CN101046682A - Method for predicting hot-rolling Nb-containing band steel organization and mechanical properties - Google Patents

Abstract

The present invention relates to a method for predicting hot-rolled Nb-contained band steel tissue and mechanical performance. Said method is characterized by that it uses physical metallurgical model as basis, adopts a method of making thermal simulation experiment be combined with industrial production actually-measured data analysis, creates mathematical models for hot-rolled Nb-contained band steel tissue and mechanical performance, including temperature model, austenite recrystallization model on the hot-rolling line, phase change model in cooling process and tissue and performance relationship model and selects VB language to originate predictive software for hot-rolled Nb-contained band steel tissue and mechanical performance.

Description

The method of a kind of predicting hot-rolled Nb-contained and mechanical property

Technical field

The invention belongs to technical field of steel rolling, be specifically related to the method for a kind of predicting hot-rolled Nb-contained and mechanical property.

Background technology

Along with the aggravation of steel products market competition, the user is more and more harsher to the price and the quality requirements of product, and this just requires steel production enterprise must improve constantly the quality of product, reduces production costs.For reaching this purpose, for the iron and steel system of processing, can manufacture experimently method repeatedly by the scene, determine optimal components and technology.But this need expend a large amount of manpower and financial resources, and instructs general the needs through long time because experimentation lacks its corresponding theory.In recent years, along with the development of computing machine, Physical Metallurgy, rolling technique, on the basis of physical metallurgy principle and a large amount of experiments, make up the mathematical model of composition, technology, microstructure and property, the steel hot rolling process is simulated and the structure property prediction, and then realized the optimization of production technology.This uses reducing survey fees; Shorten new product development cycle, reduce development cost; Stabilized product quality reduces loss due to spoiled work; Realize full-automatic accurately control, it is significant to improve productive capacity.

Microstructure evolution in the course of hot rolling and performance prediction start from Britain (the CM Sellars of the seventies in 20th century, Proc.Int.Conf.Hot Working and Forming Processes, Sheffield, ed.By CM Sellarsand GJ Davies, Met.Soc., London (1980)).The nineties is under the huge subsidy and hosting of USDOE and American National iron and steel office, metallurgical process engineering center of Univ British Columbia Canada and NBS and North America 14 tame iron and steel enterprises have developed process simulation software (the AISI-HSMM.Integ Process Group of a cover sheet material tandem rolling jointly, Inc. (USA), http://www.integpg.com).This software uses for many years in North America big steel enterprise, reacts fine.In addition, VAI engineering corporation (VAI) and Lin Ci steel mill have developed continuous-rolling strip steel quality control system (J.Andorfer cooperatively, G.Hribernig, A.Luger, et al. uses VAI-Q Strip system to realize comprehensive control of hot-strip mechanical property first, iron and steel, 2001,36:42-46), this system successively is used for the production run of mild carbon steel and Aldecor, can calculate mechanical property according to the chemical constitution of slab and the production data of measurement, and can revise goal production data (as final rolling temperature and coiling temperature etc.), to reach desired mechanical property.In addition, the Thyssen Aktiengesellschaft of Korea S Pu item company, Ying Ganglian, Siemens Company and Germany etc. have developed dissimilar mechanical properties forecast systems, and some has begun commercial the application.

Domestic structure property has been carried out a large amount of research, also set up microstructure evolution and Predicting Model for Mechanical Properties (Xu Yunbo, Liu Xianghua, Wang Guodong. prediction of hot-strip microstructure and property and controlling models and application prospect thereof, the steel research journal, 2002,14 (1): 65-68. 2. Xue Li is flat, and deer is kept reason, Dou Xiaofeng etc. the finite element analogy and the performance prediction of microstructure Evolution during the metal fever distortion, University of Science ﹠ Technology, Beijing's journal, 2000,22 (1): 34-37).In addition, also carried out structure property prediction work, combined process and Physical Metallurgy model have been developed simulation softward ROLLAN (Wang Liming, Sha Xiaochun, Li Dianzhong, in the exploitation of .Rollan hot strip rolling process organization differentiation with performance prediction software, ferrous materials international conference of new generation [c], Beijing: 2001), now online use, the needs that the off-line prediction error can satisfy inspection-free (or sampling observation).

Although existing many scientific research institutions and the Physical Metallurgy model of researcher in making up course of hot rolling, a large amount of explorations and effort have been carried out in aspects such as development organizations performance prediction system, but effect still allows of no optimist, also there are many problems, mainly show: (1) existing performance prediction system can satisfy few inspection even inspection-free requirement for the C-Mn steel, but, accomplish that accurately forecast also has certain degree of difficulty for micro alloyed steel; (2) aspect the structure property prediction that contains Nb band steel, bibliographical information both domestic and external the research of some relevant submodels, but do not see the report that comprehensive forecast contains microstructure evolution and mechanical property in the Nb band steel production run; (3) import software cost height.

Summary of the invention

The purpose of this invention is to provide a kind of cheaply, can be accurately and forecast the method for hot-rolling Nb-containing band steel organization and mechanical property fast.

For achieving the above object, the present invention is based on the Physical Metallurgy model, and the method that adopts thermal simulation experiment to combine with the analysis of commercial production measured data is set up the mathematical model at hot-rolling Nb-containing band steel organization and mechanical property; And select the VB language to work out the software of forecasting of hot-rolling Nb-containing band steel organization and mechanical property.

The present invention includes following steps:

At first, set up temperature model, comprise rolled piece temperature model on the roller-way, roughing section rolled piece temperature model, finish rolling section rolled piece temperature model, laminar flow cooling section rolled piece temperature model with method of finite difference;

Secondly, set up austenitic recrystallization model on the roll line, grow up model, roughing process austenitic recrystallization model, finish rolling process austenitic recrystallization model of austenite crystal when comprising heating;

Once more, set up and roll phase transition model in the cooling procedure of back, comprise phase transformation model incubation period, temperature model, each phase volume fraction model, ferritic grain size model when perlitic transformation finishes;

The end this, set up the microstructure and property relational model, comprise yield strength model, tensile strength model, extensibility model;

At last, select the software of forecasting of relevant hot-rolling Nb-containing band steel organization of VB language compilation and mechanical property.

Concrete steps are as follows:

One, austenitic recrystallization model

1, when heating the austenite crystal model of growing up:

$D^{1.7}=D_0^{1.7}+252.37\·\exp (-\frac{16409}{8.31T})\·t^{0.389}---\left(1\right)$

In the formula: D is the crystallite dimension μ m of temperature retention time when being t; T is temperature retention time s;

D ₀Crystallite dimension μ m for initial austenite; T is holding temperature K.

2, roughing process austenitic recrystallization model:

(1) roughing dynamic recrystallization critical strain model:

${\mathrm{\ϵ}}_{c1}=6.446\×{10}^{-5}\×D_0^{0.5}\·Z^{0.2231}---\left(2\right)$

$Z=\stackrel{\·}{\mathrm{\ϵ}}\exp \left(\frac{312000}{8.31T}\right)---\left(3\right)$

In the formula: ε _C1Be roughing dynamic recrystallization critical strain amount;

D ₀Be the austenite crystal diameter μ m before being out of shape;

Z is the Zener-Holloman parameter;

Be rate of deformation s ^-1T is deformation temperature K.

