摘要
金属材料的强度与裂纹扩展行为密切相关。裂纹扩展过程中裂纹尖端存在着应力、应变集中,这使得裂纹尖端的局部应力、应变大于材料中其它区域的应力和应变。因此,在裂纹扩展的过程中,其尖端将会发生微结构演化。相关实验和原子尺度模拟的结果表明：裂纹扩展过程中裂尖微结构演化有多种形式,包括位错发射、孪晶形成以及裂尖相变等。而且这些微结构演化行为又与裂尖场的分布密切相关,可能对控制裂纹的扩展起到决定性作用。
本文应用有限元方法计算了平面应变条件下体心立方铁中不同取向裂纹的裂尖弹性应力场和弹性应变能密度分布。三种不同取向的裂纹将体心立方铁的刚度矩阵转化为不同形式,导致裂尖应力场和弹性应变能密度分布不同。由此出发,从宏微观相结合角度分析了裂尖场分布与裂尖微结构演化的相互关联。研究表明：裂尖微结构演化与裂尖弹性应变能密度分布密切相关。裂尖应力集中所导致的局部弹性应变能密度增高可以由裂尖塑性变形所释放。同时,应用连续介质力学及有限元的方法验证了裂尖塑性变形的具体形式与体心立方铁晶体结构中滑移面上的分切应力大小密切相关。分切应力大则易发生相变,分切应力较小易发生孪晶或位错。并分别比较了弹性应力场和HRR裂尖应力场与有限元模拟结果,结合分子动力学模拟结果尝试探讨了裂尖应力场的奇异性区域。
此外,运用弹塑性状态下{110}<110>Ⅰ型裂纹的有限元分析,从裂纹系统整体能量变化以及裂尖应力场两个角度分析裂尖塑性变形与裂纹扩展行为的关系。研究发现,相对于单纯的裂纹扩展,裂尖塑性变形的存在更有助于降低裂纹系统整体的弹性应变能总量。在较大载荷或较快加载速率条件下,裂尖附近区域弹性应变能密度增高为马氏体相变提供了必需的驱动力。同时本文也考察了此类裂纹滑移面上分切应力随载荷的变化,指出距裂尖一定距离的滑移面上分切应力平台对应着裂尖相变产生的区域。并验证了非局部弹塑性连续体模型所确定的裂纹尖端附近应力分布,结果显示此类型裂纹裂尖应力最大值发生在距裂尖约1纳米处。
The strength of metals is closely related to crack propagation. There will be stress and strain concentrations at the crack tip in the process of crack propagation, thus the plastic deformation will occur at the crack tip. Experimental and atomistic simulation results show that the plastic deformation occurring at crack tip includes dislocation emission, twinning and phase transformation. The occurrence of the plastic deformation is closely related to crack tip field, and it probably plays an important role on the crack propagation behaviors.
In this paper, the finite element method is applied to calculate the elastic stress field and the elastic strain energy density distribution at the crack tip. Three types of crack in body-centered cubic (bcc) iron with different orientations are selected. The calculated elastic stress field and elastic strain energy density distribution are different for three types of crack due to the difference of their stiffness matrixes. The results indicate that the microstructure evolution at the crack tip is closely related with the elastic strain energy density distribution. The high elastic energy could be released by the plastic deformation at the crack tip. It is also proved that the shear stress on the slip plane is a decisive factor on the micro structure evolution. Moreover, the truncated distance of continuum elastic field is discussed based on the finite element method, the continuum mechanics and the analysis of the HRR crack tip field.
Furthermore, using the FEM simulation of{110}<110> mode I crack, the relationship between the plastic deformation at the crack tip and the crack propagation behavior are discussed. At a high loading rate, matensitic phase transformation is favored to occur due to the high elastic strain energy density at the crack tip. It is also found that there exist a stress plateau on the slip plane during the martensitic phase transformation, which is caused by the stress relaxation due to the phase transformation. Moreover, the maximal value of the stress is shown at the location lnm away from the crack tip.
