CN115740493A

CN115740493A - Finite element simulation method for selective electron beam melting temperature field and stress field

Info

Publication number: CN115740493A
Application number: CN202211347875.XA
Authority: CN
Inventors: 江静; 陈相均; 岳明楷; 李梅娥
Original assignee: Xian Jiaotong University
Current assignee: Xian Jiaotong University
Priority date: 2022-10-31
Filing date: 2022-10-31
Publication date: 2023-03-07

Abstract

The invention discloses a finite element simulation method of a melting temperature field and a stress field of an electron beam selection area, which develops a method for simulating the temperature field and the stress field of a forming process by a DFLUX subprogram for realizing a user-defined heat source, a UMATHT subprogram for realizing the switching of physical property parameters of materials from powder to entity, and a UEPACTIVATIONVOL subprogram for distinguishing powder and entity through an established heat-structure indirect coupling finite element model aiming at the melting process of a metal material electron beam selection area.

Description

Finite element simulation method for selective electron beam melting temperature field and stress field

Technical Field

The invention relates to the field of finite element simulation in a metal additive manufacturing process, in particular to a finite element simulation method for a melting temperature field and a stress field of an electron beam selection area.

Background

In recent years, the additive manufacturing technology which is rapidly developed is based on computer aided design, and is formed layer by layer in an accumulation mode according to a digital model file of a part, so that an opportunity is provided for preparing a complex part. After the research of recent decades, additive manufacturing technologies suitable for various occasions have appeared, taking metal powder bed additive manufacturing as an example, and the representative processes are: selective Laser Sintering (SLS), selective Laser Melting (SLM), selective Electron Beam Melting (SEBM), and the like. The SEBM has the advantages of high energy density, high energy absorption rate, high scanning speed, low residual stress, repeated use of powder and the like, so that the SEBM is rapidly distinguished from a plurality of technologies and becomes one of the most potential metal additive manufacturing technologies at present. However, the forming process has many problems, such as high instantaneous temperature, fast temperature change, difficult data collection and the like, which makes dynamic temperature and stress distribution difficult in the process of experimental research, and the final precision, surface quality and performance of the produced parts have an inseparable relationship with parameters of metal additive manufacturing process, including heat source temperature, heat source movement speed, material property and the like. Under the conditions of high experimental research cost and low efficiency, numerical simulation becomes a more appropriate and effective means for researching temperature distribution and stress evolution in the SEBM forming process at present, can directly and effectively acquire transient temperature distribution and stress distribution in the forming process, provides guidance for revealing the internal mechanism of SEBM forming and process test research, and has important significance in monitoring and detecting temperature and stress evolution in the metal additive manufacturing process and improving and optimizing part quality.

However, the simulation of the above process by means of finite element software mainly faces three technical difficulties: powder is spread layer by layer, a heat source moves and material physical property parameters are switched. The powder is spread layer by adopting a unit activation method, or a living and dead unit technology; heat source movement is typically implemented in writing a user subroutine DFLUX; both of these are easily implemented in finite element software, so relevant reports can be found in a large number of studies. The difficulty related to the switching of material physical property parameters is large. The physical property parameter is one of important and difficult to ignore factors in simulating the temperature and stress distribution condition in the metal additive manufacturing process, and comprises thermal property parameters such as thermal conductivity, specific heat capacity, density and the like and mechanical parameters such as thermal expansion coefficient, yield strength, poisson's ratio, elastic modulus and the like, and generally changes in a nonlinear way along with the change of temperature. In addition, the physical parameters are also influenced by the state of the material, for example, the powder material and the solid material have great difference in internal heat transfer mechanism, rigidity and strength, and the parameters directly influence the calculation result. However, the finite element method adopted by researchers at present is used for simulating the SEBM forming process, and is limited to the physical property parameters of a solid material which is constant or changes along with the temperature, the influence of powder is rarely considered, the thermal effect of electron beam forming of single-layer multi-channel and multi-layer multi-channel cannot be accurately reflected, and the later prediction of the residual stress is influenced.

