Vol.22 No.5 荆德君等：连铸结晶器内铸坯温度场和应力场耦合过程数值模拟 421 坯裂纹、优化结晶器锥度、改进工艺参数等具有 1.0% 重要的指导作用. 2.78% 2.40% 参考文献 1.84% 1 Naghdi P M,Stress-strain Relations in Plasticity and Ther- 1.520% 1.30% moplasticity in Plasticity.in:Lee E H,Symonds PS.eds. 1.30% 1.1% Proceedings of the Second Symposium on Naval Struc- 1.19% 1.3% tural Mechanics.New York:Pergamon Press,1960 1.5% 1.6% 2 Wimmer F,Thone H,Lindorfer B.Thermomechanically- coupled Analysis of the Steel Solidification Process as a 图8结晶器出口处还壳内部应变强度等值线分布图 Basis for the Development of a High Speed Billet Casting Fig.8 Calculated effective strain contours in solid shell at Mold.in:Proceedings of International Conference on mold exit Modelling and Simulation in Metallurgical Engineering 导致漏钢事故发生.因此，本模型可以用来预测 and Materials Science.Beijing,1996.366 3 Kelly J E,Michalek K P,Connor T G,et al.Initial Devel- 铸坯裂纹的产生 opment of Thermal and Stress Fields in Continuously Cast 4结论 Steel Billets.Metallurgical Transaction A,1988,19A: 2589 (1)将模型预测出的坯壳形貌、界面热流和 4 Zetterlund E H,Kristiansson J O.Continuous Casting-a 裂纹敏感区等，与实际测定值和文献结果作比 numerical Study of the Influence of Mmold Wear on Crack Formation.Scandinavian Journal of Metallurgy,1983,12: 较，吻合较好，故本论文所建立的热-力耦合模 211 型是可靠的. 5 Sorimachi K,Brimacombe J K.Improvements in Mathe- (2)在凝固的很早阶段（离弯月面不到 matical Modelling of Stresses in Continuous Casting of 100mm范围内)，气隙就优先在铸坯角部出现， Steel.Ironmaking and Steelmaking,1976(1):38 随着铸坯往下移动，气隙逐步向中部扩展.气隙 6荆德君，蔡开科，包晶相变对连铸坯初生坯壳凝固 主要存在于离铸坯角部20mm范围内. 收缩的影响.钢铁研究学报，1999,11(3)：9 7 Friedman E.Thermomechanical Analysis of the Welding (3)气隙的出现使铸坯和铜板界面热流急 Process Using the Finite Element Method.Journal of Pres- 剧下降，角部回热显著，其表面温度明显比中部 sure Vessel Technology,Transaction of the ASME,1975, 高 97(8):206 (4)气隙的形成使初生坯壳生长不均匀，角 8 Chong Hee Yu,Mikio Suzuki,Hiroyuki Shibata,et al. 部明显比中部薄.在角部靠近凝固前沿位置存 Simulation of Crack Formation on Solidifying Steel Shell in Continuous Casting Mold.ISIJ International,1996,36 在应力集中，应变强度达到20%，超过产生裂 (Supplement):159 纹的临界应变，为裂纹敏感区， 9 Yamanaka,Nakajima K,Okamura K.Critical Strain for In- (5)本模型可从物理本质上真实模拟结晶 ternal Crack Formation in Continuous Casting.Ironmak- 器内热和力学状态及其变化规律，对于预测铸 ing and Steelmaking,1995,22(6):508 Numerical Simulation of the Coupling Phenomenon between Thermal and Mechanical Fields of Billet in Continuous Casting Mold JING Dejun,CAI Kaike Metallurgy School,UST Beijing,Beijing 100083,China ABSTRACT Based on the solidification process of carbon steel in continuous casting mold,and considering the contact behavior between billet and mold,a fully thermomechanically coupled 2D transient thermo-elasto- plastic FEM model is established.The model is implemented