参考文献 ·11· [36]Rice J R.A path indepedent integral and the approximate analysis of strain concentra- tion by notches and cracks.J.Appl.Mech.,1968,35:379-386. (37]Cherepanov G P.On crack propagation in solids.Int.J.Solids.Structs.,1969,5: 863-871. [38]Hutchinson J W.Singular bebavior at the end of a tensile crack tip in a hardening materials.J.Mech.Phys.Solids,1968,16:13-31. [39]Rice J R,Rosengren G F.Plane strain deformation near a crack tip in a power law hardening material.J.Mech.Phys.Solids,1968,16:1-12. [40 Eshelby J D.The continuum theory of lattice defects.Solid Statc Physics,1956,3. [41 Giinther W.Uber einige randintegrae der elastomechanik Adhandlungen der Bran- schweigischen Wissenschaftlichen Gesellschaft.1962,14:53-72. [42]Begley J A,Landes J D.The J-integral as a fracture criterion.ASTM STP 514,1972: 1-20. [43 Rice J R,Paris P C,Merkle J G.Some further results of J-integral analysis and estimates, in Progress in Flaw Groth and Fracture Toughnese Testing.ASTM STP 536,American Society for Testing and Materials,Philadelphia,213-245. [44 MeMeeking R M,Parks D M.Elastic-plastic fracture.ASTM STP 668,1979:175-194. [45]Sih C F,German M D.Requirement for a one parameter characterization of crack tip fields by the HRR singularity.I.J.Fracture,1981,17:27-43. [46 Hancock J W,cowling M J.Role of state of stress in crack tip failure processes.Metal Science,1980,14:293-304. [47]De Castro P M S T,Spurrire J,Hancock P.An cxperimental study of the crack length/specimen widh ration dependence for the crack opening displacement test us- ing smale scale specimen.Fracture Mechanics,ASTM STP677,Philadelphia,486-497. [48,李尧臣，王自强.平面应变I型非线性裂纹问题的高阶渐近解.中国科学A,1986:182一194. [49李松涛，王自强.平面应力问题的高阶渐近场.中国科学A,1992:512-519. [50]Liu H W,Zhuang T.Characteristic crack tip fields and the characterizing parameter for elastic-plastic fracture mechanics.Advances in Fracture Research,ICF6,1984,2: 777-790. [51邓海涛，王自强.Plane stress elastic-plastic fracture criterion and stress-strain field around crack tip.Advances in Fracture Research,ICF7,1989:323-332. [52夏霖，王自强.非线性材料裂纹问题的高阶渐近分析.力学学报（英文版），1992,8：156-163. [53]Xia L,Wang T C,Shih CF.High order analysis of crack tip fields in power law hardening materials.J.Mech,Phys.Solids,1993,41:665-687. [54 Chao Y J,Yang S,Sutton M A.Asymptotic analysis of the crack tip fields to determine the region of dominance of the HRR solution.Proceedings of the 28th Annual Technical Meeting of the Society of Engineering Science,1991
.12. 第1章引 论 55]Yang S,Chao Y J,Sutton M A.Complete theoretical analysis for high order asymptotic terms and the HRR zone at a crack tip for Mode I and Mude II loading of a hardening material.Acta Mechanica,1993,98:79-98. [56]Betegon C.Hancock J W.Two-parameter characterizatiou of elastic-plastic crack tip fields.J.Applied Mechanics,1991,58:104. 57]Sharma S M,Aravas N.Detcrmination of high-order terms in asymptotic elastoplastic crack tip solations.J.Mech.Plys.Solids,1991,39:1043-1072. 