(2) roughing dynamic recrystallization number percent model:

$X_{d1}=1-\exp (-6.31{\left(\frac{\mathrm{\ϵ}-{\mathrm{\ϵ}}_C}{{\mathrm{\ϵ}}_S-{\mathrm{\ϵ}}_C}\right)}^{4.59})---\left(4\right)$

${\mathrm{\ϵ}}_S=A\·0.006\·D_0^{0.5}{\left(\stackrel{\·}{\mathrm{\ϵ}}\exp \left(\frac{312000}{8.31T}\right)\right)}^{0.1027}---\left(5\right)$

In the formula: X _D1Be the dynamic recrystallization percent by volume; ε is true strain;

ε _SStrain size when reaching steady state (SS) for dynamic recrystallization;

Be rate of deformation s ^-1R is a gas law constant; A is a correction factor.

(3) roughing dynamic recrystallization grain size model:

D _d1＝250000Z ^-0.34 (6)

In the formula: D _D1Be roughing dynamic recrystallization grain size;

Be rate of deformation;

T is deformation temperature K; Z is the Zener-Holloman parameter.

(4) roughing static state is the crystallization percentage model again:

$X_{s1}=1-\exp (-1.4\×{\left(\frac{t}{t_s}\right)}^{0.626})---\left(7\right)$

$t_s=0.2413{\mathrm{\ϵ}}^{-0.112}\exp \left(\frac{2836}{T}\right)---\left(8\right)$

In the formula: X _S1Static state when the residence time is t in the passage deformation gap is crystalline volume percentage again;

T is crystallization time s again; t _SBe medium-soft time s, promptly again crystallization to 50% o'clock required time;

Rolled piece temperature K when T is stop; ε is true strain.

(5) the big minimodel of the static recrystal grain of roughing:

$D_{s1}=334\×D_0^{0.4}{\mathrm{\ϵ}}^{-0.185}\exp (-\frac{45000}{8.31T})---\left(9\right)$

In the formula: D _S1Be the austenite crystal diameter μ m of static state when crystallization has just been finished again; ε is true strain;

D ₀Be the austenite crystal diameter μ m before being out of shape; T is deformation temperature K.

(6) roughing non-recrystallization grain size model:

D _n1＝D ₀ exp(-ε/12) (10)

In the formula: D _N1Equivalent diameter μ m for roughing distortion back flat crystal grain;

D ₀Be the austenite crystal diameter μ m before being out of shape; ε is true strain.

3, finish rolling process austenitic recrystallization model:

(1) finish rolling dynamic recrystallization critical strain model:

${\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20071005200700291.png"\; state="\{\{state\}\}">C</figure-callout>}2}=5.6\&times;{10}^{-4}{D}_0^{0.5}\exp \left(\frac{300000}{8.31T}\right)---\left(11\right)$

In the formula: ε _C2Be finish rolling dynamic recrystallization critical strain amount;

D ₀Be the austenite crystal diameter μ m before being out of shape; T is deformation temperature K.

(2) finish rolling dynamic recrystallization number percent model:

${\mathrm{<figure-callout\; id="2"\; label="X\; d"\; filenames="A20071005200700291.png"\; state="\{\{state\}\}">X</figure-callout>}}_d=1-\exp (-0.693{\left(\frac{\mathrm{\&epsiv;}-{\mathrm{\&epsiv;}}_c}{{\mathrm{\&epsiv;}}_{0.5}}\right)}^2)---\left(12\right)$

${\mathrm{\&epsiv;}}_{0.5}=1.3\&times;{10}^{-5}{D}_0^{0.28}{\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}}^{0.005}\exp \left(\frac{300000}{8.31T}\right)---\left(13\right)$

In the formula: X _D2Be finish rolling dynamic recrystallization percent by volume; ε _CBe dynamic recrystallization critical strain amount;

ε is true strain; ε _0.5For dynamic recrystallization reaches 50% needed dependent variable;

D ₀Be austenite crystal diameter μ m before being out of shape;

Be rate of deformation s ^-1

T is deformation temperature K.

(3) finish rolling dynamic recrystallization grain size model:

D _d2＝22600Z ^-0.27 (14)

In the formula: D _D2Be finish rolling dynamic recrystallization crystallite dimension;

Z is the Zener-Holloman parameter.

(4) model of growing up of finish rolling dynamic recrystallization crystal grain:

${\mathrm{<figure-callout\; id="2"\; label="D\; dyn"\; filenames="A20071005200700291.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\mathrm{dyn}}^2={\mathrm{<figure-callout\; id="2"\; label="D\; d"\; filenames="A20071005200700291.png"\; state="\{\{state\}\}">D</figure-callout>}}_d^2+3900{C_{\mathrm{eq}}}^{-1.43}\&CenterDot;t^{0.3}\exp (-5380/T)---\left(15\right)$

In the formula: D _Dyn2Be the later dynamic recrystallization crystallite dimension μ m of residence time t between passage;

D _D2Be finish rolling dynamic recrystallization crystallite dimension μ m; C _EqBe the C equivalent;

T is residence time s between passage.

(5) finish rolling static state is crystallization start time model again:

$t_{0.05}=6.75\&times;{10}^{-20}{\mathrm{\&epsiv;}}^{-4}\&CenterDot;D_0\&CenterDot;\exp \left(\frac{300000}{8.31T}\right)\&CenterDot;\exp \left\{(\frac{2.75\&times;{10}^5}{T}-185)\right[\mathrm{Nb}\%\left]\right\}---\left(16\right)$

In the formula: t _0.05For finish rolling static state again crystallization reach 5% o'clock needed time s,

ε is true strain; D ₀Be austenite crystal diameter μ m before being out of shape;

T is deformation temperature K; [Nb%] is the percentage composition of Nb element.

(6) finish rolling static state is the crystallization percentage model again:

X＝1-exp{0.693(t/t _0.5) ²} (17)

$t_{0.5}=2.52\&times;{10}^{-19}{\mathrm{\&epsiv;}}^p{D}_0^{1.7}\exp (\frac{325000}{8.31T}325000/\mathrm{RT})---\left(18\right)$

In the formula: finish rolling static state crystallization percentage again when X is residence time t; T is residence time s;

ε is true strain; T is deformation temperature K; D ₀Be austenite grain size μ m before being out of shape.

(7) the big minimodel of the static recrystal grain of finish rolling:

$D_{s2}=3.000\&times;D_0^{0.2}{\mathrm{\&epsiv;}}^{0.5}---\left(19\right)$

In the formula: D _S2Be the static recrystal grain size of finish rolling μ m;

D ₀Be austenite grain size μ m before being out of shape; ε is true strain.

(8) model of growing up of the static recrystal grain of finish rolling:

${\mathrm{<figure-callout\; id="2"\; label="D\; stat"\; filenames="A20071005200700291.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\mathrm{stat}}^2=D_{s2}^{4.5}+3.68\&times;{10}^7{C_{\mathrm{eq}}}^{-1.43}\&CenterDot;\exp (-7000/T)\&CenterDot;t^{0.7}---\left(20\right)$

In the formula: D _Stat2Be finish rolling crystal grain diameter μ m during through t after crystallization is finished again;

D _S2Be the static recrystal grain size of finish rolling μ m; C _EqBe the C equivalent;

T is temperature K; T is for just having finished beginning consumed time s from crystallization again.

(9) the austenite crystal model of crystallization does not again take place in finish rolling:

D _n2＝D ₀·exp(-ε/4) (21)

In the formula: D _N2The equivalent diameter μ m of finish rolling distortion back flat crystal grain;

D ₀Be austenite grain size μ m before being out of shape; ε is true strain.

