CN106484978A - A kind of method for building up of anisotropy this structure of linear elasticity based on translation gliding mechanism - Google Patents
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Abstract
The invention discloses the present invention relates to a kind of method for building up of anisotropy this structure of linear elasticity based on translation gliding mechanism, belonging to material mechanical performance finite element numerical calculating field.The method first sets up FEM mesh, and determines boundary condition and loading environment；Using project method, the transformed matrix between the coordinate system of solving finite element grid model and die coordinates system；By tensor operation, obtain monocrystal elastic stiffness matrix and the Schmidt's factor under FEM mesh coordinate system；Boundary condition according to setting and loading environment are loaded；According to the Hill Hutchinson polycrystal theory of elastic-plastic deformation, solve the instantaneous stiffness matrix in the plastic stage for the crystal grain, instantaneous stiffness matrix is replaced monocrystal elastic stiffness matrix, repeating to load the maximum load step number until setting, obtaining anisotropy this structure of linear elasticity that instantaneous stiffness matrix is crystal grain.
Description
Technical Field
The invention relates to a method for establishing an anisotropic linear elastic constitutive structure based on a crystal slip mechanism, and belongs to the field of material mechanical property finite element numerical calculation.
Background
In the aspect of simulating macro and micro mechanical properties of a polycrystalline material by using a modeling method based on a real microstructure, the selection of a material constitutive model and the parameter acquisition have decisive influence on a simulation result, and the method is also a weak link to be solved urgently. In the research of material texture at home and abroad, an isotropic texture model, namely a mesoscopic phase texture model is usually considered by a description method of a phenomenological phenomenon. The method for obtaining the phase structure is mainly that the microscopic deformation characteristics of the material are similar to those of a macroscopic structure, and then the overall performance of the material with the uniform organization structure is endowed to the phase; for each constituent phase in a multi-phase material, the macroscopic properties of a single-phase material having similar composition are used instead. The large commercial finite element software LS-DYNA is general explicit dynamic analysis software and has higher calculation reliability in the field of engineering application. The method has the explicit/implicit solving function, and the solving is stable; meanwhile, the method has the functions of nonlinear dynamic analysis and static analysis under the condition of complex boundary loading. The post-processing function can realize the visualization of various internal solution parameters, but the application of the post-processing function is mainly based on phenomenology at present, and the intrinsic mechanism of material deformation is rarely considered.
However, in order to take into account the internal physical mechanisms existing during the deformation of the material, the isotropic phase structure model has not been able to meet the requirements, and therefore the established model has been gradually developed into a grain structure model taking into account the slip mechanism, i.e. into a crystal plasticity description method from a phenomenological description method. The elastic-plastic self-consistent simulation method for researching the internal mechanism of material loading deformation is widely applied, and can be used for simulating the macroscopic stress-strain response of the whole material; researching the elastic-plastic transformation process of the material and the fitting of the characterization parameters in the process; fitting a lattice evolution process; texture evolution during deformation, etc. The main theoretical basis and assumptions of the self-consistent simulation method are: (1) adopting a Hill-Hutchinson polycrystalline elastic-plastic deformation mechanism, a Voc é hardening law and a hardening coefficient matrix; (2) the realization method of the anisotropy of the crystal grains is that the crystal grains are arranged into an ellipsoid with an anisotropic elastic constant matrix, and each crystal grain is endowed with a slippage system and characteristic parameters corresponding to the crystal structure type of the crystal grain; (3) the interaction between crystal grains is to establish an interaction function between each crystal and an assumed homogeneous matrix through an elastic-plastic Eshelby tensor; (4) and (3) adopting an incremental loading mode, wherein each loading step is small deformation loading, namely the stress-strain relation is considered as instantaneous linear elasticity.
The method not only considers the actual orientation of crystals in the polycrystalline material, but also considers different crystal structure types of multiphase materials, plastic deformation slip mechanisms, hardening effects, orientation changes and the like. However, it has some drawbacks, such as: the data corresponding to the in-situ stretching synchrotron radiation X-ray diffraction, neutron diffraction and other experiments need to be obtained, and the experiments have long period and high cost; the interaction is realized in the algorithm through the 'limit tensor', visualization cannot be carried out, and the interaction relation between adjacent grains in a real microstructure cannot be considered; the loading boundary conditions that can be set are relatively simple, typically uniaxial tension or compression at a rate governed by stress or strain, etc.
