CN105631132B - Method for calculating grain size of lath ferrite in welding and cooling process - Google Patents

Method for calculating grain size of lath ferrite in welding and cooling process Download PDF

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CN105631132B
CN105631132B CN201511008465.2A CN201511008465A CN105631132B CN 105631132 B CN105631132 B CN 105631132B CN 201511008465 A CN201511008465 A CN 201511008465A CN 105631132 B CN105631132 B CN 105631132B
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ferrite
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welding
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austenite
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童莉葛
谷京晨
白芳
王立
尹少武
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University of Science and Technology Beijing USTB
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Abstract

The invention provides a method for calculating the grain size of lath ferrite in the welding and cooling process, which combines the temperature field in the welding and cooling process with the continuous cooling phase change CCT curve chart of welding steel grade, and calculates the grain size of lath ferrite by a material method, and comprises the following steps: acquiring a CCT curve diagram of the steel grade; calculating the cooling speed of the predicted point; obtaining the diffusion coefficient Dc of carbon in the steel grade; sequentially calculating dimensionless parameters omega0Average diameter dr of austenite grains, effective grain boundary area S of austenite unitγFerrite growth rate GfFerrite nucleation rate IsTransformation ratio of ferrite at early and later phases
Figure DDA0000893827670000011
And
Figure DDA0000893827670000012
total number of ferrite nuclei
Figure DDA0000893827670000013
Ferrite grain size in the early stage of gamma → alpha transformation
Figure DDA0000893827670000014
And the growth increment at the late phase of the gamma → alpha phase transition
Figure DDA0000893827670000015
And
Figure DDA0000893827670000016
the sum is the current grain size of ferrite. The invention combines the temperature field in the welding and cooling process with the CCT curve chart of the steel grade, calculates the grain size in the welding and cooling process of the ferrite of the strip, and realizes the real-time calculation of the grain size.

Description

Method for calculating grain size of lath ferrite in welding and cooling process
Technical Field
The invention belongs to the field of metal materials and the field of weld joint and base metal structure prediction in a welding process, and relates to a method for calculating the grain sizes of weld joints and heat affected zones of lath ferrite in the welding process by combining a temperature field in a welding Cooling process and a Continuous Cooling phase transition (CCT) curve graph of steel grades.
Background
With the wider application of welding technology in engineering, research on improving the mechanical properties of high-strength steel welded joints is urgent. Predicting the grain size of the weld joint microstructure in real time during cooling is critical to analyzing and improving the mechanical properties of the weld joint. And the calculation of the grain size, particularly the calculation of the change of the grain size of the lath ferrite along with time and temperature in the welding and cooling process has important significance for analyzing the influence factors of the mechanical property of the welding joint.
The grain size of the welded joint microstructure lath ferrite is calculated by two methods at present: one is to calculate the lath ferrite grain size through a mathematical model, and the other is to measure the metallographic structure size through experiments.
The method for calculating the size of the ferrite grains of the strip by adopting the mathematical model is more basic, and can analyze factors influencing the growth of the ferrite of the strip from the mechanism. However, in the process of model building and calculation, the precondition assumption can make the calculation result deviate from the actual result. In certain cases, this deviation is acceptable, but in some cases it is not tolerable in cases where high computational accuracy is required.
The method for measuring the size of the metallographic structure by experiments can conveniently and intuitively obtain the size and other related parameters of the lath ferrite and other structures. The data obtained by the method is also true and reliable. However, the experimental method can only measure and obtain the microstructure after welding and cooling, and cannot obtain the evolution process of the microstructure and the change process of the ferrite grain size of the strip along with time and temperature. According to the method for calculating the grain size of the lath ferrite in the welding and cooling process, the dynamic evolution process of the grain size in the cooling process can be obtained, and an effective calculation method is further provided for researching the influence of the welding and cooling speed on the grains.
Disclosure of Invention
The invention aims to provide a method for calculating the grain size of lath ferrite in the welding and cooling process, so as to realize the real-time calculation of the sizes of the lath ferrite in a welding seam and a heat affected zone in the welding process.