with MARC software on PC computer,and the thermal and mechanical states in continuous casting mold are obtained,especially including the interfacial sta- tes between shell and mold,such as billet surface temperature,interfacial heat flux and the law of gap forma- tion.This analytical work can provide theoretical bases for optimizing mold taper and developing high-speed casting mold with continuously changing taper. KEY WORDS continuous casting mold;solidification;thermal-mechanical couple;contact;thermo-elasto- plastic FEM modelVb l 一 22 N 0 . 5 荆 德君 等 : 连铸 结 晶器 内铸 坯温度 场和 应 力场 祸合 过程 数值模拟 . 42 1 - 图 8 结 晶器出口 处坯 壳内部应变强度等值线分布 图 F ig . 8 C a l e u al tde e n怎e ivt e s t r a in c o n ot u sr in so il d s h e il a t m o l d e x i t 导 致漏钢 事故发生 . 因 此 , 本模型 可 以用来预测 铸坯 裂纹的 产 生 . 4 结论 ( 1) 将模型 预测 出 的坯 壳形貌 、 界 面热流和 裂 纹敏感 区 等 , 与 实际 测定值 和 文献 结果 作 比 较 , 吻合 较好 , 故本论 文所 建立 的热一 力祸 合模 型是可靠 的 . (2 ) 在 凝 固 的很 早 阶段 ( 离 弯 月 面 不 到 1 0 0 r 口幻。 范 围 内) , 气 隙就优 先在铸坯 角部 出现 , 随着铸坯往下 移动 , 气 隙逐步 向中部 扩 展 . 气隙 主要存 在于 离铸坯 角部 2 0 r n r n 范 围 内 . (3 ) 气 隙的 出 现使铸 坯和 铜板 界 面热 流急 剧下 降 , 角部回热显 著 , 其表面温度 明显 比 中部 局 . (4 ) 气隙的形成使初生坯壳 生长不 均匀 , 角 部 明 显 比 中部薄 . 在角部 靠近凝 固前 沿位置 存 在应 力集 中 , 应变 强 度达 到 .2 0 % , 超 过产生 裂 纹 的临界应变 , 为裂 纹敏感 区 . (5 ) 本模 型 可从物理 本质上真 实模拟 结 晶 器 内热 和 力 学 状态 及其变化 规律 , 对于 预测 铸 坯裂纹 、 优化结 晶器锥度 、 改进工 艺 参数等 具有 重要 的指导作 用 . 参 考 文 献 1 N a hg d i P M , S etr s s 一s atr in eR lat i o n s in P last i e iyt an d hT e -r m o P last i e i yt in P las t i e i .yt in : L e e E H , S ym on d s P S . e ds . Pr o e e e d in g s o f ht e S e e o n d S y m P o s i um on N va a l S trU e - t u r a 1M e c h an i e s . N e w OY kr : P e飞aj m o n P er s s , 1 9 6 0 Z V丙m m er F, hT o n e H , L i n d o fer r B . hT e mr o m e e h an i e a lly - e o u P l e d A n a ly s i s o f ht e S et e l S o l id iif e at i on P or e e s s as a B as i s fo r het D ve e l op m e in o f a H ihg s pe ed B i llet C as t l n g M o ld . i n : P r oc e e d i n g s o f ntI em iat o n a l C o n fe er n e e o n Mo d e ll i n g an d s诵u lat i o n in M e at l l切唱i e al E ng ine e n n g an d M aet ir a l s S e i enc e . B e ij ing , 1 99 6 . 36 6 3 eK l ly J E , M i e h a l e k K P, C o mt o r T G , e t a l . I n i it a l D ve e l - o P m e n t o f hT e mr ia an d S etr s s F i e l d s in C o n tin u o u s l y C ast Set e l B i ll e st . M e at l l u 电 i e a l T r an s a c t l o n A , 1 9 8 8 , 1 9A : 2 5 8 9 4 Z e t e r lun d E H , Kr i s ti an s s o n J O . C o nt i n u o u s C as t i n g 一 a n um e ir e a l StU dy o f ht e nI if u e n e e o f M h l o ld W七ar o n C acr k F o mr at i o n · S c an din va ian J o um ia o f M e alt l u 飞y , 19 8 3 , 12 : 2 1 1 5 S o ir m ac hi K , B ir m ac o m be J K . nI P r0 v e m e nst in M a ht e - m at i e a l M o d e l lin g o f S etr s s e s in C o in i n u o u s C ast in g o f S t e e l · orI nl ak 加 9 an d S et e ln a] 厄n g , 19 7 6 ( 1) : 3 8 6 荆 德君 , 蔡开科 . 