Disclosure of Invention
The invention aims to provide a method for establishing an anisotropic linear elastic constitutive structure based on a crystal slippage mechanism, which continues a theoretical mechanism for describing crystal plastic deformation adopted in a self-consistent model, is combined with a finite element method, not only considers the microstructure morphology of a material, but also realizes the interaction between crystal grains by using the units and nodularization of a finite element grid, makes up the defects in the self-consistent model, gives full play to the advantages of finite element simulation calculation, and realizes complex boundary loading conditions and various visual post-processing operations.
The purpose of the invention is realized by the following technical scheme:
a method for establishing an anisotropic linear elastic constitutive based on a crystal slip mechanism, the method comprising the following steps:
the method comprises the following steps:
establishing a finite element mesh model of the grain structure by adopting a finite element mesh subdivision method based on a grain structure image of the anisotropic linear elastic constitutive material to be solved, and determining the boundary condition and the loading condition of the finite element mesh model;
the loading conditions comprise a load and a maximum loading step number, wherein the initial loading step number is 0;
step two:
adopting a projection operation method, and according to intrinsic parameters of grain structures, initial stress strain state components and initial Euler angles of grain orientationsSolving for grain orientation Euler angle increments And adding the Euler angle increment and the initial Euler angle to obtain the Euler angle after the crystal grain orientation changes due to strainObtaining a transformation matrix between a coordinate system of the finite element grid model and a crystal grain coordinate system according to the changed Euler angles;
wherein the intrinsic parameters comprise crystal structure type parameters, single crystal elastic rigidity matrix and intra-grain slippage system parameters;
the slip system parameters comprise the name of a slip system, the number of equivalent slip systems and the Voc hardening index of the slip system; the Voc hardening index includes the critical value of the shear stress tau at which the slip train starts0Slip is the stress increase τ from start-up to no further increase in cumulative shear strain1Initial hardening rate of slip system0And saturated cure rate of slip system [ theta ]1；
The crystal grainThe Euler angle of orientation is defined by Bunge's method, i.e. the crystal grain coordinate system is rotated around its z-axis in the xy-planeAn angle; then, the lens rotates around the x axis through a phi angle in the yz plane; finally, rotate through the xy plane again around the z axisThe angles are finally completely overlapped with a finite element mesh model coordinate system, thereby obtaining three euler angles of spatial orientation of each crystal grainInitial Euler angle of grain orientationMeasured by an Electron Back Scattering Diffraction (EBSD) experiment;
the stress-strain state components are respectively according to sigmaxx，σyy，σzz，σyz，σxz，σxyAndxx，yy，zz，yz，xz，xygiven the order of (a), the initial values are all set to 0;
wherein, the sigmaxx，σyyAnd σzzRespectively representing the normal stress along the directions of an X axis, a Y axis and a Z axis in the space to which the crystal grains are subjected in the coordinate system of the finite element mesh model in the step one;
the above-mentionedxx，yyAndzzrespectively representing positive strain along the directions of an X axis, a Y axis and a Z axis in the space to which the crystal grains are subjected in the coordinate system of the finite element mesh model in the step one;
the sigmayzRepresenting the shear stress parallel to the X axis in the normal plane of the Y axis in the space suffered by the crystal grains in the coordinate system of the finite element mesh model in the step one;
the sigmaxzRepresenting the shear stress parallel to the Z axis in the X-axis normal plane in the space suffered by the crystal grains in the coordinate system of the finite element mesh model in the step one;
the sigmaxyRepresenting the shear stress parallel to the Y axis in the X-axis normal plane in the space to which the crystal grains are subjected in the coordinate system of the finite element mesh model in the step one;
the above-mentionedyzRepresenting the shear strain of a micro line segment included angle in the Y-axis and Z-axis directions in the space suffered by the crystal grain in the coordinate system of the finite element grid model in the step one;
the above-mentionedxzRepresenting the shear strain of a micro line segment included angle in the X-axis and Z-axis directions in the space suffered by the crystal grain in the coordinate system of the finite element grid model in the step one;
the above-mentionedxyRepresenting the shear strain of a micro line segment included angle in the X-axis and Y-axis directions in the space suffered by the crystal grain in the coordinate system of the finite element grid model in the step one;
step three:
