The many scales in fracture mechanics

Abstract

The fracture process is intimately connected with one or more length parameters, sometimes also with time parameters. The size of these parameters may be vastly different, giving rise to many different scales. Already seemingly simple cases, such as crack growth in single‐crystals, involve great complexity, due to large scale differences, and for materials of engineering and geological interest, enormous complexity is involved. This can be greatly reduced by identifying the dominant scale, which leads to the cell model, in which a cell is the smallest material unit that contains reasonably sufficient information of the crack growth properties of the material. In some cases, a single dominant scale cannot be found, such as when very high strain gradients are present in one small region of the body. This can be handled in a comprehensive way by using a modified continuum plasticity theory that considers the influence of strain gradients. For fatigue and creep, different scales dominate sequentially from initial crack growth to completed fracture. This creates extraordinarily great complexity.