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Stress-Based Criteria
The purpose of failure criteria is to predict or estimate the failure/yield of machine parts and structural members.

A considerable number of theories have been proposed. However, only the most common and well-tested theories applicable to isotropic materials are discussed here. These theories, dependent on the nature of the material in question (i.e. brittle or ductile), are listed in the following table:

Failure Theories
Ductile Maximum shear stress criterion, von Mises criterion
Brittle Maximum normal stress criterion, Mohr's theory
All four criteria are presented in terms of principal stresses. Therefore, all stresses should be transformed to the principal stresses before applying these failure criteria.

Note: 1. Whether a material is brittle or ductile could be a subjective guess, and often depends on temperature, strain levels, and other environmental conditions. However, a 5% elongation criterion at break is a reasonable dividing line. Materials with a larger elongation can be considered ductile and those with a lower value brittle.
Another distinction is a brittle material's compression strength is usually significantly larger than its tensile strength.
  2. All popular failure criteria rely on only a handful of basic tests (such as uniaxial tensile and/or compression strength), even though most machine parts and structural members are typically subjected to multi-axial loading. This disparity is usually driven by cost, since complete multi-axial failure testing requires extensive, complicated, and expensive tests.
Non Stress-Based Criteria
The success of all machine parts and structural members are not necessarily determined by their strength. Whether a part succeeds or fails may depend on other factors, such as stiffness, vibrational characteristics, fatigue resistance, and/or creep resistance.

For example, the automobile industry has endeavored many years to increase the rigidity of passenger cages and install additional safety equipment. The bicycle industry continues to decrease the weight and increase the stiffness of bicycles to enhance their performance.

In civil engineering, a patio deck only needs to be strong enough to carry the weight of several people. However, a design based on the "strong enough" precept will often result a bouncy deck that most people will find objectionable. Rather, the stiffness of the deck determines the success of the design.

Many factors, in addition to stress, may contribute to the design requirements of a part. Together, these requirements are intended to increase the sense of security, safety, and quality of service of the part.