Acta Metallurgica Sinica, 2017, 53(1): 123-128
doi: 10.11900/0412.1961.2016.00274
一种第二相析出-温度-时间曲线计算模型的建立
A Model for Precipitation-Temperature-Time Curve Calculation
杨永, 王昭东, 李天瑞, 贾涛, 李小琳, 王国栋

摘要:

基于经典形核长大理论和Johnson-Mehl-Avrami方程,假定过饱和沉淀的球形第二相分子式为Mx1Mv2M1-x-v3CyN1-y,采用平均扩散速率表征合金原子对第二相形核长大过程影响的思想,建立了计算第二相析出-温度-时间(PTT)曲线的模型。基于Adrian模型提出计算多元系全固溶温度的方法,针对Fe-0.09C-0.011Ti-0.03V-0.025Nb (质量分数,%)钢计算得到的铁素体区PTT曲线呈典型的“C”形,得到的最快析出温度为628 ℃,其值与实验结果吻合。本模型计算效率高,计算析出相体积自由能变化时无需求取复合相的溶解度公式;适用性高,适用于不同基体中不同类型析出相PTT曲线的计算。

关键词: 微合金钢 ; 经典形核长大理论 ; 析出相 ; 析出-温度-时间(PTT)曲线

Abstract:

Nanometer precipitation is of great importance to the mechanical properties of the low carbon micro-alloyed steel. Precipitation process is controlled by the driving force for precipitation and the diffusion rate of atoms. Under the influence of these two factors, the fastest precipitation temperature for (Mx1Mv2M1-x-v3)(CyN1-y) phase is available, which is also known as nose temperature. The maximum number density of precipitates can be obtained through isothermal treatment at the nose temperature. The most effective tool for getting the value of nose temperature is the precipitation-temperature-time (PTT) curve. Due to that the diffusivity of substitutional atom is several orders of magnitude smaller than that of interstitial atom, the nucleation process and growth process of complex precipitation are controlled by the diffusion of substitutional atoms. So far no model has been established for calculating PTT curve of complex precipitation. All the existing models are established for simple precipitation. In this work, a kinetic model, based on the classical nucleation and growth theories and Johnson-Mehl-Avrami equation, employing Adrian thermodynamic model and L-J model, using average diffusivity to demonstrate the effects of forming elements on precipitation process, has been adapted to describe the precipitation kinetics following high temperature deformation in micro-alloy steels alloying with V, Nb and Ti. Using this model, the PTT curves for the kinetics of second phase were easily obtained. In the experiment, within the temperature range from 660 to 540 ℃, the nose temperature of carbonitride precipitation is equal to or slightly higher than 620 ℃. The value of nose temperature estimated from PTT curve is 628 ℃ which is consistent with the experimental observation. There are enough reasons to believe that the model proposed in this work can estimate accurately the nose temperature information in relatively small experiment case. This model has outstanding advantages in comparison with existing models: the mole fraction of precipitation and the driving force for precipitation per unit volume ∆Gv can be calculated directly without calculating the solubility formula of complex carbide in matrix; The proposed model can also be used to calculate the absolute solution temperature and the constituent of initial complex precipitation forming at critical temperature of precipitation, which can be used as the iterative initial values for calculating the equilibrium information between matrix and precipitation at relatively low temperatures.

Key words: micro-alloyed steel, ; classical nucleation and growth theory, ; precipitation, ; PTT curve

近年来,为了充分挖掘钢材的潜能,研究人员[1~5]通过调节合金成分及加工工艺调控钢材组织和性能。微合金化、控制轧制及控制冷却不仅可以有效细化晶粒,还可以发挥微合金元素的析出强化作用。低碳钢中添加微量的Nb、V和Ti等合金元素会对钢的组织和性能产生重要影响[6]。Nb能通过偏聚拖拽晶界或形成碳化物钉扎晶界有效阻碍晶粒长大,从而细化铁素体晶粒,产生较强的析出强化和细晶强化效应[7~9]。V在奥氏体中有很高的溶解度,但在冷却过程中,在铁素体中析出大量的纳米粒子,产生极强的析出强化效应[6]。Ti钢兼具Nb钢和V钢的优点,且其原料成本低、性能独特,因而发展潜力巨大。相比于Nb和V,Ti具有很高的活性,在高温下极易与C或N化合产生TiC、TiN或Ti(CN)。这些高温析出相会消耗一定量的Ti,降低奥氏体或铁素体中含Ti化合物的析出量,从而降低析出强化效果。

