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摘要: 采用經典彈性力學方法建立了金屬層合板翹曲解析計算力學模型，獲得了厚度方向不均勻延伸與板形翹曲之間的定量關系；并分別建立了在線和離線兩種狀態下金屬層合板翹曲變形的有限元數值模擬模型，對解析計算力學模型進行了驗證；在此基礎上，揭示了金屬層合板產生板形翹曲缺陷的力學根源以及各因素對金屬層合板板形翹曲缺陷演變的影響規律，同時對比分析了雙層和三層結構層合板與均質板的翹曲變形差異以及銅/碳鋼層合板與不銹鋼/碳鋼層合板二者之間的翹曲變形差異。研究表明，金屬層合板翹曲高度與延伸差、厚度比呈正比關系，與厚度呈反比關系，且基層與覆層的切變模量相差越大，厚度比對金屬層合板翹曲變形的影響越大。基于數值模型，模擬研究了層合板在理想均勻分布的初始溫度下，歷經去應力退火過程時，其板形翹曲的變形行為及規律，并與均質板進行比較。最后，在工業生產現場取樣已翹曲層合板，通過測量其彎曲變形量進而反求其初始延伸差，驗證了解析計算力學模型的準確性。Abstract: The layered characteristics of the material in the thickness direction of the metal laminate make it more prone to uneven plastic extension during the thinning, rolling, flattening, and straightening process, resulting in plate-shaped warpage defects and cause the plate-shaped warpage of the metal laminate. The behavior is significantly different from that of a homogeneous metal plate. In this paper, the classical elastic mechanics method was used to establish an analytical computational mechanical model for the warpage of the metal laminate, and the quantitative relationship between the uneven extension in the thickness direction and the warpage of the plate shape was obtained; the online and offline states of the metal laminate were established, respectively. The finite element numerical simulation model of warpage deformation validated the analytical computational mechanics model; based on this, it revealed the mechanical roots of the shape warping defects of metal laminates and the effect of various factors on the shape warpage defects of metal laminates. The influence law of evolution and the difference in warpage deformation between double-layer and three-layer structure laminates and homogeneous plates, as well as the difference in warpage deformation between copper/carbon steel laminates and stainless steel/carbon steel laminates, were compared. Studies have shown that the warpage height of the metal laminate is proportional to the elongation difference and thickness ratio, and it is inversely proportional to the thickness. The greater the difference between the shear modulus of the base layer and the cladding layer is, the larger the effect of the thickness ratio on the warpage deformation of the metal laminate will be. Based on the numerical model, simulation studies were conducted on the deformation behavior and regularity of the plate shape warping of the laminated plate under the ideal uniform distribution of the initial temperature and the stress relief annealing process, and it was compared with that of the homogeneous plate. Finally, a sample of the warped laminate was taken at an industrial production site, and the initial extension difference was reversed by measuring its bending deformation. The result verifies the accuracy of the analytical computational mechanical model.
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Key words:
- metal laminate /
- warpage /
- longitudinal extension /
- analytical method /
- finite element
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圖 1 金屬層合板結構模型。（a）雙層結構的層合板；（b）三層結構的層合板
Figure 1. Structural model of metal laminate: (a) double-layer structure laminate; (b) three-layer laminate
