On the relation between the energy of a distorted crystal lattice and the bending modulus of strain gradient elasticity

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;    Bending moduli;    Electrostatic energies;    Face-centred cubic;    Linear-elastic fracture mechanics;    Strain gradient elasticity;    Stress singularities;    Surface of materials;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/790/1/012019/pdf
DOI  :  10.1088/1742-6596/790/1/012019

来源: IOP

【 摘 要 】

It is a well known fact that linear elastic fracture mechanics (LEFM) predicts stress singularities at the tips of sharp cracks, at sharp edges, at corners and at the surface of material transitions. However, from the viewpoint of the strengths of atomic bonds it is clear that only finite forces may be present at the tip of a stable crack. Therefore, theories of strain gradient elasticity were developed which reduce the values of stress concentrations. Within these theories a bending modulus is postulated which introduces an increased stiffness of the crystal lattice against bending. In the present study, the value of this bending modulus is evaluated on the basis of the electrostatic energy of a bent crystal lattice. This is done for the face centred cubic structure of NaCl. In fact, results for the bending modulus could be obtained although they depend on the crystal size.