研究人员[10~14]建立了大量的数学模型,模拟合金碳化物和合金碳氮化物在奥氏体或铁素体中的析出行为。Dutta等[10]模拟了奥氏体中Nb(CN)的应力诱导析出行为,探究了位错对第二相析出的促进作用,发现位错节能有效增加第二相形核位置,提升析出相的密度,进而细化第二相尺寸。Perrard等[12]修正了第二相形核公式和形核结束准则,建立了计算铁素体中NbC非均匀析出动力学的模型,该模型包含第二相在位错线上形核需要的临界形核功的调节因子,该因子需经过实验和模拟结果确定,模型适用性低。Perez等[13]探究了铁素体中缺位型析出相NbCxNy的析出行为,较精确地预测了析出相的成分。雍岐龙[15]建立了计算第二相析出-温度-时间(PTT)曲线和形核率-温度(NrT)曲线的模型,应用该模型可较准确地预测简单析出相最快析出温度。

复合第二相形核与长大过程由多种原子扩散控制,由于无法定量化不同原子扩散对析出的影响,所以计算该类析出相PTT曲线的模型还未建立。本工作采用平均扩散速率表征合金原子对第二相形核长大过程影响的思想,利用Adrian模型[16]计算析出相与基体间的平衡信息,利用L-J模型[17]计算析出相的体积自由能,基于经典形核长大理论[12]和Johnson-Mehl-Avrami方程[18~20],建立计算第二相PTT曲线的模型。

1 析出动力学模型的建立
1.1 热力学计算

合金组元Ti、V和Nb均为强碳氮化物形成元素,极易与钢中C、N组元结合生成TiC、TiN、VC、VN、NbC和NbN。这些二元化合物均为NaCl型fcc结构,且晶格常数较接近,可以无限互溶形成复合碳氮化物。假定析出相分子式为( M x 1 M v 2 M 1 - x - v 3 )( C y N 1 - y ) ,Adrian[16]基于规则溶体模型[21]及质量守恒定律提出了求解不同温度下基体与析出相间平衡信息的热力学模型:

y ln xy K M 1 C [ M 1 ] [ C ] + 1 - y ln x 1 - y K M 1 N [ M 1 ] [ N ] +

y 1 - y L CN R g T = 0 (1)

y ln vy K M 2 C [ M 2 ] [ C ] + 1 - y ln v 1 - y K M 2 N [ M 2 ] [ N ] +

y 1 - y L CN R g T = 0 (2)

y ln ( 1 - x - v ) y K M 3 C [ M 3 ] [ C ] + 1 - y ln ( 1 - x - v ) 1 - y K M 3 N [ M 3 ] [ N ] +

y 1 - y L CN R g T = 0 (3)

vy ln x [ M 2 ] K M 1 C v [ M 1 ] K M 2 C + 1 - x - v 1 - y ln 1 - x - v [ M 1 ] K M 3 N x [ M 3 ] K M 1 N + 1 - y ln x ( 1 - y ) K M 1 N [ M 1 ] [ N ] + y 2 1 - y L CN R g T = 0 (4)

M 0 1 = x 2 f + 1 - f [ M 1 ] (5)

M 0 2 = v 2 f + 1 - f [ M 2 ] (6)

M 0 3 = 1 - x - v 2 f + 1 - f [ M 3 ] (7)

C 0 , C = y 2 f + 1 - f [ C ] (8)

C 0 , N = 1 - y 2 f + 1 - f [ N ] (9)

式中,[M1]、[M2]、[M3]、[C]和[N]分别为温度T下相应组元的溶解度(原子分数), M 0 1 M 0 2 M 0 3 C 0 , C C 0 , N 分别为相应组元的名义含量,xvy分别表示析出相中各相应组元的占位比,Rg为理想气体常数,f为析出相的摩尔分数, L CN = - 4260 J/mol[16] K M 1 C K M 1 N K M 2 C K M 2 N K M 3 C K M 3 N 分别为用原子分数表示的相应化合物的溶解度:

K MX = M X = A Fe 2 10 4 A M A X × 10 B - A / T (10)

