CN112100702A - Additive material small crack propagation numerical simulation method considering microstructure - Google Patents

Additive material small crack propagation numerical simulation method considering microstructure Download PDF

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CN112100702A
CN112100702A CN202010940897.1A CN202010940897A CN112100702A CN 112100702 A CN112100702 A CN 112100702A CN 202010940897 A CN202010940897 A CN 202010940897A CN 112100702 A CN112100702 A CN 112100702A
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胡殿印
徐宇飞
毛建兴
王荣桥
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Abstract

The invention relates to a method for simulating a small crack propagation numerical value of an additive material by considering a microstructure, which comprises the following steps of: (1) establishing a flat piece model according to the size of a 'bone rod type' crack propagation test piece of the additive manufacturing material, partitioning the model according to whether crystal grains are introduced or not, and respectively endowing isotropic and anisotropic material properties; (2) carrying out grid division on the flat piece model, and carrying out grid local encryption on a crack expansion area in the middle of the model; (3) deriving a model geometry and grid attribute file, and combining MATLAB software to mathematically represent the crystal morphology and crystal orientation of the additive manufacturing material to complete microstructure modeling; (4) for the model prefabricated crack, adopting an expansion finite element method to simulate the small crack expansion behavior of the material, and determining the parameter value in the FATIGUE fracture criterion according to the actual condition of the material; (5) and (3) simulating the small crack propagation behavior of the material based on finite element software ABAQUS to obtain a crack propagation path and a crack propagation rate.

Description

Additive material small crack propagation numerical simulation method considering microstructure
Technical Field
The invention discloses a numerical simulation method for small crack propagation of an additive material by considering a microstructure, which is a numerical simulation method for small crack propagation of a special microstructure of an additive manufacturing material, including crystal morphology and crystal orientation influence, and belongs to the technical field of aerospace engines.
Background
The additive manufacturing is different from the traditional manufacturing process, the materials are formed by stacking from bottom to top layer by layer, and the additive manufacturing has the characteristics of quick processing, low production cost, short manufacturing period, high material utilization rate and the like, and has remarkable advantages in the aspect of processing complex structures. The structure can be further lightened and the cost can be reduced when the structure is applied to an aircraft engine.
The rapid melting and cooling solidification in the additive manufacturing process enable the formed material to have metallurgical defects such as unfused, air holes and inclusions, the crack initiation can be accelerated, and the crack propagation accounts for more than 90% of the fatigue life of the structure in three stages of fatigue failure. Research also shows that the structural fatigue crack propagation life is mostly consumed in a small crack stage which is greatly influenced by the microstructure, and the propagation mechanism of the structural fatigue crack propagation life is obviously different from that of the conventional long crack. Therefore, in the fatigue failure process of the additive manufacturing structural component, the influence of the microstructure must be considered, and the small crack propagation stage of the additive manufacturing structural component is researched intensively.
However, the additive manufacturing material is affected by high temperature gradient during processing, and the microstructure thereof is greatly different from that of the traditional manufacturing and forming. For example, the microstructure of the selective laser melting TC4 has coarse columnar original beta grains growing along the direction of the deposited layer, the inside of the grains is alpha + beta lamellar structure, and the material can show obvious anisotropy. Therefore, it becomes important how to consider the effect of a particular microstructure on the propagation of small cracks.
At present, the research on the small crack propagation of the additive manufacturing material is mainly based on tests, and the tests have the problems of high cost, difficulty in operation, low process repeatability and the like, so that the research on the numerical simulation method for the small crack propagation of the additive manufacturing material considering the microstructure is innovative.
Disclosure of Invention
The technical scheme of the invention is as follows: the method can consider the influence of the special microstructure of the additive manufacturing material, including crystal morphology and crystal orientation, realize effective simulation of the small crack propagation behavior of the additive manufacturing material, and lay a foundation for accurate prediction of the subsequent fatigue life of the additive manufacturing material.
The technical scheme of the invention is as follows: aiming at a special microstructure of an additive manufacturing material, an MATLAB script program is compiled through an INP data file of commercial finite element software ABAQUS to realize the characterization of the crystal morphology and the crystal orientation of the material, and a propagation finite element method is adopted to simulate the propagation behavior of a small crack to obtain a crack propagation path and a crack propagation rate.
