  This paper presents two main results. The first result indicates that in
materials with broadly distributed microscopic heterogeneities, the fracture
strength distribution corresponding to the peak load of the material response
does not follow the commonly used Weibull and (modified) Gumbel distributions.
Instead, a {\it lognormal} distribution describes more adequately the fracture
strengths corresponding to the peak load of the response. Lognormal
distribution arises naturally as a consequence of multiplicative nature of
large number of random distributions representing the stress scale factors
necessary to break the subsequent "primary" bond (by definition, an increase in
applied stress is required to break a "primary" bond) leading up to the peak
load. Numerical simulations based on two-dimensional triangular and diamond
lattice topologies with increasing system sizes substantiate that a {\it
lognormal} distribution represents an excellent fit for the fracture strength
distribution at the peak load. The second significant result of the present
study is that, in materials with broadly distributed microscopic
heterogeneities, the mean fracture strength of the lattice system behaves as
$\mu_f = \frac{\mu_f^\star}{(Log L)^\psi} + \frac{c}{L}$, and scales as $\mu_f
\approx \frac{1}{(Log L)^\psi}$ as the lattice system size, $L$, approaches
infinity.