式中,[M]和[X]分别代表合金原子与间隙原子的溶解度, A Fe A M A X 分别代表Fe、MX的相对原子质量。AB为相应固溶度积公式中的参数[15]

1.2 临界形核功和临界半径

假定第二相在基体中均匀析出,呈球形,则其析出时引起的能量变化 Δ G 为:

Δ G = Δ G chem + Δ G int (11)

式中, Δ G chem 为化学自由能变化[17], Δ G int 为界面能变化,其中:

Δ G chem = 4 3 π R 3 Δ G v (12)

Δ G int = 4 π R 2 γ (13)

式中,R为析出相的半径,γ为析出相与基体间的比界面能, Δ G v 为析出相的体积自由能:

Δ G v = - R g T V m [ ln [ M 1 ] 0 [ M 1 ] + ln [ M 2 ] 0 [ M 2 ] + ln [ M 3 ] 0 [ M 3 ] +

ln [ C ] 0 [ C ] + ln [ N ] 0 N ] (14)

式中, V m 为析出相的摩尔体积, [ M 1 ] 0 [ M 2 ] 0 [ M 3 ] 0 [ C ] 0 [ N ] 0 分别为析出开始前相应组元在基体中的固溶量。由式(11)对R的导数为0得到临界形核半径 R c 为:

R c = - 2 γ Δ G v (15)

R c 代入式(11)得到临界形核功为:

Δ G c = 16 π γ 3 3 Δ G v 2 (16)

1.3 形核率

由于合金原子扩散比间隙原子慢得多,假定析出相形核过程由合金原子扩散控制。依据经典形核理论,第二相的稳态形核率[12] I 为:

I = N n exp - Δ G c k B T (17)

式中, Z 为Zeldovich因子(≈0.05), N n 为有效形核位置点(=1/a3)[13], k B 为Boltzmann常数,β为临界核心吸收溶质原子的频率:

β = 4 π R c 2 D ev X 0 a 4 (18)

D ev = x D M 1 + v D M 2 + ( 1 - x - v ) D M 3 (19)

D M i = D M io exp ( - Q i R g T ) (20)

X 0 = x M 1 0 + v M 2 0 + ( 1 - x - v ) M 3 0 (21)

式中, D ev 为合金原子平均体扩散率[22],表征各成核原子对复合相形核和长大过程的影响[22]; D M i i 组元的体扩散率; D M io i组元的体扩散系数; Q i i组元的体扩散激活能; X 0 为基体中合金原子的平均浓度[22];a为基体晶格常数。晶核形成后其附近微区内的溶质过饱和度及体积自由能迅速降低,导致临界形核功大量增加,形核率迅速下降并衰减到0,故实际形核率 I t 为:

I t = I exp ( - t τ e ) (22)

式中,t为时间, τ e 为有效形核时间。t时间内形成的全部核心数 N s 为:

N s = 0 I t d t = I τ e (23)

1.4 析出相的长大

假定析出相的长大由合金原子体扩散控制,且周围基体中的合金原子向析出相核心径向扩散为稳态扩散,根据Zener长大方程[23],析出粒子长大速率 v 为:

v = d R d t = D ev R X 0 - X i X p - X i (24)

式中, X i X p 分别为界面处和第二相中合金原子的平均浓度。由上式积分得到析出相的半径与长大时间t之间的关系式为:

R 2 = 2 D ev X 0 - X i X p - X i t (25)

1.5 析出曲线

第二相的析出分数随时间的变化可以用Johnson-Mehl-Avrami方程定量描述,该方程由Johnson和Mehl[18]在研究结晶动力学时首次提出,经Avrami[19,20]发展和完善后,广泛应用于研究扩散型固态相变动力学。假定第二相的平衡析出总量为 f ,令 λ 2 = 2 ( X 0 - X i ) / ( X p - X i ) ,f可以表述为:

f = 1 - exp - W t n (26)

式中,n为Avrami指数,与形核机制和长大机制有关。将析出相的总体积 4 3 π R 3 I τ e 代入式(26),得到:

f = 1 - exp ( - 4 3 π Ι τ e λ 3 D ev 3 2 t 3 2 ) (27)

