复合轧制过程接触模型及轧制区变形特性研究

doi:10.3901/JME.2025.22.383

摘要/Abstract

摘要： 复合轧制是一种快速、高效、环保的金属复合板生产方法，具有广阔的应用前景。复合轧制过程中板材与轧辊以及板材与板材之间的接触是影响复合板变形以及结合强度的关键因素。针对复合轧制过程中复杂的接触非线性问题，基于Mortar法对接触界面进行离散，使用拉格朗日乘子法进行接触约束的施加，构建了复合轧制过程轧辊与板材以及板材与板材之间的接触模型。通过对偶基函数对拉格朗日乘子进行插值，实现了有限元刚度矩阵简化。最后，基于该接触模型对Cu/Al复合轧制过程进行了三维有限元模拟。经验证，该模型在板厚以及轧制力预测方面具有较高的精度。该接触模型能够对接触界面上接触相关参数进行模拟，结果表明：铝板与轧辊接触界面以及铜板与轧辊接触界面以滑动摩擦为主，而铜板与铝板的接触界面以粘着摩擦为主。通过对不同压下率下的复合轧制过程进行模拟，揭示了压下率对中性点以及搓轧区的影响机理以及板材结合界面接触力随压下率的变化规律。结果表明：随着压下率的增加以及与板材中心距离的减小，x_N/x_L的值减小且压下率的增加使得搓轧区两侧的摩擦力方向发生改变。在板材与板材接触界面上，压力以及摩擦力的峰值位置随着压下率的增加而逐渐远离出口。

关键词: 复合轧制, 有限元法, 接触模型, 接触力, 中性点

Abstract: Clad rolling is a rapid, efficient, and environmentally friendly method for producing composite plates, with significant potential for widespread application. The contact between the plate and the roll, as well as between plates, is a critical factor influencing the deformation and bonding strength of composite plates during the rolling process. To address the complex nonlinear contact issues inherent in clad rolling, a contact model was developed using the Mortar method to discretize the contact interfaces and the Lagrange multiplier method to enforce contact constraints. This model simulates the interactions between roll and plate, as well as between plates themselves. By interpolating the Lagrange multipliers with dual basis functions, the finite element stiffness matrix is simplified. Finally, a three-dimensional finite element simulation of the Cu/Al clad rolling process was conducted based on this contact model. The model has been verified to have high accuracy in predicting plate thickness and rolling force. The contact model can simulate the contact parameters on the contact interface. The results show that the contact interface between the aluminum plate and the roll, as well as the copper plate and the roll, is primarily characterized by sliding friction, whereas the contact interface between the copper plate and the aluminum plate is mainly characterized by stick friction. By simulating the clad rolling process under different reduction rates, the effects of the reduction rate on the neutral point and the cross shear zone were revealed, as well as the pattern of changes in the contact force at the plate interface with the reduction rate. The results indicate that as the reduction rate increases and the distance from the center of the plate decreases, the value of x_N/x_L decreases, and the increase in reduction rate causes a change in the direction of frictional forces on both sides of the cross shear zone. On the contact interface between the plates, the peak positions of pressure and frictional force gradually move away from the outlet as the reduction rate increases.

Key words: clad rolling, FEM, contact model, contact force, neutral point

中图分类号:

TG331

李志强, 张明泽, 郭宝琦, 陈鹏, 王涛, 黄庆学. 复合轧制过程接触模型及轧制区变形特性研究[J]. 机械工程学报, 2025, 61(22): 383-397.

LI Zhiqiang, ZHANG Mingze, GUO Baoqi, CHEN Peng, WANG Tao, HUANG Qingxue. Study on the Contact Model of Clad Rolling Process and Deformation Characteristics of the Rolling Zone[J]. Journal of Mechanical Engineering, 2025, 61(22): 383-397.

