This paper studies the evolution of intergranular localization and stress concentration in three dimensional micron sized specimens through the Gurtin grain boundary model (J Mech Phys Solids 56:640–662, 2008) incorporated into a three dimensional higher-order strain gradient crystal plasticity framework (Yalçinkaya et al. in Int J Solids Struct 49:2625–2636, 2012). The study addresses continuum scale dislocation-grain boundary interactions where the effect of crystal orientation mismatch and grain boundary orientation are taken into account through the grain boundary model in polycrystalline metallic specimens. Due to the higher-order nature of the model, a mixed finite element formulation is used to discretize the problem in which both displacements and plastic slips are considered as primary variables. For the treatment of grain boundaries within the solution algorithm, an interface element is formulated and implemented together with the bulk plasticity model. The capabilities of the framework is demonstrated through 3D polycrystalline examples considering grain boundary conditions, grain boundary strength, the orientation distribution and the specimen size. A detailed grain boundary condition and stress concentration analysis is presented. The advantages and the disadvantages of the model is discussed in detail through numerical examples.

本文通过将Gurtin晶界模型（J Mech Phys Solids 56：640–662，2008）并入三维高阶应变梯度晶体可塑性框架（J Mech Phys Solids 56：640–662，2008）中，研究了三维微米级试样中晶间定位和应力集中的演变。 Yalçinkayaet al。in Int J Solids Struct 49：2625-2636，2012）。该研究解决了连续尺度的位错-晶界相互作用，其中通过多晶金属试样中的晶界模型考虑了晶体取向失配和晶界取向的影响。由于模型的高阶性质，使用混合有限元公式来离散化其中位移和塑性滑移均被视为主要变量的问题。为了在求解算法中处理晶界，制定了接口元素并与整体塑性模型一起实现。通过考虑晶粒边界条件，晶粒边界强度，取向分布和试样尺寸的3D多晶实例证明了框架的功能。给出了详细的晶界条件和应力集中分析。通过数值示例详细讨论了该模型的优缺点。方向分布和试样尺寸。给出了详细的晶界条件和应力集中分析。通过数值示例详细讨论了该模型的优缺点。方向分布和试样尺寸。给出了详细的晶界条件和应力集中分析。通过数值示例详细讨论了该模型的优缺点。