For this reason the plates were placed with scratches facing downwards so that the procedure could test the effect of flaw size on fracture stress. Otherwise the experiment would have probably shown little difference between scratched and unscratched samples. The scratched samples also showed consistent directions in that they were nearly always perpendicular, this was due to linkage of cracks. Whereas for unscratched glass, the crack will propagate according to the local shape and direction of the defect. The three point bending test is used for brittle materials only for two reasons.
The first is because brittle materials cannot be tested with conventional unsocial tension tests because of early failure at the grips. The second reason is that LEE-M can only be applied in bending tests to rattle materials because yielding occurs around the same point as failure, so failure stresses can be used to calculate normal tensions in the beam using o = Mac/l. That is the stress versus strain diagrams remain nearly linear up until failure. Fracture toughness is the ability of a material to withstand brittle fracture in the presence of a crack or flaw.
The equation as mentioned earlier is derived from linear elastic fracture mechanics and stipulates that crack length is inversely proportional to fracture stress. The greater the crack length the less the stress needed to cause brittle fracture. At yield stress is the point where this equation is quite useful, if the crack length is below this critical length (the crack length at yield stress), yielding dominated behavior is expected so that there is little or no strength reduction due to a crack.
So the question remains how do we know what the distribution of flaw sizes are there in a specimen, so that fracture mechanics can be applied if necessary. Waybill statistics can be used to determine the distribution of cracks in a specimen, thereby allowing good prediction of whether the whole specimen contains cracks that are above r below the critical crack lengths. It is a useful distribution because it is non- symmetric and is better suited to the characterization of failure-relevant properties.
The results show relatively high Waybill modulo as compared to the literature which places the modulus for Glass at 2. 3, showing that for our specimens in general there is a tight distribution of flaw. Comparing scratched to unscratched, scratched exhibited a higher m, which means that the flaws that lead to failure tended to be more homogeneous in length than the flaws that caused failure in the unscratched specimens.