And feel free to ask for any question related.. Engineering Mechanics S. Bhavikatti, K. Newton solid mechanics Strength of Materials system of forces..

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Such allowable stresses are also known as "design stresses" or "working stresses. 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. Generally, higher the range stress, the fewer the number of reversals needed for failure. Failure theories Edit There are four failure theories: maximum shear stress theory, maximum normal stress theory, maximum strain theory, maximum strain energy theory, and maximum distortion energy theory. 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 most accurate results in majority of the stress conditions. 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 — This 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 — This 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 — This 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.

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 change in shape. Distortion energy is the amount of energy that is needed to change the shape. This important theory is also known as numeric conversion of toughness of material in the case of crack existence.

Fractology was proposed by Takeo Yokobori because each fracture laws including creep rupture criterion must be combined nonlinearly. The engineering processes to which a material is subjected can alter this microstructure.

The variety of strengthening mechanisms that alter the strength of a material includes work hardening , solid solution strengthening , precipitation hardening , and grain boundary strengthening and can be quantitatively and qualitatively explained.

Strengthening mechanisms are accompanied by the caveat that some other mechanical properties of the material may degenerate in an attempt to make the 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.

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 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 strength of materials, especially the problem of fatigue. Repeated loading often initiates brittle cracks, which grow until failure occurs. The cracks always start at stress concentrations , especially changes in cross-section of the product, near holes and corners at nominal stress levels far lower than those quoted for the strength of the material.

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