Two, roll phase transition model in the cooling procedure of back

1, phase transformation model incubation period:

$k_f=\exp \left\{\begin{array}{c}4.91-13.339\&CenterDot;[\%C]-1.1922\&CenterDot;[\%\mathrm{Mn}]+0.02505\&CenterDot;(T-273)-\\ 3.5067\&times;{10}^{-5}\&CenterDot;{(T-273)}^2\end{array}\right\}---\left(22\right)$

lnτ _f＝-1.6454·lnk _f+20·lnT+3.265×10 ⁴·T ^-1-174.67 (23)

$k_p=\exp \left\{\begin{array}{c}11.2-16.002\&CenterDot;[\%C]-0.9797\&CenterDot;[\%\mathrm{Mn}]+0.00791\&CenterDot;\\ (T-273)-2.313\&times;{10}^{-5}\&CenterDot;{(T-273)}^2\end{array}\right\}---\left(24\right)$

lnτ _p＝-0.91732·lnk _p+20·lnT+1.9559×10 ⁴·T ^-1-158.6 (25)

$k_b=\exp \left\{\begin{array}{c}28.9-11.484\&CenterDot;[\%C]-1.1121\&CenterDot;[\%\mathrm{Mn}]+0.13109\&CenterDot;\\ (T-273)-1.2077\&times;{10}^{-4}\&CenterDot;{(T-273)}^2\end{array}\right\}---\left(26\right)$

lnτ _b＝-0.68352·lnτ _b+20·lnT+1.6491×10 ⁴·T ^-1-155.8 (27)

In the formula: k _f, τ _fBe respectively the constant and the incubation period of ferrite transformation model incubation period;

k _p, τ _pBe respectively pearlitic transformation model constants incubation period and incubation period;

k _b, τ _bBe respectively bainitic transformation model constants incubation period and incubation period;

T is temperature K; [C%], [Mn%] are respectively the percentage composition of carbon, niobium, manganese.

Temperature model when 2, perlitic transformation finishes:

T _PE＝951.30-143.26·[％C]-86.20[Nb％]-24.15·[％Mn] (28)

In the formula: T _PETemperature K when finishing for perlitic transformation;

[C%], [Nb%], [Mn%] are respectively the percentage composition of carbon, niobium, manganese.

3, each phase volume fraction model:

$X=1-\exp (-\frac{1}{2.24}\{\frac{2.24}{D}\&times;q+0.114\&times;{\left(\mathrm{\&Delta;\&epsiv;}\right)}^2\}\&times;\{1+4\&times;\mathrm{\&Delta;\&epsiv;}\}\&times;k\&times;t^n)---\left(29\right)$

In the formula: X is the volume fraction of each phase behind the austenitic transformation;

D is austenitic crystallite dimension μ m before the phase transformation;

Q is a shape coefficient, and span is 1.2-3.8;

Δ ε is an overstrain; T is transformation time s;

N is the Avrami coefficient, and ferrite is 2.4, and pearlite is 2.0, and bainite is 2.5,

The k value can adopt formula (22) to calculate for ferrite, can adopt formula (24) to calculate for pearlite k value, can adopt formula (26) to calculate for bainite k value.

4, ferritic grain size model:

lnd _f0＝-0.4688×ln[2.24/D×q+0.144×(Δε) ²]+0.005724×Ar ₃

-0.53259×ln(1+4.0×Δε)+0.13113×lnV _f-3.95 (30)

d _f ²＝d _f0 ²+24.811×d _f0 ^0.5888exp[-181.56/(T _c-723)] (31)

In the formula: d _F0Be ferritic crystallite dimension μ m after the phase transformation,

D is austenitic crystallite dimension μ m before the phase transformation,

Δ ε is an overstrain,

Ar ₃For ferrite begins transition temperature K,

V _fBe the volume fraction of ferrite after beginning to change,

Q is a shape coefficient, and span is 1.2-3.8,

d _fBe final ferritic crystallite dimension μ m,

T _cBe coiling temperature K.

Three, microstructure and property relational model

1, yield strength model:

σ _s＝1158201[C％]+591.73[Nb％]+1559.80d _f ^-0.5+3877.34V _p-0.193T _c-10.20h-39202 (32)

2, tensile strength model:

σ _b＝7824.90[C％]+1519.10[Nb％]+1900.16d _f ^-0.5+4098.58V _p-0.34T _c-9.10h-362.29 (33)

3, extensibility model:

δ＝0.39[Mn％]-106.0[Si％]+561.74[Nb％]-0.15V _p+9.32d _f ^-0.5-0.0021T _c+26.51 (34)

[C%] in formula (32), (33), (34), [Nb%], [Mn%] are the percentage composition of carbon, niobium, manganese

d _fBe ferritic crystallite dimension μ m, V _pBe pearlitic volume fraction;

T _cFor coiling temperature K, h are belt steel thickness mm.

Four, select the software of forecasting of relevant hot-strip tissue of VB language compilation and mechanical property, the main flow of its software is:

The method that adopts thermal simulation experiment to combine with the analysis of commercial production measured data, foundation comprises and sets up temperature model at the mathematical model of hot-rolling Nb-containing band steel organization and mechanical property, sets up austenitic recrystallization model, set up phase transition model, set up the microstructure and property relational model; On this basis, adopt the software of forecasting of VB language establishment hot-rolling Nb-containing band steel organization and mechanical property;

At first, the chemical constitution and the technological parameter of input steel grade calculate according to the formula in the austenitic recrystallization model.Calculate the critical strain ε of dynamic recrystallization _CIf the passage strain stress is greater than the critical strain ε of dynamic recrystallization _C, just adopt Dynamic Recrystallization Model to calculate the dynamic recrystallization mark of roughing and finish rolling respectively; If the passage strain stress is less than the critical strain ε of dynamic recrystallization _C, just adopt static state that static crystal model again calculates roughing and finish rolling respectively crystalline fraction again.

Then, on the basis of austenite recrystallization result of calculation, the formula in the phase transition model calculates in the cooling procedure of back according to rolling.Temperature T when calculating the end of ferrite and pearlitic incubation period and perlitic transformation respectively _PE, calculate n ferritic volume fraction V constantly respectively according to stack rule and phase transition model again _FnWith pearlitic volume fraction V _PnTemperature T when temperature T finishes less than perlitic transformation _PEThe time, calculate n+1 ferritic volume fraction V constantly respectively by process of iteration _{F (n+1)}With pearlitic volume fraction V _{P (n+1)}Temperature T when temperature T finishes less than perlitic transformation _PEThe time, ferrite and pearlitic volume fraction are calculated and are finished; The volume fraction V of bainite _bCan calculate according to ferrite and pearlitic volume fraction.

At last, in rolling the back cooling procedure on the basis of phase transformation result of calculation, the formula in giving according to the microstructure and property relational model calculates, and just can calculate yield strength, tensile strength and extensibility respectively.

Because adopt technique scheme, the present invention is predicting hot-rolled Nb-contained and mechanical property quickly and accurately, for offline optimization hot-rolling Nb-containing band steel production technology provides " computer trial production " platform.The present invention coincide to the forecast and the measured value of hot-rolling Nb-containing band steel mechanical property, the yield strength of forecast and actual measurement yield strength error are at ratio 〉=85% of ± 15MPa scope, the tensile strength of forecast and actual measurement tensile strength error are at ratio 〉=90% of ± 20MPa scope, the extensibility of forecast and ratio 〉=90% of actual measurement extensibility error in ± 7% scope.And the present invention can expand or revise, enlarge its range of application easily.

