| Popis: |
The stress field close to a crack tip in an elastic isotropic solid can be expressed as an asymptotic expansion following Williams (1957): $$ {{\sigma }_{{ij}}}(r,\theta ) = {{A}_{{ij}}}(\theta ){{r}^{{ - \frac{1}{2}}}} + {{B}_{{ij}}}(\theta ) + {{C}_{{ij}}}(\theta ){{r}^{{\frac{1}{2}}}} + ... $$ (1) (r, σ)are polar co-ordinates centred at the crack tip, and σ ij are the Cartesian components of the stress tensor. Focussing interest on the non-zero terms at the crack tip, the elastic field can be expressed in the form: $$ {{\sigma }_{{ij}}}(r,\theta ) = \frac{{{{K}_{I}}}}{{\sqrt {{2\pi r}} }}{{f}_{{ij}}}(\theta ) + T{{\delta }_{{1,}}}_{j}{{\delta }_{{i,1}}} $$ (2) |
