Thermodynamically consistent continuum dislocation dynamics
Thermodynamically consistent continuum dislocation dynamics
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DOI：
10.1016/j.jmps.2015.12.015
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发表时间：
2015-08
影响因子：
5.3
通讯作者：
T. Hochrainer
中科院分区：
文献类型：
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作者：
T. Hochrainer
基于位错的塑性力学模型是材料科学与连续介质力学交叉的核心挑战之一。发展位错的连续理论需要解决两个长期存在的问题：（i）以合理数量的变量表示位错运动学，以及（ii）以这些变量导出位错动力学（即材料定律）的平均描述。最近通过引入连续位错动力学（CDD）解决了运动学问题（i），CDD提供了位错排列张量的运动学一致的演化方程，假定给定的平均位错速度（Hochrainer，T.，2015年，多极扩展的连续位错动力学方面的对齐张量。《哲学杂志》95（12），1321-1367）。在目前的文件中，我们演示了如何自由能制定可用于解决的动态封闭问题（ii）在CDD。我们这样做的最低阶CDD变种弯曲位错在一个单一的滑移的情况下。在这种情况下，一个一致的平均位错速度被发现包括五个介观剪切应力的贡献。对于一个假设的自由能表达式，我们确定这些应力贡献的背应力项和线张力项，这两个已经假定CDD。出现新的应力贡献，其在早期CDD模型中缺失，包括直平行刃位错的统计连续理论（Groma，I.，Csikor，F.F.，Zaiser，M.，2003.位错动力学连续描述中的空间相关性和高阶梯度项。材料学报51，1271-1281）。此外，两个全新的应力贡献来自位错的曲率。
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i) to represent dislocation kinematics in terms of a reasonable number of variables and (ii) to derive averaged descriptions of the dislocation dynamics (i.e. material laws) in terms of these variables. The kinematic problem (i) was recently solved through the introduction of continuum dislocation dynamics (CDD), which provides kinematically consistent evolution equations of dislocation alignment tensors, presuming a given average dislocation velocity (Hochrainer, T., 2015, Multipole expansion of continuum dislocations dynamics in terms of alignment tensors. Philos. Mag. 95 (12), 1321–1367). In the current paper we demonstrate how a free energy formulation may be used to solve the dynamic closure problem (ii) in CDD. We do so exemplarily for the lowest order CDD variant for curved dislocations in a single slip situation. In this case, a thermodynamically consistent average dislocation velocity is found to comprise five mesoscopic shear stress contributions. For a postulated free energy expression we identify among these stress contributions a back-stress term and a line-tension term, both of which have already been postulated for CDD. A new stress contribution occurs which is missing in earlier CDD models including the statistical continuum theory of straight parallel edge dislocations (Groma, I., Csikor, F.F., Zaiser, M., 2003. Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics. Acta Mater. 51, 1271–1281). Furthermore, two entirely new stress contributions arise from the curvature of dislocations.