对比式(26)和(27),得到n值为1.5, W = 4 3 π I τ e λ 3 D ev 3 / 2 。计算PTT曲线时,通常选择析出总量达到5%f作为析出开始点( t 0.05 ),95%f为结束点( t 0.95 )。受到某些难以精确计算的参数的限制,第二相开始形核的绝对起始点t0无法确定,开始点和结束点也无法准确确定。为了便于研究第二相的析出行为,采用析出时间的相对值。当析出量为5%,即f=0.05时,对f的表达式取双对数得到:

lg t 0.05 = 1 1.5 ( - 1.28994 - lg 4 π 2 τ e λ 3 N n 15 a 4 -

lg X 0 - 5 2 lg D ev - 2 lg R c + 1 ln 10 Δ G c k B T ) (28)

忽略温度对λ的影响,则上式中 lg 4 π 2 τ e λ 3 N n 15 a 4 与温度无关。终冷温度不同,析出相成分不同。随着析出相成分的改变,平均浓度会稍有改变,但其值对温度的变化不敏感。忽略温度对 lg X 0 数值的影响,令 lg t 0 = - 1 1.5 ( lg 4 π 2 τ e λ 3 N n 15 a 4 + lg X 0 ) 。式(28)变形得到相对值:

lg t 0.05 t 0 = 1 1.5 ( - 1.28994 - 5 2 lg D ev - 2 lg R c + 1 ln 10 Δ G c k B T ) (29)

lg t 0.95 t 0.05 = 1 1.5 lg ( ln 0.05 ln 0.95 ) (30)

2 模型验证与讨论

本工作针对文献[24]中的实验进行模拟计算,以验证模型的可靠性。实验材料成分为(质量分数,%): C 0.09,Mn 1.05,Si 0.25,N 0.0037,Ti 0.011,V 0.03,Nb 0.025,Fe余量。样品在K010箱式电阻炉中于1200 ℃保温72 h后淬火至室温,切取相应的试样后在MMS-300热力模拟试验机上进行测试实验。热处理及加工工艺为:以10 ℃/s的加热速率将试样加热到1200 ℃保温3 min,再以10 ℃/s的冷却速率冷却到900 ℃后施以60%的变形,再以80 ℃/s的冷却速率分别冷却到540、580、620和660 ℃之后以0.1 ℃/s的冷却速率缓慢冷却至室温。

2.1 全固溶温度的计算

将合金的名义成分代入Adrian模型中的式(1)~(4)即可解得全固溶温度及第二相开始析出时的原子占位比,将这些值作为其它温度下析出热力学计算的迭代初值,可避免迭代初值选择的盲目性,使计算过程更加高效。计算可知,实验材料中合金元素的全固溶温度为1706 K。

2.2 平衡固溶量的计算

固溶处理温度下溶质原子的实际固溶量对低温区第二相析出动力学有很大的影响作用。通过对全固溶温度的计算可知,钢在1200 ℃保温并不能使碳氮化物完全溶解,且保温72 h会使第二相达到平衡析出,该温度下试样中各合金组元的实际固溶量的计算结果如图1所示。可以看出,在固溶处理温度下,以Ti和N原子析出为主,Nb和V几乎不析出,析出相中Ti原子占位高达80%以上。

图1 不同温度下析出的热力学平衡信息

Fig.1 Thermodynamic equilibrium information of TixVvNb1-x-vCyN1-y for steel above 1473 K(a) solute concentrations in matrix(b) the occupation ratio of atoms in precipi- tate

2.3 终轧结束时实际固溶量的计算

1200 ℃保温3 min后,将钢以10 ℃/s的冷却速率冷却到900 ℃,再施加60%的变形,在此过程中会有一定量的第二相析出。由于时间较短,假定实际析出量仅为平衡析出量的20%,则900 ℃下的实际固溶量为1200 ℃下平衡固溶量减去900 ℃下平衡析出量的20%。

2.4 复合相在铁素体中的析出行为

复合析出相 T i x V v N b 1 - x - v ( C y N 1 - y ) 可看作由各二元化合物互溶形成,其摩尔体积随各组元含量的变化而变化,本工作采用线性内插法[13]求复合析出相的摩尔体积。第二相与基体间的界面能对析出相的临界半径和临界形核功起着决定作用,准确计算出界面能值是准确计算PTT曲线的前提。界面能随各组元含量及温度的变化而变化。采用线性内插法[13]求复合析出相与基体间的界面能。采用本模型计算的第二相临界晶核半径、临界形核功及相对沉淀析出时间随温度变化曲线如图2所示。由图2a和b可知,临界晶核尺寸与临界形核功均随温度降低单调减小,温度越低,其值越小。在温度低于950 K时,临界晶核尺寸已不足0.5 nm。第二相析出受到析出驱动力和成核原子扩散率的共同影响。温度越高,溶质原子扩散越快;温度越低,溶质过饱和度越大,析出驱动力越大。在二者共同作用下,存在一个最快析出温度:在该温度等温,可以获得数量最多、分布最弥散的第二相颗粒,这对于探究析出强化非常重要。