based on the transformation matrix in the second step, obtaining a single crystal elastic stiffness matrix and a Schmidt factor alpha under a finite element grid model coordinate system through tensor operation, wherein alpha is cos lambda cos phi, phi is an included angle between a slip plane and a central axis of an external force F, and lambda is an included angle between a slip direction and the external force F;
step four:
determining the Euler angle incrementWhether or not it is (0, 0, 0), if Entering the step five; if it isEntering a sixth step;
step five:
loading the current finite element grid model according to the boundary conditions and the loading load of the finite element grid model in the step one, and then calculating by adopting a finite element calculation method to obtain the stress strain state component of the loaded crystal grain aiming at the single crystal elastic stiffness matrix under the coordinate system of the current finite element grid model; replacing the initial stress-strain state component in the second step with the stress-strain state component of the loaded crystal grain, and repeating the second step to the fourth step; wherein, after each loading, the number of loading steps is increased by one; step six:
judging whether the total number n of potential to-be-started and started slip systems in the crystal grains is larger than zero or not; if n is 0, repeating the step five; if n is more than 0, entering a seventh step;
method for determining potential to actuate and actuated slip systems:
if it isThe slip is marked as potentially going on ifThe slip is marked as actuated; wherein σcIndicating the current stress value of the crystal grain in which any slip system is located,representing the critical slitting stress value of the ith slip system, αi(ii) a schmidt factor representing the ith slip series;
step seven:
according to the Hill-Hutchinson polycrystalline elastic-plastic deformation theory, solving a basis vector matrix of n slip system strain linear equation sets; then according to the basis vector matrix, solving the shear quantity distributed to each slip system, and further obtaining an instantaneous rigidity matrix of the crystal grains in a plasticity stage;
step eight:
judging whether the current loading step number is equal to the set maximum loading step number or not, if so, obtaining an instantaneous stiffness matrix which is the anisotropic linear elasticity constitutive structure of the crystal grains; and if the instantaneous stiffness matrix is smaller than the maximum loading step number, replacing the single crystal elastic stiffness matrix in the step II with the instantaneous stiffness matrix in the step III, and repeating the step II to the step III until the loading step number is equal to the maximum loading step number set in the step I.
Advantageous effects
(1) The method of the invention continues the theoretical mechanism of describing crystal plastic deformation adopted in the self-consistent model, and is combined with the finite element method; by adopting the grid model based on the grain structure, the microstructure morphology of the material is considered, and the interaction between grains is realized by using the units and the nodulation of the finite element grid, so that the defects in the self-consistent model are overcome.
(2) The method utilizes a restart technology in a finite element solver, and carries out incremental step restart loading based on a finite element grid model established by a grain structure under certain boundary conditions and loading conditions, and each loading step inherits the stress-strain state of each unit and node when the previous loading step is finished, so that step incremental loading is realized; the orientation of each crystal grain in the polycrystalline material is reflected by adopting an anisotropic linear elastic constitutive model provided in finite element solving software, and simultaneously, the stress strain state of the crystal grain after each step of loading can be realized by combining a crystal plastic deformation theory, so that the constitutive parameters (namely instantaneous modulus) of a plastic deformation mechanism layer are updated and improved in real time; the advantages of finite element simulation calculation are fully exerted, and complex boundary loading conditions and various visual post-processing operations are realized.
(3) The method can further consider the real microstructure morphology of the material, and develops the phase structure model into a grain structure model, so that the internal physical mechanism existing in the material deformation process can be further considered; by adopting the method provided by the invention, the anisotropic linear elastic constitutive of each crystal grain in the crystal grain structure finite element grid model which is continuously changed along with the loading process can be obtained through calculation, and a more accurate research method is provided for reproducing the material structure evolution process, analyzing the local stress state of the material, predicting the material failure form and the like.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic diagram of a coordinate system (left) of the finite element mesh model of the grain structure and a coordinate system (right) of the grain;
FIG. 3 is a schematic diagram showing the meaning of the Voc hardening index in example 1;
fig. 4 is a diagram illustrating schmitt factor definition as described in example 1.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments, but is not limited thereto.