Disclosure of Invention

Aiming at the problems in the prior art, the invention provides a finite element simulation method of a melting temperature field and a stress field of an electron beam selection area, so that the prediction of the temperature field and the stress field is realized, and the capital cost and the time cost of exploring the process parameters through experimental trial and error can be reduced.

The invention is realized by the following technical scheme:

a finite element simulation method of a melting temperature field and a stress field of an electron beam selection area comprises the following steps:

step 1, establishing a three-dimensional heat transfer calculation model for selective melting of metal electron beams, establishing a UMATHT subprogram which is associated with the three-dimensional heat transfer calculation model and is used for realizing the switching of thermal physical parameters from powder to solid materials, and establishing a DFLUX subprogram which is used for self-defining a heat source;

step 2, establishing a three-dimensional stress calculation model for selective melting of the metal electron beam, and establishing a UEPACTIVATIONVOL subprogram which is associated with the three-dimensional stress calculation model and is used for distinguishing powder and material mechanical parameters of a solid area;

step 3, when calculating a temperature field, sequentially acquiring the thermophysical property parameters of each grid node material by the UMATHT subprogram, acquiring the temperature of each network node according to the thermophysical property parameters, and acquiring the temperature distribution of the three-dimensional heat transfer calculation model according to the temperatures of all the network nodes;

and 4, when stress field calculation is carried out, applying temperature distribution as load to stress calculation of the three-dimensional heat transfer calculation model, sequentially acquiring the temperature of each unit node by the UEPACTIVATIONVOL subprogram, assigning corresponding mechanical parameters according to the material state attribute, obtaining the stress of the unit according to the mechanical parameters, and obtaining the stress distribution of the whole three-dimensional heat transfer calculation model according to the stress of each unit.

Preferably, the method for establishing the three-dimensional heat transfer calculation model in the step 1 is as follows:

creating a substrate and respective powder layers and imparting material properties;

assembling the substrate and each powder layer, setting heat transfer initial conditions, boundary conditions and a solver;

and respectively carrying out grid division on the powder layer and the substrate and setting unit types to obtain a three-dimensional heat transfer calculation model.

Preferably, the assembly method of the substrate and each powder layer is as follows:

the substrate and the powder layers and the adjacent powder layers are restrained by Tie contact, and the powder layers are activated layer by layer through Model Change to simulate the powder paving process.

Preferably, the initial and boundary conditions and solver types are as follows:

the electron beam selection area is melted in the vacuum cavity, the initial temperature of the three-dimensional heat transfer calculation model is the temperature in the cavity, only radiation heat dissipation exists on the top surface and the side surface of the three-dimensional heat transfer calculation model, and constant temperature boundary conditions are applied to the bottom surface of the substrate; the solver was set to "Heat Transfer".

Preferably, the method for mesh division and the cell type are set as follows:

dense grids are adopted at the top of the powder layer and the top of the substrate, loose grids are adopted at the bottom of the substrate, and transition grids are divided between the dense grids and the loose grids; the cell type is set to DC3D8.

Preferably, the establishment method of the umat subroutine is as follows:

setting MAT _ ID as a state variable of a material, wherein a node with MAT _ ID of 0 is endowed with a powder material attribute, a node with MAT _ ID of 1 is endowed with a solid material attribute, and MAT _ ID values of all powder areas are 0 in an initial state; and the UMATHT subroutine reads the MAT _ ID value of each node when the analysis step starts, judges whether the node meets the solidification condition or not, updates the MAT _ ID value of the node meeting the condition and endows the updated MAT _ ID value to a corresponding thermophysical property parameter of the solid material.

Preferably, the method for establishing the stress calculation model in step 2 is as follows:

assembling the substrate and each powder layer, and setting a boundary condition and a solver;

and respectively carrying out grid division on the powder layer and the substrate, and setting unit types to obtain a stress calculation model.

Preferably, the boundary conditions and solver types are as follows:

the substrate and the powder layer are freely placed in a vacuum cavity before the electron beam is loaded, the initial stress and the strain are both equal to 0, the degree of freedom of all nodes in the bottom surface of the substrate along the forming direction is set to be zero, and the translational degree of freedom of any two adjacent sides in the x or y direction is restricted; the solver selects "Static General".

