STUDY OF CONFINED LAYER PLASTICITY BASED ON HIGHER-ORDER STRAIN GRADIENT PLASTICITY THEORY
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摘要: 针对受限金属薄层在剪切塑性变形时出现明显尺度效应这一问题, 现有理论分析多采用纯剪切假设和传统钝化边界条件, 其理论预测与实验结果不符. 文章采用黏弹塑性本构模型, 对Gudmundson高阶应变梯度塑性理论进行了有限元实现, 深入研究了金属薄层受限剪切的塑性变形机理. 考虑因界面倾斜引起的附加压应力, 采用自定义平面单元对材料的压缩−剪切组合变形进行了有限元模拟. 根据表面解锁的物理机制, 引入“软−硬”中间态的边界条件. 结果表明, 在压缩−剪切组合变形条件下, 受限薄层的剪切流动应力明显低于纯剪切条件下的流动应力, 而压应力的存在降低了剪切屈服强度. 利用周期性钝化边界条件, 能够定量描述界面处几何必需位错饱和引起的边界条件变化, 理论预测与实验结果吻合. 相关研究揭示了加载方式和高阶边界条件在受限薄层剪切尺度效应问题中的重要作用.Abstract: In addressing the size effect observed in the plastic deformation of confined metallic thin layers, existing theoretical analyses have relied on pure shear assumptions and traditional passivation boundary conditions. However, their theoretical predictions are not in agreement with experimental results. In this paper, the finite element implementation of Gudmundson's theory of higher-order strain gradient plasticity is carried out based on the elasto-viscoplastic constitutive model. The method is then applied to study the plastic deformation mechanism in the shear of confined metallic layers. This study considers the additional compressive stress resulting from the inclined interface, and the combined compression-shear deformations are modeled through the user-defined plane element. In addition, a "soft-hard" boundary condition corresponding to the intermediate state is also introduced according to the physical context of surface unlocking. The results demonstrate that the shear flow stress of the confined layer under combined compressive and shear loads is significantly lower than that of the confined layer under pure shear, indicating that compressive stress dramatically reduces the yielding shear stress. The transition of the boundary condition due to the saturation of geometrically necessary dislocations at the interface is quantitatively characterized using the periodically passivated boundary condition. The theoretical predictions are in agreement with experimental data. The study emphasizes the importance of loading and boundary conditions in the size-dependent plasticity of confined layers.
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图 2 压缩和剪切组合作用下的金属薄层
Figure 2. Thin metallic layer under combined compressive and shear loads
图 3 压缩−剪切组合作用下归一化的切应力−位移关系
Figure 3. Normalized shear stress-displacement relation under combined compression and shear
图 4 ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$时塑性切应变$ {\gamma _{\text{P}}} $的分布云图
Figure 4. Contours of the plastic shear strain $ {\gamma _{\text{P}}} $ at ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$
图 7 不同周期下归一化切应力与位移的变化关系
Figure 7. Normalized shear stress-displacement relation under different periods
图 8 ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$时不同周期下塑性切应变$ {\gamma _{\text{P}}} $分布云图
Figure 8. Contours of the plastic shear strain $ {\gamma _{\text{P}}} $ at ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$ under different periods
图 9 ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$时不同周期下储能高阶应力$\tau _{122}^{\text{E}}$分布云图
Figure 9. Contours of the higher-order stress $\tau _{122}^{\text{E}}$ at ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$ under different periods
图 11 不同边界条件下归一化的切应力−位移关系
Figure 11. Normalized shear stress-displacement relation under different boundary conditions
图 12 ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$时的塑性切应变$ {\gamma _{\text{P}}} $分布云图
Figure 12. Contours of the plastic shear strain $ {\gamma _{\text{P}}} $ at ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$
Attribute ${{{\sigma _Y}} \mathord{\left/ {\vphantom {{{\sigma _Y}} E}} \right. } E}$ $N$ $ \nu $ ${\dot \varepsilon _0}$ ${\ell / H}$ ${L / H}$ Value 0.003 0 0.3 0.0001 $ \in \left[ {0,1} \right]$ $ \in \left[ {0,1} \right]$ 
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