The effects of stress and temperature gradients on fatigue life

Abstract

A method is developed that establishes a lower bound on fatigue life due to non-uniform multiaxial stress (strain) and temperature distributions. The method allows prediction of fatigue crack initiation at notches, where stress (strain) gradients are always present, from isothermal uniaxial fatigue tests. In addition, the method enables prediction of fatigue life due to multiaxial, non-uniform thermal stresses (strains) associated with temperature gradients. By considering the strain energy density distribution associated with the non-uniform stress (strain) field, it is shown that if the actual distribution is replaced by a series of thin strips, each at an average temperature with a chordwise linear strain energy density distribution, then the actual strain energy is always less than that associated with the chordwise approximation. The concept of “specific damage” (per cycle) is then introduced as linearly proportional to strain energy. Specific damage is then related to fatigue life through the life fraction rule, which leads to a lower bound on actual fatigue life.