Preferably, the grid division of the powder layer and the substrate is kept consistent with the temperature field calculation model, and the cell type is changed into C3D8R.

Preferably, the UEPACTIVATIONVOL subroutine is established as follows:

and applying a temperature field as a load to a corresponding stress model, sequentially judging whether each grid node meets the solidification condition or not according to a UEPACTIVATIONVOL subprogram, activating the entity units meeting the solidification condition, applying corresponding mechanical parameters to the solid materials, calculating the stress values of the entity units, and obtaining the stress distribution of the whole model according to the stress of each unit.

Compared with the prior art, the invention has the following beneficial technical effects:

the invention provides a finite element simulation method of a melting temperature field and a stress field of an electron beam selection area, which develops a DFLUX subprogram for realizing a user-defined heat source, a UMATHT subprogram for realizing the switching of material from powder to physical property parameters and a method for simulating the temperature field and the stress field of a forming process by a UEPACTIVATIONVOL subprogram for distinguishing the difference of mechanical properties of the powder and the physical material through an established heat-structure indirect coupling finite element model aiming at the melting process of the electron beam selection area of a metal material.

Drawings

FIG. 1 shows the process of selective melting and powder layer-by-layer powder spreading by electron beams according to the present invention.

FIG. 2 shows a physical model of the selective electron beam melting process and a dual ellipsoid heat source model used in the present invention.

FIG. 3 is a schematic diagram of the deformation of the present invention due to different temperature gradients.

FIG. 4 is a schematic diagram of a calculation model and a partial mesh division adopted in the selective melting process of the pure tungsten electron beam simulation of the present invention.

FIG. 5 is a flow chart of the UMATHT process of the present invention.

FIG. 6 is a temperature cloud chart of the pure tungsten electron beam selective melting single-layer multi-pass forming method at different moments solved by the calculation model of FIG. 4. NT11 denotes temperature in K.

Fig. 7 is a flowchart of UEPACTIVATIONVOL programming according to the present invention.

FIG. 8 is a graph of stress component distribution along the x-direction (scan line direction) centerline, along the y-direction (perpendicular to scan line direction) centerline, and along the z-direction (forming direction) centerline of the upper surface of the model calculated in FIG. 4 for multiple passes of selective melting of a single layer for a pure tungsten electron beam. S represents the Von Mises stress, and S11, S22, and S33 represent the stress components in the x, y, and z directions, in MPa.

Detailed Description

The present invention will now be described in further detail with reference to the attached drawings, which are illustrative, but not limiting, of the present invention.

Referring to fig. 1-7, a finite element simulation method of melting temperature field and stress field of a selected area of a metal electron beam comprises the following steps:

step 1, establishing a three-dimensional heat transfer calculation model aiming at selective melting of a metal electron beam, which specifically comprises the following processes:

creating a substrate and respective powder layers, the substrate imparting physical metallic material properties and the powder layers imparting metallic powder material properties, the material thermophysical parameters including density, thermal conductivity, specific heat, and the like as a function of temperature.

Assembling a substrate and each powder layer, wherein the substrate is in contact with the powder layers and adjacent powder layers through Tie to restrain the powder layers so as to carry out layer-by-layer activation simulation powder paving process on the powder layers through Model Change, and FIG. 1 is a schematic diagram for simulating an electron beam selective melting process;

and setting a solver, initial conditions and boundary conditions. Selecting Heat Transfer by a temperature field solver, and selecting a transient Heat Transfer type; the selective melting of the electron beam is carried out in a vacuum cavity, the initial temperature of the heat transfer calculation model is the temperature in the cavity, only radiation heat dissipation exists on the top surface and the side surface of the powder, and constant temperature boundary conditions are applied to the bottom surface of the substrate;

and respectively carrying out grid division and unit arrangement on the powder layer and the substrate. The top of the powder layer and the top of the substrate adopt dense grids to analyze the melting condition, the rest parts adopt loose grids, and transition grids are divided between the powder layer and the substrate; the unit type of the heat transfer calculation process is set to DC3D8;

