Inherent crack size

The second approach to fracture is different in that it treats the material as a continuum rather than as an assembly of molecules. In this case it is recognised that failure initiates at microscopic defects and the strength predictions are then made on the basis of the stress system and the energy release processes around developing cracks. From the measured strength values it is possible to estimate the size of the inherent flaws which would have caused failure at this stress level. In some cases the flaw size prediction is unrealistically large but in many cases the predicted value agrees well with the size of the defects observed, or suspected to exist in the material. 

The probability of crack propagation can be calculated for the classic hexagonal cell and can be related to cell dimensions and the applied stress.9 A new constant is involved in the resultant equations it is related to cell size (since crack propagation is a combination of tensile stress and bending moment). For CMP pads, the equivalent areas of concern will be the cell density (related to the relative density) and the cell size distribution (visualized in Figure 6.33). It is the cell proximity or overlap probability that will determine the material s inherent propensity to support crack propagation. Also, since much of the shear stress concentration is at the top frictional surface, the damage done to the inherent cell structure by the CMP process is likely to determine much of the material s wear response. It is probable that the shape, size, and distribution of abrasives play an important role in the material s wear characteristics. 

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