A numerical simulation method for mesoscopic-scale crack propagation behavior

Abstract

The present invention discloses a numerical simulation method for the mesoscopic-scale crack propagation behavior, and the steps are as follows: First, obtain the mechanical property parameters of the material through strain-controlled low-cycle fatigue tests, then use the Voronoi algorithm to obtain the mesoscopic model, and then use the commercial finite element software ABAQUS for sub-region modeling, mesh division, static solution, and set boundary conditions according to the test load conditions. Write scripts in Python to randomly distribute the elastic modulus and pores in the mesoscopic model elements; use the USDFLD subroutine developed by the secondary development of ABAQUS to write the Basquin–Coffin–Manson program to predict the fatigue life of the material, and then use the continuous damage mechanics model to calculate the low-cycle fatigue damage; finally, submit the job in ABAQUS, view the simulated crack propagation results, analyze the crack evolution process, and perform data processing on the simulated results to obtain the stress intensity factor at the crack tip and the crack propagation rate curve of the simulation.

Description

Technical Field

[0001] The present invention relates to the field of strain-controlled low-cycle fatigue, and specifically to a numerical simulation method for mesoscopic-scale crack propagation behavior. Background Art

[0002] Additive manufacturing technology is different from traditional manufacturing technologies. Additive manufacturing is a technology that uses a laser or electron beam as a heat source, metal powder particles or metal wire as the forming raw material, and prints layer by layer according to the three-dimensional modeling data of the required part along a set scanning path. Compared with traditional subtractive manufacturing technologies, this manufacturing technology can greatly save raw materials, shorten the production cycle, and reduce production costs. At the same time, it is found that the mechanical properties of parts manufactured by additive manufacturing are excellent. Therefore, additive manufacturing technology is widely used in the fields of aerospace and medical devices.

[0003] According to research reports, it is known that there are randomly distributed defects in parts manufactured by additive manufacturing, such as unfused particles, pores, and microcracks. The reason for the formation of unfused particles is that there is an overlapping area between adjacent laser tracks, and the depth of this overlapping area is less than the powder layer thickness, resulting in the powder layer under the overlapping area not being melted. The formation of pores is due to the fact that the cooling rate of the forming material is too fast, making the internal gas unable to escape. Therefore, the formation of unfused particles and pores is closely related to process parameters. Additive manufacturing is a process of rapid melting and solidification in a local area. In this process, the melting and solidification rate of the powder raw material in the molten pool is faster than that of the surrounding area, ultimately resulting in the generation of residual stress. When the residual stress is higher than the strength limit of the material, microcracks will appear. Through heat treatment, this residual stress can be eliminated, but the internal pores still exist.

[0004] It is found that pores are often the source of crack initiation, and their existence will shorten the service life of parts. Therefore, it becomes particularly important to study the influence of pores inside parts after heat treatment on crack evolution. The present invention proposes a numerical simulation method for crack propagation behavior that considers randomly distributed pores and elastic modulus factors within the mesoscopic scale range. Summary of the Invention

[0005] The purpose of the present invention is to provide a numerical simulation method for mesoscopic-scale crack propagation behavior. By considering the non-uniformity of the cell distribution, the anisotropy of the internal direction of the cell, the non-uniformity of the elastic modulus distribution within the cell, and the randomness of the pore distribution, it is possible to effectively simulate the mesoscopic structure inside heat-treated SLM Ti-6Al-4V and simulate the low-cycle fatigue crack propagation behavior affected by the non-uniformity of the elastic modulus distribution within the cell and the randomness of the pore distribution within the mesoscopic scale range.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions.

[0007] A numerical simulation method for the crack propagation behavior at the mesoscopic scale, comprising the following steps:

[0008] Step S1: Prepare a test round bar specimen SLM Ti-6Al-4V using selective laser melting technology, perform heat treatment at 800 °C, conduct a low-cycle fatigue test on the heat-treated round bar specimen SLM Ti-6Al-4V under strain control to obtain its mechanical properties, and then obtain the cyclic stress-strain curve according to the Ramberg–Osgood equation and material-related mechanical parameters. The damage coefficient can be obtained by combining the damage evolution equation with experimental data;

[0009] Step S2: Obtain the microstructure morphology information of the round bar specimen SLM Ti-6Al-4V material, and obtain a mesoscopic model according to the Voronoi algorithm with the aid of MATLAB software;