实验结果[24]表明,第二相在620 ℃析出最快,在660 ℃比在580 ℃析出快。由于实验中采用的温度点较分散,无法确定理论最快析出温度就是620 ℃,但可以确定的是最快析出温度一定在620~660 ℃之间,且非常靠近620 ℃。采用式(29)和(30)计算得到的复杂析出相在铁素体区析出的PTT曲线如图2c所示。可以看出,该曲线呈典型的“C”型[25],且最快析出温度为901 K,即628 ℃,这与实验结果吻合。应用式(14)计算析出相体积自由能变化,无需求取不同温度下析出相的溶解度公式,计算效率高。此外,本模型具有较好的适用性,适用于铁素体或奥氏体中简单析出相PTT曲线的计算,也适用于复合析出相PTT曲线的计算。

图2 复合析出相在铁素体中析出的临界晶核半径、临界形核功及相对沉淀析出时间随温度变化的曲线

Fig.2 Kinetic behaviors of complex precipitates precipitated in ferrite (t0 is the absolute time when second phase begins to precipitate, t0.05 and t0.95 are the times of volume fraction of second phase reaching 5% and 95% equilibrium precipitation amount at given temperatures, respectively) (a) critical nucleus radius(b) critical nucleation energy(c) PTT diagram

3 结论

(1) 基于经典形核长大理论和Johnson-Mehl-Avrami方程,采用平均扩散率表征成核原子对第二相形核长大过程影响的思想,建立了计算第二相PTT曲线的模型。计算结果与实验结果吻合良好。

(2) 该模型适用于不同基体中各类第二相析出动力学的计算,也可用于计算全固溶温度及不同温度下第二相平衡析出量。

The authors have declared that no competing interests exist.