step 2, constructing a DFLUX subprogram and a UMATHT subprogram which are associated with the three-dimensional heat transfer calculation model;

the DFLUX subroutine is used to simulate the moving heat source in the selective melting process of the electron beam, and define the functional relationship between the heat flow and the time and space by using built-in functions FLUX (1) and FLUX (2), so as to realize the self-definition of the radius, power, speed, scanning time, scanning strategy and the like of the heat source, referring to fig. 2, and the adopted heat source is a double-ellipsoid heat source model.

In addition, fig. 2 also shows a heat transfer model when the electron beam scans the shaping layer, the interior of the model follows a three-dimensional unsteady heat transfer law, and the heat conduction equation is as follows:

λ is thermal conductivity (W/(m.K)), and ρ is density (kg/m) ³ )、c _p Are specific heats (J/(kg. K)) which all vary with temperature, and q represents the heat flux absorbed from a moving heat source in J/m ³ . In order to simulate the temperature of the forming cabin, a constant temperature boundary condition is set on the base; in order to simulate the preheating of the powder layers, each powder layer defines a predefined field with a temperature of the preheating temperature when activated; the surfaces of the shaping layer other than the bottom surface are provided as radiation heat dissipation boundary conditions.

In addition, the temperature variation range in the SEBM forming process is large, the metal powder undergoes the transformation from a powder state to a liquid state and a solid state under the action of electron beams, and the difference of thermophysical property parameters of the material at different temperatures and states is large. Therefore, the calculation should take into account both the variation of the thermophysical property of the material with temperature and the variation of the thermophysical property of the material with state. The thermal physical property parameters changing along with the temperature can be realized in finite element software, the thermal physical property parameters changing along with the material state are realized by virtue of a UMATHT subprogram based on ABAQUS secondary development of the finite element software, built-in functions related to heat conductivity, specific heat and the like in UMATHT are realized by only endowing each material parameter to a corresponding function and calling the function. Referring to fig. 5, the umat subroutine is established as follows:

defining MAT _ ID as a state variable of a material, endowing a grid node with MAT _ ID of 0 with a powder material attribute, endowing a node with MAT _ ID of 1 with a solid material attribute, and endowing all powder areas with MAT _ ID values of 0 in an initial state, wherein during calculation of a temperature field, an UMATHT subprogram reads the MAT _ ID value of each grid node and judges whether the grid node meets a solidification condition (T is less than or equal to T) _m &dT/dt<0) For nodes meeting the condition, the MAT _ ID value is addedThe rows are updated and assigned their corresponding solid state material properties. Once the solid material property is endowed, when the temperature continues to drop until the room temperature, the thermophysical property parameter of the material only changes according to the solid material and does not change back to the powder state parameter, so that the unidirectional conversion of the material from the powder state to the liquid state to the solid state is realized. And giving corresponding thermophysical parameters according to the material state attribute so as to obtain the temperature of the grid node, and obtaining the temperature distribution of the whole three-dimensional heat transfer model according to the temperature of each grid node.

Step 3, establishing a stress calculation model aiming at selective melting of the metal electron beam, which specifically comprises the following processes:

creating a substrate and each powder layer, wherein the substrate endows the solid metal material with the property, the powder layers endow the metal powder material with the property, and the material mechanical parameters comprise Poisson's ratio, young modulus, thermal expansion coefficient and yield stress which change along with temperature;

the connection mode between the substrate and the powder layers and between the adjacent powder layers is unchanged, and the substrate and the powder layers are still connected by adopting 'Tie';

and setting a solver of stress calculation, initial conditions and boundary conditions. Setting a stress solver as "Static General"; because the substrate and the powder layer are freely placed in the vacuum cavity before the electron beam is loaded, the initial stress and the strain are both considered to be equal to 0, the degree of freedom of all nodes in the bottom surface of the substrate along the forming direction is set to be zero, and the translational degree of freedom of any two adjacent edges in the x or y direction is restrained;

