Ultimate strength is an attribute related to a material, rather than just a specific specimen made of the material, and as such it is quoted as the force per unit of cross section area (N/m2). The ultimate strength is the maximum stress that a material can withstand before it breaks or weakens.{{cite book A
factor of safety is a design criteria that an engineered component or structure must achieve. FS = F/f, where FS: the factor of safety, Rf The applied stress, and F: ultimate allowable stress (psi or MPa){{cite book Margin of Safety is the common method for design criteria. It is defined MS = Pu/P − 1. For example, to achieve a factor of safety of 4, the allowable stress in an AISI 1018 steel component can be calculated to be F = UTS/FS = 440/4 = 110 MPa, or F = 110×106 N/m2. Such allowable stresses are also known as "design stresses" or "working stresses". Design stresses that have been determined from the ultimate or yield point values of the materials give safe and reliable results only for the case of static loading. Many machine parts fail when subjected to a non-steady and continuously varying loads even though the developed stresses are below the yield point. Such failures are called fatigue failure. The failure is by a fracture that appears to be brittle with little or no visible evidence of yielding. However, when the stress is kept below "fatigue stress" or "endurance limit stress", the part will endure indefinitely. A purely reversing or cyclic stress is one that alternates between equal positive and negative peak stresses during each cycle of operation. In a purely cyclic stress, the average stress is zero. When a part is subjected to a cyclic stress, also known as stress range (Sr), it has been observed that the failure of the part occurs after a number of stress reversals (N) even if the magnitude of the stress range is below the material's yield strength. Generally, higher the range stress, the fewer the number of reversals needed for failure.
Failure theories There are four failure theories: maximum shear stress theory, maximum normal stress theory, maximum strain energy theory, and maximum distortion energy theory (von Mises criterion of failure). Out of these four theories of failure, the maximum normal stress theory is only applicable for brittle materials, and the remaining three theories are applicable for ductile materials. Of the latter three, the distortion energy theory provides the most accurate results in a majority of the stress conditions. The strain energy theory needs the value of
Poisson's ratio of the part material, which is often not readily available. The maximum shear stress theory is conservative. For simple unidirectional normal stresses all theories are equivalent, which means all theories will give the same result. •
Maximum shear stress theory postulates that failure will occur if the magnitude of the maximum shear stress in the part exceeds the shear strength of the material determined from uniaxial testing. •
Maximum normal stress theory postulates that failure will occur if the maximum normal stress in the part exceeds the ultimate tensile stress of the material as determined from uniaxial testing. This theory deals with brittle materials only. The maximum tensile stress should be less than or equal to ultimate tensile stress divided by factor of safety. The magnitude of the maximum compressive stress should be less than ultimate compressive stress divided by factor of safety. •
Maximum strain energy theory postulates that failure will occur when the strain energy per unit volume due to the applied stresses in a part equals the strain energy per unit volume at the yield point in uniaxial testing. •
Maximum distortion energy theory, also known as maximum distortion energy theory of failure or
von Mises–Hencky theory. This theory postulates that failure will occur when the distortion energy per unit volume due to the applied stresses in a part equals the distortion energy per unit volume at the yield point in uniaxial testing. The total
elastic energy due to strain can be divided into two parts: one part causes change in volume, and the other part causes a change in shape. Distortion energy is the amount of energy that is needed to change the shape. •
Fracture mechanics was established by
Alan Arnold Griffith and
George Rankine Irwin. This important theory is also known as numeric conversion of toughness of material in the case of crack existence. A material's strength depends on its
microstructure. The engineering processes to which a material is subjected can alter its microstructure.
Strengthening mechanisms that alter the strength of a material include
work hardening,
solid solution strengthening,
precipitation hardening, and
grain boundary strengthening. Strengthening mechanisms are accompanied by the caveat that some other mechanical properties of the material may degenerate in an attempt to make a material stronger. For example, in grain boundary strengthening, although
yield strength is maximized with decreasing grain size, ultimately, very small grain sizes make the material brittle. In general, the yield strength of a material is an adequate indicator of the material's mechanical strength. Considered in tandem with the fact that the yield strength is the parameter that predicts
plastic deformation in the material, one can make informed decisions on how to increase the strength of a material depending on its microstructural properties and the desired end effect. Strength is expressed in terms of the limiting values of the
compressive stress,
tensile stress, and
shear stresses that would cause failure. The effects of dynamic loading are probably the most important practical consideration of the theory of elasticity, especially the problem of
fatigue. Repeated loading often initiates cracks, which grow until failure occurs at the corresponding residual strength of the structure. Cracks always start at a
stress concentrations especially changes in cross-section of the product or defects in manufacturing, near holes and corners at nominal stress levels far lower than those quoted for the strength of the material. ==See also==