In order to solve the above technical problems, an embodiment of the present invention provides a method for calculating a grain size of lath ferrite in a welding cooling process, wherein a temperature field in the welding cooling process and a CCT (continuous cooling transformation) curve of a welding steel grade are combined, and the grain size of the lath ferrite is calculated by a material science method, which specifically comprises the following steps:
(1) obtaining CCT curve chart of steel grade, and obtaining temperature T when phase change mechanism is changed in welding cooling processcFerrite initial precipitation temperature Ar3And an end temperature Tf；
(2) Obtaining the temperature field of a welding seam and a heat affected zone in the welding and cooling process, obtaining a thermal cycle curve of the temperature of a certain predicted point changing along with time, converting the time of the abscissa of the thermal cycle curve into a logarithmic coordinate, drawing the logarithmic coordinate on the CCT curve chart in the step (1), calculating the cooling speed of the predicted point by a formula (1),
Vc＝(Tmax-T)/t0(1)；
wherein, VcIs the cooling rate in ° C.s-1；
TmaxThe highest temperature in the welding and cooling process is measured in units of temperature;
t is the current temperature in units of;
t0is the cooling time in units of s;
(3) obtaining the diffusion coefficient D of carbon in the steel gradecIn units of cm2·s-1；
(4) Obtaining the equilibrium mole fraction of carbon in the austenite side and the ferrite side at the austenite-ferrite phase boundary and the mole fraction of carbon in the austenite at different temperatures, respectively:
Figure GDA0002271887520000021
and
Figure GDA0002271887520000022
then calculating the growth rate G of ferrite according to the formula (2)fRelated dimensionless parameter omega0，
Figure GDA0002271887520000023
Wherein omega0Is a dimensionless parameter related to the ferrite growth rate;
Figure GDA0002271887520000024
is the equilibrium mole fraction of carbon at the austenite side at the austenite to ferrite phase boundary at different temperatures;
Figure GDA0002271887520000025
is the equilibrium mole fraction of carbon at the ferrite side at the austenite-ferrite phase boundary at different temperatures;
Figure GDA0002271887520000031
is the mole fraction of carbon in austenite at different temperatures;
(5) solving the average diameter d of the austenite grains by adopting an iterative calculation method through a formula (3)rCalculating the unit austenite effective grain boundary area S by the formula (4)γ，
Figure GDA0002271887520000032
Figure GDA0002271887520000033
Wherein d is0The austenite starting average grain diameter at constant temperature is expressed in cm;
drthe average grain diameter of austenite at the current moment is in cm;
k is a constant;
n is an index;
t0is the cooling time in units of s;
Sγis the unit austenite effective grain boundary area, and the unit is cm2；
π is the circumference ratio, 3.1415926;
(6) calculating ferrite growth rate G according to equation 5f，
Figure GDA0002271887520000034
Wherein G isfIs the growth rate of ferrite in cm s-1；
DcIs the diffusion coefficient of carbon in the steel grade, and the unit is cm2·s-1；
r0Is the ultimate radius of curvature of the ferrite growing section, and is 1.8 multiplied by 10-6cm；
Ω0Is a parameter related to the growth rate of ferrite, and is obtained by the formula (2);
(7) calculating ferrite nucleation rate I according to formula (6)s，
Figure GDA0002271887520000035
Wherein, IsIs the ferrite nucleation rate in cm s-1；
K2、K3K is constant, and is 2.07 × 103、1.14×109And 1.38X 10-23；
DcIs the diffusion coefficient of carbon in the steel grade, and the unit is cm2·s-1；
T is the current temperature in units of;
Gfis the growth rate of ferrite in cm s-1From scratchObtaining a compound of formula (5);
(8) calculating the transformation ratio of the ferrite at the early and later phase transformation
Figure GDA00022718875200000410
In the early phase of ferrite phase transition, the phase transition is mainly driven by a nucleation growth mechanism, the kinetic equation is shown as a formula (7), in the later phase of ferrite phase transition, the kinetic equation accords with a position saturation mechanism, and is shown as a formula (8),
Figure GDA00022718875200000411
wherein the content of the first and second substances,
Figure GDA0002271887520000042