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The yield strength and impact energy properties for martensitic steel fabricated by vacuum induction melting are investigated. It is found that the addition of Ti can improve the yield strength property of the martensitic steel after reheat quenching process, which can be attributed to increase in precipitation hardening from formation of TiC precipitates in the martensitic matrix and a superfine sized (~8 渭m) grains in the martensitic structure. Moreover, the yield strength can be further enhanced by tempering and reheat quenching process, which can be ascribed to a large amount of freshly nano-sized (1鈥10 nm) precipitates in the final martensitic structure for martensitic steel-containing Ti. The experimental and theoretical results on the contribution of TiC precipitates to hardening of the martensitic steel are in excellent agreement. In addition, the impact toughness also has been improved along with yield strength followed by the heat treatment, which can be attributed to the high ratio of high-angle grain boundaries after tempering and reheat quenching process.
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The grain refinement and mechanical properties improvement resulted from Ti addition and reheating quenching were demonstrated in this study. The direct quenched medium manganese steel with low carbon content (0.05C) was treated by reheating quenching process. The yield strength and Charpy impact energy were measured. The microstructures and the second precipitated particles were examined by optical microscopy (OM), scanning electron microscopy (SEM), electron back-scattered diffraction (EBSD), transmission electron microscopy (TEM), X-rays diffraction and phase analysis method. It was found that reheating quenching at 900鈥1000掳C resulted in significant grain refinement, especially the refinement of effective grain size (EGS), which was attributed to the large amount nano-sized precipitation of TiC. In addition, high elastic modulus was also obtained from the large amount TiC precipitated from the matrix. It is concluded that reheating quenching process is a useful method to refine the grain size and improve the combined mechanical properties of the martensitic steel through Ti addition.
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The diffusion-controlled growth of proeutectoid ferrite ({alpha}) from austenite ({gamma}) in an Fe-C-Mn alloy was simulated incorporating the possible drag effect of Mn on the migration of {alpha}:{gamma} interphase boundaries. The magnitude of drag force or the dissipation of free energy by drag was evaluated by means of Cahn and Purdy-Brechet models. The growth rate of ferrite was calculated from the flux balance equation for carbon taking into account the fact that the carbon concentration at the boundary in austenite varied with time. Whereas the time exponent of growth deviated from one-half at each moment, the overall time dependence was dictated by carbon volume diffusion in austenite. The reported differences of experimental growth rates from those calculated assuming paraequilibrium were reduced considerably by incorporating the drag of Mn, although simulation results may largely depend on the shape and depth of solute interaction potential with {alpha}:{gamma} boundaries and Mn diffusivity within the boundary, etc.
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The microstructures and properties of hot-rolled low-carbon ferritic steel have been investigated by optical microscopy, field-emission scanning electron microscopy, transmission electron microscopy, and tensile tests after isothermal transformation from 600掳C to 700掳C for 60 min. It is found that the strength of the steel decreases with the increment of isothermal temperature, whereas the hole expansion ratio and the fraction of high-angle grain boundaries increase. A large amount of nanometer-sized carbides were homogeneously distributed throughout the material, and fine (Ti, Mo)C precipitates have a significant precipitation strengthening effect on the ferrite phase because of their high density. The nanometer-sized carbides have a lattice parameter of 0.411-0.431 nm. After isothermal transformation at 650掳C for 60 min, the ferrite phase can be strengthened above 300 MPa by precipitation strengthening according to the Ashby-Orowan mechanism.
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We have constructed a computer model of the precipitation kinetics of vanadium carbonitride in steel that takes into account the composition evolution of the precipitates with time. The model takes advantage of the fast diffusion of nitrogen and carbon compared to niobium to derive the composition, size and rate of formation of the precipitates during their nucleation. A local equilibrium condition is used at the precipitate–matrix interface to derive the growth rate of each precipitate as a function of its size and the current matrix composition. Coarsening occurs naturally on account of the Gibbs–Thomson capillarity effect. For isothermal heat treatments, the calculations show that the precipitates nucleate as almost pure vanadium nitrides. They subsequently grow at the expense of solute nitrogen. When nitrogen is exhausted, the solute carbon precipitates and progressively transforms the nitrides into carbonitrides. The coarsening stage leads to a steady-state size distribution of niobium carbonitrides of the equilibrium composition.
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A model has been developed for describing the precipitation of NbC on dislocations in ferrite in an Fe–C–Nb steel. This model is a continuous description of the classical laws for nucleation growth and coarsening, which are adapted to the specific case where precipitates only form on dislocations. This model is successfully applied on an extensive data set obtained by small-angle neutron scattering for a wide temperature range and two alloy contents. Using this model, it is possible to estimate the effects of process parameters on the final microstructure and, notably, it is shown that the initial dislocation density has a pronounced influence on the maximum precipitate density.