圖 2 金屬層合板翹曲有限元模型。（a）工業在線有張力帶狀層合板翹曲模型；（b）離線裁切后塊狀層合板翹曲模型
Figure 2. Finite element model for warping of metal laminates: (a) industrial online warpage model of tensioned ribbon laminate; (b) warping model of block laminate after offline cutting
圖 3 金屬層合板翹曲模態。（a）C翹翹曲模態；（b）L翹翹曲模態
Figure 3. Warping mode of metal laminate: (a) C warping mode; (b) L warping mode
圖 4 延伸差對不同翹曲模態變形的影響。（a）C翹；（b）L翹
Figure 4. Effect of extension difference on the warpage height of C warping (a) and L warping (b)
圖 5 厚度對不同翹曲模態變形的影響。（a）C翹；（b）L翹
Figure 5. Effect of thickness on warpage height of C warping (a) and L warping (b)
圖 6 厚度比對不同翹曲模態變形的影響。（a）C翹；（b）L翹
Figure 6. Effect of the thickness ratio on warpage height of C warping (a) and L warping (b)
圖 7 金屬層合板不同翹曲后界面處應力分布情況。（a）C翹；（b）L翹
Figure 7. Stress distribution at the interface of metal laminate after C warping (a) and L warping (b)
圖 8 層合板與均質板冷卻過程熱變形行為對比。（a）工業在線有張力帶狀層合板和均質板對比；（b）離線裁切后塊狀層合板和均質板對比
Figure 8. Comparison of the thermal deformation behavior of laminated and homogeneous plates during cooling: (a) comparison of industrial online tension band laminate and homogeneous board; (b) comparison of block laminate and homogeneous board after offline cutting
圖 9 不銹鋼?碳鋼雙金屬層合板翹曲模態。（a）工業在線有張力層合板翹曲模態；（b）離線裁切后塊狀層合板翹曲模態
Figure 9. Stainless steel?carbon steel bimetal laminate warpage mode: (a) warping mode of industrial online tension laminate; (b) warping mode of block laminate after offline cutting
圖 10 終冷溫度對C翹（a）和四角翹（b）翹曲變形的影響
Figure 10. Effect of the final cooling temperature on warpage height of C warpage (a) and four corners warpage (b)
圖 11 冷卻后層合板界面處應力分布。（a）工業在線有張力時帶狀金屬層合板；（b）離線裁切后塊狀金屬層合板
Figure 11. Stress distribution at the interface of the laminate after cooling: (a) strip metal laminate with tension in the industrial line; (b) bulk metal laminate after offline cutting
表 1 金屬層合板力學性能
Table 1. Mechanical properties of metal laminates
Metal laminates Material E / GPa G/GPa $\nu $ Copper / carbon steel T2/ Q235 108/210 41/81 0.32/0.3 Stainless steel/carbon steel 304/ Q235 202/210 78/81 0.3/0.3 
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表 2 解析計算與有限元計算C翹翹曲高度結果對比
Table 2. Comparison between analytical calculation and finite element calculation of C warpage height
Metal laminate Laminate structure Extension difference / 10?5 Finite element results / mm Analytical calculation results / mm Relative error / % Copper / carbon steel Double layer 50/100 7.41/14.82 7.23/14.46 2.43/2.43 Three layers 50/100 5.20/10.41 5.28/10.55 1.52/1.33 Stainless steel / carbon steel laminate Double layer 50/100 8.40/16.80 8.36/16.72 0.48/0.48 Three layers 50/100 7.77/15.53 8.20/16.40 5.24/5.31
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表 3 解析計算與有限元計算L翹翹曲高度結果對比
Table 3. Comparison between analytical calculation and finite element calculation of L warpage height
Metal laminate Laminate structure Extension difference /
10?5Finite element results / mm Analytical calculation results / mm Relative error / % Copper / carbon steel Double layer 50/100 93.73/186.65 94.34/188.68 0.65/1.08 Three layers 50/100 66.57/132.92 68.37/136.75 2.63/2.80 Stainless steel / carbon steel laminate Double layer 50/100 111.77/222.35 111.44/222.87 0.30/0.23 Three layers 50/100 105.45/210.17 109.36/218.72 3.58/3.91
