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张旭, 秦聪, 屈腾飞, 马竞. 考虑应力梯度效应的金属微梁屈服模型研究. 力学学报, 2024, 56(4): 1-12. DOI: 10.6052/0459-1879-23-516
引用本文: 张旭, 秦聪, 屈腾飞, 马竞. 考虑应力梯度效应的金属微梁屈服模型研究. 力学学报, 2024, 56(4): 1-12. DOI: 10.6052/0459-1879-23-516
Zhang Xu, Qin Cong, Qu Tengfei, Ma Jing. Research on the yield model for metal microbeams considering the stress gradient effects. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(4): 1-12. DOI: 10.6052/0459-1879-23-516
Citation: Zhang Xu, Qin Cong, Qu Tengfei, Ma Jing. Research on the yield model for metal microbeams considering the stress gradient effects. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(4): 1-12. DOI: 10.6052/0459-1879-23-516

考虑应力梯度效应的金属微梁屈服模型研究

RESEARCH ON THE YIELD MODEL FOR METAL MICROBEAMS CONSIDERING THE STRESS GRADIENT EFFECTS

  • 摘要: 一系列微加载测试结果表明, 金属微梁的弯曲强度会随着材料外部几何特征尺寸的减小而显著升高, 呈现出明显的尺寸相关性. 基于位错塞积模型, 探讨了纯金属单晶微梁的初始屈服应力, 并提出了描述其尺寸相关性行为的关键内禀特征长度. 通过综合分析现有的微梁弯曲实验及其离散位错动力学数值模拟结果, 并考虑到位错−自由表面交互作用的影响, 提出了一种仅涉及位错源的位错塞积构型. 在此构型下, 对线性应力梯度作用下的位错塞积行为进行了连续性分析, 并建立了一个由位错源主导的应力梯度屈服模型. 该模型有效地解释了微梁初始屈服应力的尺寸相关性, 并与实验结果一致. 研究结果表明, 针对外部几何特征尺寸在数微米及以下的纯金属单晶微梁, 位错塞积行为是其尺寸相关性行为的主导机制, 而且刻画这种行为需要两个内禀特征长度参数, 即位错源长度和位错塞积长度. 为解释非均匀加载条件下微尺度晶体材料屈服应力的尺寸相关性行为, 特别是纯金属单晶微梁, 提供了新的视角.

     

    Abstract: A series of micro-loading tests on metal microbeams have revealed a significant increase in bending strength as specimen sizes decrease, demonstrating a remarkable size effect. In this study, we systematically investigate the initial yielding strength of pure metal single-crystal microbeams, utilizing a novel dislocation pile-up model that incorporates stress gradient effects. This model allows us to identify the key intrinsic length scales behind the underlying strengthening mechanisms, which are pivotal in determining the size-dependent behavior of microbeams when subjected to either pure or transverse bending. Through a synthesis of existing micro-bending experimental observations and discrete dislocation dynamic (DDD) simulation results, we firstly propose a new dislocation pile-up configuration, which is exclusively focused on dislocation sources and comprehensively accounts for the interactions between free surfaces and dislocations. Within such a pile-up configuration, we then conduct a detailed continuum analysis of dislocation pile-up behavior under linear stress gradients, which leads us to finally establish a source-controlled stress gradient yield model. Applying this yield model to micro- and submicron copper beams under bending conditions, we observe that it could effectively capture the size-dependent behavior of the initial yielding stress in microbeams within the specified size range (spanning from several micrometers to hundreds of nanometers). Notably, our model shows good agreement with corresponding experimental results. These findings suggest that, for pure metal single-crystal microbeams with specimen size of several micrometers or smaller, the dislocation pile-up strengthening mechanism plays a dominant role in the observed size-dependent behavior. Moreover, our results emphasize the importance of two material length scales — the source length and the dislocation pile-up length — in accurately quantifying the size-dependent bending strength at micro- and submicron scales. This study offers an insightful perspective in understanding the size-dependent yield stress in micro-scale crystalline materials under non-uniform loading conditions, particularly in the case of pure metal single-crystal microbeams.

     

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