the transformation ratios of the ferrite at the early stage and the later stage are respectively expressed in kg-cm-3·s-1；
IsIs the ferrite nucleation rate in cm s-1；
GfIs the growth rate of ferrite in cm s-1；
t is ferrite phase change current time, and the unit is s;
Sγis the unit austenite effective grain boundary area, and the unit is cm2；
IsObtained by the formula (6), GfObtained from the formula (5), SγObtained from formula (4);
(9) calculating the total ferrite nucleation number according to the formula (9)
Figure GDA0002271887520000043
Figure GDA0002271887520000044
Wherein the content of the first and second substances,
Figure GDA0002271887520000045
is the total ferrite nucleation number;
Tcthe temperature when the phase change mechanism is changed is expressed in units of ℃;
Ar3the initial precipitation temperature of ferrite is expressed in unit of ℃;
Isis the ferrite nucleation rate in cm s-1；
VcIs the cooling rate in ° C.s-1；
Figure GDA0002271887520000046
Is the transformation ratio of ferrite at the early stage of transformation, and the unit is kg cm-3·s-1；
T is the current temperature in units of;
Isobtained by the following formula (6),
Figure GDA0002271887520000047
obtained from the formula (7), Ar3Obtaining the CCT curve chart of the steel variety in the step (1);
(10) the ferrite grain size in the early stage of the γ → α transformation is calculated by the equations (10) and (11), respectively
Figure GDA0002271887520000048
And the growth increment at the late phase of the gamma → alpha phase transition
Figure GDA0002271887520000049
Figure GDA0002271887520000051
Figure GDA0002271887520000052
Wherein the content of the first and second substances,
Figure GDA0002271887520000053
is the ferrite grain size in cm at the early stage of gamma → alpha phase transformation;
is the growth increment of the later phase change of gamma → alpha, and the unit is cm;
the transformation ratios of the ferrite at the early stage and the later stage are respectively expressed in kg-cm-3·s-1；
π is the circumference ratio, 3.1415926;
Figure GDA0002271887520000056
is the total ferrite nucleation number;
Sγis the unit austenite effective grain boundary area, and the unit is cm2；
TfThe ferrite phase transition finishing temperature is expressed in units of ℃;
Tcthe temperature when the phase change mechanism is changed is expressed in units of ℃;
Gfis the growth rate of ferrite in cm s-1；
VcIs the cooling rate in ° C.s-1；
T is the current temperature in units of;
Sγobtained from the formula (4), GfObtained from the formula (5) in the following way,
Figure GDA0002271887520000057
obtained from the formula (7) in the following way,
Figure GDA0002271887520000058
obtained from the formula (8) in the following way,
Figure GDA0002271887520000059
obtained by formula (9), Ar3Obtaining the CCT curve chart of the steel variety in the step (1);
(11) the current grain size of ferrite is the grain size of ferrite in the phase prior to gamma → alpha transformation
Figure GDA00022718875200000510
And the growth increment at the late phase of the gamma → alpha phase transition
Figure GDA00022718875200000511
And, as shown in equation (12),
wherein, the steel grade is high-strength low-alloy steel, X65, X70, X80, X90, X100 or X120, and the steel grade is widely applied to natural gas and petroleum transmission pipelines.
And (2) in the step (1), simulating and analyzing the tissue composition and hardness at different cooling speeds through a thermal simulation testing machine, drawing a CCT curve, and obtaining a CCT curve graph of the steel grade.
And (3) calculating the temperature fields of the welding seam and the heat affected zone in the welding cooling process in the step (2) by CFD software. The temperature fields of the welding seam and the heat affected zone in the welding and cooling process in the step (2) can also be obtained by measuring through an infrared thermal imager or a thermocouple.
Preferably, the CFD software is Fluent finite element analysis software.
Wherein, in the step (3), the diffusion coefficient D of the carbon in the steel grade is measured by a method for manufacturing a diffusion couplecThe diffusion couple is prepared by connecting steel sheets and carbon sheets of the same type by molybdenum wires, and heating to the highest welding temperature TmaxThen cooling treatment is carried out, and then the diffusion coefficient Dc is measured. DcAnd can also be obtained by consulting relevant literature.
