Indeed, fracture or breakdown studies might be the oldest physical science studies, which still remain intriguing and very much alive. Leonardo da Vinci, more than 500 years ago, observed that the tensile strengths of nominally identical specimens of iron wire decrease with increasing length of the wires (see e.g., for a recent discussion). Similar observations were made by Galileo Galilei more than 400 years ago. This is the manifestation of the extreme statistics of failure (bigger sample volume can have larger defects due to cumulative fluctuations where failures nucleate and induce lower strength of the sample). Types
There are two types of fractures: brittle and ductile fractures respectively without or with plastic deformation prior to failure. Brittle
In brittle fracture, no apparent plastic deformation takes place before fracture. Brittle fracture typically involves little energy absorption and occurs at high speeds—up to 2,133.6 m/s (7,000 ft/s) in steel. In most cases brittle fracture will continue even when loading is discontinued.In brittle crystalline materials, fracture can occur by cleavage as the result of tensile stress acting normal to crystallographic planes with low bonding (cleavage planes). In amorphous solids, by contrast, the lack of a crystalline structure results in a conchoidal fracture, with cracks proceeding normal to the applied tension.
The Weibull distribution predicts the survival probability of a fraction of samples with a certain volume that survive a tensile stress sigma, and is often used to better assess the success of a ceramic in avoiding fracture. Fiber bundles
To model fracture of a bundle of fibers, the Fiber Bundle Model was introduced by Thomas Pierce  in 1926 as a model to understand the strength of composite materials. The bundle consists of a  large number of parallel Hookean springs of identical length and each having identical spring constants. They have however different breaking stresses. All these springs are suspended from a rigid horizontal platform. The load is attached  to a horizontal platform, connected to the lower ends of the springs. When this lower platform is absolutely rigid, the load at any point of time is shared equally (irrespective of how many fibers or springs have broken and where) by all the surviving fibers. This mode of load-sharing is called Equal-Load-Sharing mode. The lower platform can also be assumed to have finite rigidity, so that local deformation of the platform occurs wherever springs fail and the surviving neighbor fibers have to share a larger fraction of that transferred from the failed fiber. The extreme case is that of local load-sharing model, where load of the failed spring or fiber is shared (usually equally) by the surviving nearest neighbor fibers. Disasters
Failures caused by brittle fracture have not been limited to any particular category of engineered structure.