Theoretical development of continuum dislocation dynamics for finite-deformation crystal plasticity at the mesoscale
Theoretical development of continuum dislocation dynamics for finite-deformation crystal plasticity at the mesoscale
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DOI：
10.1016/j.jmps.2020.103926
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发表时间：
2020-06
影响因子：
5.3
通讯作者：
K. Starkey;G. Winther;A. El-Azab
中科院分区：
文献类型：
--
作者：
K. Starkey;G. Winther;A. El-Azab
建立了晶体有限变形时位错输运方程，着重讨论了位错的矢量密度表示。一个同伴的热力学分析产生了一个广义的表达的驱动力的位错，依赖于曼德尔（柯西）应力在参考（空间）配置和贡献的位错核心能量的自由能的晶体。我们的配方依赖于几个位错密度张量的措施链接到晶体中的塑性变形的不相容性。虽然以前的作品开发这样的张量从乘法分解的变形梯度，我们开发的位错密度和位错通量的位移梯度和晶体速度场的加法分解的张量措施。由塑性变形的参考旋度和逆弹性变形的空间旋度以及相关位错电流定义的两点位错密度测量被发现在推导位错矢量密度的输运方程的参考和空间形式中更有用。本文提出了几个试验问题，说明了有限变形对静态位错场的影响，特别注意了晶格转动。开发的框架提供了理论基础，调查晶体塑性和位错图案在介观尺度上，它承担了现实的数值解与实验比较的潜力。
The equations of dislocation transport at finite crystal deformation were developed, with a special emphasis on a vector density representation of dislocations. A companion thermodynamic analysis yielded a generalized expression for the driving force of dislocations that depend on Mandel (Cauchy) stress in the reference (spatial) configurations and the contribution of the dislocation core energy to the free energy of the crystal. Our formulation relied on several dislocation density tensor measures linked to the incompatibility of the plastic distortion in the crystal. While previous works develop such tensors starting from the multiplicative decomposition of the deformation gradient, we developed the tensor measures of the dislocation density and the dislocation flux from the additive decomposition of the displacement gradient and the crystal velocity fields. The two-point dislocation density measures defined by the referential curl of the plastic distortion and the spatial curl of the inverse elastic distortion and the associate dislocation currents were found to be more useful in deriving the referential and spatial forms of the transport equations for the vector density of dislocations. A few test problems showing the effect of finite deformation on the static dislocation fields are presented, with a particular attention to lattice rotation. The framework developed provides the theoretical basis for investigating crystal plasticity and dislocation patterning at the mesoscale, and it bears the potential for realistic comparison with experiments upon numerical solution.