Wherein, in the step (4), the balance mole fraction of the carbon at different temperatures at the austenite side at the austenite-ferrite phase boundary is
Figure GDA0002271887520000061
Equilibrium mole fraction of carbon at different temperatures on the ferrite side at the austenite-ferrite phase boundary
Figure GDA0002271887520000062
Molar fraction of carbon in austenite at different temperatures
Figure GDA0002271887520000063
The method is obtained by inquiring an iron-carbon phase diagram in the material science foundation. The iron-carbon phase diagram is described in the materials science foundation (Hu 36179;, Seitz 29667, Yonghua treaty, Shanghai university of transportation Press, 2010).
Wherein d in the step (5)0The values of K and n are referred to in Table 1, and the temperatures not listed in the table can be calculated by intermediate interpolation0K and n.
TABLE 1
Predicted Point temperature (. degree. C.) n K d0(cm×10-4)
1010 4.44988 2340.1 12.87
1030 4.21522 2387.5 15.50
1050 3.92269 2478.2 17.33
1160 2.48619 19834.9 25.1
1200 2.48339 25485.8 30.3
。
The technical scheme of the invention has the following beneficial effects:
in the scheme, the temperature field in the welding and cooling process is combined with the CCT curve chart of the steel grade, and the grain size in the welding and cooling process of the strip ferrite is calculated, so that the real-time calculation of the sizes of the weld joint and the strip ferrite in the heat affected zone in the welding process is realized.
Drawings
FIG. 1 is a flow chart of the calculation of the present invention;
fig. 2 is a graph showing the dynamic evolution of grain size during cooling.
Description of reference numerals:
1. welding seams;
2. a fusion zone;
3. a coarse-grained region;
4. a normalizing zone;
5. an incomplete recrystallization zone;
6. a base material.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, a method for calculating the grain size of lath ferrite in the welding cooling process combines the temperature field in the welding cooling process and the continuous cooling phase transformation CCT curve chart of the welding steel type, and calculates the grain size of lath ferrite by a material method, which comprises the following specific steps:
(1) obtaining CCT curve chart of steel grade, and obtaining temperature T when phase change mechanism is changed in welding cooling processcFerrite initial precipitation temperature Ar3And an end temperature Tf；
The CCT curve can be obtained by analyzing the tissue composition and the hardness at different cooling speeds through a thermal simulation test model, drawing a CCT curve and obtaining the CCT curve of the steel. Other methods can be adopted to obtain the CCT curve according to actual conditions.
(2) Obtaining the temperature field of a welding seam and a heat affected zone in the welding and cooling process, obtaining a thermal cycle curve of the temperature of a certain predicted point changing along with time, converting the time of the abscissa of the thermal cycle curve into a logarithmic coordinate, drawing the logarithmic coordinate on the CCT curve chart in the step (1), calculating the cooling speed of the predicted point by a formula (1),
Vc＝(Tmax-T)/t0(1)；
wherein, VcIs the cooling rate in ° C.s-1；
TmaxThe highest temperature in the welding and cooling process is measured in units of temperature;
t is the current temperature in units of;
t0is the cooling time in units of s;
the temperature fields of the welding seam and the heat affected zone in the welding and cooling process can be obtained through calculation of CFD software such as Fluent finite element analysis software. The temperature field of the welding seam and the heat affected zone in the welding and cooling process can also be measured by an infrared thermal imager or a thermocouple.
(3) Measuring the diffusion coefficient D of carbon in the steel grade by a method for manufacturing a diffusion couplecIn units of cm2·s-1. The method of the diffusion couple isConnecting the steel sheets and carbon sheets of the same kind to be welded together by molybdenum wires to form a diffusion couple, and heating to the highest welding temperature TmaxThen cooling treatment is carried out, and then the diffusion coefficient Dc is measured. Of course, DcAnd can also be obtained by consulting relevant literature.
(4) Obtaining the equilibrium mole fraction of carbon in the austenite side and the ferrite side at the austenite-ferrite phase boundary and the mole fraction of carbon in the austenite at different temperatures, respectively:
Figure GDA0002271887520000081
and
Figure GDA0002271887520000082
can be obtained by inquiring an iron-carbon phase diagram in the material science foundation. Then calculating the growth rate G of ferrite according to the formula (2)fRelated dimensionless parameter omega0，
Figure GDA0002271887520000083
Wherein omega0Is a dimensionless parameter related to the ferrite growth rate;
Figure GDA0002271887520000084
is the equilibrium mole fraction of carbon at the austenite side at the austenite to ferrite phase boundary at different temperatures;
Figure GDA0002271887520000085
is the equilibrium mole fraction of carbon at the ferrite side at the austenite-ferrite phase boundary at different temperatures;
is the mole fraction of carbon in austenite at different temperatures.
