Weibull stress distribution for static mechanical stress and its stress/strength analysis

The method's steps to estimate the Weibull shape (β) and scale (η) parameters, based only on the ratio of the maximal and minimal principal stresses (σ₁/σ₂) and on the designed reliability (R(t)) are given in Section 4.1 . The method's efficiency is based on the following facts: (1) The square root of σ₁/σ₂ represents the base life on which the Weibull lifetimes are estimated (see Equation  61 ). (2) The mean of the logarithms of the expected lifetimes (g(x)) is completely determined by the determinant of the analyzed stress matrix (see Equation  13 ). (3) The Weibull distribution is a circle centered on the arithmetic mean (μ), and it covers the whole principal stresses' span (see Figure  5 ). (4) σ₁/σ₂ and g(x) completely determine the σ_1i and σ_2i values, which correspond to any lifetime in the Weibull analysis (see Equation  54 ). And (5) σ₁/σ₂ and η completely determine the minimal and maximal lifetime, which corresponds to any σ_1i and σ_2i values (see Equation  57 ). Additionally, by using the addressed stress β and η parameters, when the stress is either constant or variable, the formulation to estimate the designed R(t) index is given. The steps to determine both the material's strength average (μ_M) for a desired R(t) index and the R(t) index, which corresponds to a used μ_M value, are given.