The method comprises the following implementation steps:
the method comprises the steps of firstly, establishing a flat plate model by only reserving the minimum section part of the stepped shape of a test piece and combining the Saint-Venn principle to improve the calculation efficiency on the basis of the size of a 'bone-rod-shaped' crack propagation test piece made of an additive manufacturing material. In order to further reduce the number of grid cells and reduce the calculation amount, a model area is divided according to whether crystal grains are introduced, only a crack propagation area in the middle part of the model is defined as an area considering a microstructure, and anisotropic material properties are given to the crack propagation area; the remaining regions do not take into account microstructural effects, i.e. no grains need to be introduced, giving isotropic material properties.
And secondly, carrying out grid division on the established flat piece model, wherein the linear reduction integration unit is more accurate in displacement solving result, so that the unit type is an 8-node hexahedron linear reduction integration unit (C3D 8R). The model has high requirement on the calculation precision of the middle imported grain region, so that the grid units in the region need to be encrypted, the number of seed points on each side of the grid units is increased, a local precise grid is established, and the solving precision of the numerical simulation method on the small crack propagation behavior of the material is ensured; in addition, a unit transition area is arranged around the area, so that the size of the unit is transited from dense to sparse.
And thirdly, deriving an INP data file in ABAQUS finite element software based on the flat piece model after meshing, extracting three-dimensional coordinates of mesh unit nodes and serial numbers corresponding to 8 nodes of each unit, generating a corresponding number of crystal core points in an area needing to be led in the crystal grains according to information such as real crystal grain size and crystal morphology of the additive manufacturing material, and partitioning each mesh unit by using a Voronoi algorithm to finish crystal morphology characterization. And (2) writing an MATLAB script program according to the corresponding position coordinates and the strength of each position in the additive manufacturing material EBSD pole figure, wherein the program comprises the following steps:
the Euler angle method is selected to represent a sufficient number of randomly generated crystal orientations passing through the Euler angle
Figure BDA0002673604260000021
φ、
Figure BDA0002673604260000022
The rotating XYZ sample coordinate system can be expressed as g in hkl crystal coordinate system, with the expression:
Figure BDA0002673604260000023
wherein three crystal axes of the hkl crystal coordinate system are firstly rotated around the Z axis from the XYZ sample coordinate system
Figure BDA0002673604260000024
Angle, the rotated coordinate system being rotated again about the X-axis
Figure BDA0002673604260000025
Angle, finally rotation about Z axis
Figure BDA0002673604260000026
The angle is obtained. Then, the hkl crystal coordinate system can be expressed as g in the XYZ sample coordinate system-1I.e. the crystal orientation can be expressed as g-1。
Regarding the representation of the position coordinates of a certain crystal orientation in each projection plane in the XYZ sample coordinate system, taking the XOY plane as the projection plane as an example, the expression of the position coordinates (x, y) is as follows:
Figure BDA0002673604260000031
wherein, alpha is the included angle between the crystal direction and the Z axis, beta is the included angle between the crystal direction and the X axis, and gamma is the included angle between the crystal direction and the Y axis.
And screening out crystal orientations which meet the positions and the texture strength of the EBSD pole figures of the material according to the number of crystal grains required by the middle introduced crystal grain area, and endowing the crystal orientations to the crystal grains to finish the crystal orientation characterization. And importing the grid unit partition information obtained by running an MATLAB script program and the screened crystal orientation information into an INP file so as to update the established basic model.
Fourthly, prefabricating cracks for a flat piece model with introduced crystal grains, simulating the small crack propagation behavior of the material by adopting a finite element propagation method, wherein the analysis step adopts a direct cycle analysis step, the fracture criterion adopts a FATIGUE criterion, and the conditions for starting the crack propagation of an enrichment unit in a certain layer are as follows:
Figure BDA0002673604260000032
ΔG＝Gmax-Gmin
wherein G ismax、GminThe strain energy release rates corresponding to the maximum load and the minimum load during cyclic loading, c1、c2The number of cycles N required for the crack to start propagating is determined as a material parameter. Taking the value c, irrespective of crack initiation, due to the presence of pre-cracks1＝0、c 20. The propagation rate of the layer of enrichment units after the crack begins to propagate is as follows:
Figure BDA0002673604260000033
Gthresh＜Gmax＜Gpl
wherein G isthresh、GplRespectively satisfying the upper and lower limits of the strain energy release rate of Paris area, c3、c4Determining the propagation rate of the crack after the crack begins to propagate as a material parameter
Figure BDA0002673604260000034
c3、c4The value is calculated by C, m in the Paris formula of the material, and the expression is as follows:
Figure BDA0002673604260000035
Figure BDA0002673604260000036
wherein E is the elastic modulus of the material, and mu is the Poisson's ratio.