Description of drawings

Fig. 1 is a main-process stream block diagram of the present invention;

Fig. 2 is an austenite recrystallization calculation process block diagram;

Fig. 3 rolls phase transformation calculation process block diagram in the cooling procedure of back;

Fig. 4 is a microstructure and property calculation process block diagram;

Fig. 5 is the software of forecasting parameter setting interface;

Fig. 6 is that software of forecasting is to austenite recrystallization forecast result in the rolling process of rough rolling;

Fig. 7 is that software of forecasting is to austenite recrystallization forecast result in the finish rolling operation of rolling;

Fig. 8 is the forecast result of software of forecasting to final tissue;

Fig. 9 is the forecast result of software of forecasting to the finished product mechanical property.

Embodiment

A kind of method of predicting hot-strip tissue and mechanical property is an example with the production of the 1700mm hot continuous rolling WL510 of certain steel mill band steel, and the present invention is further detailed explanation with example in conjunction with the accompanying drawings.

Present embodiment as shown in Figure 1, based on the Physical Metallurgy model, the method that adopts thermal simulation experiment to combine with the analysis of commercial production measured data, foundation is at the mathematical model of hot-rolling Nb-containing band steel organization and mechanical property; And adopt the VB language to work out the software of forecasting of hot-rolling Nb-containing band steel organization and mechanical property.

Present embodiment may further comprise the steps:

At first, set up temperature model, comprise rolled piece temperature model on the roller-way, roughing section rolled piece temperature model, finish rolling section rolled piece temperature model, laminar flow cooling section rolled piece temperature model with method of finite difference;

Secondly, set up austenitic recrystallization model on the roll line, grow up model, roughing process austenitic recrystallization model, finish rolling process austenitic recrystallization model of austenite crystal when comprising heating;

Once more, set up and roll phase transition model in the cooling procedure of back, comprise phase transformation model incubation period, temperature model, each phase volume fraction model, ferritic grain size model when perlitic transformation finishes;

The end this, set up the microstructure and property relational model, comprise yield strength model, tensile strength model, extensibility model;

At last, select the software of forecasting of relevant hot-rolling Nb-containing band steel organization of VB language compilation and mechanical property.

Concrete steps are as follows:

One, austenitic recrystallization model

1, when heating the austenite crystal model of growing up:

$D^{1.7}=D_0^{1.7}+252.37\&CenterDot;\exp (-\frac{16409}{8.31})\&CenterDot;t^{0.389}---\left(1\right)$

In the formula: D is the crystallite dimension μ m of temperature retention time when being t; T is temperature retention time s;

D ₀Crystallite dimension μ m for initial austenite; T is holding temperature K.

2, roughing process austenitic recrystallization model:

(1) roughing dynamic recrystallization critical strain model:

${\mathrm{\&epsiv;}}_{c1}=6.446\&times;{10}^{-5}\&times;D_0^{0.5}\&CenterDot;Z^{0.2231}---\left(2\right)$

$Z=\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}\exp \left(\frac{312000}{8.31T}\right)---\left(3\right)$

In the formula: ε _C1Be roughing dynamic recrystallization critical strain amount;

D ₀Be the austenite crystal diameter μ m before being out of shape;

Z is the Zener-Holloman parameter; Be rate of deformation s ^-1T is deformation temperature K.

(2) roughing dynamic recrystallization number percent model:

$X_{d1}=1-\exp (-6.31{\left(\frac{\mathrm{\&epsiv;}-{\mathrm{\&epsiv;}}_C}{{\mathrm{\&epsiv;}}_S-{\mathrm{\&epsiv;}}_C}\right)}^{4.59})---\left(4\right)$

${\mathrm{\&epsiv;}}_S=A\&CenterDot;0.006\&CenterDot;D_0^{0.5}{\left(\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}\exp \left(\frac{312000}{8.31T}\right)\right)}^{0.1027}---\left(5\right)$

In the formula: X _D1Be the dynamic recrystallization percent by volume; ε is true strain;

ε _sStrain size when reaching steady state (SS) for dynamic recrystallization;

Be rate of deformation s ^-1R is a gas law constant; A is a correction factor.

(3) roughing dynamic recrystallization grain size model:

D _d1＝250000Z ^-0.34 (6)

In the formula: D _D1Be roughing dynamic recrystallization grain size;

Be rate of deformation;

T is deformation temperature K; Z is the Zener-Holloman parameter.

(4) roughing static state is the crystallization percentage model again:

$X_{s1}=1-\exp (-1.4\&times;{\left(\frac{t}{t_s}\right)}^{0.626})---\left(7\right)$

$t_s=0.2413{\mathrm{\&epsiv;}}^{-0.112}\exp \left(\frac{2836}{T}\right)---\left(8\right)$

In the formula: X _S1Static state when the residence time is t in the passage deformation gap is crystalline volume percentage again;

T is crystallization time s again; t _SBe medium-soft time s, promptly again crystallization to 50% o'clock required time;

Rolled piece temperature K when T is stop; ε is true strain.

(5) the big minimodel of the static recrystal grain of roughing:

$D_{s1}=334\&times;D_0^{0.4}{\mathrm{\&epsiv;}}^{-0.185}\exp (-\frac{45000}{8.31T})---\left(9\right)$

In the formula: D _S1Be the austenite crystal diameter μ m of static state when crystallization has just been finished again; ε is true strain;

D ₀Be the austenite crystal diameter μ m before being out of shape; T is deformation temperature K.

(6) roughing non-recrystallization grain size model:

D _n1＝D ₀ exp(-ε/12) (10)

In the formula: D _N1Equivalent diameter μ m for roughing distortion back flat crystal grain;

D ₀Be the austenite crystal diameter μ m before being out of shape; ε is true strain.

3, finish rolling process austenitic recrystallization model:

(1) finish rolling dynamic recrystallization critical strain model:

${\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20071005200700291.png"\; state="\{\{state\}\}">C</figure-callout>}2}=5.6\&times;{10}^{-4}{D}_0^{0.5}\exp \left(\frac{300000}{8.31}\right)---\left(11\right)$

In the formula: ε _C2Be finish rolling dynamic recrystallization critical strain amount;

D ₀Be the austenite crystal diameter μ m before being out of shape; T is deformation temperature K.

(2) finish rolling dynamic recrystallization number percent model:

${\mathrm{<figure-callout\; id="2"\; label="X\; d"\; filenames="A20071005200700291.png"\; state="\{\{state\}\}">X</figure-callout>}}_d=1-\exp (-0.693{\left(\frac{\mathrm{\&epsiv;}-{\mathrm{\&epsiv;}}_c}{{\mathrm{\&epsiv;}}_{0.5}}\right)}^2)---\left(12\right)$

${\mathrm{\&epsiv;}}_{0.5}=1.3\&times;{10}^{-5}{D}_0^{0.28}{\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}}^{0.005}\exp \left(\frac{300000}{8.31T}\right)---\left(13\right)$

In the formula: X _D2Be finish rolling dynamic recrystallization percent by volume; ε _CBe dynamic recrystallization critical strain amount;

ε is true strain; ε _0.5For dynamic recrystallization reaches 50% needed dependent variable;

D ₀Be austenite crystal diameter μ m before being out of shape;

Be rate of deformation s ^-1

T is deformation temperature K.

(3) finish rolling dynamic recrystallization grain size model:

D _d2＝22600Z ^-0.27 (14)

In the formula: D _D2Be finish rolling dynamic recrystallization crystallite dimension;

Z is the Zener-Holloman parameter.

