Abstract Upon employing the conservation theorem and continuum theory, the configurational force on a singularity, or a defect, is given by a path-independent integral called the J integral. According to the continuum elasticity theory, the J integral around a steadily moving dislocation is equal to the Peach–Koehler force acting on the dislocation and is independent of the integration path. However, using a discrete lattice dynamics method, we theoretically prove that the J integral is not path-independent in practice even under uniform motion. This is because of the generation of phonons during the dislocation motion. In general, phonons are generated upon localized oscillation of the dislocation, and they dissipate energy from the dislocation core; consequently, a drag force is produced. As the drag force disturbs the dislocation motion, the J integral around the moving dislocation is smaller than that around a stationary one, and its deviation from the stationary one corresponds to the drag force. In this study, we analytically derive the drag force for each oscillation mode by adopting dislocation–phonon coordinates. We classify the oscillation mode simply as symmetric or anti-symmetric after assuming the dislocation to be a localized defect having a finite core width. Consequently, the drag force is numerically calculated upon consideration of the discrete nature of the dislocation core. In particular, our study reveals that the anti-symmetric oscillation mode mainly contributes to the drag force in the limit of high dislocation velocity. Furthermore, we show that the resulting relation between the drag force and dislocation frequency can reproduce the dislocation velocity-stress curve. This work is expected to contribute to meso- and macro-scale plasticity when the material is loaded under extreme conditions or transient dislocation motion can be assumed.

中文翻译：

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具有局域振荡的动态位错上的构型力

摘要 根据守恒定理和连续统理论，奇异点或缺陷上的构型力由称为 J 积分的与路径无关的积分给出。根据连续弹性理论，稳定移动位错周围的 J 积分等于作用在位错上的 Peach-Koehler 力，与积分路径无关。然而，使用离散晶格动力学方法，我们从理论上证明了 J 积分在实践中即使在匀速运动下也不是路径无关的。这是因为在位错运动过程中产生了声子。一般来说，声子是在位错的局域振荡下产生的，它们从位错核心耗散能量；因此，产生了阻力。由于阻力干扰了位错运动，移动位错周围的 J 积分小于静止位错周围的 J 积分，其与静止位错的偏差对应于阻力。在这项研究中，我们通过采用位错-声子坐标来分析推导每种振荡模式的阻力。在假设位错是具有有限核心宽度的局部缺陷之后，我们将振荡模式简单地分类为对称或反对称。因此，在考虑位错核心的离散特性的情况下数值计算阻力。特别是，我们的研究表明，反对称振荡模式主要有助于高位错速度极限下的阻力。此外，我们表明，阻力和位错频率之间的最终关系可以再现位错速度-应力曲线。当材料在极端条件下加载或可以假设瞬态位错运动时，预计这项工作将有助于中观和宏观尺度的塑性。