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High-resolution transmission electron microscopy and electron-energy loss spectroscopy have been used to characterize the structure and chemical composition of niobium carbonitrides in the ferrite of a Fe-Nb-C-N model alloy at different precipitation stages. Experiments seem to indicate the coexistence of two types of precipitates: pure niobium nitrides and mixed sub-stoichiometric niobium carbonitrides. In order to understand the chemical composition of these precipitates, a thermodynamic formalism has been developed to evaluate the nucleation and growth rates (classical nucleation theory) and the chemical composition of nuclei and existing precipitates. A model based on the numerical solution of thermodynamic and kinetic equations is used to compute the evolution of the precipitate size distribution at a given temperature. The predicted compositions are in very good agreement with experimental results.
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Three ways of implementing classical nucleation and growth theories for precipitation are presented and discussed: (i) the “mean radius approach” (particle size distribution is restricted to its mean radius and density); (ii) the “Euler-like multi-class approach” (the particle size distribution is discretized in several size classes and its time evolution is calculated evaluating the fluxes between neighboring classes); and (iii) the “Lagrange-like multi-class approach” (the particle size distribution is again discretized in several size classes, whose radius time evolution are calculated). In some simple cases, the three approaches lead to similar results, but when more complex heat treatments are involved, multi-class approaches are required. Although the Euler-like approach involves a more complex class number management, it is more adapted to the modeling of precipitate chemistry. Some examples of implementation are presented: Cu precipitation in ferrite, Al 3 Sc precipitation in aluminum, VC and NbVC precipitation in austenite.
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ABSTRACT To control austenite grain growth in high strength low alloy (HSLA) steels, additions of micro alloying elements showing chemical affinity for interstitial elements (C and N) are used. These elements have a significant effect on the mechanical properties of the steels. The mechanical properties of HSLA steels depend both on the amounts of the microalloying elements dissolved in the austenite and on undissolved carbonitrides. In the present work, a thermodynamic model enabling calculation of the composition of the austenite as well as the composition and quantity of the carbonitrides in HSLA steels containing up to four microalloying elements is presented. This model can be a useful tool in determining the optimum chemical compositions for steels as well as the heat treatment parameters required to maximise hardenability and to control austenite grain growth.MST/1471
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Ti(CN) precipitation data determined by stress relaxation are analyzed using the classical theory of diffusion controlled nucleation. For this purpose, the interface energy 纬 and strain energy 螖 G accompanying nucleus formation are estimated using a new approach, and the driving force for Ti(CN) nucleation is calculated with the aid of a thermodynamic model. The analysis indicates that the critical nucleus is richer in N than the bulk precipitate at equilibrium at a given holding temperature. The results also show that trace amounts of nitrogen dissolved in austenite can significantly increase the chemical driving force for Ti(CN) nucleation and thereby accelerate the rate of precipitation. On the basis of this analysis, a kinetic model is developed for predicting start times ( P ) for the strain-induced precipitation of Ti(CN) in austenite. Such predictions are in reasonably good agreement with measured P times.
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The theory of the kinetics of phase change is developed with the experimentally supported assumptions that the new phase is nucleated by germ nuclei which already exist in the old phase, and whose number can be altered by previous treatment. The density of germ nuclei diminishes through activation of some of them to become growth nuclei for grains of the new phase, and ingestion of others by these growing grains. The quantitative relations between the density of germ nuclei, growth nuclei, and transformed volume are derived and expressed in terms of a characteristic time scale for any given substance and process. The geometry and kinetics of a crystal aggregate are studied from this point of view, and it is shown that there is strong evidence of the existence, for any given substance, of an isokinetic range of temperatures and concentrations in which the characteristic kinetics of phase change remains the same. The determination of phase reaction kinetics is shown to depend upon the solution of a functional equation of a certain type. Some of the general properties of temperature‐time and transformation‐time curves, respectively, are described and explained.