Example 1
As shown in fig. 1, a method for establishing an anisotropic linear elastic constitutive based on a crystal slip mechanism includes the following steps:
the method comprises the following steps:
establishing a finite element mesh model of the grain structure by adopting a finite element mesh subdivision method based on a grain structure image of the anisotropic linear elastic constitutive material to be solved and based on a finite element software LS-DYNA, and determining the boundary condition and the loading condition of the finite element mesh model;
the loading conditions comprise load and loading step number, wherein the initial loading step number is 0;
the coordinate system of the finite element mesh model of the grain structure and the coordinate system schematic diagram of the grains are shown in FIG. 2;
step two:
reading intrinsic parameters of grain structure, initial stress strain state component and initial Euler angle of grain orientation by using Fortran programAnd according to the projection relation of the strain increment, the Euler angle increment is calculated by the strain increment of the crystal grain according to the following formula:
and adding the Euler angle increment and the initial Euler angle to obtain the Euler angle after the crystal grain orientation changes due to strainObtaining a transformation matrix R between a coordinate system OXYZ of the finite element grid model and a crystal grain coordinate system OXYZ according to the changed Euler angles;
wherein the intrinsic parameters comprise crystal structure type parameters, single crystal elastic rigidity matrix and intra-grain slippage system parameters;
the crystal structure type parameters comprise crystal structure type and axial ratio c/a of unit cell; the crystal structure type is represented by ihcp, and the ihcp is 1 and is represented by a close-packed hexagonal crystal structure (HCP), and the crystal orientation index and the crystal plane index of the crystal structure type are represented by four coordinates; ihcp ═ 0 is expressed as CUBIC crystal structure (CUBIC), with the crystal orientation index and the plane index being plotted in three coordinates; the axial ratio c/a of the unit cell is represented by rca, taking alpha and beta phases in the TC6 titanium alloy as an example, and rca is 1.597 for the alpha phase; for the β phase, rca ═ 1.0.
The single crystal elastic stiffness matrix Cij6 x 6 matrix in GPa with symmetry C for a close-packed hexagonal crystal structure11＝C22，C13＝C23，C44＝C55＝C66(ii) a And C for cubic crystal structure11＝C22＝C33，C12＝C13＝C23，C44＝C55＝C66Wherein, the α phase in the TC6 titanium alloy has the crystal structure type parameters of hexagonal close-packed (HCP), the crystal structure type ihcp is 1, the axial ratio of unit cell is rca to 1.597, and the elastic stiffness matrix of the single crystal is as follows:
for the beta phase in the TC6 titanium alloy, the crystal structure type parameters are as follows: CUBIC, crystal structure type ihcp 1, unit cell axial ratio rca 1.0, single crystal elastic stiffness matrix:
the slip system parameters comprise the name of a slip system, the number of equivalent slip systems and the Voc hardening index of the slip system; all slip systems to be considered in the grain, including the total number of slip systems in the file, the total number of slip systems to be read (Num _ slip);
name of slip system: four slip systems are common for the close-packed hexagonal crystal structure, respectively: the {0002} <11-20> basal plane slip system, {10-10} <11-20> cylindrical plane slip system, {10-11} <11-20> first order cone slip system and {10-11} <11-23> second order cone slip system, the common slip systems for body-centered cubic crystal structures are three: {1-10} <111>, {11-2} <111> and {12-3} <111 >;
the number of equivalent slip systems is expressed by (m _ slip);
voc hardening index of the slip system: which includes the critical value of the slitting stress tau for the start of the slip system0Slip is the stress increase τ from start-up to no further increase in cumulative shear strain1Initial hardening rate of slip system0Slip system saturation hardening ratio theta1The coefficient of interaction h between the slip systems to be readij(i ≠ j denotes a self-hardening coefficient, and i ≠ j denotes mutual hardening); the specific meaning is represented by a stress-strain curve, as shown in fig. 3; sequentially marking all equivalent slip systems of all slip systems needing to be read in a Fortran program; by slip system {0001}<11-20>For example, there are 6 equivalent slip systems (including negative slip) as shown in table 1;
TABLE 1 parameter settings of the slip system in the crystal
The Euler angle of the grain orientation is defined by Bunge method, i.e. the coordinate system of the grain is rotated around the z-axis in the xy planeAn angle; rotating around the x axis through a phi angle in the yz plane; finally, rotate through the xy plane again around the z axisThe angles are finally completely overlapped with a finite element mesh model coordinate system, thereby obtaining three euler angles of spatial orientation of each crystal grainInitial Euler angle of grain orientation Measured by an EBSD experiment;