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表 4 L翹翹曲高度測量值與計算值對比
Table 4. Comparison of the measured values and calculated values of the L warpage height
Working condition Sampling parameters / mm Measurement results / mm Calculation results /
mmRelative error /
%d1 d2 h1 h2 1 299.8 300.2 15.8 12.5 14.15 13.40 5.3 2 399.6 400.4 35.7 31.2 33.45 31.84 4.8 3 499.4 500.3 65.9 63.1 64.50 62.18 3.6
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參考文獻
[1] Shi H J, Ding X, Luo H L, et al. Research progress of preparation technology of heterogeneous nonferrous metal composite plate. Hot Work Technol, 2019, 48(6): 1史豪杰, 丁旭, 羅海龍, 等. 異種有色金屬復合板制備技術的研究進展. 熱加工工藝, 2019, 48(6):1 [2] Liu Y, Zhang T Z, Sun A X, et al. Research status of compounding technology for Cu/Steel bimetal. Mater Rev, 2015, 29(15): 10劉越, 張太正, 孫愛新, 等. 銅/鋼雙金屬復合制備工藝技術研究現狀. 材料導報, 2015, 29(15):10 [3] Li L, Bi J H, Zhou D J. Production and application of metal clad plate and strip in China. Steel Roll, 2017, 34(2): 43李龍, 畢建華, 周德敬. 我國金屬復合板帶材的生產及應用. 軋鋼, 2017, 34(2):43 [4] Qin Q, Deng J C, Zang Y, et al. Factors influencing the combined performance of hot-rolled bimetallic composite plates prepared via hot compression. Chin J Eng, 2018, 40(4): 469秦勤, 鄧俊超, 臧勇, 等. 熱壓316L/Q345R復合板的結合性能. 工程科學學報, 2018, 40(4):469 [5] Ji C, Huang H G, Sun J N, et al. Research progresses on cast-rolling bonding technology of laminated metal clad strips. China Mech Eng, 2019, 30(15): 1873 doi: 10.3969/j.issn.1004-132X.2019.15.014季策, 黃華貴, 孫靜娜, 等. 層狀金屬復合板帶鑄軋復合技術研究進展. 中國機械工程, 2019, 30(15):1873 doi: 10.3969/j.issn.1004-132X.2019.15.014 [6] Wang D. The Research on Simulation of Composite Cold Rolling Plate of Stainless Steel [Dissertation]. Qinhuangdao: Yanshan University, 2011王丹. 不銹鋼復合板冷軋模擬研究 [學位論文]. 秦皇島: 燕山大學, 2011 [7] Ma J Z, Zhou C L, Zhang X C. The effect of different reduction and speed rate on the flatness of asymmetrical rolling clad plate. Heavy Mach, 2016(3): 20 doi: 10.3969/j.issn.1001-196X.2016.03.005馬江澤, 周存龍, 張校誠. 壓下率和異速比對異步軋制復合板平直度影響. 重型機械, 2016(3):20 doi: 10.3969/j.issn.1001-196X.2016.03.005 [8] He B L, Zhang X J, He Y, et al. Simulation of head warping in hot rolling of carbon steel and stainless steel clad plate. Steel Roll, 2016, 33(2): 16何冰冷, 張心金, 何毅, 等. 碳鋼/不銹鋼復合厚板熱軋頭部翹曲有限元模擬. 軋鋼, 2016, 33(2):16 [9] Zan X L, Wang F Q, Liu Z Y, et al. Mechanism analysis and research measures of residual stress-related plate shape defects in hot rolled strip. China Metall, 2020, 30(5): 35昝現亮, 王鳳琴, 劉子英, 等. 熱軋帶鋼殘余應力相關板形缺陷機理分析及攻關措施. 中國冶金, 2020, 30(5):35 [10] Masui T, Kaseda Y, Ando K. Warp control in strip processing plant. ISIJ Int, 1991, 31(3): 262 doi: 10.2355/isijinternational.31.262 [11] Li H, Zhang L Y, Zhang B Y, et al. Microstructure characterization and mechanical properties of stainless steel clad plate. Materials, 2019, 12(3): 509 doi: 10.3390/ma12030509 [12] He J F. Cause analysis of tinplate warp and our countermeasures. Baosteel Technol, 2004(1): 36 doi: 10.3969/j.issn.1008-0716.2004.01.010何建鋒. 寶鋼鍍錫板翹曲原因分析與對策. 