[0010] Step S3: Import the mesoscopic model obtained in Step S2 into ABAQUS software, establish a simulation model in ABAQUS according to the specimen size, divide the simulation model according to the crack propagation region, and obtain a mesoscopic model region and a non-mesoscopic model region;

[0011] Step S4: Perform mesh division on the simulation model established in Step S3. To ensure the accuracy of the simulation results, use a transitional mesh drawing method for mesh division in the transition region between the mesoscopic model region and the non-mesoscopic model region;

[0012] Step S5: Assign material properties: Input the mechanical property parameters and cyclic stress-strain curve of the round bar specimen SLM Ti-6Al-4V material obtained in Step S1 into the material properties of ABAQUS software;

[0013] Step S6: Set the analysis step: Adopt a static general analysis step;

[0014] Step S7: Use Python scripts in ABAQUS to achieve the random distribution of elastic modulus and pores; Script 1: Random distribution of elastic modulus. First, make the elastic modulus follow a normal distribution, then randomly select several elastic moduli from the normal distribution, and finally randomly assign the selected several elastic moduli to each element of the model; Script 2: Random distribution of pores. First, randomly select the corresponding number of elements in the mesoscopic region, then establish a set of these elements, and finally kill this set using the birth-death element technology;

[0015] Step S8: Set the boundary conditions in the simulation according to the actual load conditions of the experiment;

[0016] Step S9: Write the USDFLD subroutine. First, use the Basquin–Coffin–Manson general method to predict the fatigue life of the material. Then, use the continuous damage mechanics model to calculate the damage value of each element in each cycle, accumulate the damage values of each cycle of the element. If the accumulated damage value exceeds the set threshold, finally, use the element deletion technology in ABAQUS to delete the corresponding element, so as to simulate the crack propagation;

[0017] Step S10: Submit the job, view the simulated crack propagation results, analyze the crack evolution process and process the simulated result data to obtain the stress intensity factor at the crack tip and the crack propagation rate curve.

[0018] Specifically, in step S1, the cyclic stress-strain curve is obtained according to the Ramberg–Osgood equation and the mechanical parameters related to the material. The Ramberg–Osgood expression is as follows:

[0019]

[0020] In the formula, k ′ and n ′ are the cyclic strength coefficient and the cyclic strain hardening index respectively, and E is the cyclic elastic modulus.

[0021] Specifically, the expression of the Basquin–Coffin–Manson general method in step S9 is as follows:

[0022]

[0023] In the formula, σ ′ f and ε ′ f represent the fatigue strength coefficient and the fatigue ductility coefficient respectively, and b and c are the fatigue strength index and the fatigue ductility index.

[0024] Specifically, the expression for calculating the fatigue damage of each cycle by the continuous damage mechanics model in step S9 is as follows:

[0025]

[0026] In the formula, p is the damage coefficient;

[0027] Integrating the above formula can obtain the damage evolution equation:

[0028]

[0029] The advantages and beneficial effects of the present invention are:

[0030] The method of the present invention combines experimental data with numerical simulation in the mesoscopic scale range, simulates the crack propagation behavior of heat-treated SLM Ti-6Al-4V, and realizes the analysis and calculation of the entire process of crack evolution, which is of great significance for studying the crack propagation behavior of heat-treated SLM Ti-6Al-4V. Description of the Drawings

[0031] Figure 1 The specific flowchart for simulating the low-cycle fatigue crack propagation of heat-treated SLM Ti-6Al-4V;

[0032] Figure 2 The dimensions of the round bar specimen;

[0033] Figure 3 The mesoscopic model with a notch;

[0034] Figure 4 The fitted cyclic stress-strain curve;

[0035] Figure 5 The simulated random distribution of pores;

[0036] Figure 6 The simulated random distribution of elastic modulus;

[0037] Figure 7 The results of the simulated low-cycle fatigue crack propagation path under the random distribution of pores;

[0038] Figure 8 The results of the simulated low-cycle fatigue crack propagation path under the random distribution of elastic modulus;

[0039] Figure 9 The curve of crack propagation rate - stress intensity factor. Detailed Embodiment

[0040] The present invention will be further described below in conjunction with specific embodiments.