(4) model of growing up of finish rolling dynamic recrystallization crystal grain:

${\mathrm{<figure-callout\; id="2"\; label="D\; dyn"\; filenames="A20071005200700291.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\mathrm{dyn}}^2={\mathrm{<figure-callout\; id="2"\; label="D\; d"\; filenames="A20071005200700291.png"\; state="\{\{state\}\}">D</figure-callout>}}_d^2+3900{C_{\mathrm{eq}}}^{-1.43}\&CenterDot;t^{0.3}\exp (-5380/T)---\left(15\right)$

In the formula: D _Dyn2Be the later dynamic recrystallization crystallite dimension μ m of residence time t between passage;

D _D2Be finish rolling dynamic recrystallization crystallite dimension μ m; C _EqBe the C equivalent;

T is residence time s between passage.

(5) finish rolling static state is crystallization start time model again:

$t_{0.05}=6.75\&times;{10}^{-20}{\mathrm{\&epsiv;}}^{-4}\&CenterDot;D_0\&CenterDot;\exp \left(\frac{300000}{8.31T}\right)\&CenterDot;\exp \left\{(\frac{2.75\&times;{10}^5}{T}-185[\mathrm{Nb}\%\left]\right)\right\}---\left(16\right)$

In the formula: t _0.05For finish rolling static state again crystallization reach 5% o'clock needed time s,

ε is true strain; D ₀Be austenite crystal diameter μ m before being out of shape;

T is deformation temperature K; [Nb%] is the percentage composition of Nb element.

(6) finish rolling static state is the crystallization percentage model again:

X＝1-exp{0.693(t/t _0.5) ²} (17)

$t_{0.5}=2.52\&times;{10}^{-19}{\mathrm{\&epsiv;}}^p{D}_0^{1.7}\exp (\frac{325000}{8.31T}325000/\mathrm{RT})---\left(18\right)$

In the formula: finish rolling static state crystallization percentage again when X is residence time t; T is residence time s;

ε is true strain; T is deformation temperature K; D ₀Be austenite grain size μ m before being out of shape.

(7) the big minimodel of the static recrystal grain of finish rolling:

$D_{s2}=3.000\&times;D_0^{0.2}{\mathrm{\&epsiv;}}^{0.5}---\left(19\right)$

In the formula: D _S2Be the static recrystal grain size of finish rolling μ m;

D ₀Be austenite grain size μ m before being out of shape; ε is true strain.

(8) model of growing up of the static recrystal grain of finish rolling:

${\mathrm{<figure-callout\; id="2"\; label="D\; stat"\; filenames="A20071005200700291.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\mathrm{stat}}^2=D_{s2}^{4.5}+3.68\&times;{10}^7{C_{\mathrm{eq}}}^{-1.43}\&CenterDot;\exp (-70000/T)\&CenterDot;t^{0.7}---\left(20\right)$

In the formula: D _Stat2Be finish rolling crystal grain diameter μ m during through t after crystallization is finished again;

D _S2Be the static recrystal grain size of finish rolling μ m; C _EqBe the C equivalent;

T is temperature K; T is for just having finished beginning consumed time s from crystallization again.

(9) the austenite crystal model of crystallization does not again take place in finish rolling:

D _n2＝D ₀·exp(-ε/4) (21)

In the formula: D _N2The equivalent diameter μ m of finish rolling distortion back flat crystal grain;

D ₀Be austenite grain size μ m before being out of shape; ε is true strain.

Two, roll phase transition model in the cooling procedure of back:

1, phase transformation model incubation period:

$k_f=\exp \left\{\begin{array}{c}4.91-13.339\&CenterDot;[\%C]-1.1922\&CenterDot;[\%\mathrm{Mn}]+0.02505\&CenterDot;(T-273)-\\ 3.5067\&times;{10}^{-5}\&CenterDot;{(T-273)}^2\end{array}\right\}---\left(22\right)$

lnτ _f＝-1.6454·lnk _f+20·lnT+3.265×10 ⁴·T ^-1-174.67 (23)

$k_p=\exp \left\{\begin{array}{c}11.2-16.002\&CenterDot;[\%C]-0.9797\&CenterDot;[\%\mathrm{Mn}]+0.00791\&CenterDot;\\ (T-273)-2.313\&times;{10}^{-5}\&CenterDot;{(T-273)}^2\end{array}\right\}---\left(24\right)$

lnτ _p＝-0.91732·lnk _p+20·lnT+1.9559×10 ⁴·T ^-1-158.6 (25)

$k_b=\exp \left\{\begin{array}{c}28.9-11.484\&CenterDot;[\%C]-1.1121\&CenterDot;[\%\mathrm{Mn}]+0.13109\&CenterDot;\\ (T-273)-1.2077\&times;{10}^{-4}\&CenterDot;{(T-273)}^2\end{array}\right\}---\left(26\right)$

lnτ _b＝-0.68352·lnτ _b+20·lnT+1.6491×10 ⁴·T ^-1-155.8 (27)

In the formula: k _f, τ _fBe respectively the constant and the incubation period of ferrite transformation model incubation period;

k _p, τ _pBe respectively pearlitic transformation model constants incubation period and incubation period;

k _b, τ _bBe respectively bainitic transformation model constants incubation period and incubation period;

T is temperature K; [C%], [Mn%] are respectively the percentage composition of carbon, niobium, manganese.

Temperature model when 2, perlitic transformation finishes:

T _PE＝951.30-143.26·[％C]-86.20[Nb％]-24.15·[％Mn] (28)

In the formula: T _PETemperature K when finishing for perlitic transformation;

[C%], [Nb%], [Mn%] are respectively the percentage composition of carbon, niobium, manganese.

3, each phase volume fraction model:

$X=1-\exp (-\frac{1}{2.24}\{\frac{2.24}{D}\&times;q+0.114\&times;{\left(\mathrm{\&Delta;\&epsiv;}\right)}^2\}\&times;\{1+4\&times;\mathrm{\&Delta;\&epsiv;}\}\&times;k\&times;t^n)---\left(29\right)$

In the formula: X is the volume fraction of each phase behind the austenitic transformation;

D is austenitic crystallite dimension μ m before the phase transformation;

Q is a shape coefficient, and span is 1.2-3.8;

Δ ε is an overstrain; T is transformation time s;

N is the Avrami coefficient, and ferrite is 2.4, and pearlite is 2.0, and bainite is 2.5,

The k value can adopt formula (22) to calculate for ferrite, can adopt formula (24) to calculate for pearlite k value, can adopt formula (26) to calculate for bainite k value.

4, ferritic grain size model:

lnd _f0＝-0.4688×ln[2.24/D×q+0.144×(Δε) ²]+0.005724×Ar ₃

-0.53259×ln(1+4.0×Δε)+0.13113×lnV _f-3.95 (30)

d _f ²＝d _f0 ²+24.811×d _f0 ^0.5888exp[-181.56/(T _c-723)] (31)

In the formula: d _F0Be ferritic crystallite dimension μ m after the phase transformation,

D is austenitic crystallite dimension μ m before the phase transformation,

Δ ε is an overstrain,

Ar ₃For ferrite begins transition temperature K,

V _fBe the volume fraction of ferrite after beginning to change,

Q is a shape coefficient, and span is 1.2-3.8,

d _fBe final ferritic crystallite dimension μ m,

T _cBe coiling temperature K.

