Methodology to Determine the Stress Distribution Based on Fatigue Data with Bilinear Behavior and Its P–S–N Field and Testing Plan

Abstract

In this paper, based on the Weibull Inverse Power Law, we present a methodology to determine the following: (1) the failure percentiles, referred to as the P–S–N field, of an S–N curve for a 42CrMo4 steel material exhibiting bilinear (𝑠1 and 𝑠2) behavior (e.g., a competence failure mode); (2) the Weibull family that characterizes the entire bilinear behavior; and (3) the zero-vibration test plan that meets the required vibration reliability index of 𝑅⁡(𝑡) =0.97 with a reliability confidence level of 𝐶⁢𝐿 =0.75. From the application, based on the formulated normal–Weibull relationship, we determine the failure percentiles for the normal (one, two, and three) sigma levels, as well as those failure percentiles corresponding to the capability (𝐶⁢𝑝) and ability (𝐶⁢𝑝⁢𝑘) indices. Finally, we present the formulation to determine the 𝑅⁡(𝑡) index and the 𝐶⁢𝐿 level associated with each normal percentile, along with their numerical values.