CN105653822A - Cellular automaton method simulating static recrystallization behavior of GH4169 alloy - Google Patents

Abstract

The invention discloses a cellular automaton method simulating the static recrystallization behavior of GH4169 alloy. The method includes the following steps that firstly, an initial microstructure is generated; secondly, the static recrystallization behavior is simulated. The cellular automaton method simulating the static recrystallization behavior of GH4169 alloy is a static recrystallization behavior simulating method based on a physical mechanism, the static recrystallization behavior of GH4169 alloy can be accurately simulated, and technological support is provided for reasonably formulating the hot working technology of GH4169 alloy.

Description

A kind of cellular automation method simulating GH4169 alloy Static Recrystallization behavior

Technical field

The present invention relates to a kind of cellular automation method simulating GH4169 alloy Static Recrystallization behavior, belong to hot-working field of engineering technology.

Background technology

GH4169 alloy has the elevated temperature strength of excellence, resisting fatigue, creep resistant, antioxidation and decay resistance, is widely used in manufacturing the key components and parts of aero-engine: such as the turbine disk, compressor disc, casing etc. Large complicated GH4169 alloyed components generally adopts the multi-stage deep drawing modes such as forging, rolling, extruding to shape. In the forming process of these parts, the Microstructure evolution of alloy is sufficiently complex. Holding stage after hot formed passage interval time and deformation, static recovery, Static Recrystallization or meta-dynamic recrystallization etc. all can occur. This can significantly change the microstructure of alloy, and then affects the quality of forging. In order to obtain the GH4169 alloyed components of high-quality, need a kind of method that can accurately predict alloy Microstructure evolution badly, provide reliable microstructure Prediction means for heat forming technology optimization.

But, owing to GH4169 alloy structure development law in Static Recrystallization process is sufficiently complex, still lack at present and can accurately simulate the method for Microstructure evolution in GH4169 alloy passage interval time. For this difficult problem, the invention provides a kind of cellular automation method that can simulate GH4169 alloy Static Recrystallization behavior. The novelty of the present invention is in that, cellular models introduces the main physical factors affecting recrystallization behavior, drastically increase the precision of prediction of model, it is proposed to method verified by embodiment, result shows that this method can simulate GH4169 alloy Static Recrystallization behavior effectively.

Summary of the invention

It is an object of the invention to provide a kind of cellular automation method simulating GH4169 alloy Static Recrystallization behavior, the method is based on physical mechanism and sets up, it is possible to the forming core of grain structure and rule of growing up in the Static Recrystallization process of the GH4169 that calculates to a nicety.

For reaching above-mentioned purpose, the present invention adopts the technical scheme that: a kind of cellular automation method simulating GH4169 alloy Static Recrystallization behavior, and the method comprises the following steps:

Step 1: generate the step of initial microstructure;

Step 2: the step of simulation Static Recrystallization behavior;

Step 1 includes following sub-step:

(1) selected simulated domain, by discrete for the simulated domain grid for being made up of cellular, sets total simulation step number;

(2) composing initial value to cellular state variable, cellular state variable includes crystal grain numbering variable and grain orientation variable;

(3) in selected simulated domain, N is randomly selected_gIndividual cellular, and give selected N_gIndividual cellular composes different crystal grain numbering variablees and grain orientation variable;

(4) all cellulars are carried out one by one calculated below: assuming the state that state transfer is neighbours' cellular of current cellular, the change of computing system energy, if system capacity reduces, then by state that the state transfer of current cellular is neighbours' cellular;

(5) sub-step (4) of step 1 is repeated, until completing total simulation step number;

Step 2 includes following sub-step:

(1) time step �� t and total simulated time t is determined_total, compose initial value for cellular state variable; Cellular state variable includes dislocation density variable, recrystallization degree variables, crystal boundary migration distance variable, crystal grain numbering variable and grain orientation variable; Dislocation density initial guess is ��₁, recrystallization degree variables initial value is 0, and crystal boundary migration distance initial guess is 0, and crystal grain numbering variable and grain orientation variable are with the result of calculation of step 1 for initial value;

