Investigation of the stress distribution around a mode 1 crack with a novel strain gradient theory

2nd International Conference on Rheology and Modeling of Materials

Lederer, M.^1 ; Khatibi, G.^1

Institute of Chemical Technologies and Analytics, Vienna University of Technology, Christian Doppler Laboratory for Lifetime and Reliability of Interfaces, Complex Multi-Material Electronics, Wien, Austria^1

关键词: Atomic bonds;    Linear-elastic fracture mechanics;    Mesh refinement;    Multi-scale modelling;    Novel strains;    Size effects;    Strain gradient elasticity;    User subroutine;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/790/1/012018/pdf
DOI  :  10.1088/1742-6596/790/1/012018

来源: IOP

【 摘 要 】

Stress concentrations at the tip of a sharp crack have extensively been investigated in the past century. According to the calculations of Inglis, the stress ahead of a mode 1 crack shows the characteristics of a singularity. This solution is exact in the framework of linear elastic fracture mechanics (LEFM). From the viewpoint of multiscale modelling, however, it is evident that the stress at the tip of a stable crack cannot be infinite, because the strengths of atomic bonds are finite. In order to prevent the problem of this singularity, a new version of strain gradient elasticity is employed here. This theory is implemented in the commercial FEM code ABAQUS through user subroutine UEL. Convergence of the model is proved through consecutive mesh refinement. In consequence, the stresses ahead of a mode 1 crack become finite. Furthermore, the model predicts a size effect in the sense "smaller is stronger".