On the computational solution of vector-density based continuum dislocation dynamics models: A comparison of two plastic distortion and stress update algorithms
On the computational solution of vector-density based continuum dislocation dynamics models: A comparison of two plastic distortion and stress update algorithms
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DOI：
10.1016/j.ijplas.2021.102943
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
P. Lin;Vignesh Vivekanandan;K. Starkey;B. Anglin;C. Geller;A. El-Azab
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文献类型：
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作者：
P. Lin;Vignesh Vivekanandan;K. Starkey;B. Anglin;C. Geller;A. El-Azab
连续介质位错动力学模型由位错输运-反应方程和晶体力学方程耦合而成。这两组方程之间的耦合是这样的位错输运引起的塑性变形（应变）的演变，而后者的演变固定的应力，从其中的位错速度场被发现通过迁移率法。早期的解决方案，这些方程采用交错的解决方案的两套方程，其中的塑性变形更新通过时间积分的速率，发现从奥罗万定律。在这项工作中，我们表明，这样一个直接的时间积分方案可以遭受积累的数值误差。我们介绍了一种替代方案的基础上，确保一致性的晶体中的塑性变形和位错含量的位错力学。新格式将塑性变形的相容部分和非相容部分分开计算，非相容部分由位错密度场计算。应力场和位错输运计算是在基于有限元的控制方程离散化中实现的，晶体力学部分由传统的Galerkin方法求解，位错输运方程由最小二乘法求解。首先通过简单的试验验证了两种修正方案的精度，结果表明基于场位错力学的求解方法更精确。然后，该方法被用来模拟单轴载荷和多滑移条件下的奥氏体钢晶体。通过考虑结引起的位错相互作用，得到了与离散位错动力学模拟结果相似的硬化率。模拟结果表明，随着应变的增加，位错呈现出一些自组织结构。
Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport gives rise to the evolution of plastic distortion (strain), while the evolution of the latter fixes the stress from which the dislocation velocity field is found via a mobility law. Earlier solutions of these equations employed a staggered solution scheme for the two sets of equations in which the plastic distortion was updated via time integration of its rate, as found from Orowan's law. In this work, we show that such a direct time integration scheme can suffer from accumulation of numerical errors. We introduce an alternative scheme based on field dislocation mechanics that ensures consistency between the plastic distortion and the dislocation content in the crystal. The new scheme is based on calculating the compatible and incompatible parts of the plastic distortion separately, and the incompatible part is calculated from the current dislocation density field. Stress field and dislocation transport calculations were implemented within a finite element based discretization of the governing equations, with the crystal mechanics part solved by a conventional Galerkin method and the dislocation transport equations by the least squares method. A simple test was first performed to show the accuracy of the two schemes for updating the plastic distortion, which shows that the solution method based on field dislocation mechanics is more accurate. This method then was used to simulate an austenitic steel crystal under uniaxial loading and multiple slip conditions. By considering dislocation interactions caused by junctions, a hardening rate similar to discrete dislocation dynamics simulation results was obtained. The simulations show that dislocations exhibit some self-organized structures as the strain is increased.