(2) sub-step of Static Recrystallization forming core is simulated;

(3) sub-step of Static Recrystallization grain growth is simulated;

(4) judge whether to reach total simulated time, if not up to, then again performing sub-step (2) and sub-step (3), if having reached total simulated time, stopping simulation;

The sub-step (2) of step 2 comprises the steps:

A. the cellular number N in statistics original grain boundary_pg;

B. Static Recrystallization nucleation rate is calculated, computing formula is:

$\stackrel{\·}{N}=C_1{(G-G_0)}^{C_2}\exp (-Q_n/RT)$

Wherein, C₁��C₂And Q_nFor material parameter, G is deformation energy, G₀For the critical energy storage needed for Static Recrystallization forming core, R is ideal gas constant, and T is deformation temperature; Material parameter C₁Span be 900-1500, material parameter C₂Span be 0-100, material parameter Q_nSpan be 10⁵-10⁶;

C. the cellular number N of Static Recrystallization forming core is calculated_n, and, A in formula_cFor single cell density;

Compose a forming core probability P d. to all cellulars being positioned in original grain boundary_n, and P_n=N_n/N_pg, by forming core probability P_nThe random number generated with computer contrasts, if forming core probability P_nLess than the random number that computer generates, then current cellular is chosen to be Static Recrystallization nucleus, and the dislocation density variable of current cellular is reset to ��₀, the recrystallization degree variables of current cellular adds 1, the crystal boundary migration distance variable zero setting of current cellular;

E. the step d of the sub-step (2) of step 2 is repeated, until selecting N_nIndividual Static Recrystallization nucleus;

The sub-step (3) of step 2 comprises the steps:

A. crystal boundary migration driving force P, P=�� (�� is calculated₁-��₀), the �� in formula is dislocation line energy;

B. calculating crystal boundary migration speed V, V=MP, the M in formula is crystal boundary migration rate, and computing formula is

$M=\frac{{\mathrm{\δD}}_{0b}\exp (-Q_b/RT)}{kT}b$

Wherein, �� D_0bAnd Q_bFor material parameter, �� D_0bSpan be 10^-11-10^-10, Q_bSpan be 10⁵-10⁶, b is Bai Shi vector, and k is Boltzmann constant;

C. crystal boundary migration distance variables L, L=V �� t are calculated;

If d. crystal boundary migration distance variables L is more than the distance between adjacent two cellulars, then by state that the state transfer of current cellular is recrystallization degree variables neighbours' cellular more than 1.

The novelty of the present invention and have the beneficial effect that (1) incorporates, in Static Recrystallization nucleation rate computing formula, the main physical factors affecting nucleation process, it is possible to describe the nucleation of GH4169 Static Recrystallization exactly; (2) result of calculation of crystal boundary migration rate can reflect the effect of dragging of solute element, meets the development law of alloy crystal boundary migration rate; (3) present invention is the Static Recrystallization analogy method of a kind of physically based deformation mechanism, it is possible to relatively accurately simulation GH4169 alloy Static Recrystallization behavior.

Accompanying drawing explanation

Contrast between crystallite dimension predictive value and the measured value of Fig. 1 this method;

The microstructure predicting result of Fig. 2 this method and the contrast of experimental result;

Detailed description of the invention

Below in conjunction with accompanying drawing, the present invention is described further.