and carrying out grid division on the stress calculation model and setting the unit type. The grid division is consistent with the temperature calculation process, and the unit type is changed into C3D8R;

step 4, building a UEPACTIVATIONVOL subprogram associated with the stress calculation model;

specifically, the young's modulus, the thermal expansion coefficient and the yield stress of the powder are different from those of solid tungsten before the powder reaches the melting point, although the powder also changes with the temperature, the influence is almost negligible compared with that of the solid tungsten, the mechanical property is almost zero from the preheating temperature to the impending solidification, the influence on deformation is negligible, the mechanical parameters of the tungsten powder can be regarded as zero values to participate in calculation, but the strength and the rigidity of the solid tungsten are very large, and the calculation process is not negligible, so that a uepactivionovol subprogram shown in fig. 7 is designed for distinguishing the mechanical parameters of materials on a melted area and an unmelted area on a powder layer.

In the initial stage, the whole forming layer is not activated, the UEPACTIVATIONVOL subprogram sequentially judges whether the temperature at the node is lower than the melting point of the material and the temperature change rate is less than zero (namely whether the solidification condition is met), if a certain unit node meets the condition, the unit is completely activated and is endowed with the entity material attribute. Similarly, the units that do not satisfy the coagulation condition are not activated and are in an unconstrained free state. And assigning corresponding mechanical parameters according to the material state attributes, thereby calculating the stress values of the materials and obtaining the stress distribution of the whole model according to the stress of each unit.

Referring to fig. 1, the first technical difficulty of simulating the selective melting process of the electron beam of the powder bed is the problem of powder spreading layer by layer, and fig. 1 shows the basic idea of the invention to solve the problem, and a calculation model containing a substrate and a powder layer is established in advance, and the assembly and the constraint are set. Before forming, making all powder layers not activated; after the forming is started, activating each powder layer by layer according to the set powder laying time, scanning the powder layers in a selective area by an electron beam in a powder laying gap, and forming the whole part by proper cooling solidification and circulation alternation.

Referring to fig. 3, the forming layer is deformed by the influence of temperature in the selective melting process of the electron beam, the electron beam reaches the surface of the sample, the powder layer absorbs heat, the temperature rises suddenly to expand, the bottom layer material must restrict the top part due to the continuity of the material, so that the top part is subjected to elastic pressure stress, when the yield strength of the material is reached, the top part is subjected to plastic deformation, and the hot top layer and even the whole test piece can bend away from the electron beam; after the beam exits, the top begins to cool and contract, also constrained by the underlying material, and the top is pulled, causing the specimen to bend toward the beam.

Fig. 4 shows a computational model for selective melting forming of a pure tungsten electron beam in this example, the model comprising a forming layer consisting of a pure tungsten substrate and a single layer of pure tungsten powder. The dimensions of the substrate were 6.0mm x 2.0 mm, the dimensions of the powder bed 6.0mm x 0.05mm, and the frame of the powder bed was an electron beam scanning area of 4.2mm x 0.05mm. The pitch of the scanning lines was 0.05mm, so that the number of scanning tracks on the forming layer was 21. And (4) carrying out mesh division of density transition on the model by comprehensively considering two aspects of calculation precision and efficiency. The cell size of the powder layer was set to 0.15mm x 0.025mm, the grid size of the solid tungsten substrate was set to 0.9mm x 0.15mm x 0.4mm, and the final grid model contained 15200 cells. And solving the temperature field and the stress in the forming process by adopting sequential coupling, wherein all grids adopt a DC3D8 grid type during the temperature field calculation, all grids adopt a hexahedral grid type with eight C3D8 nodes during the stress field calculation, and the grid division of the two processes is kept unchanged.

FIG. 6 shows the temperature distribution at different times during the forming process calculated using the model of FIG. 4, (a) is a temperature cloud when scanning to the midpoint of the first trace; (b) is a temperature cloud when scanning to the central point of the forming layer; (c) The temperature cloud picture is a temperature cloud picture when the middle point of the last trace is scanned, and the temperature peak value is gradually increased along with the continuous scanning due to the preheating of the front scanning trace; (d) Is a temperature cloud picture of the electron beam cooled to a certain moment after leaving; (e) A temperature cloud of the entire formed layer cooled to the preheat temperature.

