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How Things Break Solids fail through the propagation of cracks, whose speed is controlled by instabilities at the smallest scales

Galileo was seventy-two years old, his life nearly shattered by a trial for heresy before the Inquisition, when he retired in 1635 to Florence to construct the Dialogues Concerning Two New Sciences. His first science is the study of the forces that hold objects together, and the conditions that cause them to fall apart, the dialogue taking place in a shipyard, triggered by observations of craftsmen building the Venetian fleet. The second science concerns ``local motions:'' laws governing the movement of projectiles. The two subjects Galileo founded have fared differently. One is a respectable branch of mechanical engineering, while the other is a core subject that physicists learn at the beginning of their education. Although now, as in Galileo's time, ship-builders need good answers to questions about the strength of materials, the subject has never yielded easily to basic analysis. Galileo identified the main difficulty: ``one cannot reason from the small to the large, because many mechanical devices succeed on a small scale that cannot exist in great size.[1]'' Nearly three hundred years elapsed after Galileo wrote these lines before science reached the atomic scale and began to answer the questions he had posed on the origins of strength, and the relation between large and small. Despite the tremendous development of solid state physics in this century, attention physicists paid to how things break has been slight. In part, the subject seems too hard. Cracks form at the atomic scale, extend to the macroscopic level, are irreversible, and travel far from equilibrium. Many of the tools with which solid state physics was built do not work: for example, there is no perfect lattice left in which to calculate the quantum mechanical motion of electrons, and cracks move so quickly that even basic quantities such as temperature are ill-defined near their tips. There is also the embarrassment of explaining to colleagues that one is working on failure. The strength of solids calculated from an excessively idealized starting point comes out completely wrong; it is not determined by performance under ideal conditions, but instead by the survival of the most vulnerable spot under the most adverse of conditions. Failure of Perfect Solids Here is how a perfect solid would break.