the stress-strain state components are respectively according to sigmaxx，σyy，σzz，σyz，σxz，σxyAndxx，yy，zz，yz，xz，xygiven the order of (a), the initial values are all set to 0; the number of crystal grains contained in the file is stored by using a variable n _ grain;
wherein, the sigmaxx，σyyAnd σzzRespectively representing the normal stress along the directions of an X axis, a Y axis and a Z axis in the space to which the crystal grains are subjected in the coordinate system of the finite element mesh model in the step one;
the above-mentionedxx，yyAndzzrespectively representing positive strain along the directions of an X axis, a Y axis and a Z axis in the space to which the crystal grains are subjected in the coordinate system of the finite element mesh model in the step one;
the sigmayzRepresenting the shear stress parallel to the X axis in the normal plane of the Y axis in the space suffered by the crystal grains in the coordinate system of the finite element mesh model in the step one;
the sigmaxzRepresenting said finite element mesh model at step oneIn a coordinate system, the space in which the crystal grains are subjected to the shear stress parallel to the Z axis in an X-axis normal plane;
the sigmaxyRepresenting the shear stress parallel to the Y axis in the X-axis normal plane in the space to which the crystal grains are subjected in the coordinate system of the finite element mesh model in the step one;
the above-mentionedyzRepresenting the shear strain of a micro line segment included angle in the Y-axis and Z-axis directions in the space suffered by the crystal grain in the coordinate system of the finite element grid model in the step one;
the above-mentionedxzRepresenting the shear strain of a micro line segment included angle in the X-axis and Z-axis directions in the space suffered by the crystal grain in the coordinate system of the finite element grid model in the step one;
the above-mentionedxyRepresenting the shear strain of a micro line segment included angle in the X-axis and Y-axis directions in the space suffered by the crystal grain in the coordinate system of the finite element grid model in the step one;
step three:
based on the transformation matrix in the second step, obtaining a single crystal elastic stiffness matrix Cij' and a schmitt factor alpha in a finite element grid model coordinate system through tensor operation, wherein alpha is cos lambda cos phi, phi is an included angle between a slip plane and a central axis of an external force F, and lambda is an included angle between a slip direction and the external force F, as shown in fig. 4;
the tensor operation formula is as follows: cij ═ R-1·Cij；
Step four:
determine Euler angle incrementWhether or not it is (0, 0, 0), if Entering the step five; if it isEntering a sixth step;
step five:
loading the current finite element grid model according to the boundary conditions and the loading load of the finite element grid model in the step one, and then calculating by adopting a finite element calculation method to obtain the stress strain state component of the loaded crystal grain aiming at the single crystal elastic stiffness matrix under the coordinate system of the current finite element grid model; replacing the initial stress-strain state component in the second step with the stress-strain state component of the loaded crystal grain, and repeating the second step to the fourth step; wherein, after each loading, the number of loading steps is increased by one; step six:
judging whether the total number n of potential to-be-started and started slip systems in the crystal grains is larger than zero or not; if n is 0, the crystal grain is still in the elastic deformation stage, and repeating the step five; if n is more than 0, indicating that the crystal grain enters a plastic deformation stage, entering a seventh step;
method for determining potential to actuate and actuated slip systems:
if it isThe slip is marked as potentially going on ifThe slip is marked as actuated; wherein σcIndicating the current stress value of the grain in which the slip system is located,representing the critical slitting stress value of the ith slip system, αi(ii) a schmidt factor representing the ith slip series;
step seven:
according to the Hill-Hutchinson polycrystal elastic-plastic deformation theory, the plastic strain of each crystal grain is consideredIs the dependent variable (gamma) of all slip systemsi) The accumulated value of (a):
according to Hooke's law, each loading state corresponds to an instantaneous modulus (L) that links grain stress to strainc) I.e. the instantaneous stress (σ) of the grainc) And is given byc) The relationship satisfies:
wherein the total strain of the crystal grains: (c) Is elastically strainedAnd plastic strainAnd (2) are substituted into (1) and (2) to obtain:
wherein M iscIs LcThe inverse matrix of (c).
And the critical actuation stress value (tau) of the theoretical slip system according to Hill (1996)i) And the amount of strain (gamma) of slip systemi) The following relationships exist:
substituting (1) to (4) into the relational expression of the slitting stress:
τi＝σcαi(5)
and (4) obtaining:
wherein, the finally obtained basis vector matrix X of the n slip system strain linear equation setsijComprises the following steps:
Xij＝hij+αiLcαj(9)
substituting (9) into (8), solving the shear quantity gamma assigned to each potential slip systemi：
γi＝fi c(10)
Wherein,
Yijis XijThe inverse of (c).
