  Through controlled numerical simulations in a one dimensional fiber bundle
model with local stress concentration, we established an inverse correlation
between the strength of the material and the cracks which grow inside it - both
the maximum crack and the one that set in instability within the system,
defined to be the critical crack. Through Pearson correlation function as well
as probabilistic study of individual configurations, we found that the maximum
and the critical crack often differ from each other unless the disorder
strength is extremely low. A phase diagram on the plane of disorder vs system
size demarcates between the regions where the largest crack is the most
vulnerable one and where they differ from each other but still shows moderate
correlation.
