This work considers a recently developed finite-deformation elastoplasticity theory that assumes distinct tensorial fields describing macro-plasticity and micro-plasticity, where the latter is determined by a higher-order balance equation with associated boundary conditions. Specifically, micro-plasticity evolves according to a contribution to the Helmholtz free-energy density that depends on a Nye–Kröner-like dislocation density tensor and is referred to as the defect energy. The theory is meant to set the onset of micro-plasticity at a stress level lower than that activating macro-plasticity, such as micro-plasticity aims at explaining and characterizing the increase in yield stress with diminishing size. Additionally, the formulation relies on smooth elastic–plastic transitions for both plasticity fields, even if focusing on rate-independent response. This investigation demonstrates the capability of the proposed theory to predict size-effects of interest in small-scale metal plasticity by focusing on multiple loading cycles and, prominently, on the scaling of the apparent yield stress with sample size, the latter being a crucial open issue in the recent literature on modeling size-dependent plasticity. To this end, this work considers the specialization of the theory to small deformations and proposes a finite element implementation for the constrained simple shear problem. Importantly, it is shown that the simplest treatment of plastic strain gradients, which consists of adopting a quadratic defect energy, can be conveniently used to predict reliable size-effects, although in the literature on strain gradient plasticity quadratic defect energies have always been associated with a relatively poor description of size-effects. In fact, in the present theory the limits of the quadratic defect energy are overcome by leveraging on the complex interplay between micro- and macro-plasticity fields. The capability of the proposed theory is quantitatively demonstrated by predicting results from the literature that are obtained from discrete dislocation dynamics simulations on planar polycrystals of grains with variable size subjected to macroscopic pure shear.

中文翻译：

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使用具有两个塑性率场的尺寸相关理论对屈服应力缩放和循环响应进行建模


这项工作考虑了最近开发的有限变形弹塑性理论，该理论假设描述宏观塑性和微塑性的不同张量场，其中微塑性由具有相关边界条件的高阶平衡方程决定。具体来说，微塑性根据对亥姆霍兹自由能密度的贡献而演变，该贡献取决于类似 Nye-Kröner 的位错密度张量，称为缺陷能量。该理论旨在将微可塑性的开始设置在低于激活宏观可塑性的应力水平，例如微可塑性旨在解释和表征产量应力的增加与尺寸的减小。此外，该公式依赖于两个塑性场的平滑弹塑性转变，即使专注于与速率无关的响应。这项研究证明了所提出的理论能够通过关注多个加载循环来预测小规模金属塑性中感兴趣的尺寸效应，尤其是表观屈服应力随样本量的缩放，后者是最近关于建模尺寸依赖性塑性的文献中一个关键的开放问题。为此，本文考虑了该理论对小变形的专业化，并提出了约束简单剪切问题的有限元实现。重要的是，研究表明，塑性应变梯度的最简单处理，包括采用二次缺陷能量，可以方便地用于预测可靠的尺寸效应，尽管在关于应变梯度塑性的文献中，二次缺陷能量总是与相对较差的尺寸效应描述相关联。 事实上，在本理论中，通过利用微观和宏观塑性场之间复杂的相互作用，克服了二次缺陷能量的限制。通过预测文献中的结果，定量地证明了所提出的理论的能力，这些结果是从对受到宏观纯剪切作用的可变尺寸的晶粒的平面多晶进行离散位错动力学模拟中获得的。