A proper design includes the prediction of circumstances under which failure is likely to occur. In the most general terms, failure refers to any action that causes the member of the structure or machine to cease to function satisfactorily. The strength, stiffness, and stability of various load-carrying members are possible types or modes of failure. Failure may also be associated with poor appearance, poor adaptability to new demands, or other considerations not directly related to the ability of the structure to carry a load. Important variables associated with the failure include the type of material, configuration and rate of loading, the shape and surface peculiarities, and the operational environment.

This chapter is devoted to study of static failure criteria and the reliability method in design. We are concerned mainly with the failure of homogeneous and isotropic materials by yielding and fracture. The mechanical behavior of materials associated with failure also is discussed. In addition to possible failure by yielding or fracture, a member can fail at much lower stresses by crack propagation, should a crack of sufficient size be present. The fracture mechanics theory provides a means to predict a sudden failure on the basis of a computed stress intensity factor compared to a tested toughness criterion for the material (Sections 7.2 through 7.4). Other modes of failure include excessive elastic deflection of some element, rendering the machine or structure useless, or failure of a component by buckling. Various types of failure are considered in the problems presented as the subject unfolds [1-5].

Unless we are content to overdesign members, it is necessary to predict the most probable modes of failure and product reliability. Of necessity, the strength theories of failure are used in the majority of machine and structural designs. The actual failure mechanism in an element may be quite complicated; each failure theory is only an attempt to model the mechanism of failure for a given class of material. In each case, a factor of safety is employed to provide the required safety and reliability. Clearly, composite materials that do not exhibit uniform properties require more complex failure criteria [4].