The stress at which a metal fails by fatigue lies

ANS:C - in the elastic range.

elastic range" of a material's stress-strain curve, we are referring to the portion where the material deforms elastically, meaning it can return to its original shape after the stress is removed. In this range, the material behaves according to Hooke's Law, which states that the strain (deformation) is directly proportional to the stress applied, with a linear relationship. In the elastic range, the material undergoes reversible deformation, and no permanent changes occur in its structure. Fatigue failure, on the other hand, occurs due to the accumulation of small, localized deformations and microstructural changes that eventually lead to crack initiation and propagation, resulting in failure. Fatigue failure typically occurs in the plastic range of the stress-strain curve or at stress levels beyond the yield point, where permanent deformation begins to occur in the material. In this range, the material undergoes irreversible deformation, and the cyclic loading leads to the initiation and growth of fatigue cracks, eventually resulting in failure. Therefore, to clarify, fatigue failure usually occurs in the plastic range of the stress-strain curve, rather than in the elastic range where the material behaves elastically and returns to its original shape after the stress is removed.