(5) Solving the average diameter d of the austenite grains by adopting an iterative calculation method through a formula (3)rCalculating the unit by the formula (4)Effective austenite grain boundary area Sγ，
Figure GDA0002271887520000087
Wherein d is0The austenite starting average grain diameter at constant temperature is expressed in cm;
drthe average grain diameter of austenite at the current moment is in cm;
k is a constant;
n is an index;
t0is the cooling time in units of s;
Sγis the unit austenite effective grain boundary area, and the unit is cm2；
π is the circumference ratio, 3.1415926;
wherein d is0The values of K and n are shown in Table 1. Temperatures not tabulated, d being calculated by intermediate interpolation0K and n.
TABLE 1
Predicted Point temperature (. degree. C.) n K d0(cm×10-4)
1010 4.44988 2340.1 12.87
1030 4.21522 2387.5 15.50
1050 3.92269 2478.2 17.33
1160 2.48619 19834.9 25.1
1200 2.48339 25485.8 30.3
。
(6) Calculating the ferrite growth rate G according to the formula (5)f，
Wherein G isfIs the growth rate of ferrite in cm s-1；
DcIs the diffusion coefficient of carbon in the steel grade, and the unit is cm2·s-1；
r0Is the ultimate radius of curvature of the ferrite growing section, and is 1.8 multiplied by 10-6cm；
Ω0Is a parameter related to the growth rate of ferrite, and is obtained by the formula (2);
(7) root of herbaceous plantCalculating ferrite nucleation rate I according to formula (6)s，
Figure GDA0002271887520000092
Wherein, IsIs the ferrite nucleation rate in cm s-1；
K2、K3K is constant, and is 2.07 × 103、1.14×109And 1.38X 10-23；
DcIs the diffusion coefficient of carbon in the steel grade, and the unit is cm2·s-1；
T is the current temperature in units of;
Gfis the growth rate of ferrite in cm s-1Obtained from formula (5);
(8) calculating the transformation ratio of the ferrite at the early and later phase transformation
Figure GDA0002271887520000093
In the early phase of ferrite phase transition, the phase transition is mainly driven by a nucleation growth mechanism, the kinetic equation is shown as a formula (7), in the later phase of ferrite phase transition, the kinetic equation accords with a position saturation mechanism, and is shown as a formula (8),
Figure GDA0002271887520000101
Figure GDA0002271887520000102
wherein the content of the first and second substances,
Figure GDA0002271887520000103
the transformation ratios of the ferrite at the early stage and the later stage are respectively expressed in kg-cm-3·s-1；
IsIs the ferrite nucleation rate in cm s-1；
GfIs the growth rate of ferrite in units ofcm·s-1；
t is ferrite phase change current time, and the unit is s;
Sγis the unit austenite effective grain boundary area, and the unit is cm2；
IsObtained by the formula (6), GfObtained from the formula (5), SγObtained from formula (4);
(9) calculating the total ferrite nucleation number according to the formula (9)
Figure GDA0002271887520000104
Figure GDA0002271887520000105
Wherein the content of the first and second substances,
Figure GDA0002271887520000106
is the total ferrite nucleation number;
Tcthe temperature when the phase change mechanism is changed is expressed in units of ℃;
Ar3the initial precipitation temperature of ferrite is expressed in unit of ℃;
Isis the ferrite nucleation rate in cm s-1；
VcIs the cooling rate in ° C.s-1；
Figure GDA0002271887520000107
Is the transformation ratio of ferrite at the early stage of transformation, and the unit is kg cm-3·s-1；
T is the current temperature in units of;
Isobtained by the following formula (6),
Figure GDA0002271887520000108
obtained from the formula (7), Ar3 is obtained from the CCT curve chart of the steel type in the step (1);
(10) ferrite grains in the early stage of the gamma → alpha transformation are calculated by the equations (10) and (11), respectivelySize ofAnd the growth increment at the late phase of the gamma → alpha phase transition
Figure GDA00022718875200001011
Wherein the content of the first and second substances,is the ferrite grain size in cm at the early stage of gamma → alpha phase transformation;
Figure GDA0002271887520000112
is the growth increment of the later phase change of gamma → alpha, and the unit is cm;
Figure GDA0002271887520000113
the transformation ratios of the ferrite at the early stage and the later stage are respectively expressed in kg-cm-3·s-1；
