Penny-shaped crack in elastic medium with surface energy effects
In this paper, a penny-shaped crack in an infinite elastic medium subjected to vertical pressure loading at the crack surface under the influence of surface stress is considered. The Gurtin–Murdoch continuum theory of elastic material surfaces is adopted, and the Hankel integral transform is employed to solve this axisymmetric boundary value problem. A set of simultaneous dual integral equations is solved by employing an appropriate numerical solution scheme. Selected numerical results are presented to portray the influence of the surface stress on the elastic field. Numerical results reveal that the surface stress has a significant influence on both stress and displacement fields. It is also found that the material becomes tougher with the presence of surface stress. In addition, the elastic field also shows size-dependent behavior deviating from the classical crack solution. The solutions presented in this study provide fundamental understanding of the influence of surface stress on fracture mechanics problems. It can also be used as a benchmark solution for the development of numerical techniques, such as FEM and BEM, for analysis of more complicated problems associated with cracks under the influence of surface stress.
Intarit, P., Senjuntichai, T., Rungamornrat, J., & Rajapakse, N. (2017). Penny-shaped crack in elastic medium with surface energy effects. Acta Mechanica, 1–14. doi:10.1007/s00707-016-1728-9