direction. Set the cutting speeds to be: 50 m / min, 500 m / min, 1000 m / min, 1500 m / min, and 2500 m / min. In each cutting speed experimental group, divide the gradients for D1 - D5: keep D2 - D5 unchanged, and let D1 take the original value, increase by 50%, increase by 100%, decrease by 50%, and decrease by 100% respectively; perform the same operations on D2, D3, D4, and D5, and the experimental parameters are as follows:

[0050]

[0051] Conduct a simulation experiment each time the parameters are changed.

[0052] S6. Measure the obtained simulation results. Using Inventor 2022 to measure the data, as shown in Figure 2, mark the top, valley, and bottom of the serrated chips obtained from the simulation. Make circles that intersect the above three points respectively, and use the formula to calculate the serration degree parameter of the simulation results. By calling the regress() function in MATLAB software, five regression equations of G s with respect to

[0053] D1, D2, D3, D4, and D5 can be obtained under each cutting speed experimental group, that is, five regression equations of G sj with respect to D i (i = 1, 2, 3, 4, 5) can be obtained under each cutting speed experimental group, where j is the number of the experimental group. Five cutting speed experimental groups can obtain five equations of G s with respect to D1 - D5. At this time, substitute the actually measured G s values, and solve the non-homogeneous linear equations simultaneously. The Johnson-Cook damage model parameters of the required material can be obtained as shown in the following table:

[0054]

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for obtaining the parameters of the JC damage model of a material, characterized in that, The following steps are involved: S1. Consider the Johnson-Cook damage model parameter D i Obtain the relationship model between the serration degree parameter and the Johnson-Cook damage model parameter considering the influence relationship on the serration degree of the chip The equation of the sawtooth degree related to the sawtooth degree parameter is obtained through subsequent simulation fitting, which is expressed as follows: Among them, G s represents the serration degree parameter, i represents the i-th Johnson-Cook damage model parameter, j represents the j-th group of experiments, A ij is the correlation coefficient obtained by fitting, and ε j is the constant term; S2. Determine the cutting speed range and divide the speed gradient according to the formation law of serrated chips, carry out cutting experiments, and after the processing is completed, measure the serration degree of the serrated chips obtained during the processing; S3, determining the parameter range of the Johnson-Cook damage model of the material under test according to the type of the material under test; S4, expand the parameter range by x%; S5. Gradient division of Johnson-Cook damage model parameters, design simulation schemes under different gradients, combine cutting parameters, material properties and other factors, and establish simulation models through finite element analysis software; S6. The simulation results under different Johnson-Cook damage model parameters are measured to obtain the jagged degree parameters, the Johnson-Cook damage model parameters are fitted one by one to obtain the regression equation, and the experimental data are substituted to obtain the Johnson-Cook damage model parameters by solving the simultaneous equations.

2. The method for obtaining the JC damage model parameters of the material according to claim 1, wherein, In step S2, the cutting experiment is specifically carried out at different gradient cutting speeds. The steps are as follows: S21. Determine the cutting speed range according to the conditions for forming serrated chips, formulate experimental plans under different cutting speeds and carry out cutting experiments, and collect the chips generated during the cutting process; S22. Observe the obtained chips and measure the parameters of the serration degree.

3. The method for obtaining the JC damage model parameters of the material according to claim 2, characterized in that, In step 3, determining the parameter range of the Johnson-Cook damage model required for the simulation of the material under test includes the following steps: S31. Determine the parameter range of the Johnson-Cook damage model of the material being tested by using the parameters of the Johnson-Cook damage model of similar types of materials.

4. The method for obtaining the JC damage model parameters of the material according to claim 3, characterized in that, In step S4, the parameter range is expanded by x%, and the following steps are included: S41. On the basis of determining the parameter range of the Johnson-Cook damage model of the material to be measured according to the category of the material to be measured, expand the range of each damage parameter to [(1 - x%)D i , (1 + x%)D i , where i = 1, 2, 3, 4, 5, and D i , where i = 1, 2, 3, 4, 5 respectively represent the initial failure strain, the exponential factor, the stress triaxiality factor, the strain rate factor, and the temperature factor.

5. The method for obtaining the JC damage model parameters of the material according to claim 4, characterized in that: In step 5, establishing a simulation model comprises the following steps: S51. Use finite element analysis software to build a model, set up thermal-mechanical coupling analysis, set the tool as a rigid body, and use unit deletion technology; S52. Gradient division is performed on the variable values ​​of the five Johnson-Cook damage models, and the variables are controlled. Each parameter is set with n gradients, and its range is expanded by y times, so as to obtain a total of 2n+1 simulation experiments including itself.

6. A method for obtaining the JC damage model parameters of a material according to claim 5, characterized in that: The step 6 specifically includes the following steps: S61. Use the measurement software to measure the serrated chips obtained by simulation, mark the serration tips, serration valleys, and the bottom of the chips, draw circles C1, C2, and C3, and record the distances from the centers of the circles to the above three marked points as R1, R2, and r3 respectively. The calculation formula for the serration degree parameter is as follows: S62. The serration degree parameter G obtained by simulation s is linearly fitted with five groups of Johnson-Cook damage model parameters to establish a non-homogeneous linear equation system: where G s represents the serration degree parameter, i represents the i-th Johnson-Cook damage model parameter, j represents the j-th group of experiments, and A ij is the correlation coefficient obtained by fitting, and ε j is the constant term; S63. Substitute the actual value of the serration parameter G measured in the experiment in step 2, and solve the Johnson-Cook damage model parameter D by simultaneously solving the equations s . i .

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