Piecewise reliability-dependent hazard rate for composites under fatigue loading adjustment

Based on the derived transition period and reliability drop, this paper proposes a method of piecewise combination of the reliability-dependent hazard rate function named $ (e_ocp)$ model to describe the dynamical reliability in a two-stage fatigue loading process. First, the parameters $ e_o$, $c$, $p$ are fitted through simulated failure data under various constant-amplitude cyclic stresses. The reliability of the high-low loading process is described piecewise with the corresponding values of $ (e_o,c,p)$ for each respective stress level, and maintains $ R_a$ in the transition period while $ R_a$ denotes the reliability at which the stress level changes. The reliability of the low-high process is determined by subtracting the portion of reliability drop at $ R_a$ from the piecewise fitted curves. The proposed reliability behavior is verified successfully. The linear damage sum is found to be larger than unity for the high-low loading, and on the contrary for the low-high cases. A larger difference between the stress level changed results in larger deviation of damage sum from unity, especially when $ R_a$ near 0.9.