Higher order Cauchy–Born rule based multiscale cohesive zone model and prediction of fracture toughness of silicon thin films
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- 作者：Shingo Urata ; Shaofan Li
- 关键词：Cohesive zone model ; Crack ; Fracture toughness ; Multiscale simulation ; Silicon thin film
- 刊名：International Journal of Fracture
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：203
- 期：1-2
- 页码：159-181
- 全文大小：
- 刊物类别：Chemistry and Materials Science
- 刊物主题：Characterization and Evaluation of Materials; Classical Mechanics; Civil Engineering; Automotive Engineering; Mechanical Engineering;
- 出版者：Springer Netherlands
- ISSN：1573-2673
- 卷排序：203
文摘
In this work, we extend the multiscale cohesive zone model (MCZM) (Zeng and Li in Comput Methods Appl Mech Eng 199:547–556, 2010), in which interatomic potential is embedded into constitutive relation to express cohesive law in fracture process zone, to include the hierarchical Cauchy–Born rule in the process zone and to simulate three dimensional fracture in silicon thin films. The model has been applied to simulate fracture stress and fracture toughness of single-crystal silicon thin film by using the Tersoff potential. In this study, a new approach has been developed to capture inhomogeneous deformation inside the cohesive zone. For this purpose, we introduce higher order Cauchy–Born rules to construct constitutive relations for corresponding higher order process zone elements, and we introduce a sigmoidal function supported bubble mode in finite element shape function of those higher order cohesive zone elements to capture the nonlinear inhomogeneous deformation inside the cohesive zone elements. Benchmark tests with simple 3D models have confirmed that the present method can predict the fracture toughness of silicon thin films. Interestingly, this is accomplished without increasing of computational cost, because the present model does not require quadratic elements to represent heterogeneous deformation, which is the inherent weakness of the previous MCZM model. Quantitative comparisons with experimental results are performed by computing crack propagation in non-notched and initially notched silicon thin films, and it is found that our model can reproduce essential material properties, such as Young’s modulus, fracture stress, and fracture toughness of single-crystal silicon thin films.