固体力学学报 2000年第21卷 参考文献 I Cook J, Gordon J E. A mechanism for the control of crack propagation in all-brittle materials. Proc R Soc, London 964,A282:508~520 2 Baskaran S et al. Fibrous monolithic ceramic. J Am Ceram Soc. 1993. 76: 2209--2216 3 Clegg wJ et al. A simple way to take tough ceramic. Nature (London), 1990, 357[Oct 4]: 455-457 4 Liu Haiyan, Hsu S M. Fracture behaviour of multilayer silicon nitride/ boron nitride ceramics. J Am Ceram Soc 996,79(9):2452~2457 5郭海,黄勇,李建保.层状氮化硅陶瓷的性能与结构.硅酸盐学报,1997,25(5):532~536 6 Cao H C, Evans A G An experimental study of the fracture resistance bimaterial interface. Mech Mater, 1989 7 Charalamibides P Get al. A test specimen for determining the fracture resistance of bimaterial interface. J Appl Mech,1989,56:77~82 8 Phillipps AJ, Clegg WJ, Clyne T W. Fracture behaviour of ceramic laminates in bending I. Modelling of crack propagation. Acta Metall Mater, 1993, 41(3): 805-817 9 Kovar D, King b H, Trice R Wet al. Fibrous mplithie ceramics. J Am Ceram Soc, 1997,80(10): 2471--2487 10 He Mingyuan, Hutchinson J W. Kinking of a crack out of an interface. J Appl Mech, 1989, 56(6): 270-278 1中国航空研究院主编应力强度因子手册北京:科学出版社,1981,120~121 A MECHANICS ANALYSIS OF STRENGTHENING TOUGHENING DESIGN OF MUL TILAY ER STRUCTURE CERAMICS Department d Engineening Mechanics, Tsinghua University, Bejing, 100084/ Wang Changan Huang Yong Department d Material Science and Engineening, Tsinghua University, Bejing, 100084) Abstract Based on theory of beam and cracking and kinking condition of crack in bimaterial ir terfaces, the mechanics analysis is made on strength and toughness of multilayer structure ceramics in symmetric fourpoint bending. An analytic relation that relates strength, toughness of the bending specimen and material properties, structure s geometric parameters of the ceramic sheet and interfacial layer is obtained. Finally, the corresponding relative curves are given and the theoretical value of frac- ture work for Si3 N4/BN multilayer structure is compared with the experimental result Key words multilayer structure ceramics, load-displacement curve, interface fracture tough ness, strengthening- toughening design 附录A梁的挠度、柔度与相应的能量释放率表达式的推导 图5所示梁的挠度曲线方程与加载点位移可利用梁的理论得出图中∑为界面裂纹作 第i次扩展后,相应扩展长度为a的区域内梁的等效抗弯刚度,1=1,2,3,…,n.i=1时,2 为界面裂纹未扩展时的原始抗弯刚度.现分a扩展至AB段L≤xs+D和OA段0≤x )01994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreservedhttp:/www.cnki参 考 文 献 1 Cook J , Gordon J E. A mechanism for the control of crack propagation in all2brittle materials. Proc R Soc , London , 1964 , A282 :508～520 2 Baskaran S et al. Fibrous monolithic ceramic. J Am Ceram Soc , 1993 , 76 :2209～2216 3 Clegg W J et al. A simple way to take tough ceramic. Nature (London) , 1990 , 357[Oct. 4 ] :455～457 4 Liu Haiyan , Hsu S M. Fracture behaviour of multilayer silicon nitride/ boron nitride ceramics. J Am Ceram Soc , 1996 , 79 (9) :2452～2457 5 郭海 ,黄勇 ,李建保. 层状氮化硅陶瓷的性能与结构. 硅酸盐学报 ,1997 ,25 (5) :532～536 6 Cao H C , Evans A G. An experimental study of the fracture resistance bimaterial interface. Mech Mater , 1989 , (7) :295～304 7 Charalamibides P G et al. A test specimen for determining the fracture resistance of bimaterial interface. J Appl Mech , 1989 , 56 :77～82 8 Phillipps A J , Clegg W J , Clyne T W. Fracture behaviour of ceramic laminates in bending2Ⅰ. Modelling of crack propagation. Acta Metall Mater , 1993 , 41 (3) :805～817 9 Kovar D , King B H , Trice R W et al. Fibrous monolithic ceramics. J Am Ceram Soc , 1997 , 80 (10) :2471～2487 10 He Mingyuan , Hutchinson J W. Kinking of a crack out of an interface. J Appl Mech , 1989 , 56 (6) :270～278 11 中国航空研究院主编. 应力强度因子手册. 北京 :科学出版社 ,1981 ,120～121 A MECHANICS ANALYSIS OF STRENGTHENING2TOUGHENING DESIGN OF MULTILAYER STRUCTURE CERAMICS Guo Xianghua Cai Qianhuang ( Department of Engineering Mechanics , Tsinghua University , Beijing , 100084) Wang Changan Huang Yong ( Department of Material Science and Engineering , Tsinghua University , Beijing , 100084) Abstract Based on theory of beam and cracking and kinking condition of crack in bimaterial in2 terfaces , the mechanics analysis is made on strength and toughness of multilayer structure ceramics in symmetric four2point bending. An analytic relation that relates strength , toughness of the bending specimen and material properties , structureπs geometric parameters of the ceramic sheet and interfacial layer is obtained. Finally , the corresponding relative curves are given and the theoretical value of frac2 ture work for Si3N4/ BN multilayer structure is compared with the experimental result. Key words multilayer structure ceramics , load2displacement curve , interface fracture tough2 ness , strengthening2toughening design 附录 A 梁的挠度、柔度与相应的能量释放率表达式的推导 图 5 所示梁的挠度曲线方程与加载点位移可利用梁的理论得出. 图中Σi 为界面裂纹作 第 i 次扩展后 ,相应扩展长度为 ai 的区域内梁的等效抗弯刚度 , i = 1 ,2 ,3 , …, n. i = 1 时 ,Σ1 为界面裂纹未扩展时的原始抗弯刚度. 现分 ai 扩展至 AB 段 ( L ≤x ≤L + l) 和 OA 段 (0 ≤x ·322 · 固体力学学报 2000 年 第 21 卷