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Following upon the general theory in Part I, a considerable simplification is here introduced in the treatment of the case where the grain centers of the new phase are randomly distributed. Also, the kinetics of the main types of crystalline growth, such as result in polyhedral, plate‐like and lineal grains, are studied. A relation between the actual transformed volume V and a related extended volume V1 ex is derived upon statistical considerations. A rough approximation to this relation is shown to lead, under the proper conditions, to the empirical formula of Austin and Rickett. The exact relation is used to reduce the entire problem to the determination of V1 ex, in terms of which all other quantities are expressed. The approximate treatment of the beginning of transformation in the isokinetic range is shown to lead to the empirical formula of Krainer and to account quantitatively for certain relations observed in recrystallization phenomena. It is shown that the predicted shapes for isothermal transformation‐time curves correspond well with the experimental data.
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A series of sodium 2-sulfoethyl alkanoates RCOO(CH2)(2)SO3Na was prepared from sodium isethionate and fatty acids containing 9, 11, 13, and 15 carbon atoms. The Krafft point, the critical micelle concentration (CMC), the surface tension, the emulsifying power, the wetting time, the resistance to acid hydrolysis, and the calcium-ion stability of this series of surfactants were examined, and the results were compared with those of the corresponding sodium alkyl beta-sulfopropionates ROCO(CH2)(2)SO3Na, which have another structure of ester-linkage. The CMC values of sodium 2-sulfoethyl alkanoates almost coincide with those value of the sodium alkyl beta-sulfopropionates with the same number of carbon atoms. However, the Krafft point and surface tension at the CMC of sodium 2-sulfoethyl alkanoates were lower than those of the sodium alkyl beta-sulfopropionates with the same number of carbon atoms. Sodium 2-sulfoethyl alkanoates are more stable than sodium alkyl beta-sulfopropionates in their resistance to hydrolysis and to the calcium-ion.
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[22] Okaguchi S, Hashimoto T.Computer model for prediction of carbonitride precipitation during hot working in Nb-Ti bearing HSLA steels[J]. ISIJ Int., 1992, 32: 283
Abstract A computer model which predicts complex precipitation behavior quantitatively in Nb-Ti bearing steel has been developed on a theoretical basis. The solubility and composition of the complex precipitates, and the chemical driving force of the precipitates from supersaturated austenite are estimated by means of thermodynamic analysis of regular solution composed of four-binary compounds. The change in dislocation density which acts as a nucleation site during hot working is calculated by using dislocation theory. And the time dependence of volume fraction and the particle radius of strain induced precipitation are also predicted on the basis of classical nucleation theory. In order to estimate the effect of deformation on nucleation, the change in elastic energy of dislocation with nucleation is calculated. Experimental results showed that combination of Nb and Ti addition, decreased the solubility of carbonitrides and accelerated the precipitation rate from supersaturated austenite because of the formation of complex precipitates. Such experimental results are in good agreement with the prediction by the present model. And both the acceleration of precipitation rate and the refinement of precipitates particles due to hot deformation are also quantitatively explained.
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The radius of a spherical precipitate particle growing in a solid solution of initially uniform composition may be shown to be equal to α(Dt)05, where D is the atomic diffusion coefficient, t the time of growth, and α, the growth coefficient, is a dimensionless function of the pertinent compositions. In this paper the precise dependence is found of this function upon the pertinent concentrations. A similar computation is made for the growth coefficient corresponding to the one‐dimensional growth of a plate.
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[24] Li X L, Wang Z D, Deng X T, et al.Effect of final temperature after ultra-fast cooling on microstructural evolution and precipitation behavior of Nb-V-Ti bearing low alloy steel[J]. Acta Metall. Sin., 2015, 51: 784
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(李小琳, 王昭东, 邓想涛. 超快冷终冷温度对含Nb-V-Ti微合金钢组织转变及析出行为的影响[J]. 金属学报, 2015, 51: 784)
<p>以复合添加Nb, V和Ti的低碳微合金钢为研究对象, 采用热模拟试验机模拟高温轧制+超快速冷却+缓冷工艺, 采用OM, HRTEM和显微硬度计等对超快冷至不同温度实验钢的组织转变和析出规律进行研究. 结果表明, 随着超快冷终冷温度的升高, 显微组织由贝氏体向珠光体和铁素体转变, 碳化物形核位置从贝氏体转变为铁素体, 铁素体中的析出物密度大于贝氏体中的, 且在620 ℃达到最大. 超快冷至不同温度时析出物的尺寸均小于10 nm, 纵横比均接近于1, 即析出物形态更接近于球形, 且随终冷温度的降低, 析出物尺寸逐渐减小. 利用Orowan机制计算了析出强化增量, 得出在620 ℃析出强化对屈服强度的贡献最大, 可达到25.6%.</p>
DOI:10.11900/0412.1961.2014.00606      Magsci     URL    
[25] Quispe A, Medina S F, Gómez M, et al.Influence of austenite grain size on recrystallisation-precipitation interaction in a V-microalloyed steel[J]. Mater. Sci. Eng., 2007, A447: 11
By means of torsion tests using small specimens, the influence of austenite grain size on strain induced precipitation kinetics has been determined in a vanadium microalloyed steel. Determination of recrystallisation–precipitation–time–temperature (RPTT) diagrams for two austenite grain sizes allows values of the aforementioned magnitudes to be determined. An ample discussion is made of the quantitative influence found and its relation with nucleation and growth mechanisms of precipitates. The results are compared with the quantitative influence exerted by the other variables, reaching the conclusion that the austenite grain size has a notable influence on strain induced precipitation kinetics which should not be underestimated. Finally, the influence of austenite grain size is included in a strain induced precipitation model constructed by the authors of this work and which also takes into account the other aforementioned variables.
DOI:10.1016/j.msea.2006.11.036      URL     [本文引用:1]
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关键词(key words)
微合金钢
经典形核长大理论
析出相
析出-温度-时间(PTT)曲线

micro-alloyed steel,
classical nucleation and ...
precipitation,
PTT curve

作者
杨永
王昭东
李天瑞
贾涛
李小琳
王国栋

YANG Yong
WANG Zhaodong
LI Tianrui
JIA Tao
LI Xiaolin
WANG Guodong