离散位错动力学算法及其在材料塑性行为模拟中的应用

Discrete dislocation dynamics algorithms and their application in modeling of plastic behaviors of crystalline materials

晶体材料的塑性变形由位错的运动演化而引起.离散位错动力学(discrete dislocation dynamics, DDD)通过直接模拟大量位错的演化而研究材料的塑性变形,因此能够揭示材料微结构-位错微结构-塑性力学行为之间内在的物理关联,并能够自然而然地捕捉塑性变形微米/亚微米特征尺度下本征的尺度效应.它所能模拟的尺度介于微观分子动力学模拟和宏观有限元模拟之间,在多尺度算法中起到承上启下的作用.本文首先系统地发展、完善和丰富了离散位错动力学-有限元(finite element method, FEM)叠加算法、DDD-FEM直接耦合算法(discrete-continuous method, DCM)以及离散位错动力学-扩展有限元(extended finite element method, XFEM)耦合算法等框架体系.在此基础上,利用这些方法对单晶镍基高温合金的塑性变形机理、晶体材料的断裂和损伤变形行为以及塑性行为的微尺度和微结构效应3个方面开展了系统的研究.所得模拟结果指导了基于微结构和位错机制的单晶镍基高温合金晶体塑性本构模型的建立,丰富和加深了人们对材料强化、循环塑性、断裂、损伤、尺度效应和微结构效应的认识.此外,离散位错动力学可进一步应用于诸如高温、高压、高应变率、化学腐蚀环境、高辐照等极端条件下晶体材料塑性行为的研究,是材料力学行为多尺度模拟研究中的重要一环.

The plastic behaviors of crystalline materials are induced by the evolution of a series of dislocations. Discrete dislocation dynamics(DDD) can be used to model plastic deformation by taking into account the nucleation, annihilation, motion of dislocations, and formation of jogs, junctions, networks, and other dislocation structures directly. As a result, it can be used to investigate the physical correlation between material microstructures, dislocation structures, and plastic responses. It can also model the intrinsic size effect of plastic behaviors at the micron/submicron scales. Since its modeling scale is much larger than that of the microscopic molecular dynamics but is smaller than that of the macroscopic finite element method(FEM), DDD plays a connecting link role in multiscale modeling.In the present manuscript, three categories of DDD schemes, i.e., the DDD-FEM superposition algorithm, the DDD-FEM direct coupling algorithm, and DDD-extended FEM(XFEM) coupling algorithm, are further developed and optimized. In the DDD-FEM superposition algorithm, the consideration of dislocation climb is specifically included to take into account the high-temperature effect. In the DDD-FEM direct coupling algorithm, the so-called virtual dislocations are introduced to distribute the Eigen plastic strain by dislocation evolution to the FEM module more appropriately, and a special scheme is developed to calculate the Peach-Koehler force on the dislocation efficiently. To model the problems with strong or weak interfaces(such as cracks, voids, particles, and grain boundaries), the scheme coupling the DDD and XFEM, which is not sensitive to the finite element mesh, is further developed carefully. Each of these three DDD schemes has its own special characteristics, and so they are suitable for solving different plastic problems.Based on these three kinds of DDD algorithms, the plastic deformation mechanisms of nickel-based superalloy, the damage and fracture behaviors of crystalline materials, and the size effect and microstructure dependency of heterogeneous crystalline materials have been investigated systematically. For the nickel-based superalloy, the dislocation mechanisms for the hardening responses, the abnormal yielding behavior with increasing temperature, the loading rate effect, the lattice misfit effect, and the crystalline orientation effect and the dislocation climb effect have been studied in detail. Based on these dislocation mechanisms and the special two-phase material microstructures, a crystal plasticity constitutive law informed by dislocation and microstructure mechanisms suitable for single crystal nickel-based superalloy was here developed. Further, the microvoid growth mechanism, the crack tip-microvoid interaction, the crack tip ratchetting responses, the crack shielding effect by dislocation, and the effect of crack-tip dislocation emission on crack growth have also been investigated systematically through DDD simulations. In addition, the plastic behavior, its size effect, and intrinsic dislocation mechanisms for materials with heterogeneous structures, such as particle-enhanced metal matrix composites, multilayered metallic films, and polycrystalline materials, have also been studied carefully using DDD models, especially at elevated temperature. This type of DDD research has facilitated better understanding of the intrinsic mechanisms of hardening response, cyclic plasticity, fracture, damage evolution, size effect, and microstructure dependency. DDD can be further used to study the plastic behaviors of crystals under the extreme environmental conditions, such as high temperature, high pressure, high loading rate(shocking), chemical erosion environment, and high neutron irradiation. DDD has recently become a powerful model of the behavior of metallic materials at microscale in a more physical manner than existing plasticity models.