58 O'Dowd N P.Shih CF.Family of crack tip ficlds characterized by a triaxially parameter- I.Structure of fields.J.Mech.Phys.Solids,1991,39:989-1015. (59O'Dowd N P,Shih C F,Dodds.The role of geometry and crack growth on constraint and iplications for ductile/brittle fracture.ASTM STP 1224,Philadelphia,1994. [60 Wei Y G,Wang T C.Fracture criterion based on the higher-order asymptotic fields. Inter.J.Fracture,1995,73:39-50. [61]Kirk M J,Koppenhoefer K C,Shih C F.Effect of constraint on specimen dimension nceded to obtain structurely relevant toughness measure.ASTM-STP 1171,1993. [62 Burderkin F M,Stone D E W.The crack opening displacement approach to fracture mechanics in yiclding materials.J.Strain Analysis,1966,1:145;Daws M G.The COD design curve,in Advances in elastic-plastic fracture mechanics.Applied Science Publishers8,1980:279-300. [63]徐纪林，王自强.平面应力的弹塑性断裂模型及其有限元分析，固体力学学报，1980,2： 183-193. (64]Hutchinson J W,Paris P C.Stability analysis of J-controlled crack growth,ASTM STP 668,Philadelphia.Ame,Soc.Testing Mater.,1979:37-64. [65]Paris P C,Tada H,Zahoor A et al.Instability of the tearing model of elastic-plastic crack growth.ASTM STP 668,Philadelphia,Ame Soc.Testry Mate.,1979:5-36. [66]Chitaley A D,McClintock F A.Elastic-plastic mechanics of steady crack growth under anti-plane shear.J.Mech.Phys.Solids,1971,19:147-163. (67]Slepyan L 1.Growing crack during plane deformation of an elastic plastic body.Izv. Akad Nauk.SSSR,Mekn,Tverd Tcla.1974,9:51-67. [68]Rice JR,Drugan W J;Sham T L.Elastic-plastic analysis of growing cracks.ASTM STP 700,Philadelphia,Ame.Soc.Testing Mate.,1980:189-221. [6!高玉臣.理想塑性介质中裂纹定常扩展的弹塑性场.力学学报，1980,12：48-56， [70)Drugan W J,Rice J R,Sham T L.Asymptotic analysis of growing plane strain tensile crack in elastic ideally plastic solids.J.Mech.Phys.Solids,1982,30:447-473. [71].The influence of compressibility on the elastic-plastic field of a growing crack. In the second Int.Symposium,On Elastic-Plastic Fracture Mechanics,Philadelphia, 1981.ASTM STP803,1983:176-190
参考文献 ·13· [?2岁学盆，黄克智.可压缩弹塑性扩展裂纹尖端场问题的正确提法及其解.中国科学，A,1988, 31:1275-1282. [73]Amazigo J C,Hutchinson J W.Crack tip fields in steady crack growth with linear strain hardening.J.Mech.Phys.Solids,1977,25:81-97. [74]Hui C Y,Reidel H.The asymptotic stress and strain field near the tip of a growing crack under creep condition.Int.J.Fracture,1981,17:409-425. [75]杨卫.宏微观断裂力学，北京：国防工业出版杜，1995， [76]黄克智，余寿文.弹塑性断裂力学.北京：清华大学出版社，1985. [77]匡震邦，马法尚.裂纹端部场.西安：西安交通大学出版社，2002. [781沈成康.断裂力学.上海：同济大学出版社，1996. 791范天佑.断裂理论基础.北京：科学出版社，2003. [80]王铎.断裂力学.哈尔滨：哈尔滨工业大学出版社，1987 [81]程靳，赵树山.断裂力学.北京：科学出版社，2006
第2章 线弹性断裂力学 断裂力学的早期发展是建立在线弹性理论基础之上的，也就是设想材料是理想 的线弹性材料.如陶瓷、玻璃等非常脆的材料，在一定条件下可以看作是理想的线 弹性材料，然后通过Irwin1!,2]和Orowanl个的修正，引入塑性功，在设想裂纹尖端 塑性区尺寸远远小于裂纹尺寸和其他特征尺寸的前提下，可以将线弹性断裂理论成 功用到常用的工程材料中 线弹性断裂力学主要研究裂纹起始扩展，亚临界扩展及失稳扩展的规律.通常 采用两种不同的观点处理裂纹扩展问题：一种是能量平衡观点，认为在裂纹扩展过 程中，外力所做的功减去物体应变能的增加应该等于产生新裂纹表面所需要的能 量：另一种是应力强度因子观点，认为裂纹尖端应力场强度因子达到表征材料断裂 韧性的临界应力强度因子时，裂纹就起始扩展、这两种观点有紧密的内在联系，在 很多情况下，这两种观点可以得到相同的结果. 2.1裂纹尖端弹性应力场 2.1.1平面问题 弹性力学平面问题，可以归结为求解应力函数(x,以，它满足办调方程： V4U=0 2.1) 考察图2.1所示的有限裂纹的一端.直角坐标系Oxy的原点选在裂纹尖端处 x轴与裂纹共线，y轴与裂纹垂直. 图2.1
2.1裂纹尖端弹性应力场 .15 裂纹面上，面力为零： 06=Tr9-0 (2.2) 式中，g和1r6分别是极坐标系中的周向正应力和剪应力， 本节只讨论裂纹尖端附近的奇性场.设想应力函数U可用分离变量的形式表 示为 U(r,)=x1+入F(0) (2.3) 将(2.3)式代入(2.1)式，得到关于的控制方程： F"()+2(A2+1)FY(0)+(2-1)2F(0)=0 (2.4) 该方程的通解为 F(0)=Acos(+1)0+Bsin(+1)0+Ccos(-1)0+Dsin(-1)0 (2.5) 极坐标系中的应力分量为 x= 1a2U+1aU=rA-1[F+A+1)] 2a82+r0r a2U 8三 =rA-1入+1)F (2.6) 0r2 10U r80 -A-1λF 由边界条件(2.2)导得 Fx(土元)=0，F(±π)=0 (2.7) 将(2.5)式代入(2.7)式，得到关于系数A,B,C和D的4个线性齐次代数方程： A cos An +C cos At =0 2.8) A(+1)sin+C(-1)sin=0 B sin.An+Dsin An =0 (2.9) B(+1)cos+D(-1)cos =0 这4个线性代数方程组成两组方程组.这两个方程组有非零解的充要条件是它们 的系数行列式分别为零，由此得到一个相同的特征方程： sin2λ元=0 (2.10) 相应的特征根为 2, n=0,1,2, (2.11)