MECHANICS OF HERTZIAN CRACKING

We review the progress made at Oxford in recent years in the quantific ation of surface damage of ceramics by application of the Hertzian ind entation test. This includes using micro-indenters to search out the s urface density of flaws, as well as assessing the size distribution. M any analytical tools have been developed for processing the data obtai ned, including refined methods of analysing the cone crack using distr ibuted strain nuclei techniques which accurately model the behaviour o f cracks in steep stress gradients, and in particular the use of eigen strain methods to quantify the growth of an initial surface thumbnail crack. The influence of elastic mismatch on the state of stress induce d by the indenter is also discussed, and it is shown that the use of a n indenter more compliant than the substrate leads to a more extensive annular zone of tension, thereby encouraging the formation of a ring crack. The remaining problem is an accurate analysis of the full cone crack itself, which has already been analysed using a special finite e lement formulation, and which is currently being re-examined by the us e of axi-symmetric ring nuclei: this promises to provide a more comple te and precise solution.