And fifthly, setting load and boundary conditions according to actual conditions, simulating the small crack propagation behavior of the additive manufacturing material by adopting an expansion finite element method of ABAQUS finite element software based on the established model, and acquiring a small crack propagation path and a crack propagation rate in a visualization module.
Compared with the prior art, the invention has the advantages that:
according to the method, the influence of the special microstructure of the additive manufacturing material is introduced into the numerical simulation of the small crack propagation of the material, and the microstructure modeling is completed through the characterization of the crystal morphology and the crystal orientation of the material, so that the simulation of the small crack propagation behavior of the additive manufacturing material is more accurate, and the related research deficiency is made up.
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FIG. 1 is a flow chart of an embodiment of a method for simulating a small crack propagation value of an additive material considering a microstructure according to the present invention;
FIG. 2 is a schematic diagram of a finite element model of additive material small crack propagation according to an embodiment;
FIG. 3(a) is a simulation result of a small crack propagation path of an additive material according to an embodiment;
fig. 3(b) is a simulation result of a small crack propagation rate of an additive material according to an embodiment.
Detailed Description
The technical scheme of the additive material small crack propagation numerical simulation method considering the microstructure is further explained below with reference to the accompanying drawings. The material to be investigated in this example was SLM (selective laser melting) TC4 alloy.
As shown in fig. 1, the specific implementation process of the present invention is as follows:
in the first step, a flat plate piece basic model with the size of 4.5mm by 1.5mm by 0.05mm is established for improving the calculation efficiency according to the size of an SLM TC4 material 'bone bar type' crack propagation test piece. The width of the basic model only keeps the minimum section part of the test piece in the step shape, namely 1.5 mm; the Saint Vietnam principle is combined, and the length of the model is only kept 4.5 mm; the model is changed from a 3-dimensional model to a 2.5-dimensional model, namely, the thickness of the model is reduced, and the dimension in the direction is only kept 0.05 mm. In order to further reduce the number of grid cells and the calculation amount, the model area is divided according to whether the crystal grains are introduced, only the area 1.0mm x 0.2mm in the middle of the model is defined as the area considering the microstructure, and anisotropic material properties are given to the area, as shown in table 1; the remaining regions do not take into account microstructural effects, i.e. no grains need to be introduced, giving isotropic material properties, as shown in table 2.
TABLE 1 SLM TC4 Material Anisotropic elastic constant
Figure BDA0002673604260000041
Figure BDA0002673604260000051
TABLE 2 SLM TC4 Material Isotropic Material Properties
Figure BDA0002673604260000052
And secondly, carrying out grid division on the established flat piece model, wherein the linear reduction integration unit is more accurate in displacement solving result, so that the unit type is an 8-node hexahedron linear reduction integration unit (C3D 8R). The model has high requirement on the calculation accuracy of the middle imported grain region, so that the grid cells in the region need to be encrypted, the number of seed points on each side of the grid cells is increased, a local precise grid is established, the cell size is finally determined to be 0.005mm through simulation verification, and the calculation amount is reduced as much as possible on the premise of ensuring the solving accuracy of the numerical simulation method on the small crack propagation of the material; in addition, a cell transition region is arranged around the region, so that the cell size is transited from dense to sparse, and 12524 grid cells are formed by combining models.