Three, microstructure and property relational model

1, yield strength model

σ _s＝1158201[C％]+591.73[Nb％]+1559.80d _f ^-0.5+3877.34V _p-0.193T _c-10.20h-39202 (32)

2, tensile strength model

σ _b＝7824.90[C％]+1519.10[Nb％]+1900.16d _f ^-0.5+4098.58V _p-0.34T _c-9.10h-36229 (33)

3, the extensibility model is

δ＝0.39[Mn％]-106.0[Si％]+561.74[Nb％]-0.15V _p+9.32d _f ^-0.5-0.0021T _c+26.51 (34)

[C%] in formula (32), (33), (34), [Nb%], [Mn%] are the percentage composition of carbon, niobium, manganese;

d _fBe ferritic crystallite dimension μ m, V _pBe pearlitic volume fraction;

T _cFor coiling temperature K, h are belt steel thickness mm.

Four, select the software of forecasting of relevant hot-strip tissue of VB language compilation and mechanical property, structure property is forecast.

1, forecasts crystallization again

Austenite recrystallization calculation process block diagram is imported the chemical constitution and the technological parameter of steel grade as shown in Figure 2, and formula (1)～(21) formula that provides according to austenitic recrystallization model calculates, and calculates the critical strain ε of dynamic recrystallization earlier _CIf the passage strain stress is greater than the critical strain ε of dynamic recrystallization _C, just adopt Dynamic Recrystallization Model to calculate the dynamic recrystallization mark of roughing and finish rolling respectively; If the passage strain stress is less than the critical strain ε of dynamic recrystallization _C, just adopt static state that static crystal model again calculates roughing and finish rolling respectively crystalline fraction again.Software of forecasting is forecast the result as shown in Figure 6 to austenite recrystallization in the rolling process of rough rolling, and software of forecasting to austenite recrystallization forecast result in the finish rolling operation of rolling as shown in Figure 7.

2, forecast final room temperature texture

Roll the back cooling procedure in phase transformation calculation process block diagram as shown in Figure 3, on the basis of austenite recrystallization result of calculation, calculate the temperature T when calculating the end of ferrite and pearlitic incubation period and perlitic transformation respectively according to rolling formula (22)～(31) that phase transition model provides in the cooling procedure of back _PE, calculate n ferritic volume fraction V constantly respectively according to stack rule and phase transition model again _FnWith pearlitic volume fraction V _PnTemperature T when temperature T finishes less than perlitic transformation _PEThe time, calculate (n+1) ferritic volume fraction V constantly respectively by process of iteration _{F (n+1)}With pearlitic volume fraction V _{P (n+1)}Temperature T when temperature T finishes less than perlitic transformation _PEThe time, ferrite and pearlitic volume fraction are calculated and are finished; The volume fraction V of bainite _bCan calculate according to ferrite and pearlitic volume fraction.Result of calculation as shown in Figure 8, result of calculation shows that ferritic beginning transition temperature is 676.69 ℃, volume fraction is 84.76%, average grain size is 5.56 μ m, pearlitic beginning transition temperature is 655.53 ℃, volume fraction is 11.81%, and the beginning transition temperature of bainite is 553.99 ℃, and volume fraction is 3.42%.

3, the mechanical property of forecast finished product

Microstructure and property calculation process block diagram as shown in Figure 4, in rolling the back cooling procedure on the basis of phase transformation result of calculation, calculate formula (32)～(34) in giving according to the microstructure and property relational model, just can calculate yield strength, tensile strength and extensibility respectively.Result of calculation as shown in Figure 9, yield strength is 457.16MPa, tensile strength is 545.01MPa, extensibility is 29.33%.

Work out the accuracy of software of forecasting in order to verify, collected part end properties check data at the scene, predicted value and measured value to mechanical property compares (seeing attached list 1), the error that the result shows yield strength is less than ± 10.5MPa, the error of tensile strength is less than ± 16MPa, the error of extensibility illustrates that less than ± 1.1% predicted value and measured value coincide better.Further the measured data that contains the Nb steel that certain 2002-2006 of steel mill is produced is analyzed and is compared, the yield strength of finding forecast and actual measurement yield strength error are at ratio 〉=85% of ± 15MPa scope, the tensile strength of forecast and actual measurement tensile strength error are at ratio 〉=90% of ± 20MPa scope, the extensibility of forecast and ratio 〉=90% of actual measurement extensibility error in ± 7% scope.

Table 1 mechanical properties forecast value and measured value are relatively

Sequence number	Nominal thickness	The yield strength measured value	The yield strength predicted value	The tensile strength measured value	The tensile strength prediction value	The extensibility measured value	The extensibility predicted value
								1	4.0	475.32	458.00	560.66	545.00	28.26	29.30
2	5.0	460.59	459.00	548.12	544.00	29.52	29.00
								3	6.0	453.06	451.00	547.76	539.00	27.71	28.80
4	7.0	423.2	443.00	521.00	534.00	29.46	28.70
								5	8.0	425.62	430.00	533.92	525.00	28.32	28.70

Because adopt technique scheme, the present invention is predicting hot-rolled Nb-contained and mechanical property quickly and accurately, for offline optimization hot-rolling Nb-containing band steel production technology provides " computer trial production " platform.The present invention coincide to the forecast and the measured value of hot-rolling Nb-containing band steel mechanical property, the yield strength of forecast and actual measurement yield strength error are at ratio 〉=85% of ± 15MPa scope, the tensile strength of forecast and actual measurement tensile strength error are at ratio 〉=90% of ± 20MPa scope, the extensibility of forecast and ratio 〉=90% of actual measurement extensibility error in ± 7% scope.And the present invention can expand or revise, enlarge its range of application easily.

Claims (12)

1, the method for a kind of predicting hot-rolled Nb-contained and mechanical property is characterized in that may further comprise the steps:

(1) sets up temperature model with method of finite difference, comprise rolled piece temperature model on the roller-way, roughing section rolled piece temperature model, finish rolling section rolled piece temperature model, laminar flow cooling section rolled piece temperature model;

(2) set up austenitic recrystallization model on the roll line, comprise when heating austenite crystal grow up model, roughing process austenitic recrystallization model, finish rolling process austenitic recrystallization model;

(3) phase transition model in the cooling procedure of back is rolled in foundation, comprises phase transformation model incubation period, temperature model, each phase volume fraction model, ferritic grain size model when perlitic transformation finishes;

(4) set up the microstructure and property relational model, comprise yield strength model, tensile strength model, extensibility model;

(5) software of forecasting of selection relevant hot-rolling Nb-containing band steel organization of VB language compilation and mechanical property.

2, the method for predicting hot-rolled Nb-contained according to claim 1 and mechanical property, the austenite crystal model of growing up when it is characterized in that the heating of described austenitic recrystallization model:

$D^{1.7}=D_0^{1.7}+252.37\&CenterDot;\exp (-\frac{16409}{8.31T})\&CenterDot;t^{0.398}...\left(1\right)$

In the formula: D is the crystallite dimension μ m of temperature retention time when being t; T is temperature retention time s;

D ₀Crystallite dimension μ m for initial austenite; T is holding temperature K.

3, the method for predicting hot-rolled Nb-contained according to claim 1 and mechanical property is characterized in that the roughing process austenitic recrystallization model of described austenitic recrystallization model:

(1) roughing dynamic recrystallization critical strain model:

${\mathrm{\&epsiv;}}_{c1}=6.446\&times;{10}^{-5}\&times;D_0^{0.5}\&CenterDot;Z^{0.2231}...\left(2\right)$

$Z=\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}\exp \left(\frac{312000}{8.31T}\right)...\left(3\right)$

In the formula: ε _C1Be roughing dynamic recrystallization critical strain amount; D ₀Be the austenite crystal diameter μ m before being out of shape;

Z is the Zener-Holloman parameter;

Be rate of deformation s ^-1T is deformation temperature K.

