微纳米尺度位错与晶界相互作用的理论和计算研究

The interactions between dislocations and grain boundaries play an important role in controlling the strength and ductility of polycrystalline metals at micro/nano scale. This project aims at investigating the mechanism of dislocation-grain boundary interactions across the scales: from the atomistic level via the level of discrete dislocations to the continuum level-coupled by means of proper scale transitions. First, the interactions between single dislocation and grain boundary will be studied on the atomistic scale at the greatest detail to find the key factors which control the dislocation/grain boundary behavior. The critical values of the local stress/energy and the Burgers vector information after reaction will be extracted to serve as the input for the study at upper discrete dislocation level. Then a new 3D discrete dislocation dynamics (DDD) method will be developed to calculate the stress field of dislocations near the anisotropic interface. The short range interactions between dislocation and grain boundary will be treated according to the atomistic information. The interface properties like displacement and traction jump will be obtained from interfacial computational homogenization method and will be passed to the study at the micrometer scale. Next, a higher-order crystal plasticity theory considering interface effect will be developed and the corresponding higher-order boundary conditions will be proposed to describe the piling-up, transmission, absorption and reflection of dislocations at the grain boundary. At last, the extended finite element method (XFEM) will be employed to capture the jump of displacement and plastic strain field at the grain boundary. The influence of dislocation-grain boundary interactions on the plastic deformation of polycrystalline metals will be studied by solving the higher-order crystal plasticity equation using XFEM.

位错-晶界作用是控制微纳米尺度多晶材料强度和延性的关键要素。本项目将从原子、离散位错、连续介质三个层次研究位错-晶界相互作用机理，分析其对多晶材料强度和延性的影响。在原子尺度研究单个位错和界面相互作用机制，确定控制位错/晶界行为的主要因素，通过粗粒化方法提取位错和晶界反应的临界应力及反应后的Burgers矢量信息，用于亚微米尺度离散位错模拟；在此基础上发展新的离散位错模拟方法，准确求解各向异性界面处位错应力场，根据原子尺度信息处理位错和晶界的近程相互作用，并通过均匀化理论提取位移和塑性应变间断等界面参数，作为微米尺度研究的输入信息；进而在连续介质层次上发展考虑界面效应的高阶晶体塑性理论，根据离散位错输入信息在界面处提出高阶边界条件描述位错在界面处的堆积、透射等机理。最后应用扩展有限元来捕捉界面位移、塑性应变间断，求解高阶晶体塑性方程，研究位错界面相互作用对多晶材料塑性变形影响。

本项目结合原子、离散位错和连续介质力学理论和方法，建立连续介质位错-晶界相互作用模型，并应用该模型揭示位错-晶界作用对晶体材料力学性能影响规律。取得的主要成果包括：1）发展了大变形离散-连续晶体塑性模型，提出高效高精度的塑性应变局部化方案，准确计算界面镜像力和滑移系转动，弥补了现有离散位错动力学方法的不足。2）揭示了含涂层界面亚微米单晶柱中截获位错密度的演化规律，以及背应力与截获位错密度的线性关系；建立了考虑背应力效应和涂层钉扎效应的单臂源开动应力公式，发展了预测含涂层界面单晶柱力学响应的理论模型。3）从位错的运动方程出发，建立能够描述位错与晶界相互作用的微观连续介质晶体塑性模型，研究由界面引起的尺寸效应和包辛格效应。发表SCI论文8篇，其中包括固体力学顶级期刊Journal of the Mechanics and Physics of Solids2篇，塑性力学的重要期刊International Journal of Plasticity4篇。研究成果得到了国内外学者的广泛关注，欧洲材料力学委员会(EMMCC)主席M.G.D. Greers教授认为该项目建立的连续化位错-晶界相互作用模型：“迈出了从连续介质层次在应变梯度晶体塑性框架下考虑晶界界面力学的第一步，可以自然地考虑晶界处晶体方向的变化，这对处理位错和晶界相互作用非常重要”。