参考文献

[1] XU X,ZHOU J,CUI H,et al.A new method for joining Incoloy825/X65 composite plate by laser and CMTwelding[J].Journal of Manufacturing Processes,2024,129:11-23.
[2] SHI C,LUO X,SUN Z,et al.Experimental and numerical study of interface and mechanical properties of TA1/5083/TA1 vacuum creep pressure bonding composites[J].Journal of Manufacturing Processes,2024,124:458-478.
[3] ZHAO H,SHENG L.Microstructure and mechanical properties of the Ag/316L composite plate fabricated by explosive welding[J].Journal of Manufacturing Processes,2021,64:265-275.
[4] 任忠凯,郭雄伟,李宁,等.脉冲电流对TA1/304复合板结合性能的改性机制研究[J].机械工程学报,2022,58(6):62-72.REN Zhongkai,GUO Xiongwei,LI Ning,et al.Study on the modification mechanism of pulse current on the bonding properties of TA1/304 composite plate[J].Journal of Mechanical Engineering,2022,58(6):62-72.
[5] 马艺星,杨蔚涛,关肖虎,等.TWIP钢/IF钢热轧复合板材的微观结构和界面结合性能[J].机械工程学报,2024,60(4):345-356.MA Yixing,YANG Weitao,GUAN Xiaohu,et al.Microstructure and interfacial bonding property of a hotroll-bonded TWIP/IF steel composite plate[J].Journal of Mechanical Engineering,2024,60(4):345-356.
[6] 杨旭东,张全鑫,张晓波.铝/铜复合材料累积叠轧组织及力学性能研究[J].塑性工程学报,2025,32(6):248-256.YANG Xudong,ZHANG Quanxin,ZHANG Xiaobo.Study on microstructure and mechanical properties of aluminium/copper composites prepared by accumulated roll bonding[J].Journal of Plasticity Engineering,2025,32(6):248-256.
[7] 刘元铭,刘延啸,申宏卓,等.Mg/Al复合板波纹轧变形特点与微观组织演变[J].机械工程学报,2025,61(8):85-97.LIU Yuanming,LIU Yanxiao,SHEN Hongzhuo,et al.Deformation characteristic and microstructure evolution of Mg/Al clad plate in corrugated rolling[J].Journal of Mechanical Engineering,2025,61(8):85-97.
[8] 刘锦华,刘鹏,栾欠欠,等.波纹界面钛/钢复合板热轧制备与界面组织性能研究[J].精密成形工程,2025,17(7):31-40.LIU Jinhua,LIU Peng,LUAN Qianqian,et al.Hot roll bonding fabrication and interfacial microstructure and properties of titanium/steel clad plates with corrugated interface[J].Journal of Netshape Forming Engineering,2025,17(7):31-40.
[9] 郭允畅,路明昊,祁梓宸,等.表面处理方式对热轧钢/铝复合板结合强度的影响[J].精密成形工程,2025,17(7):41-51.GUO Yunchang,LU Minghao,QI Zichen,et al.Influence of surface treatment methods on bonding strength of hot-rolled steel-aluminum composite plates[J].Journal of Netshape Forming Engineering,2025,17(7):41-51.
[10] 孙建亮,刘宏民,彭艳,等.考虑非均匀应力分布的大型筒节轧制力计算模型[J].机械工程学报,2015,51(18):50-56.SUN Jianliang,LIU Hongmin,PENG Yan,et al.Rolling force model of heavy cylinder based on non-uniform stress distribution[J].Journal of Mechanical Engineering,2015,51(18):50-56.
[11] 黄华贵,季策,杜凤山.双金属复合管固-液铸轧复合轧制力模型研究[J].机械工程学报,2017,53(10):10-17.HUANG Huagui,JI Ce,DU Fengshan.Research on cast-rolling force calculation model in solid-liquid cast-rolling bonding (SLCRB) process of bimetallic clad pipe[J].Journal of Mechanical Engineering,2017,53(10):10-17.
[12] QWAMIZADEH M,KADKHODAEI M,SALIMI M.Slab analysis of asymmetrical rolling of bonded two-layer sheets[J].ISIJ International,2013,53(2):265-273.
[13] WANG S,GAO H T,WANG X G,et al.Rolling force model of V-shaped variable thickness rolling based on energy approach[J].Journal of Materials Processing Technology,2024,326:118336.
[14] 陈宇,刘文文,王涛,等.预制波纹工艺对钢/铝/铝合金复合板界面影响机制研究[J].机械工程学报,2023,59(8):74-82.CHEN Yu,LIU Wenwen,WANG Tao,et al.Study on influence mechanism of prefabricating corrugation process on interface of Steel/Aluminum/Aluminum alloy laminated plate[J].Journal of Mechanical Engineering,2023,59(8):74-82.
[15] PAPADOPOULOS P,TAYLOR R L.A mixed formulation for the finite element solution of contact problems[J].Computer Methods in Applied Mechanics and Engineering,1992,94(3):373-389.
[16] PUSO M A,LAURSEN T A,SOLBERG J.Asegment-to-segment mortar contact method for quadratic elements and large deformations[J].Computer Methods in Applied Mechanics and Engineering,2008,197(6-8):555-566.
[17] WOPSCHALL S R,RASHID M M.A novel face-on-face contact method for nonlinear solid mechanics[J].Computer Methods in Applied Mechanics and Engineering,2019,348:356-376.
[18] WRIGGERS P,VU VAN T,STEIN E.Finite element formulation of large deformation impact-contact problems with friction[J].Computers&Structures,1990,37(3):319-331.
[19] HEINTZ P,HANSBO P.Stabilized Lagrange multiplier methods for bilateral elastic contact with friction[J].Computer Methods in Applied Mechanics and Engineering,2006,195(33-36):4323-4333.
[20] ZHOU M,ZHANG B,PENG C.Numerical evaluation of soft inter-slab joint in concrete-faced rockfill dam with dual mortar finite element method[J].International Journal for Numerical and Analytical Methods in Geomechanics,2018,42(5):781-805.
[21] HARTMANN S,RAMM E.A mortar based contact formulation for non-linear dynamics using dual Lagrange multipliers[J].Finite Elements in Analysis and Design,2008,44(5):245-258.
[22] PUSO M A,LAURSEN T A.A mortar segmentto-segment contact method for large deformation solid mechanics[J].Computer Methods in Applied Mechanics and Engineering,2004,193(6-8):601-629.
[23] POPP A,GITTERLE M,GEE M W,et al.A dual mortar approach for 3D finite deformation contact with consistent linearization[J].International Journal for Numerical Methods in Engineering,2010,83(11):1428-1465.
[24] SITZMANN S,WILLNER K,WOHLMUTH B I.A dual Lagrange method for contact problems with regularized contact conditions[J].International Journal for Numerical Methods in Engineering,2014,99(3):221-238.
[25] SITZMANN S,WILLNER K,WOHLMUTH B I.A dual Lagrange method for contact problems with regularized frictional contact conditions:Modelling micro slip[J].Computer Methods in Applied Mechanics and Engineering,2015,285:468-487.