(2) roughing dynamic recrystallization number percent model:

$X_{d1}=1-\exp (-6.31{\left(\frac{\mathrm{\&epsiv;}-{\mathrm{\&epsiv;}}_C}{{\mathrm{\&epsiv;}}_S-{\mathrm{\&epsiv;}}_C}\right)}^{4.59})...\left(4\right)$

${\mathrm{\&epsiv;}}_S=A\&CenterDot;0.006\&CenterDot;D_0^{0.5}{\left(\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}\exp \left(\frac{312000}{8.31T}\right)\right)}^{0.1027}...\left(5\right)$

In the formula: X _D1Be the dynamic recrystallization percent by volume; ε is true strain;

ε _SStrain size when reaching steady state (SS) for dynamic recrystallization;

Be rate of deformation s ^-1R is a gas law constant; A is a correction factor.

(3) roughing dynamic recrystallization grain size model:

D _d1＝250000Z ^-0.34 (6)

In the formula: D _D1Be roughing dynamic recrystallization grain size;

Be rate of deformation;

T is deformation temperature K; Z is the Zener-Holloman parameter.

(4) roughing static state is the crystallization percentage model again:

$X_{s1}=1-\exp (-1.4\&times;{\left(\frac{t}{t_S}\right)}^{0.626})...\left(7\right)$

$t_s=0.2413{\mathrm{\&epsiv;}}^{-0.112}\exp \left(\frac{2836}{T}\right)...\left(8\right)$

In the formula: X _S1Static state when the residence time is t in the passage deformation gap is crystalline volume percentage again;

T is crystallization time s again; t _SBe medium-soft time s, promptly again crystallization to 50% o'clock required time;

Rolled piece temperature K when T is stop; ε is true strain.

(5) the big minimodel of the static recrystal grain of roughing:

$D_{s1}=334\&times;D_0^{0.4}{\mathrm{\&epsiv;}}^{-0.185}\exp (-\frac{45000}{8.31T})...\left(9\right)$

In the formula: D _S1Be the austenite crystal diameter μ m of static state when crystallization has just been finished again; ε is true strain;

D ₀Be the austenite crystal diameter μ m before being out of shape; T is deformation temperature K.

(6) roughing non-recrystallization grain size model:

D _n1＝D ₀exp(-ε/12) (10)

In the formula: D _N1Equivalent diameter μ m for roughing distortion back flat crystal grain;

D ₀Be the austenite crystal diameter μ m before being out of shape; ε is true strain.

4, the method for predicting hot-rolled Nb-contained according to claim 1 and mechanical property is characterized in that the finish rolling process austenitic recrystallization model of described austenitic recrystallization model:

(1) finish rolling dynamic recrystallization critical strain model:

${\mathrm{\&epsiv;}}_{C2}=5.6\&times;{10}^{-4}{D}_0^{0.5}\exp \left(\frac{300000}{8.31T}\right)...\left(11\right)$

In the formula: ε _C2Be finish rolling dynamic recrystallization critical strain amount;

D ₀Be the austenite crystal diameter μ m before being out of shape; T is deformation temperature K.

(2) finish rolling dynamic recrystallization number percent model:

$X_{d2}=1-\exp (-0.693{\left(\frac{\mathrm{\&epsiv;}-{\mathrm{\&epsiv;}}_c}{{\mathrm{\&epsiv;}}_{0.5}}\right)}^2)...\left(12\right)$

${\mathrm{\&epsiv;}}_{0.5}=1.3\&times;{10}^{-5}{D}_0^{0.28}{\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}}^{0.005}\exp \left(\frac{300000}{8.31T}\right)...\left(13\right)$

In the formula: X _D2Be finish rolling dynamic recrystallization percent by volume; ε _CBe dynamic recrystallization critical strain amount;

ε is true strain; ε _0.5For dynamic recrystallization reaches 50% needed dependent variable;

D ₀Be austenite crystal diameter μ m before being out of shape;

Be rate of deformation s ^-1

T is deformation temperature K.

(3) finish rolling dynamic recrystallization grain size model:

D _d2＝22600Z ^-0.27 (14)

In the formula: D _D2Be finish rolling dynamic recrystallization crystallite dimension;

Z is the Zener-Holloman parameter.

(4) model of growing up of finish rolling dynamic recrystallization crystal grain:

$D_{\mathrm{dyn}2}^2=D_{d2}^2+3900{C_{\mathrm{eq}}}^{-1.43}\&CenterDot;t^{0.3}\exp (-5380/T)...\left(15\right)$

In the formula: D _Dyn2Be the later dynamic recrystallization crystallite dimension μ m of residence time t between passage;

D _D2Be finish rolling dynamic recrystallization crystallite dimension μ m; C _EqBe the C equivalent;

T is residence time s between passage.

(5) finish rolling static state is crystallization start time model again:

$t_{0.05}=6.75\&times;{10}^{-20}{\mathrm{\&epsiv;}}^{-4}\&CenterDot;D_0\&CenterDot;\exp \left(\frac{300000}{8.31T}\right)\&CenterDot;\exp \left\{(\frac{2.75\&times;{10}^5}{T}-185)\right[\mathrm{Nb}\%\left]\right\}...\left(16\right)$

In the formula: t _0.05For finish rolling static state again crystallization reach 5% o'clock needed time s,

ε is true strain; D ₀Be austenite crystal diameter μ m before being out of shape;

T is deformation temperature K; [Nb%] is the percentage composition of Nb element.

(6) finish rolling static state is the crystallization percentage model again:

X＝1-exp{0.693(t/t _0.5) ²} (17)

$t_{05}=2.52\&times;{10}^{-19}{\mathrm{\&epsiv;}}^p{D}_0^{1.7}\exp (\frac{325000}{8.31T}325000/\mathrm{RT})...\left(18\right)$

In the formula: finish rolling static state crystallization percentage again when X is residence time t; T is residence time s;

ε is true strain; T is deformation temperature K; D ₀Be austenite grain size μ m before being out of shape.

(7) the big minimodel of the static recrystal grain of finish rolling:

$D_{s2}=3.000\&times;D_0^{0.2}{\mathrm{\&epsiv;}}^{0.5}...\left(19\right)$

In the formula: D _S2Be the static recrystal grain size of finish rolling μ m;

D ₀Be austenite grain size μ m before being out of shape; ε is true strain.

(8) model of growing up of the static recrystal grain of finish rolling:

$D_{\mathrm{stat}2}^{4.5}=D_{s2}^{4.5}+3.68\&times;{10}^7{C_{\mathrm{eq}}}^{-1.43}\&CenterDot;\exp (-70000/T)\&CenterDot;t^{0.7}...\left(20\right)$

In the formula: D _Stat2Be finish rolling crystal grain diameter μ m during through t after crystallization is finished again;

D _S2Be the static recrystal grain size of finish rolling μ m; C _EqBe the C equivalent;

T is temperature K; T is for just having finished beginning consumed time s from crystallization again.

(9) the austenite crystal model of crystallization does not again take place in finish rolling:

D _n2＝D ₀·exp(-ε/4) (21)

In the formula: D _N2The equivalent diameter μ m of finish rolling distortion back flat crystal grain;

D ₀Be austenite grain size μ m before being out of shape; ε is true strain.