Finally, the stress strain instantaneous modulus (L) of the original crystal grain is obtainedc) On the basis of the method, an instantaneous rigidity matrix considering the plastic deformation stage is solved
Step eight:
judging whether the current loading step number is equal to the set maximum loading step number or not, if so, obtaining an instantaneous stiffness matrix which is the anisotropic linear elasticity constitutive structure of the crystal grains; and if the instantaneous stiffness matrix is smaller than the maximum loading step number, replacing the single crystal elastic stiffness matrix in the step II with the instantaneous stiffness matrix in the step III, and repeating the step II to the step III until the loading step number is equal to the maximum loading step number set in the step I.
(1) Assuming an oriented 8-grain model, 4 of which are α phase grains and 4 of which are β phase grains, the finite element has a 10-3The strain rate is loaded with 0.1% of strain in each step, after 10 steps of loading, 4 crystal grains in α phase crystal grains can be judged to completely enter a plastic deformation stage, 3 crystal grains in β phase enter the plastic deformation stage, whether each crystal grain enters the plastic stage or not under the current loading step can be judged from an output result, the plastic stage is entered or not entered, information such as which slip systems in the crystal grains are started and a mark number and a starting amount corresponding to each slip system can be known, and the starting information of all the slip systems in the crystal grains is shown in tables 2 and 3:
TABLE 2 information on the start-up results of the slip system in alpha-phase grains of titanium alloys in an 8-grain model assuming orientation
TABLE 3 information on the start-up results of the titanium alloy beta-phase intragranular slip system in the 8-grain model assuming orientation
Taking crystal grain 1 of alpha phase as an example, 6 slip systems are actuated, namely 3 rd, 5 th, 7 th, 29 th, 39 th and 40 th, and the actuating amount corresponding to each slip system is respectively as follows: 0.1155E-01, 0.4345E-02, 0.1872E-01, 0.2221E-01, 0.3231E-02 and 0.1375E-01;
meanwhile, the anisotropic linear elastic constitutive of each crystal grain is also given, namely a Cij matrix (the unit is GPa, see tables 4 and 5) of 6 x 6, and after comparison, the crystal grains with larger starting amount and larger starting amount of the slip system are found, and the anisotropic linear elastic constitutive change is larger.
TABLE 4C for each grain of titanium alloy α phase in 8-grain model phase assuming orientationijMatrix array
TABLE 5C for each grain of titanium alloy α phase in 8-grain model phase assuming orientationijMatrix array
(2) Assuming an oriented 108 grain model, 70 of which are α phase grains and 38 of which are β phase grains, the finite element has a 10-3The strain rate is loaded with 0.1% strain in each step, and after 10 steps of loading, 61 crystal grains in α -phase crystal grains can be judged to enterSimilarly to (1), whether each grain enters the plastic stage or not under the current loading step can be judged, the more the number of the grains in the model is, the closer the stress distributed on each grain is to the real stress situation, at this time, the grains can enter the plastic stage and do not enter the plastic stage, but a certain grain enters the plastic stage when being loaded at the previous step, but the slip system hardening effect in the grain causes the stress increased by the current loading step to be insufficient to start any slip system again, the grain is embodied as the solution-free basis vector equation set in the calculation process, namely, the state of the grain is returned from the plastic to the elastic state under the current loading step, secondly, the starting information of all intra-grain slip systems, such as the started slip systems in the grains and the corresponding labels and starting momentum of each slip system can be known, and finally, the anisotropic line elastic constitution of each grain can be given, namely, the C6ijThe matrix (unit is GPa) lists α phase 27 th crystal grain slip system start result information and anisotropic linear elastic constitutive CijThe matrix information is shown in table 6.
Table 6 set forth slip system start-up result information and anisotropic linear elastic constitutive C of α phase 27 th crystal grain in 108 crystal grain model of orientationijMatrix array
The present invention includes, but is not limited to, the above embodiments, and any equivalent substitutions or partial modifications made under the principle of the spirit of the present invention are considered to be within the scope of the present invention.
