Mechanical behavior of a μm-sized single crystal silicon structure with sharp notches
Mechanical behavior of a μm-sized single crystal silicon structure with sharp notches
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DOI：
10.1016/s0022-5096(98)00112-4
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发表时间：
1999-08
影响因子：
5.3
通讯作者：
E. Mazza;J. Dual
中科院分区：
文献类型：
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作者：
E. Mazza;J. Dual
本文研究了微米级单晶硅结构的力学行为。采用一种新的微试样拉伸试验装置测定了单晶硅微棒的力学性能。力和伸长率可独立测量，精度高。弹性常数以及临界载荷的确定。样品的失效发生在微棒末端的尖锐缺口处。因此，在缺口尖端附近的应力场进行分析，以表征结构的承载能力。为此，有限元计算结合近似解析解的基础上的斯特罗形式主义。考虑了平面应力和二维位移的情况。与有限元解的比较表明，平面应力假设是更好的，从而确定了这种情况下的临界应力强度因子Fcr。由于Fcr依赖于几何形状，一个新的标量破坏准则，即一个临界半径Rcr的介绍，并从计算的应力场在切口。它是基于存储的弹性能量和表面能在关键位置的比较。由于它是一个标量准则，它可以适用于具有任意缺口角的单晶微结构。对于所考虑的情况，实验产生Rcr= 0.8 nm。所提出的标准可以被认为是一个步骤的定义的设计规则，在单晶结构中，这是所需的微机械器件的优化设计的尖锐缺口。
The mechanical behavior of μm-sized single crystal silicon structures is investigated in this paper. A new apparatus for microsample tensile testing is used to determine the mechanical properties of single crystal silicon microbars. Force and elongation are measured independently with high accuracy. Elastic constants as well as critical loads are determined. Failure of the sample occurs at the extremities of the microbar at a sharp notch. The stress field in the notch tip vicinity is therefore analyzed to characterize the load capacity of the structure. For this purpose, finite element computations are combined with approximate analytic solutions based on the Stroh formalism. Both the case of plane stress and two-dimensional displacements are considered. Comparison with the FEM solution shows that the plane stress assumption is better, leading to the determination of the critical stress intensity factor Fcrfor this case. Because Fcris dependent on the geometry, a new scalar failure criterion—i.e. a critical radius Rcr—is introduced and derived from the calculated stress field at the notch. It is based on a comparison of stored elastic energy and surface energy at the critical location. Because it is a scalar criterion, it can be applied to single crystal microstructures with notches of arbitrary notch angle. For the case considered, experiments yield Rcr= 0.8 nm. The proposed criterion can be considered as a step towards the definition of a design rule for sharp notches in single crystal structures, which is required for the optimized design of micromechanical devices.