Theories of Failure:

Various people have prescribed various criteria for failure of a solid and therefore, a number of failure theories (also called strength theories) have been created.

In what is called as Principal Stress Theory, if the maximum principal stress (or minimum principal stress in the case of compression) reaches the similar value of maximum principal stress at failure in uniaxial strength test, after that the yield of failure limit is considered as reached.

According to Principal Strain Theory, a material is considered to have reached the yield or failure limit while the maximum principal strain within the material has reached the value of the maximum principal strain at failure as observed within the uniaxial strength test.

According to Shear Stress Theory, a material is considered to have reached the yield or failure limit while the maximum shear stress in the material has reached the value of the maximum shear stress at failure as observed within the uniaxial strength test.

 Except from the stress or strain limits as governing criteria for failure then the capacity of the material to store energy is also considered as criteria for failure and theories have been created based on these criteria.

As per to Total Strain Energy Theory, a material is considered to have reached the yield or failure limit while the total strain energy density (anywhere within the material) has reached the total strain energy density observed at failure within the case of uniaxial strength test.

Yet another failure theory has been created, along with the assumption in which the distortion energy density, rather than the total strain energy density, is important as failure criteria. According to this theory, called as Distortion Energy Theory, a material is considered to have reached the yield or failure limit while the distortion energy density (anywhere inside the solid) reaches the value of distortion energy density at failure as observed within the case of uniaxial strength test.

Some other theories are not so popular and thus, are not dealt along with here. Now, you might get a doubt, whether the various theories really set various criteria for failure or are these theories only various ways of expressing the same criteria and thus, are fundamentally the similar? Let us examine a few easy cases and ascertain the answer.