[0041] As Figure 1 shown, a numerical simulation method for mesoscopic scale crack propagation behavior includes the following steps:

[0042] Step S1: Prepare a test round bar specimen SLM Ti-6Al-For V using selective laser melting technology, heat-treat it at 800 °C, conduct a low-cycle fatigue test on the heat-treated round bar specimen SLM Ti-6Al-4V under strain control to obtain its mechanical properties, and then obtain the cyclic stress-strain curve according to the Ramberg–Osgood equation and material-related mechanical parameters. The damage coefficient can be obtained by combining the damage evolution equation with experimental data;

[0043] Step S11: Prepare a test round rod specimen SLM Ti-6Al-4V using selective laser melting technology, and then heat treat it at 800°C. Low-cycle fatigue testing is performed on the heat-treated SLM Ti-6Al-4V specimen under strain control, and the obtained mechanical properties, density, and damage coefficient are shown in Table 1 below:

[0044] Table 1 Obtained mechanical properties, density and damage coefficient

[0045]

[0046] Step S12: Fitting the cyclic stress-strain curve according to the Ramberg–Osgood equation (e.g. Figure 2 As shown), the Ramberg–Osgood equation is as follows:

[0047]

[0048] Where k ′ and n ′ are the cyclic strength coefficient and cyclic strain hardening exponent, respectively, and E is the cyclic elastic modulus;

[0049] Step S2, obtaining the microstructure information of the round rod sample SLM Ti-6Al-4V material, and obtaining a mesoscopic model according to the Voronoi algorithm using MATLAB software;

[0050] Step S21, obtaining material tissue morphology information such as the number of unit cells, the width of grain boundaries, the average radius of unit cells, and the regularity of unit cells;

[0051] Step S22: Based on the above information, a mesoscopic model is obtained using the Voronoi algorithm with the help of MATLAB software;

[0052] Step S23, determine the size of the notch: R-notch root radius, H-notch depth, θ-notch angle. On the basis of the mesoscopic model, establish a mesoscopic model with notches (such as Figure 3 shown).

[0053] Step 3: Import the mesoscopic model obtained in step S2 into ABAQUS software, establish a simulation model in ABAQUS according to the sample size, and divide the simulation model according to the crack extension area to obtain a mesoscopic model area and a non-mesoscopic model area;

[0054] Step S31: import the mesoscopic model generated by MATLAB into ABAQUS software through Python script, and then Figure 4 (As shown) a simulation model is established in ABAQUS;

[0055] Step S32: Divide the simulation model into regions, determine the mesoscopic model region according to the crack propagation position, and the other places are non-mesoscopic model regions;

[0056] Step S33: Use the Boolean operation function in ABAQUS to embed the mesoscopic model into the simulation model;

[0057] Step S4: Mesh the simulation model established in Step S3. To ensure the accuracy of the simulation results, the transition grid drawing method is used for meshing in the transition region between the mesoscopic model region and the non-mesoscopic model region;

[0058] Step S5: Assign material properties: Input the mechanical property parameters and cyclic stress-strain curve of the SLM Ti-6Al-4V material of the round bar specimen obtained in Step S1 into the material properties of the ABAQUS software, and then set the field variables;

[0059] Step S6: Set the analysis step: Adopt the static general analysis step;

[0060] Step S7: Use Python scripts in ABAQUS to achieve the random distribution of elastic modulus and pores; Script 1: Random distribution of elastic modulus. First, make the elastic modulus follow a normal distribution, then randomly select several elastic moduli from the normal distribution, and finally randomly assign the selected several elastic moduli to each element of the model. The assignment results are as Figure 5 shown; Script 2: Random distribution of pores. First, randomly select the corresponding number of elements in the mesoscopic region, then establish a set of these elements, and finally kill this set using the birth-death element technique; The results of randomly distributing pores are as Figure 6 shown;

[0061] Step S8: Set the boundary conditions in the simulation according to the actual load conditions of the experiment; The actual load conditions are shown in Table 2 below:

[0062] Table 2 Actual load conditions of the experiment

[0063]

[0064] Step S9: Write the USDFLD subroutine. First, use the Basquin–Coffin–Manson general method to predict the fatigue life of the material, then use the continuous damage mechanics model to calculate the damage value of each element in each cycle, accumulate the damage values of each cycle of the element, and if the accumulated damage value exceeds the set threshold, finally use the element deletion technique in ABAQUS to delete the corresponding element, so as to simulate the crack propagation;

[0065] Step S91. The relationship between the low-cycle fatigue crack formation life and strain under strain control can be described by the Basquin–Coffin–Manson equation:

[0066]

[0067] where σ ′ f and ε ′ f represent the fatigue strength coefficient and fatigue ductility coefficient, b and c are the fatigue strength exponent and fatigue ductility exponent, and E is the cyclic elastic modulus;

[0068] Step S92. Use the continuous damage mechanics model to calculate the damage value of each cycle of the element. The equation is as follows:

[0069]

[0070] where p is the damage coefficient;

[0071] Step S93. Accumulate the damage values of each cycle to obtain the equation:

[0072]

[0073] Step S94. If the accumulated damage value exceeds the set threshold, delete the corresponding element by means of the element deletion technology in ABAQUS;

[0074] Step S10. Submit the job, and finally obtain the simulated crack propagation path (as shown in Figure 7 、 Figure 8 ). Analyze the crack evolution process and then process the simulated result data to obtain the stress intensity factor at the crack tip and the crack propagation rate curve (as shown in Figure 9 ).