The present invention is a kind of cellular automation method simulating GH4169 alloy Static Recrystallization behavior, and the method comprises the following steps:

Step 1: generate the step of initial microstructure;

Step 2: the step of simulation Static Recrystallization;

Step 1 includes following sub-step:

(1) selected simulated domain 920 �� 920 ��m², it being divided into 460 �� 460 grids, the length of side of each square cellular is L_cIt is 2 ��m, sets total simulation step number as 300;

(2) composing initial value to cellular state variable, cellular state variable includes crystal grain numbering variable and grain orientation variable;

(3) in selected simulated domain, randomly select 178 cellulars, and compose different crystal grain numbering variablees and grain orientation variable to 178 selected cellulars;

(4) all cellulars are carried out one by one calculated below: assuming the state that state transfer is neighbours' cellular of current cellular, the change of computing system energy, if system capacity reduces, then by state that the state transfer of current cellular is neighbours' cellular;

(5) sub-step (4) of step 1 is repeated, until it reaches total simulation step number;

Step 2 includes following sub-step:

(1) time step �� t, �� t=L is determined_c/(M��(��₁-��₀)), total simulated time t_totalFor 600s, compose initial value to cellular state variable; Cellular state variable includes dislocation density variable, recrystallization degree variables, crystal boundary migration distance variable, crystal grain numbering variable and grain orientation variable; Dislocation density initial guess is ��₁, can be obtained by interrupt experiments; Recrystallization degree variables initial value is 0, and crystal boundary migration distance initial guess is 0, and grain orientation variable and grain orientation variable are with the result of calculation of step 1 for initial value;

(2) sub-step of Static Recrystallization forming core is simulated;

(3) sub-step of Static Recrystallization grain growth is simulated;

(4) judge whether to reach total simulated time, if not up to, then again performing sub-step (2) and sub-step (3), if having reached total simulated time, stopping simulation;

The sub-step (2) of step 2 comprises the steps:

A. the cellular number N in statistics original grain boundary_pg;

B. Static Recrystallization nucleation rate is calculated, computing formula is:

$\stackrel{\·}{N}=C_1{(G-G_0)}^{C_2}\exp (-Q_n/RT)$

Wherein, C₁��C₂And Q_nFor material parameter, C₁It is 994, C₂It is 5.42, Q_nBe 669286, G it is deformation energy, G₀For the critical energy storage needed for Static Recrystallization forming core, R is ideal gas constant, and T is deformation temperature;

C. the cellular number N of Static Recrystallization forming core is calculated_n,, A in formula_cFor single cell density;

Compose a forming core probability P d. to all cellulars being positioned in original grain boundary_n, and P_n=N_n/N_pg, by forming core probability P_nThe random number generated with computer contrasts, if forming core probability P_nLess than the random number that computer generates, then current cellular is chosen to be Static Recrystallization nucleus, and the dislocation density variable of current cellular is reset to ��₀, ��₀Can obtaining according to yield stress reverse, the recrystallization degree variables of current cellular adds 1, the crystal boundary migration distance variable zero setting of current cellular;

E. the step d of the sub-step (2) of step 2 is repeated, until selecting N_nIndividual Static Recrystallization nucleus;

The sub-step (3) of step 2 comprises the steps:

A. crystal boundary migration driving force P, P=�� (�� is calculated₁-��₀), the �� in formula is dislocation line energy;

B. calculating crystal boundary migration speed V, V=MP, the M in formula is crystal boundary migration rate, and computing formula is

$M=\frac{{\mathrm{\δD}}_{0b}\exp (-Q_b/RT)}{kT}b$

Wherein, �� D_0bAnd Q_bFor material parameter, �� D_0bAnd Q_bValue respectively 6.79 �� 10^-11With 2.97 �� 10⁵, b is Bai Shi vector, and k is Boltzmann constant;

C. crystal boundary migration distance variables L, L=V �� t are calculated;

If d. crystal boundary migration distance variables L is more than the distance between adjacent two cellulars, then by state that the state transfer of current cellular is recrystallization degree variables neighbours' cellular more than 1.

Adopting said method, GH4169 Static Recrystallization behavior within the scope of 1253-1313K is simulated, Fig. 1 is that crystallite dimension predicts the outcome the contrast with measurement result, and Fig. 2 is the contrast of microstructure predicting result and experimental result. By the comparing result of Fig. 1 and Fig. 2 it can be seen that the present invention can relatively accurately describe the Static Recrystallization behavior of GH4169 alloy.