Claims (5)
1. A method for establishing an anisotropic linear elastic constitutive structure based on a crystal slip mechanism is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps:
establishing a finite element mesh model of the grain structure by adopting a finite element mesh subdivision method based on a grain structure image of the anisotropic linear elastic constitutive material to be solved, and determining the boundary condition and the loading condition of the finite element mesh model;
the loading conditions comprise a loading load and a maximum loading step number, wherein the initial loading step number is 0;
step two:
using projection operation method, according to intrinsic parameters of grain structure, initial stress strain state component and initial Euler angle of grain orientation ()φ0、) Solving for the Euler angle increment of the grain orientation (Δφ、) (ii) a And adding the Euler angle increment and the initial Euler angle to obtain the Euler angle after the crystal grain orientation changes due to strainObtaining a transformation matrix between a coordinate system of the finite element grid model and a crystal grain coordinate system according to the changed Euler angles;
step three:
based on the transformation matrix in the second step, obtaining a monocrystal elastic stiffness matrix and a Schmitt factor alpha under a finite element grid model coordinate system through tensor operation;
step four:
determining the Euler angle increment (Δφ，) Whether or not it is (0, 0, 0), if Entering the step five; if it isEntering a sixth step;
step five:
loading the current finite element grid model according to the boundary conditions and the loading load of the finite element grid model in the step one, and then calculating by adopting a finite element calculation method to obtain the stress strain state component of the loaded crystal grain aiming at the single crystal elastic stiffness matrix under the coordinate system of the current finite element grid model; replacing the initial stress-strain state component in the second step with the stress-strain state component of the loaded crystal grain, and repeating the second step to the fourth step; wherein, after each loading, the number of loading steps is increased by one;
step six:
judging whether the total number n of potential to-be-started and started slip systems in the crystal grains is larger than zero or not; if n is 0, repeating the step five; if n is more than 0, entering a seventh step;
step seven:
according to the Hill-Hutchinson polycrystalline elastic-plastic deformation theory, solving a basis vector matrix of n slip system strain linear equation sets; then according to the basis vector matrix, solving the shear quantity distributed to each slip system, and further obtaining an instantaneous rigidity matrix of the crystal grains in a plasticity stage;
step eight:
judging whether the current loading step number is equal to the set maximum loading step number or not, if so, obtaining an instantaneous stiffness matrix which is the anisotropic linear elasticity constitutive structure of the crystal grains; and if the instantaneous stiffness matrix is smaller than the maximum loading step number, replacing the single crystal elastic stiffness matrix in the step II with the instantaneous stiffness matrix in the step III, and repeating the step II to the step III until the loading step number is equal to the maximum loading step number set in the step I.
2. The method for establishing the anisotropic linear elastic constitutive based on the crystal slip mechanism as claimed in claim 1, wherein: and in the second step, the intrinsic parameters comprise crystal structure type parameters, a single crystal elastic rigidity matrix and intra-grain slippage system parameters.
3. The method for establishing the anisotropic linear elastic constitutive based on the crystal slip mechanism as claimed in claim 2, wherein: the slip system parameters comprise the name of a slip system, the number of equivalent slip systems and the Voc hardening index of the slip system; the Voc hardening index includes the critical value of the shear stress tau at which the slip train starts0Slip is the stress increase τ from start-up to no further increase in cumulative shear strain1Initial hardening rate of slip system0And saturated cure rate of slip system [ theta ]1。
4. The method for establishing the anisotropic linear elastic constitutive based on the crystal slip mechanism as claimed in claim 1, wherein: the Euler angle of the grain orientation is defined by Bunge method, i.e. the coordinate system of the grain rotates around the z-axis in the xy planeAn angle; then, the lens rotates around the x axis through a phi angle in the yz plane; finally, rotate through the xy plane again around the z axisThe angle is finally completely coincided with the coordinate system of the finite element mesh model, thereby obtaining three Euler angles of spatial orientation of each crystal grain (c) ((φ，) (ii) a Initial euler angle of grain orientation (φ0，) Measured by an EBSD experiment.
5. The method for establishing the anisotropic linear elastic constitutive based on the crystal slip mechanism as claimed in claim 1, wherein: the method for judging whether the slip system is to be started or started in the sixth step is as follows:
if it isThe slip is marked as potentially going on ifThe slip is marked as actuated; wherein σcIndicating the current stress value of the crystal grain in which any slip system is located,representing the critical slitting stress value of the ith slip system, αiThe Schmidt factor of the i-th slip system is shown.
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