纳米悬臂梁Si/Cu界面破坏的弹塑性内聚力模拟

ELASTO-PLASTIC COHESIVE ZONE MODELING OF DELAMINATION OF Si/Cu INTERFACE IN A NANO-CANTILEVER

实验测试表明[Thin Solid Fil ms 516:1925-1930],纳米悬臂梁Si/Cu/Si N/Pt/C在弯曲载荷作用下发生沿Si/Cu界面的分层破坏,其载荷-位移曲线表现出明显的非线性行为.本文基于连续介质力学模型,对该实验观察到的界面裂纹萌生和沿界面扩展过程进行了数值模拟计算与分析.模拟计算中,采用指数型内聚力来表征Si/Cu界面本构关系,对Cu薄层分别按照线弹性和遵守Ramberg-Osgood型弹塑性本构关系来处理.通过与实验结果校准的方法,确定了该纳米悬臂梁中Si/Cu界面的结合强度诸参数.研究发现,内聚强度和内聚能是该内聚力模型的主导性参数;Cu薄膜层遵从线弹性本构关系更为适合于描述Si/Cu界面的分层破坏;与块体材料相比,纳米尺寸的Cu材料表现出很高的屈服应力和硬化指数,因此在整个过程中产生的塑性变形很小,这与前述的实验结果是一致的.

Previous experimental tests [Thin Solid Films 516：1925-1930] have shown that nano-cantilever Si/Cu/SiN/Pt/C tends to delaminate along the interface between Cu and Si layers when subject to monotonically bending load,the measured load-displacement curve shows a clear nonlinear behavior. Based on the continuum mechanics model, this study carries out numerical simulation and analysis of the crack initiation and propagation along the interface Si/Cu,which was observed in the above tests. Exponential type cohesive zone model （CZM） using finite element method was adopted to characterize the constitutive relationship of the interface Si/Cu,where Cu layer obeys either linear elastic or Ramberg-Osgood elasto-plastic constitutive relationship. The characteristic parameters of interface bonding strength are extracted through calibration via experimental results. The simulation results show that （i） cohesive strength and cohesive energy are the dominating CZM parameters,and exponential CZM is suitable to describe the interfacial delamination between Cu and Si layers when Cu layer is linear elastic（ii） compared with bulk Cu,nano-scale Cu has a much higher yield stress and hardening rate,which leads to little plastic deformation of the nanocantilever specimen during the whole delamination process. These predictions are in accordance with the experimental results.