固体材料的尺度效应和离散位错理论模拟

IMECH-IR > 力学所知识产出(1956-2008)

	固体材料的尺度效应和离散位错理论模拟
	唐山
导师	魏悦广
	2003
学位授予单位	中国科学院研究生院
学位授予地点	北京
学位类别	硕士
学位专业	固体力学
关键词	尺度效应离散位错理论微梁弯曲微杆扭转有限元方法四点弯曲试验
摘要	固体材料在微米和亚微米尺度将表现出和宏观尺度不同的力学性能。因尺度的不同材料所表现出的力学行为的不同通常被称为尺度效应。对于尺度效应的模拟，由于传统的弹塑性理论中不包含任何尺度参量，因此无法由该理论对材料在微米和亚微米尺度所表现的尺度效应进行预测。塑性应变梯度理论中引入了尺度参量，可以对尺度效应进行比较好的模拟。但是塑性应变梯度理论的特征尺度因子物理意义又不甚明确。虽然人们从直接的微观位错理论出发，对材料的塑性变形行为进行过大量的研究，但运用位错理论对材料尺度效应进行研究却不多。本文的主要工作就是运用离散位错理论和弹性有限元方法相结合，对材料在微尺度下的基本实验（扭转和弯曲）结果中所展示出的强烈尺度效应进行模拟。首先对于该基本力学问题（微梁弯曲和微杆扭转），以Mtlra的一维模型为基础，推导出一简单的但能够刻划尺度效应的一维模型，其次基于试验结果假定微梁弯曲和微杆扭转时其中部始终存在一弹性核。基于该模型的分析，得到了微梁弯曲和微杆扭转的应力应变关系。结果显示出，当材料的尺寸缩小到一定大小时，微梁弯曲和微杆扭转呈现出强烈的尺度效应，实现了对己有实验结果的成功模拟。以Needieman及其合作者的工作为基础，针对二维平面应变问题，模拟了滑移面方位、位错障碍密度、位错源密度和材料尺寸对微梁弯曲的影响，模拟出了尺度效应。本文工作基于严格的纯弯曲边界条件，得出了与Needleman等人不同的位错分布模式，而与Hsia的实验结果吻合。本文还针对铜和铝合金材料的小尺度试样进行了三点弯曲和四点弯曲实验，通过对表面滑移线的观察，进一步证实了梁杆中部弹性核的存在。
英文摘要	Different behaviors of mechanics are manifested in solids at the length scale of micron or submicron with at the macron scale. The discrepancy of mechanics behaviors due to different size scales is often referred to as the size effect. On the modeling of the size effect, since conventional elastic-plastic theory does not include any length scale parameters inside it, one can not predict the size effect phenomenon using it. Although the strain gradient plasticity theory includes some length parameters and can be used to model the size effect well, the physical meaning of the length parameters in the strain gradient plasticity theory is a little ambiguous. Although great deal of researches for material plastic behaviors have been preformed in past decades directly based on the microscopic dislocation theory, employing the dislocation theory for studying size effect is still lacking. Intention of the present research is focused on modeling the strong size effect displayed in the fundamental micro-scale experiments (torsion and bend), by adopting the combination method of discrete dislocation theory with elastic finite element method. Firstly, for the basic mechanics problems (micro-bend and micro-torsion), a one-dimensional model, by which the size effect can be characterized, is derived out by using the Mura's one-dimensional formula. Secondly, based on the experimental results and measurements, propose that an elastic core exists within the central zone of beam and bar when they undergo the micro-bending and micro-torsion, respectively. Through analysis based on the model, stress-strain relations of the micro-bend and micro-torsion are attained. The results show that when specimen size decreases and attains to a small value a strong size effect is displayed in the micro-bend and micro-torsion tests. A successful modeling for the known experimental results is realized. Based on the researches of Needleman and his collaborators, two-dimensional plane strain problems are used to model the effects of the slip-plane location, dislocation obstacle density, dislocation source density and specimen size on the micro-bend beam results. In the results, the size effect is displayed in the results. Based on the rigorous boundary conditions for pure bend, we obtain the dislocation distribution different from that of Needleman et al. However our result is comparable with the experimental observation of Hsia. Furthermore, the three- or four-point bend experiments for Cu and for Al-alloy specimens are preformed in the present research. Through observing the distribution of slip-lines on the surface, the existence of the elastic core within the central zone of beam is verified.
索取号	30052
语种	中文
文献类型	学位论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/23750
专题	力学所知识产出(1956-2008)
推荐引用方式 GB/T 7714	唐山. 固体材料的尺度效应和离散位错理论模拟[D]. 北京. 中国科学院研究生院,2003.

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