Abstract A dislocation mechanics based isotropic strain gradient plasticity model is developed. The model is derived from self-energies of dislocations and the Taylor model for plastic dissipation. It is shown that the same microstructural length scale emerges for both the energetic and the dissipative parts of the model. Apart from a non-dimensional factor of the order of unity, the length scale is defined as the Burgers vector divided by the strain for initiation of plastic deformation. When the structural length scale approaches this microstructural length scale, strengthening effects result. The present model predicts an increased initial yield stress that is controlled by the energetic contribution. For larger plastic strains, the hardening is governed by the dissipative part of the model. The theory is specialized to the simple load cases of tension with a passivation layer that prohibits plastic deformation on the surfaces as well as pure bending with free and fixed boundary conditions for plastic strain. Simulations of initial yield stress for varying thicknesses are compared to experimental observations reported in the literature. It is shown that the model in a good way can capture the length scale dependencies. Also upper bound solutions are presented for a spherical void in an infinite volume as well as torsion of a cylindrical rod. The model is as well applied to derive a prediction for the Hall–Petch effect.

中文翻译：

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基于位错自能和塑性耗散的泰勒模型的各向同性应变梯度塑性模型

摘要 建立了基于位错力学的各向同性应变梯度塑性模型。该模型源自位错的自能和塑性耗散的泰勒模型。结果表明，模型的能量部分和耗散部分都出现了相同的微观结构长度尺度。除了统一量级的无量纲因子外，长度尺度定义为 Burgers 矢量除以引发塑性变形的应变。当结构长度尺度接近这个微观结构长度尺度时，就会产生强化效应。本模型预测由能量贡献控制的增加的初始屈服应力。对于较大的塑性应变，硬化由模型的耗散部分控制。该理论专门用于具有钝化层的简单拉伸载荷情况，该钝化层阻止了表面的塑性变形以及具有塑性应变的自由和固定边界条件的纯弯曲。对不同厚度的初始屈服应力的模拟与文献中报道的实验观察进行了比较。结果表明，该模型可以很好地捕获长度尺度依赖性。还给出了无限体积中的球形空隙以及圆柱杆扭转的上限解。该模型也适用于推导出霍尔-佩奇效应的预测。对不同厚度的初始屈服应力的模拟与文献中报道的实验观察进行了比较。结果表明，该模型可以很好地捕获长度尺度依赖性。还给出了无限体积中的球形空隙以及圆柱杆扭转的上限解。该模型也适用于推导出霍尔-佩奇效应的预测。对不同厚度的初始屈服应力的模拟与文献中报道的实验观察进行了比较。结果表明，该模型可以很好地捕获长度尺度依赖性。还给出了无限体积中的球形空隙以及圆柱杆扭转的上限解。该模型也适用于推导出霍尔-佩奇效应的预测。