π is the circumference ratio, 3.1415926;
Figure GDA0002271887520000114
is the total ferrite nucleation number;
Sγis the unit austenite effective grain boundary area, and the unit is cm2；
TfThe ferrite phase transition finishing temperature is expressed in units of ℃;
Tcthe temperature when the phase change mechanism is changed is expressed in units of ℃;
Gfis the growth rate of ferrite in cm s-1；
VcIs the cooling rate in ° C.s-1；
T is the current temperature in units of;
Sγobtained from the formula (4), GfObtained from the formula (5) in the following way,
Figure GDA0002271887520000115
obtained from the formula (7) in the following way,
Figure GDA0002271887520000116
obtained from the formula (8) in the following way,
Figure GDA0002271887520000117
obtained from formula (9), Ar3 is obtained from the CCT curve of the steel species in the step (1);
(11) the current grain size of ferrite is the grain size of ferrite in the phase prior to gamma → alpha transformation
Figure GDA0002271887520000118
And the growth increment at the late phase of the gamma → alpha phase transition
Figure GDA0002271887520000119
And, as shown in equation (12),
Figure GDA00022718875200001110
the invention combines the temperature field in the welding and cooling process with the CCT curve chart of the steel grade, and calculates the grain size in the welding and cooling process of the lath ferrite so as to realize the real-time calculation of the sizes of the lath ferrite in the welding seam and the heat affected zone in the welding process.
By utilizing the method for calculating the grain size of the lath ferrite in the welding and cooling process, the dynamic evolution process of the grain size in the cooling process can be obtained, as shown in fig. 2, and an effective calculation method is further provided for researching the influence of the welding and cooling speed on the grain. FIG. 2(a) is a schematic diagram of each region of a welding part, which includes a welding seam 1, a fusion region 2, a coarse grain region 3, a normalizing region 4, an incomplete recrystallization region 5, and a base material 6; FIG. 2(b) is a grain diagram at the weld; FIG. 2(c) is a grain diagram of the fusion zone; FIG. 2(d) is a grain diagram of a coarse-grained region; FIG. 2(e) is a grain diagram of the normalizing region; FIG. 2(f) is a diagram of the grains of the incomplete recrystallization zone; FIG. 2(g) is a crystal grain diagram of the base material.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (3)

1. A method for calculating the grain size of lath ferrite in the welding and cooling process is characterized in that a temperature field in the welding and cooling process is combined with a continuous cooling phase change CCT curve chart of a welding steel grade, and the grain size of the lath ferrite is calculated by a material method, and the method comprises the following specific steps:
(1) obtaining CCT curve chart of steel grade, and obtaining temperature T when phase change mechanism is changed in welding cooling processcFerrite initial precipitation temperature Ar3And an end temperature Tf；
(2) Obtaining the temperature field of a welding seam and a heat affected zone in the welding and cooling process, obtaining a thermal cycle curve of the temperature of a certain predicted point changing along with time, converting the time of the abscissa of the thermal cycle curve into a logarithmic coordinate, drawing the logarithmic coordinate on the CCT curve chart in the step (1), calculating the cooling speed of the predicted point by a formula (1),
Vc＝(Tmax-T)/t0(1)；
wherein, VcIs the cooling rate in ° C.s-1；
TmaxThe highest temperature in the welding and cooling process is measured in units of temperature;
t is the current temperature in units of;
t0is the cooling time in units of s;
(3) the diffusion coefficient Dc of carbon in the steel grade is obtained and is expressed in cm2·s-1；
(4) Obtaining the equilibrium mole fraction of carbon in the austenite side and the ferrite side at the austenite-ferrite phase boundary and the mole fraction of carbon in the austenite at different temperatures, respectively:
Figure FDA0002271887510000011
and
Figure FDA0002271887510000012