[0075] The above specifically describes the preferred implementation method of the present invention. However, the present invention is not limited to the described embodiments. Those skilled in the art can make various equivalent variations or substitutions without departing from the spirit of the present invention, and these equivalent variations or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A numerical simulation method for mesoscopic-scale crack propagation behavior, characterized in that, It includes the following steps: Step S1: Prepare a test round bar specimen SLM Ti-6Al-4V using selective laser melting technology. After heat treatment at 800 °C, conduct a low-cycle fatigue test on the heat-treated round bar specimen SLM Ti-6Al-4V under strain control to obtain its mechanical properties. Then, obtain the cyclic stress-strain curve according to the Ramberg–Osgood equation and material-related mechanical parameters. The damage coefficient can be obtained from the damage evolution equation combined with test data; Step S2: Obtain the microstructure morphology information of the round bar specimen SLM Ti-6Al-4V material, and obtain the mesoscopic model according to the Voronoi algorithm with the help of MATLAB software; Step S3: Import the mesoscopic model obtained in Step S2 into ABAQUS software, establish a simulation model in ABAQUS according to the specimen size, and divide the simulation model according to the crack propagation region to obtain the mesoscopic model area and the non-mesoscopic model area; Step S4: Mesh the simulation model established in Step S3. To ensure the accuracy of the simulation results, use the transition mesh drawing method for meshing in the transition region between the mesoscopic model area and the non-mesoscopic model area; Step S5: Assign material properties: Input the mechanical property parameters and cyclic stress-strain curve of the round bar specimen SLM Ti-6Al-4V obtained in Step S1 into the material properties of ABAQUS software; Step S6: Set the analysis step: Adopt the static general analysis step; Step S7: Use Python scripts in ABAQUS to achieve the random distribution of elastic modulus and pores; Script 1: Random distribution of elastic modulus. First, make the elastic modulus follow a normal distribution, then randomly select several elastic moduli from the normal distribution, and finally randomly assign the selected several elastic moduli to each element of the model; Script 2: Random distribution of pores. First, randomly select the corresponding number of elements in the mesoscopic area, then establish a set of these elements, and finally kill this set using the birth and death element technology; Step S8: Set the boundary conditions in the simulation according to the actual load conditions of the test; Step S9: Write the USDFLD subroutine. First, use the Basquin–Coffin–Manson general method to predict the fatigue life of the material, then use the continuous damage mechanics model to calculate the damage value of each element in each cycle, accumulate the damage values of each cycle of the element. If the accumulated damage value exceeds the set threshold, finally use the element deletion technology in ABAQUS to delete the corresponding element to simulate the crack propagation; Step S10: Submit the job, view the simulated crack propagation results, analyze the crack evolution process and process the simulated result data to obtain the stress intensity factor at the crack tip and the crack propagation rate curve.

2. The numerical simulation method for mesoscopic scale crack propagation behavior according to claim 1, characterized in that In Step S1, the cyclic stress-strain curve is obtained according to the Ramberg–Osgood equation and material-related mechanical parameters. The Ramberg–Osgood expression is as follows: where k ′ and n ′ are the cyclic strength coefficient and cyclic strain hardening exponent respectively, and E is the cyclic elastic modulus.

3. A numerical simulation method for mesoscopic scale crack propagation behavior according to claim 1, characterized in that, The Basquin–Coffin–Manson general method expression described in step S9 is as follows: where σ ′ f and ε ′ f represent the fatigue strength coefficient and the fatigue ductility coefficient, and b and c are the fatigue strength exponent and the fatigue ductility exponent.

4. A numerical simulation method for mesoscopic-scale crack propagation behavior according to claim 1, characterized in that The fatigue damage expression calculated by the continuous damage mechanics model described in step S9 for each cycle is as follows: In the formula, p is the damage coefficient; Integrating the above formula gives the damage evolution equation:

Images