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

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 Rt=0.97 with a reliability confidence level of CL=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 (Cp) and ability (Cpk) indices. Finally, we present the formulation to determine the Rt index and the CL level associated with each normal percentile, along with their numerical values.