5, the method for predicting hot-rolled Nb-contained according to claim 1 and mechanical property is characterized in that described phase transformation model incubation period that rolls phase transition model in the cooling procedure of back is:

$k_f=\exp \{4.91-13.339\&CenterDot;[\%C]-1.1922\&CenterDot;[\%\mathrm{Mn}]+0.02505\&CenterDot;(T-273)-3.5067\&times;{10}^{-5}\&CenterDot;{(T-273)}^2\}...\left(22\right)$

lnτ _f＝-1.6454·lnk _f+20·lnT+3.265×10 ⁴·T ^-1-174.67 (23)

$k_p=\exp \{11.2-16.002\&CenterDot;[\%C]-0.9797\&CenterDot;[\%\mathrm{Mn}]+0.00791\&CenterDot;(T-273)-2.313\&times;{10}^{-5}\&CenterDot;{(T-273)}^2\}...\left(24\right)$

lnτ _p＝-0.91732·lnk _p+20·lnT+1.9559×10 ⁴·T ^-1-158.6 (25)

$k_b=\exp \{28.9-11.484\&CenterDot;[\%C]-1.1121\&CenterDot;[\%\mathrm{Mn}]+0.13109\&CenterDot;(T-273)-1.2077\&times;{10}^{-4}\&CenterDot;{(T-273)}^2\}...\left(26\right)$

lnτ _b＝-0.68352·lnτ _b+20·lnT+1.6491×10 ⁴·T ^-1-155.8 (27)

In the formula: k _f, τ _fBe respectively the constant and the incubation period of ferrite transformation model incubation period;

k _p, τ _pBe respectively pearlitic transformation model constants incubation period and incubation period;

k _b, τ _bBe respectively bainitic transformation model constants incubation period and incubation period;

T is temperature K; [C%], [Mn%] are respectively the percentage composition of carbon, niobium, manganese.

6, the method for predicting hot-rolled Nb-contained according to claim 1 and mechanical property is characterized in that the temperature model when the described perlitic transformation that rolls phase transition model in the cooling procedure of back finishes is:

T _PE＝951.30-143.26·[％C]-86.20[Nb％]-24.15·[％Mn] (28)

In the formula: T _PETemperature K when finishing for perlitic transformation;

[C%], [Nb%], [Mn%] are respectively the percentage composition of carbon, niobium, manganese.

7, the method for predicting hot-rolled Nb-contained according to claim 1 and mechanical property is characterized in that described each phase volume fraction model that rolls phase transition model in the cooling procedure of back is:

$X=1-\exp (-\frac{1}{2.24}\{\frac{2.24}{D}\&times;q+0.114\&times;{\left(\mathrm{\&Delta;\&epsiv;}\right)}^2\}\&times;\{1+4\&times;\mathrm{\&Delta;\&epsiv;}\}\&times;k\&times;t^n)...\left(29\right)$

In the formula: X is the volume fraction of each phase behind the austenitic transformation;

D is austenitic crystallite dimension μ m before the phase transformation;

Q is a shape coefficient, and span is 1.2-3.8;

Δ ε is an overstrain; T is transformation time s;

N is the Avrami coefficient, and ferrite is 2.4, and pearlite is 2.0, and bainite is 2.5,

The k value can adopt formula (22) to calculate for ferrite, can adopt formula (24) to calculate for pearlite k value, can adopt formula (26) to calculate for bainite k value.

8, the method for predicting hot-rolled Nb-contained according to claim 1 and mechanical property is characterized in that described ferritic grain size model of rolling phase transition model in the cooling procedure of back is:

lnd _f0＝-0.4688×ln[2.24/D×q+0.144×(Δε) ²]+0.005724×Ar ₃

-0.53259×ln(1+4.0×Δε)+0.13113×lnV _f-3.95 (30)

d _f ²＝d _f0 ²+24.811×d _f0 ^0.5888exp[-181.56/(T _c-723)] 31)

In the formula: d _F0Be ferritic crystallite dimension μ m after the phase transformation,

D is austenitic crystallite dimension μ m before the phase transformation,

Δ ε is an overstrain,

Ar ₃For ferrite begins transition temperature K,

V _fBe the volume fraction of ferrite after beginning to change,

Q is a shape coefficient, and span is 1.2-3.8,

d _fBe final ferritic crystallite dimension μ m,

T _cBe coiling temperature K.

9, the method for predicting hot-rolled Nb-contained according to claim 1 and mechanical property is characterized in that the yield strength model of described microstructure and property relational model is:

σ _s＝11582.01[C％]+591.73[Nb％]+1559.80d _f ^-0.5+3877.34V _p-0.193T _c-10.20h-392.02 (32)

10, the method for predicting hot-rolled Nb-contained according to claim 1 and mechanical property is characterized in that the tensile strength model of described microstructure and property relational model is:

σ _b＝7824.90[C％]+1519.10[Nb％]+1900.16d _f ^-0.5+4098.58V _p-0.34T _c-9.10h-362.29 (33)

11, the method for predicting hot-rolled Nb-contained according to claim 1 and mechanical property is characterized in that the extensibility model of described microstructure and property relational model is:

δ＝0.39[Mn％]-106.0[Si％]+561.74[Nb％]-0.15V _p+9.32d _f ^-0.5-0.0021T _c+26.51 (34)

[C%] in formula (32), (33), (34), [Nb%], [Mn%] are the percentage composition of carbon, niobium, manganese;

d _fBe ferritic crystallite dimension μ m, V _pBe pearlitic volume fraction;

T _cFor coiling temperature K, h are belt steel thickness mm.

12, the method for predicting hot-rolled Nb-contained according to claim 1 and mechanical property, the software of forecasting that it is characterized in that described selection relevant hot-strip tissue of VB language compilation and mechanical property is: the method that adopts thermal simulation experiment to combine with the analysis of commercial production measured data, foundation is at the mathematical model of hot-rolling Nb-containing band steel organization and mechanical property, comprise and set up temperature model, set up austenitic recrystallization model, set up phase transition model, set up the microstructure and property relational model; On this basis, adopt the software of forecasting of VB language establishment hot-rolling Nb-containing band steel organization and mechanical property;

At first, the chemical constitution and the technological parameter of input steel grade calculate according to the formula in the austenitic recrystallization model, calculate the critical strain ε of dynamic recrystallization _CIf the passage strain stress is greater than the critical strain ε of dynamic recrystallization _C, just adopt Dynamic Recrystallization Model to calculate the dynamic recrystallization mark of roughing and finish rolling respectively; If the passage strain stress is less than the critical strain ε of dynamic recrystallization _C, just adopt static state that static crystal model again calculates roughing and finish rolling respectively crystalline fraction again;

Then, on the basis of austenite recrystallization result of calculation, the formula in the phase transition model calculates in the cooling procedure of back according to rolling, the temperature T when calculating the end of ferrite and pearlitic incubation period and perlitic transformation respectively _PE, calculate n ferritic volume fraction V constantly respectively according to stack rule and phase transition model again _FnWith pearlitic volume fraction V _PnTemperature T when temperature T finishes less than perlitic transformation _PEThe time, calculate n+1 ferritic volume fraction V constantly respectively by process of iteration _{F (n+1)}With pearlitic volume fraction V _{P (n+1)}Temperature T when temperature T finishes less than perlitic transformation _PEThe time, ferrite and pearlitic volume fraction are calculated and are finished; The volume fraction V of bainite _bCan calculate according to ferrite and pearlitic volume fraction.

At last, in rolling the back cooling procedure on the basis of phase transformation result of calculation, the formula in giving according to the microstructure and property relational model calculates, and just can calculate yield strength, tensile strength and extensibility respectively.

Images