Claims (1)

1. the cellular automation method simulating GH4169 alloy Static Recrystallization behavior, it is characterised in that: the method comprises the following steps:

Step 1: generate the step of initial microstructure;

Step 2: the step of simulation Static Recrystallization behavior;

Described step 1 includes following sub-step:

(1) selected simulated domain, by discrete for the simulated domain grid for being made up of cellular, sets total simulation step number;

(2) composing initial value to cellular state variable, described cellular state variable includes crystal grain numbering variable and grain orientation variable;

(3) in selected simulated domain, N is randomly selected_gIndividual cellular, and give selected N_gIndividual cellular composes different crystal grain numbering variablees and grain orientation variable;

(4) all cellulars are carried out one by one calculated below: assuming the state that state transfer is neighbours' cellular of current cellular, the change of computing system energy, if system capacity reduces, then by state that the state transfer of current cellular is neighbours' cellular;

(5) sub-step (4) of repeating said steps 1, until completing described total simulation step number;

Described step 2 includes following sub-step:

(1) time step �� t and total simulated time t is determined_total, compose initial value for cellular state variable; Described cellular state variable includes dislocation density variable, recrystallization degree variables, crystal boundary migration distance variable, crystal grain numbering variable and grain orientation variable; Institute's dislocation density initial guess is ��₁, described recrystallization degree variables initial value is 0, and described crystal boundary migration distance initial guess is 0, and described crystal grain numbering variable and described grain orientation variable are with the result of calculation of described step 1 for initial value;

(2) sub-step of Static Recrystallization forming core is simulated;

(3) sub-step of Static Recrystallization grain growth is simulated;

(4) judge whether to reach described total simulated time, if not up to, then again performing described sub-step (2) and described sub-step (3), if having reached described total simulated time, then stopping simulation;

The described sub-step (2) of described step 2 comprises the steps:

A. the cellular number N in statistics original grain boundary_pg;

B. Static Recrystallization nucleation rate is calculatedComputing formula is:

$\stackrel{\·}{N}=C_1{(G-G_0)}^{C_2}\exp (-Q_n/RT)$

Wherein, C₁��C₂And Q_nFor material parameter, G is deformation energy, G₀For the critical energy storage needed for Static Recrystallization forming core, R is ideal gas constant, and T is deformation temperature; Described material parameter C₁Span be 900-1500, described material parameter C₂Span be 0-100, described material parameter Q_nSpan be 10⁵-10⁶;

C. the cellular number N of Static Recrystallization forming core is calculated_n, andA in formula_cFor single cell density;

Compose a forming core probability P d. to all cellulars being positioned in original grain boundary_n, and P_n=N_n/N_pg, by described forming core probability P_nThe random number generated with computer compares, if described forming core probability P_nLess than the random number that described computer generates, then current cellular is chosen to be Static Recrystallization nucleus, and the dislocation density variable of described current cellular is reset to ��₀, recrystallization degree variables add 1 and crystal boundary migration distance variable zero setting;

E. the step d of the sub-step (2) in repeating said steps 2, until selecting N_nIndividual Static Recrystallization nucleus;

Sub-step (3) in described step 2 comprises the steps:

A. crystal boundary migration driving force P, P=�� (�� is calculated₁-��₀), the �� in formula is dislocation line energy;

B. calculating crystal boundary migration speed V, V=MP, the M in formula is crystal boundary migration rate, and computing formula is

$M=\frac{{\mathrm{\δD}}_{0b}\exp (-Q_b/RT)}{kT}b$

Wherein, �� D_0bAnd Q_bFor material parameter, �� D_0bSpan be 10^-11-10^-10, Q_bSpan be 10⁵-10⁶, b is Bai Shi vector, and k is Boltzmann constant;

C. described crystal boundary migration distance variables L, L=V �� t are calculated;

If d. crystal boundary migration distance variables L is more than the distance between adjacent two cellulars, then by state that the state transfer of current cellular is recrystallization degree variables neighbours' cellular more than 1.