Statistical strength variation
Preliminary remarks. Strength is known to vary with specimen size, a
phenomenon pointed out long ago by Weibull [69]. He used the weakest
link concept for determining a critical imperfection in a given material,
the size of which increases by increasing the volume. This is a simple model
that does not account for details of the imperfections nor the constitutive
relation of the material. J ayatilaka [70] and Freudenthal [71] considered
a linear elastic material with a great number of embedded Griffith cracks
and indicated that the variability of strength with specimen volume may be
related to the probability density of crack size distribution. The strength
size effect in structures with re-entrant corners was considered by Leicester
[72] who included the effect of stress-singularity at the corner vertex. He
showed that the strength size effect is due to the existence of one or more
stress singularity sources in the body. These sources can arise from macro-
scopic notches or partially debonded interfaces. Bazant [73] also explained
size effects in the brittle failure of concrete structures by application of
Linear Elastic Fracture Mechanics and contrasted his results with those of
Weibull.