寶鋼技術, 2004(1):36 doi: 10.3969/j.issn.1008-0716.2004.01.010 [13] Tang W, Du F S, Wen J, et al. Research and application of warping control strategy on tinplate. Iron Steel, 2019, 54(12): 55唐偉, 杜鳳山, 文杰, 等. 鍍錫板翹曲控制策略研究與應用. 鋼鐵, 2019, 54(12):55 [14] Zhang Q D, Dai J T. Simulation of warping deformation in thin steel strips. J Univ Sci Technol Beijing, 2011, 33(8): 1006張清東, 戴杰濤. 帶鋼板形翹曲變形行為的仿真. 北京科技大學學報, 2011, 33(8):1006 [15] Zhang Q D, Lu X F, Zhang X F. Analysis of buckling deformation for thin cold-rolled strip with initial warping defect. Eng Mech, 2014, 31(8): 243 doi: 10.6052/j.issn.1000-4750.2013.04.0340張清東, 盧興福, 張曉峰. 具有初始翹曲缺陷冷軋薄帶鋼板形瓢曲變形行為研究. 工程力學, 2014, 31(8):243 doi: 10.6052/j.issn.1000-4750.2013.04.0340 [16] Zhang Q D, Lu X F, Dai J T, et al. Analysis of warping deformation for cold-rolled strips. J Univ Sci Technol Beijing, 2014, 36(3): 378張清東, 盧興福, 戴杰濤, 等. 冷軋帶鋼板形翹曲變形過程及規律的解析. 北京科技大學學報, 2014, 36(3):378 [17] Zhang Q D, Zhou S, Yin J C. Numerical simulation on the wave-shaped defect generation and tension straightening process of thin strips. Chin J Eng, 2015, 37(6): 789張清東, 周歲, 銀家琛. 薄帶材浪形缺陷生成與拉伸矯直過程數值仿真. 工程科學學報, 2015, 37(6):789 [18] Li B, Zhang Q D, Zhang X F. Heredity and evolution laws of flatness defects in steel strip temper rolling processes. Chin J Eng, 2015, 37(2): 231李博, 張清東, 張曉峰. 帶鋼平整軋制過程中板形缺陷的遺傳和演變規律. 工程科學學報, 2015, 37(2):231 [19] Dai J T, Zhang Q D. Analysis and experiment on central buckling and post buckling of thin cold-rolled sheet. J Mech Eng, 2011, 47(2): 44 doi: 10.3901/JME.2011.02.044戴杰濤, 張清東. 冷軋薄板中浪板形缺陷的屈曲及后屈曲理論與軋制試驗研究. 機械工程學報, 2011, 47(2):44 doi: 10.3901/JME.2011.02.044 [20] Dai J T, Li L J, Zhang Z J. Warping analysis of medium plate based on symplectic elasticity method. Chin J Solid Mech, 2015, 36(3): 215戴杰濤, 李烈軍, 張祖江. 基于辛彈性力學方法的中厚板板形翹曲行為分析. 固體力學學報, 2015, 36(3):215 [21] Zhang B Y, Lu X F, Zhang L Y, et al. Analysis of complex warping deformation for cold-rolled strip. J Mech Eng, 2018, 54(12): 184 doi: 10.3901/JME.2018.12.184張勃洋, 盧興福, 張立元, 等. 冷軋極薄帶鋼復雜板形翹曲變形行為研究. 機械工程學報, 2018, 54(12):184 doi: 10.3901/JME.2018.12.184 [22] Lu X F. Study on Buckling and Warping Deformation of Steel Strip [Dissertation]. Beijing: University of Science and Technology Beijing, 2015盧興福. 鋼板帶板形瓢曲與翹曲變形行為研究 [學位論文]. 北京: 北京科技大學, 2015 [23] Zhang Q D, Lu X F, Zhang X F. Deformation of warping in apparent straight strip after shearing process. Eng Mech, 2014, 31(Suppl 1): 217張清東, 盧興福, 張曉峰. 表觀平直帶鋼裁切加工后翹曲變形行為研究. 工程力學, 2014, 31(增刊 1):217 [24] Zhang Q D, Lin X, Liu J Y, et al. Modelling of Q& P steel heat treatment process based on finite element method. Acta Metall Sin, 2019, 55(12): 1569 doi: 10.11900/0412.1961.2019.00082張清東, 林瀟, 劉吉陽, 等. Q& P鋼熱處理過程有限元法數值模擬模型研究. 金屬學報, 2019, 55(12):1569 doi: 10.11900/0412.1961.2019.00082 [25] Yu W, Wang Y F. Relationship between cooling parameters and warping of hot rolled strips. Chin J Eng, 2016, 38(12): 1734余偉, 王乙法. 熱軋帶鋼的冷卻參數與翹曲關系. 工程科學學報, 2016, 38(12):1734 [26] Wang C H. Research on Warping Behavior and Flatness/Straightening Deformation of Metal Laminates [Dissertation]. Beijing: University of Science and Technology Beijing, 2020王春海. 金屬層合板翹曲行為與平整/矯直變形規律研究 [學位論文]. 北京: 北京科技大學, 2020 -
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