And thirdly, deriving an INP data file of ABAQUS finite element software based on the flat piece model after the meshing is finished, and extracting the three-dimensional coordinates of the mesh unit nodes and the serial numbers corresponding to 8 nodes of each unit. The microstructure of the SLM TC4 material has columnar original beta grains growing along the direction of a deposited layer, the grains are in an alpha cluster-like structure, and the same alpha cluster has the same or similar crystal orientation, so that the alpha cluster is used as a basic unit for characterization of crystal morphology. Based on the above, a corresponding number of crystal nucleus points are generated in the region of 1.0mm x 0.2mm in the middle of the crystal grains to be introduced, 8000 grid units are partitioned by using a Voronoi algorithm, and the crystal morphology characterization is completed. Writing an MATLAB script program by taking the corresponding position coordinates and the intensity of each position in the SLM TC4 material EBSD pole figure as the basis, wherein the calculation steps of the program comprise:
the Euler angle method is selected to represent a sufficient number of randomly generated crystal orientations passing through the Euler angle
Figure BDA0002673604260000053
φ、
Figure BDA0002673604260000054
The rotating XYZ sample coordinate system can be expressed as g in hkl crystal coordinate system, with the expression:
Figure BDA0002673604260000055
wherein three crystal axes of the hkl crystal coordinate system are firstly rotated around the Z axis from the XYZ sample coordinate system
Figure BDA0002673604260000056
Angle, the rotated coordinate system being rotated again about the X-axis
Figure BDA0002673604260000057
Angle, finally rotation about Z axis
Figure BDA0002673604260000058
The angle is obtained. Then, the hkl crystal coordinate system can be expressed as g in the XYZ sample coordinate system-1I.e. the crystal orientation can be expressed as g-1。
Regarding the representation of the position coordinates of a certain crystal orientation in each projection plane in the XYZ sample coordinate system, taking the XOY plane as the projection plane as an example, the expression of the position coordinates (x, y) is as follows:
Figure BDA0002673604260000061
wherein, alpha is the included angle between the crystal direction and the Z axis, beta is the included angle between the crystal direction and the X axis, and gamma is the included angle between the crystal direction and the Y axis.
And screening out crystal orientations which meet the positions and the texture strength of the EBSD pole figure of the SLM TC4 material according to the number of crystal grains required by the area of the middle introduced crystal grains, and endowing the crystal orientations to the crystal grains to finish the crystal orientation characterization. And importing the grid unit partition information obtained by running an MATLAB script program and the screened crystal orientation information into an INP data file so as to update the established basic model.
The model was created as shown in figure 2. The middle part displays the whole situation of the basic model of the flat piece; the right side of the figure shows the area after the crystal grains are led in the middle in an enlarged manner, and unit areas with different colors and gray levels represent different crystal grains; the left side of the figure shows the crystal orientation of the model after screening by the MATLAB script program.
And fourthly, prefabricating a crack with the length of 0.1mm for a flat piece model with the introduced crystal grains, simulating the small crack propagation behavior of the material by adopting a finite element expansion method, wherein the analysis step adopts a direct cyclic analysis step, the increment of the analysis step is 0.01, and the initial value of the Fourier series is 24. The fracture criterion is FATIGUE criterion, and the condition that the crack of a certain layer of enrichment unit begins to expand is as follows:
Figure BDA0002673604260000062
ΔG＝Gmax-Gmin
wherein G ismax、GminThe strain energy release rates corresponding to the maximum load and the minimum load during cyclic loading, c1、c2The number of cycles N required for the crack to start propagating is determined as a material parameter. Taking the value c, irrespective of crack initiation, due to the presence of pre-cracks1＝0、c 20. The propagation rate of the layer of enrichment units after the crack begins to propagate is as follows:
Figure BDA0002673604260000063
Gthresh＜Gmax＜Gpl
wherein G isthresh、GplRespectively satisfying the upper and lower limits of the strain energy release rate of Paris area, c3、c4Determining the propagation rate of the crack after the crack begins to propagate as a material parameter
Figure BDA0002673604260000064
c3、c4The value is calculated by C, m in the Paris formula of the material, and the expression is as follows:
Figure BDA0002673604260000065
Figure BDA0002673604260000071
wherein E is the elastic modulus of the material, and mu is the Poisson's ratio. The SLM TC4 material Paris formula has C corresponding to a value of 3.311 × 10-8M corresponds to a value of 2.99, E115 GPa, μ 0.324, and E' 128.488GPa in a plane strain state. From this, c can be obtained3＝1.495，c4＝4.70663×10-5。
Fifthly, setting boundaries and load conditions according to actual conditions, wherein the boundary conditions of the model are that the left side is hinged, the right side is circularly loaded, and the maximum stress sigma of the circular load ismax380MPa, stress ratio R of 0.06 and loading frequency of 1 Hz. Based on the established model, simulating the small crack propagation behavior of the SLM TC4 material by adopting an ABAQUS finite element software propagation finite element method, and acquiring a small crack propagation path and a crack propagation rate in a visualization module. The simulation results are shown in fig. 3.
