This paper proposes an elastic-gap free strain gradient crystal plasticity model that addresses dissipation caused by plastic slip gradient and grain boundary (GB) Burger tensor. The model involves splitting plastic slip gradient and GB Burger tensor into energetic dissipative quantities. Unlike conventional models, the bulk and GB defect energy are considered to be a quadratic functional of the energetic portion of slip gradient and GB Burgers tensor. The higher-order stresses for each individual slip systems and GB stresses are derived from the defect energy, following a similar evolution as the Armstrong-Frederick type backstress model in classical plasticity. The evolution equations consist of a hardening and a relaxation term. The relaxation term brings the nonlinearity in hardening and causes an additional dissipation. The applicability of the proposed model is numerically established with the help of two-dimensional finite element implementation. Specifically, the bulk and GB relaxation coefficients are critically evaluated based on various circumstances, considering single crystal infinite shear layer, periodic bicrystal shearing, and bicrystal tension problem. In contrast to the Gurtin-type model, the proposed model smoothly captures the apparent strengthening at saturation without causing any abrupt stress jump under non-proportional loading conditions. Moreover, when subjected to cyclic loading, the stress-strain curve maintains its curvature during reverse loading. The numerical simulation reveals that the movement of geometrically necessary dislocation (GND) towards the GB is influenced by the bulk recovery coefficient, while the dissipation and amount of accumulation of GND near the GB are controlled by the GB recovery coefficient.

翻译：本文提出一种无弹性间隙的应变梯度晶体塑性模型，用于处理由塑性滑移梯度与晶界（GB）伯格斯矢量引起的耗散。该模型将塑性滑移梯度与晶界伯格斯矢量分解为能量耗散相关量。与传统模型不同，本模型将体缺陷能与晶界缺陷能视为滑移梯度能量分量与晶界伯格斯矢量能量分量的二次泛函。基于缺陷能推导出各滑移系的高阶应力及晶界应力，其演化规律类似于经典塑性理论中Armstrong-Frederick型背应力模型。演化方程包含硬化项与松弛项，其中松弛项引入硬化非线性并产生额外耗散。通过二维有限元数值实现验证了所提模型的适用性。具体而言，基于单晶无限剪切层、周期性双晶体剪切及双晶体拉伸等不同工况，对体松弛系数与晶界松弛系数进行了系统评估。相较于Gurtin型模型，本模型在非比例加载条件下能平滑捕捉饱和阶段的表观强化效应，且不会引发应力突变。此外，在循环加载过程中，应力-应变曲线在反向加载阶段仍保持曲率连续性。数值模拟表明：几何必需位错（GND）向晶界的迁移受体恢复系数影响，而晶界附近GND的耗散与累积量则由晶界恢复系数控制。