then calculating the growth rate G of ferrite according to the formula (2)fRelated dimensionless parameter omega0，
Figure FDA0002271887510000013
Wherein omega0Is a dimensionless parameter related to the ferrite growth rate;
Figure FDA0002271887510000014
is the equilibrium mole fraction of carbon at the austenite side at the austenite to ferrite phase boundary at different temperatures;
is the equilibrium mole fraction of carbon at the ferrite side at the austenite-ferrite phase boundary at different temperatures;
Figure FDA0002271887510000016
is the mole fraction of carbon in austenite at different temperatures;
(5) solving the average diameter d of the austenite grains by adopting an iterative calculation method through a formula (3)rCalculating the unit austenite effective grain boundary area S by the formula (4)γ，
Figure FDA0002271887510000021
Figure FDA0002271887510000022
Wherein d is0The austenite starting average grain diameter at constant temperature is expressed in cm;
drthe average grain diameter of austenite at the current moment is in cm;
k is a constant;
n is an index;
t0is the cooling time in units of s;
Sγis the unit austenite effective grain boundary area, and the unit is cm2；
π is the circumference ratio, 3.1415926;
(6) calculating the ferrite growth rate G according to the formula (5)f，
Figure FDA0002271887510000023
Wherein G isfIs the growth rate of ferrite in cm s-1；
DcIs the diffusion coefficient of carbon in the steel grade, and the unit is cm2·s-1；
r0Is the ultimate radius of curvature of the ferrite growing section, and is 1.8 multiplied by 10-6cm；
Ω0Is a parameter related to the growth rate of ferrite, and is obtained by the formula (2);
(7) calculating ferrite nucleation rate I according to formula (6)s，
Figure FDA0002271887510000024
Wherein, IsIs the ferrite nucleation rate in cm s-1；
K2、K3K is constant, and is 2.07 × 103、1.14×109And 1.38X 10-23；
DcIs the diffusion coefficient of carbon in the steel grade, and the unit is cm2·s-1；
T is the current temperature in units of;
Gfis the growth rate of ferrite in cm s-1Obtained from formula (5);
(8) calculating the transformation ratio of the ferrite at the early and later phase transformation
Figure FDA0002271887510000025
In the early phase of ferrite phase transition, the phase transition is mainly driven by a nucleation growth mechanism, the kinetic equation is shown as a formula (7), in the later phase of ferrite phase transition, the kinetic equation accords with a position saturation mechanism, and is shown as a formula (8),
Figure FDA0002271887510000031
Figure FDA0002271887510000032
wherein the content of the first and second substances,
Figure FDA0002271887510000033
the transformation ratios of the ferrite at the early stage and the later stage are respectively expressed in kg-cm-3·s-1；
IsIs the ferrite nucleation rate in cm s-1；
GfIs the growth rate of ferrite in cm s-1；
t is ferrite phase change current time, and the unit is s;
Sγis the unit austenite effective grain boundary area, and the unit is cm2；
IsObtained by the formula (6), GfObtained from the formula (5), SγObtained from formula (4);
(9) calculating the total ferrite nucleation number according to the formula (9)
Figure FDA0002271887510000034
Figure FDA0002271887510000035
Wherein the content of the first and second substances,
Figure FDA0002271887510000036
is the total ferrite nucleation number;
Tcthe temperature when the phase change mechanism is changed is expressed in units of ℃;
Ar3the initial precipitation temperature of ferrite is expressed in unit of ℃;
Isis the ferrite nucleation rate in cm s-1；
VcIs the cooling rate in ° C.s-1；
Figure FDA0002271887510000037
Is the transformation ratio of ferrite at the early stage of transformation, and the unit is kg cm-3·s-1；
T is the current temperature in units of;
Isobtained by the following formula (6),
Figure FDA0002271887510000038
obtained from the formula (7), Ar3Obtaining the CCT curve chart of the steel variety in the step (1);
(10) the ferrite grain size in the early stage of the γ → α transformation is calculated by the equations (10) and (11), respectively
Figure FDA0002271887510000039
And the growth increment at the late phase of the gamma → alpha phase transition
Figure FDA00022718875100000310
Figure FDA0002271887510000041