引文
[1]冯瑞等.金属物理学(第三卷)[M].科学出版社：北京,1999.
[2]冯瑞等.金属物理学(第一卷)[M].科学出版社：北京,1999.
[3]S.T.Pantelides, D.Maroudas, D.B.Laks. Defects in Heterogeneous Solids:From Microphysics to Macrophysics [J].Mater.Sci.Forum,1994,143:1-8.
[4]K.C.Hwang, S.W.Yu, W.Yang. Theoretical investigation of crack-tip singularity fields [J].Appl.Mech.,1990:19-33.
[5]W. Yang, T.F.Guo, H.L.Tan. Evolution of crack tip process zones [J].Computational Mechanics of Materials,1993:15-18.
[6]杨卫,孙庆平,黄克智,余寿文.固体的宏细观本构理论与断裂[J]. 自然科学进展,1993.
[7]杨卫.细观力学与细观损伤力学[J].力学进展,1992.
[8]W. Yang, W. B. Lee. Mesoplasticity and Its Applications [M].Springer-Verlag,1993.
[9]Suo Z., Varias A.G., Shih C. F. A theory for cleavage cracking in the presence of plastic flow [J]. Acta Metall.,1993.
[10]刘冰,胡松青.晶体线缺陷—位错的发现过程[J].青岛大学学报,2003,16：82-84.
[11]S.M.Ohr, J. Narayan. Electron microscope observation of shear cracks in stainless steel single crystals[J]. Phil.Mag.A.,1980,41:81-95.
[12]Kobayashi.S.,S.M..Ohr. In situ observation of formation of plastic zone ahead of crack tip in copper [J]. Scripta metal.,1981,15 (3):343～348.
[13]S.M. Ohr. An electron microscope study of crack tip deformation and its on the dislocation theory of fracture[J]. Mater.Sci.Eng.,1985,72(1):1.
[14]褚武扬,乔利杰,陈奇志,高克玮.断裂与环境断裂[M].科学出版社：北京,2000：20-34.
[15]钱才富.位错和位错偶沿单一滑移系从裂纹尖端的发射[J].金属学报,1999,35(5)546-550.
[16]T. Zhu, W. Yang, T. Gao. Quasi-cleavage process driven by dislocation pileup[J]. Acta Mater., 1996,44:3049-3058.
[17]K.Ogawa. Edge Dislocations Dissociated in{112} Planes and Twinning Mechanism of bcc Metals[J]. Philos.Mag.1965,217-239.
[18]P.M.Ilner. On the effect of deformation twinning on defect densities[J].Mater.Sci.Eng.A. 1997,230:107-115.
[19]T.Smida, J.Bosansky. Micromechanism of cleavage fracture in ferritic steels[J]. Kovove Mater.,2002,40:146～160.
[20]Q.Chen, Y.Huang, L.Qiao, W.Chu. Failure modes after exhaustion of dislocation glide ability in thin crystals[J]. Sci.China,Ser.E.,1999,42:1-9.
[21]B.D.Celis, A.S.Ardon, S.Yip. Molecular dynamics simulation of crack tip processes in alpha-iron and copper[J]. J Appl Phys.,1983,54:4864.
[22]X.Wei, J.A.Moriarty. Atomistic simulation of point defects and dislocation in bcc transition metals from first principles[J]. Computer-Aided Mate.Desi.,1996,3:245-252
[23]V.Shastry,D.Farkas. Molecular statics simulation of fracture in a-iron Modell Simul[J]. Mater. Sci. Eng. A.,1996,4:473-492.
[24]Y.F.Guo, C.Y.Wang, D.L.Zhao. Atomistic simulation of crack cleavage and blunting in bcc-Fe[J]. Mater.Sci.Eng.A.,2003,349:29-35.
[25]S.Hai, E.B.Tadmor. Deformation twinning at aluminum crack tips [J]. Acta.Mater.,2003, 51:117-131.