The above examples are provided only for the purpose of describing the present invention, and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications can be made without departing from the spirit and principles of the invention, and are intended to be within the scope of the invention.

Claims (4)

1. A method for simulating a small crack propagation value of an additive material by considering a microstructure is characterized by comprising the following steps:
step (1): establishing a flat piece model according to the size of a 'bone rod type' crack propagation test piece of the additive manufacturing material, partitioning the model according to whether crystal grains are introduced or not, and respectively endowing isotropic and anisotropic material properties; the bone-bar-type crack propagation test piece is a test piece used in an in-situ fatigue test of an additive manufacturing material, and a flat piece model is established based on the Saint-Venn principle on the basis of the size of the test piece, so that the calculation efficiency can be improved on the premise of ensuring the accuracy of a result compared with a complete bone-bar-type crack propagation model; the step of partitioning the model according to whether the grains are introduced or not refers to that the microstructure modeling is only carried out in the crack expansion area in the middle of the model, the influence of the microstructure is not considered in the rest areas, and compared with the mode that the grains are introduced into the whole model, the subsequent calculation amount can be reduced; the respectively endowed material properties are that anisotropic material properties are endowed to the region in which the crystal grains are introduced, and isotropic material properties are endowed to the rest regions;
step (2): carrying out mesh division on the flat piece model established in the step (1), and carrying out local mesh unit encryption on the middle introduced grain region; the grid division refers to directly distributing and dividing the grid for each side aiming at the flat piece model, and establishing an integral rough grid, wherein the unit type is an 8-node hexahedron linear reduction integral unit C3D 8R; the grid cell encryption is to increase the number of seed points on each side of a grain region led into the middle of the grain region, establish a local precise grid, and set a cell transition region around the region to ensure that the cell size is transited from dense to sparse so as to ensure the solving precision of the numerical simulation method on the small crack propagation behavior of the material;
and (3): deriving an INP file in ABAQUS finite element software based on the flat piece model after the gridding division is completed, and characterizing the crystal morphology and the crystal orientation of the additive manufacturing material by using MATLAB software to complete the microstructure modeling; the step of exporting the INP file in the ABAQUS finite element software is to extract the three-dimensional coordinates of the grid unit nodes and the serial numbers corresponding to 8 nodes of each unit; the characterization of the crystal morphology of the additive manufacturing material by using MATLAB software refers to the generation of a corresponding number of crystal nucleus points in an area in which crystal grains need to be introduced according to the actual crystal grain size, crystal morphology and material texture information of the additive manufacturing material, and the division of grid units of the additive manufacturing material by using a Voronoi algorithm, wherein the units in the same area form one crystal grain; the characterization of the crystal orientation of the additive manufacturing material by using MATLAB software refers to extracting position coordinates and intensity of each position in an electron back scattering diffraction EBSD polar diagram, screening out qualified orientation from a sufficient number of randomly generated crystal orientations on the basis of the position coordinates and the intensity, and endowing the qualified orientation to each crystal grain; the step of finishing the microstructure modeling is to run an MATLAB script program, introduce the obtained grid unit partition information and the crystal orientation information into an INP file and update the established basic model according to the grid unit partition information and the crystal orientation information;
and (4): prefabricating cracks for the updated flat piece model in the step (3), simulating the small crack propagation behavior of the material by adopting a finite element propagation method, and determining each relevant parameter value in the FATIGUE fracture criterion according to the actual condition of the material; the updated flat piece model is a model after the microstructure modeling is completed, and comprises the representation of the crystal morphology and the crystal orientation in the middle area; the prefabricated crack refers to an initial crack which needs to be inserted into a flat piece model for a certain length when a FATIGUE fracture criterion is used;
and (5): simulating the small crack propagation behavior of the additive manufacturing material based on ABAQUS finite element software to obtain a crack propagation path and a crack propagation rate; the crack propagation path is acquired by directly displaying the options of PHILSM and STATUS SXFEM in ABAQUS software field variable output in a visualization module; the crack growth rate is obtained by obtaining the curve relation between the crack growth rate da/dN and the crack length a through a secant method based on the simulation result.