Wherein the content of the first and second substances,
Figure FDA0002271887510000042
is the ferrite grain size in cm at the early stage of gamma → alpha phase transformation;
Figure FDA0002271887510000043
is the growth increment of the later phase change of gamma → alpha, and the unit is cm;
Figure FDA0002271887510000044
the transformation ratios of the ferrite at the early stage and the later stage are respectively expressed in kg-cm-3·s-1；
π is the circumference ratio, 3.1415926;
Figure FDA0002271887510000045
is the total ferrite nucleation number;
Sγis the unit austenite effective grain boundary area, and the unit is cm2；
TfThe ferrite phase transition finishing temperature is expressed in units of ℃;
Tcthe temperature when the phase change mechanism is changed is expressed in units of ℃;
Gfis the growth rate of ferrite in cm s-1；
VcIs the cooling rate in ° C.s-1；
T is the current temperature in units of;
Sγobtained from the formula (4), GfObtained from the formula (5) in the following way,
Figure FDA0002271887510000046
obtained from the formula (7) in the following way,
Figure FDA0002271887510000047
obtained from the formula (8) in the following way,obtained by formula (9), Ar3Obtaining the CCT curve chart of the steel variety in the step (1);
(11) the current grain size of ferrite is the grain size of ferrite in the phase prior to gamma → alpha transformation
Figure FDA0002271887510000049
And the growth increment at the late phase of the gamma → alpha phase transition
Figure FDA00022718875100000410
And, as shown in equation (12),
Figure FDA00022718875100000411
in the step (1), the composition and hardness of the structure at different cooling speeds are simulated and analyzed through a thermal simulation testing machine, a CCT curve is drawn, and a CCT curve graph of the steel grade is obtained;
the temperature fields of the welding seam and the heat affected zone in the welding and cooling process in the step (2) are obtained through calculation of CFD software;
in the step (3), the diffusion coefficient Dc of the carbon in the steel grade is measured by a method for manufacturing a diffusion couple, wherein the method for manufacturing the diffusion couple is to connect steel sheets and carbon sheets which are welded in the same kind together by molybdenum wires to manufacture the diffusion couple, and the diffusion couple is heated to the highest welding temperature TmaxThen cooling treatment is carried out, and then the diffusion coefficient Dc is measured;
the steel grade is high-strength low-alloy steel, and is X65, X70, X80, X90, X100 or X120;
measuring the temperature fields of the welding seam and the heat affected zone in the welding and cooling process in the step (2) by an infrared thermal imager or a thermocouple;
d in the step (5)0The temperatures at the predicted points at which K and n are taken are shown below, and the temperatures at the predicted points which are not included can be calculated by intermediate interpolation0K and n;
when the predicted point temperature is 1010 ℃, n is 4.44988, K is 2340.1, d0Is 12.87cm × 10-4；
When the predicted point temperature is 1030 ℃, n is 4.21522, K is 2387.5, d0Is 15.50cm × 10-4；
When the predicted point temperature is 1050 ℃, n is 3.92269, K is 2478.2, d0Is 17.33cm × 10-4；
When the predicted point temperature is 1160 ℃, n is 2.48619, K is 19834.9, d0Is 25.1cm × 10-4；
When the predicted point temperature is 1200 ℃, n is 2.48339, K is 25485.8, d0Is 30.3cm × 10-4。
2. The method for calculating the grain size of lath ferrite during welding cooling according to claim 1, wherein the CFD software is Fluent finite element analysis software.
3. The method of calculating the grain size of lath ferrite during weld cooling according to claim 1, wherein in step (4), the equilibrium mole fraction of carbon at different temperatures at the austenitic-to-ferritic phase boundary on the austenitic side is calculated
Figure FDA0002271887510000051
Equilibrium mole fraction of carbon at different temperatures on the ferrite side at the austenite-ferrite phase boundary
Figure FDA0002271887510000052
Molar fraction of carbon in austenite at different temperatures
Figure FDA0002271887510000053
Obtained by inquiring an iron-carbon phase diagram.
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