[26]A. Machova, GE. Beltz, M. Chang. Atomistic simulation of stacking fault formation in bcc iron[J]. Mater. Sci. Eng.,1999,7:949.
[27]D.Bancroft, E.Peterson, S.Minshall. Polymorphism of Iron an High Pressure [J]. Appl. Phys.,1956,27:291-298.
[28]H.Fujiwara, H.Inomoto, R.Sanada, K.Ameyama. Nano-ferrite formation and strain-induced ferrite transformation in an SUS316L austenitic stainless steel [J]. Scripta Mater.,2001, 44:2093-2042.
[29]J.Zhang, F.Guyot. Experimental study of the bcc-fcc phase transformations in the Fe-rich system Fe-Si at high pressures[J]. Phys.Chem.Minerals,1999,26:419-424.
[30]Y. Ivanisenko, I.MacLaren, X.Sauvage, R.Valiev,H.Fecht. Phase transformations in pearlitic steels induced by severe plastic deformation [J]. Solid state Phen.,2006,114:133-144.
[31]D. W. De Bruin et al. Second-order Effects in Self-testable Accelerometers[J]. Sensors and Actuators.,1989,20:53.
[32]U.D. Hangen, G. Sauthoff. The effect of martensite formation on the mechanical behaviour of NiAl [J]. Intermetallics.,1999,7:501～510.
[33]Y.F. Guo, D.L. Zhao. Atomistic simulation of structure evolution at a crack tip in bcc-iron[J]. Mater Sci Eng A.,2007,448:281～286.
[34]Y.F. Guo,Y.S.Wang, D.L.Zhao Atomistic simulation of stress-induced phase transformation and recrystallzation at the crack tip in bcc iron[J]. Acta Mater.,2007,55:401～407.
[35]Y.F.Guo,Y.S.Wang,W.P.Wu,D.L.Zhao.Atomistic simulation of martensitic phase transforma-tion at the crack tip in B2NiAl[J].Acta.Mater.,2007,55:3891-3897.
[36]毛卫民,张新民.晶体材料织构定量分析[M].冶金工业出版社：北京,1993.
[37]D. Rittel, G Ravichandran, A. Venkert.The mechanical response of pure iron at high strain rates under dominant shear [J].Mater.Sci.Eng.A.,2006:191-201.
[38]叶志明.各向异性材料与混凝土材料断裂力学引论[M].中国铁道出版社：北京,2000.
[39]G.Z.Wang, J.H.Chen. A statistical model for cleavage fracture in notched specimens of C-Mn steel [J]. Mattre.Struct.,2001,24:451-459.
[40]A.C.Eringen.Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics [M].Christensen,1974:81-105.
[41]A.C.Eringen., C.G.Spezial,B.S.Kim. [J].Mech. Phys. Solids,1977,25:339-355.
[42]A.C.Eringen.[M] Crystal Lattice Defects,1977:109～130.
[43]J.C.Fisher, J.H.Hollomon, D.Turnbull. [J].Metal.Trans.,1949:185-691.
[44]R.E. Cech, D.Turnbull.[J] Trans. AIME,1956:124.
[45]L. Kaufman, M.Cohen.Progress in Metallurgy Physics [M].New York,1958:165.
[46]C.L.Magee. Phase Transfomation [M].Ohio.Metals Park,1970:115.
[47]KC. Russell, [M].Ohio, Metals Park,1970:219
[48]A.H.Onodera,H.Goto,I.Tamura.JIM Inter Symp on New Aspects of Martensitic Transformat-ion[J].Suppl.Trans.,1996:1507.
[49]D.Rittel,G.Ravichandran,A.Venkert.The mechanical response of pure iron at high strain rates under dominant shear[J]. Mater.Sci.Eng.A.,2006,432:191-201.
[50]Y.F.Guo,Y.C.Gao.Combined atomistic simulation and continuum mechanics:Size-dependent behavior of atomistic simulation for brittle fracture in bcc-iron [J].Computational Mater.Sci., 2006,36:432-439.