2. The method for simulating the small crack propagation value of the additive material considering the microstructure according to claim 1, wherein:
the characterization of the material crystal morphology in the step (3) is based on the real microstructure of the material, and an MATLAB script program is further compiled by extracting the grid unit information in the INP data file, and specifically comprises the following steps:
the Euler angle method is selected to represent a sufficient number of randomly generated crystal orientations passing through the Euler angle
Figure FDA0002673604250000021
φ、
Figure FDA0002673604250000022
The rotating XYZ sample coordinate system can be expressed as g in hkl crystal coordinate system, with the expression:
Figure FDA0002673604250000023
wherein three crystal axes of the hkl crystal coordinate system are firstly rotated around the Z axis from the XYZ sample coordinate system
Figure FDA0002673604250000024
Angle, the rotated coordinate system being rotated again about the X-axis
Figure FDA0002673604250000027
Angle, finally rotation about Z axis
Figure FDA0002673604250000025
Obtaining an angle; then, the hkl crystal coordinate system is expressed as g in the XYZ sample coordinate system-1I.e. the crystal orientation is expressed as g-1；
Regarding the representation of the position coordinates of a certain crystal orientation in each projection plane in the XYZ sample coordinate system, taking the XOY plane as the projection plane as an example, the expression of the position coordinates (x, y) is as follows:
Figure FDA0002673604250000026
wherein, alpha is the included angle between the crystal direction and the Z axis, beta is the included angle between the crystal direction and the X axis, and gamma is the included angle between the crystal direction and the Y axis;
and screening out crystal orientations which meet the positions and the texture strength of the EBSD pole figures of the material according to the number of crystal grains required by the middle introduced crystal grain area, and endowing the crystal orientations to the crystal grains to finish the crystal orientation characterization.
3. The method for simulating the small crack propagation value of the additive material considering the microstructure according to claim 1, wherein:
the characterization of the material crystal orientation in the step (3) is based on the material texture of the EBSD pole figure, and the random orientation is screened by writing an MATLAB script program, so as to obtain the crystal orientation according with the position coordinates and the strength at each position.
4. The method for simulating the small crack propagation value of the additive material considering the microstructure according to claim 1, wherein:
in the step 4, cracks are prefabricated for a flat piece model with the introduced crystal grains, the expansion finite element method is adopted to simulate the small crack expansion behavior of the material, the analysis step adopts a direct circulation analysis step, the fracture criterion adopts a FATIGUE criterion, and the conditions for starting the crack expansion of a certain layer of enrichment units are as follows:
Figure FDA0002673604250000031
ΔG＝Gmax-Gmin
wherein G ismax、GminThe strain energy release rates corresponding to the maximum load and the minimum load during cyclic loading, c1、c2Determining the number of cycles N required for the crack to start to propagate as a material parameter; taking the value c, irrespective of crack initiation, due to the presence of pre-cracks1＝0、c20; the propagation rate of the layer of enrichment units after the crack begins to propagate is as follows:
Figure FDA0002673604250000032
Gthresh＜Gmax＜Gpl
wherein G isthresh、GplRespectively satisfying the upper and lower limits of the strain energy release rate of Paris area, c3、c4Determining the propagation rate of the crack after the crack begins to propagate as a material parameter
Figure FDA0002673604250000033
c3、c4The value is calculated by C, m in the Paris formula of the material per se, and the value is obtainedThe expression is as follows:
Figure FDA0002673604250000034
Figure FDA0002673604250000035
wherein E is the elastic modulus of the material, and mu is the Poisson's ratio.
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CN114065553A (en) * 2021-12-31 2022-02-18 华侨大学 Method for establishing molecular dynamics model of anisotropic single crystal material
CN114186461A (en) * 2021-12-08 2022-03-15 北京理工大学 Multi-axial fatigue life prediction method
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CN117150858A (en) * 2023-09-06 2023-12-01 天津大学 Crack-containing continuous fiber reinforced resin matrix composite three-dimensional finite element modeling method
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