The Basic Solutions Of The Indentation-Induced Initial Fracture Based On The 3-D Method

Various complicated fracture modes can be easily observed in the traditionalindentation/scratch tests and in the micro/nano indentation/scratch tests developed inthe past decades. Given that the fracture analysis is concerned, the traditional 2Danalysis can provide the accurate results. But for the 3D method of analysis, generallyspeaking, the traditional methods like the weighted-function can not lead to thesatisfactory conclusion. Especially in the micro/scratch indention/scratch test, thesmall size of the film generates much more difficulties in 3D analysis. It is, therefore,necessary to develop effective 3D method of analysis.The project is concerned with the toughness in the indentation/scratch test. Bymeans of the equality of the physical pictures between the crack and the physicalsingularity, the 3D fracture analysis method is given based on the interaction energy ofsingularity. The method is applied to obtain the general Green functions of 3D fractureproblem and the initial crack problem in the indentation/scratch test. As a conclusion,a general 3D method is presented to deal with the complicated fracture problem; andon the other hand, the 3D method is used to solve the axially-symmetric fractureproblem in the indentation/scratch test, and this helps to extend the method to themore complicated fracture modes.The main contributions include:1) Achieving the Green function of the general 3D fracture problems throughselecting any point forces as a measurement in the 3D space and basing the theory ofthe singularity energy interaction.2) According to the axial symmetry properties of the crack configuration, basingthe theory of the singularity energy interaction, we obtain the Green function of initialcrack by using two different methods to analysis the initial fracture problem in theindentation/scratch test.3) Solving the interaction of singularity configuration in (2) and free surface toanalysis model of initial crack problems in the indentation/scratch test, we obtain thecomplete Green function that can apply directly to solve initial crack problems.