Abstract
The relation between the extent of mirror surface appearing at the starting point of crack produced in glass rod by bending and the applied stress is studied. Two series of experiments are carried out: (a) the load is increased linearly with time, (b) the load is kept constant. There is a tendency that the greater the stress at the moment of rupture, the smaller the mean extent of mirror surface. Under the same condition of stress, however, the marked fluctuations are observed on the extent of mirror as well as on the mode of successive ramifications. For the problems of these fluctuations, statistical theory of fracture is applied. If the probability of the first occurrence of ramification which determines the boundary of the mirror after the crack develops for the distance l from the starting point is denoted by μ(l), the following relations are proved to hold good.
μ(l)=A(l−l0)exp(αf) when l>l0,
=0 when l≤l0,
\barl−l0=Cexp(−α⁄2·f),
where, f being the tensile stress at the starting point of crack, l0 the minimum extent of the mirror produced under stress f, \barl the mean value of l, and A, C, α, some constants.
