• • • • • • • • • • • • • • Failure theory is the science of predicting the conditions under which solid materials fail under the action of external loads. The failure of a material is usually classified into brittle failure () or ductile failure (). Depending on the conditions (such as temperature, state of stress, loading rate) most materials can fail in a brittle or ductile manner or both.

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However, for most practical situations, a material may be classified as either brittle or ductile. Though failure theory has been in development for over 200 years, its level of acceptability is yet to reach that of continuum mechanics. In mathematical terms, failure theory is expressed in the form of various failure criteria which are valid for specific materials. Failure criteria are functions in stress or strain space which separate 'failed' states from 'unfailed' states. A precise physical definition of a 'failed' state is not easily quantified and several working definitions are in use in the engineering community. Quite often, phenomenological failure criteria of the same form are used to predict brittle failure and ductile yield.

Main article: Criteria used to predict the failure of ductile materials are usually called criteria. Commonly used failure criteria for ductile materials are: • the or maximum shear stress criterion • the or distortional strain energy density criterion • the for pressure-dependent metals • the for metals • the • various criteria based on the invariants of the Cauchy stress tensor The of a ductile material usually changes as the material experiences increased. Models for the evolution of the yield surface with increasing strain, temperature, and strain rate are used in conjunction with the above failure criteria for,,.

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Some such models are: • the • the • the • the • the There is another important aspect to ductile materials - the prediction of the of a ductile material. Several models for predicting the ultimate strength have been used by the engineering community with varying levels of success. For metals, such failure criteria are usually expressed in terms of a combination of porosity and strain to failure or in terms of a parameter.

See also [ ] • • • • • • • • • • • • References [ ].

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