Fig. 8 shows the residual stress component distribution curves of the upper surface of the model of fig. 4 along the x-direction (scan line direction) center line, along the y-direction (perpendicular to the scan line direction) center line, and along the z-direction (forming direction) center line. The stress component along the path in the x-direction is nearly equal to the peak stress component along the path in the y-direction.

The invention has the following beneficial technical effects:

firstly, the powder layer is activated layer by using 'Model Change', and the preheating of the powder bed is simulated by taking the radiation heat dissipation of the activated part into consideration and applying a predefined field, so that the selective melting process of the metal electron beam is more truly reduced.

Secondly, the thermophysical parameters and the mechanical parameters of the material directly influence the calculation result, and the accurate material parameters have important influence on the simulation result. According to the invention, by developing the UMATHT subprogram and the UEPACTIVATIONVOL subprogram of the user subprogram, the influence of material parameters under different temperatures and states on the temperature and the stress is considered in the temperature field calculation and the stress field calculation, so that the accuracy of simulation is improved.

In addition, in the selective melting process of the electron beams, the influence of forming parameters on results is crucial, and the influence of different process parameters on the selective melting thermal coupling behavior of the metal electron beams is conveniently researched by controlling heat source parameters through a DFLUX subprogram. Such as the radius of the electron beam, the scanning speed, the power of the heat source, the scanning distance, the absorption rate, the phase angle between layers, the length of the scanning line, the overlapping rate, the cooling time between layers and the like.

Finally, compared with experiments, the method can obtain the residual stress and deformation after the forming is finished, can extract the temperature change, melting condition, stress distribution and the like at each moment in the forming process, and provides great convenience for researching the heat-force behavior of the material.

The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims

1. A finite element simulation method for a melting temperature field and a stress field of an electron beam selection area is characterized by comprising the following steps:

2. A finite element simulation method of electron beam selective melting temperature field and stress field according to claim 1, wherein the three-dimensional heat transfer calculation model in step 1 is established by the following method:

assembling the substrate and each powder layer, setting heat transfer initial conditions, boundary conditions and setting a solver;

3. The finite element simulation method of electron beam selective melting temperature field and stress field of claim 2, the method for assembling the substrate and each powder layer is characterized by comprising the following steps:

4. A finite element simulation method of electron beam selective melting temperature and stress fields according to claim 2, wherein the initial and boundary conditions and solver types are as follows:

5. A finite element simulation method of electron beam selective melting temperature field and stress field according to claim 2, wherein the gridding method and element types are set as follows:

6. A finite element modeling method for selective electron beam melting temperature and stress fields as claimed in claim 1, wherein the umat subroutine is established as follows:

setting MAT _ ID as a state variable of a material, wherein a node with MAT _ ID of 0 is endowed with a powder material attribute, a node with MAT _ ID of 1 is endowed with a solid material attribute, and MAT _ ID values of all powder areas are 0 in an initial state; and the UMATHT subroutine reads the MAT _ ID value of each node when the analysis step is started, judges whether the node meets the solidification condition or not, updates the MAT _ ID value of the node meeting the condition and gives the MAT _ ID value to a corresponding solid material thermophysical property parameter.

7. A finite element simulation method of electron beam selective melting temperature field and stress field according to claim 1, wherein the stress calculation model in step 2 is established by the following method:

8. A finite element simulation method of melting temperature field and stress field of electron beam selection area established according to claim 7, wherein the boundary conditions and solver type are as follows:

9. A finite element simulation method of electron beam selective melting temperature field and stress field established according to claim 7, characterized in that the grid division of the powder layer and the substrate is kept consistent with the temperature field calculation model, and the cell type is changed to C3D8R.

10. A finite element simulation method of selective electron beam melting temperature and stress fields according to claim 1, wherein the UEPACTIVATIONVOL subroutine is established as follows: