Introduction to Fracture Mechanics

When an engineer designs a structure or piece of equipment, there are two basic forms of mechanical failure which must be considered. These are brittle fracture and, if the material employed is metallic, yielding. The second is by far the easier to take into account: it is necessary to know only the state of stress at every point in order to assemble the appropriate yield parameter. The maximum value of this quantity is found within the structure and set equal to the yield stress, which is taken as a true material property, i.e. it is independent of geometry. Usually the loading or stresses are reduced by a so-called factor of safety, which allows for unexpected overloads during the life of the structure. The load level corresponding to the onset of first yield is known as the elastic limit. There are considerable reserves of strength in any real structure if the elastic limit is moderately exceeded, partly because most real structures exhibit a high degree of redundancy, partly because cyclic loading will induce beneficial residual stresses, promoting shakedown, and partly because most common metals and alloys exhibit work hardening to a greater or lesser degree. By far the most important characteristics of yield from the point of view of design are: (a) that the yield stress is a highly repeatable true material property, being very insensitive to the geometry of the component under consideration. (b) that given the yield stress under uniaxial loading, the combination of stresses which will cause local failure under multiaxial conditions is well defined — assumptions of isotropy, independence of yield from hydrostatic stress and convexity of the yield surface (Paul, 1968) being necessary to obtain excellent bounding values for physically acceptable yield criteria.