包 晶相 变对 连铸 坯初 生坯 壳凝 固 收缩 的影 响 . 钢 铁研 究学 报 , 19 9 , 1 (:3) 9 7 F ir e dm an E · hT erm o m e c h耐 e ia A n a ly s i s o f hte W七ld ign P r o c e s s U s in g ht e F in ite E l e m e n t M e ht od . J o urn ia o f rP e s - s ur e Ve s s e l eT e lm o l o gy, T r an s a e tl on o f ht e A SM E , 197 5 , 9 7( 8 ) : 2 06 8 C h o n g H e e yu , M 沉o s u z u k i , H i r o y u k 1 Sh lb a at, et a l . Si m u lat i o n o f C acr k F omr at ion o n S o l iid fy 1 n g Set e l She l l i n C o n tin ou u s C as int g M o ld . I S I J I n et m at i o n a l , 1 9 9 6 , 3 6 ( S u PP l e m e n t ) : 1 5 9 9 、油n l an ak a, N a kaj 而a K , o k aj m uar .K C irt ic al Str a l n for ln - et ma l C ar c k F o mr iat o n in C o nt l n u ous C as tl n g . I r o n j n ak - in g an d St e e ln 山 n g , 1 9 9 5 , 2 2 ( 6 ) : 5 0 8 N um e ir e a l S im u l at i o n o f ht e C o uP li n g P h e n o m e n o n b e wt e e n hT e mr a l an d M e e h an i e a l F i e ld s o f B i ll e t i n C o n t i n u o u s C a s t i n g M o ld 刀界G D ’ej u n, CA I K d ike M e alt l l l年守 S e h o l , U S T B e ij in g B e ij in g 10 0 0 8 3 , C h in a A B S T R A C T B a s e d o n ht e s o lid iif e iat o n P ocr e s s o f e ar b on s et e l i n e o nt i n u o u s e a s t in g m o ld , an d e o n s id e n n g t h e e o n t a e t b e h a v ior b e wt e e n b ill e t an d m o ld , a ful ly ht e mr o m e e h an i e a ll y e o uP l e d 2 D tr an s i e nt ht e n n o 一 e l a s ot - Pl a s it e F E M m o d e l 1 5 e s t a b li s h e d . hT e m do e l i s im P l e m e n t e d w iht M A[ R C s o ft w ar e o n P C e o m Put er , an d ht e ht e mr a l an d m e e h an i e a l s at e s in e o nt in uo us e a st in g m o ld aer o b at i n e d , e s P e e i a lly i n e l u d i n g ht e I n t e r fa e i a l s at - t e s b e wt e e n s h e l l an d m o ld , s u e h as b ill et s u r fa e e et m Pe r a ut r e , int e ir 五e l a l he at fl ux an d ht e l aw o f g ap fo n n a - it o n . Th i s an ilyt e a l w o r k e an Por v id e ht e o er t i e a l b a s e s fo r o Pt而l z l n g m o ld at Per an d d e v e lop in g hi hg 一 s Pe e d e a st ign m o ld w iht e o n t l n u o u s l y e h an g in g at ep .r K E Y W O R D S e o n t lun ou s e a st in g m o ld : s o liid if e at i o n : ht emr a l 一 m e e h an i e a l e o u Pl e ; e o n at c t ; t h e mr o 一 e l a s ot - Plas it e F E M m o d e l