In this paper we extend the phase-field model of crystallographic slip of Ortiz (1999 J. Appl. Mech. ASME 66 289–98) and Koslowski et al (2001 J. Mech. Phys. Solids 50 2957–635) to slip processes that require the activation of multiple slip systems, and we apply the resulting model to the investigation of finite twist boundary arrays. The distribution of slip over a slip plane is described by means of multiple integer-valued phase fields. We show how all the terms in the total energy of the crystal, including the long-range elastic energy and the Peierls interplanar energy, can be written explicitly in terms of the multi-phase field. The model is used to ascertain stable dislocation structures arising in an array of finite twist boundaries. These structures are found to consist of regular square or hexagonal dislocation networks separated by complex dislocation pile-ups over the intervening transition layers.
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机译：在本文中，我们将Ortiz（1999 J. Appl。Mech。ASME 66 289-98）和Koslowski等人（2001 J. Mech。Phys。Solids 50 50 2957-635）的晶体滑移的相场模型扩展到滑移过程需要激活多个滑移系统，我们将结果模型应用于有限扭转边界阵列的研究。滑移在滑移面上的分布通过多个整数值的相位场来描述。我们展示了如何用多相场来明确地写出晶体总能量中的所有项，包括远距离弹性能和Peierls平面内能。该模型用于确定在有限扭转边界阵列中产生的稳定位错结构。发现这些结构由规则的正方形或六边形位错网络组成，这些位错网络被中间过渡层上的复杂位错堆积所分隔。
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