Cumulative fretting fatigue damage model for steel wire ropes

Fretting fatigue contributes significantly to the fatigue failure process in steel wire ropes at the wire‐to‐wire trellis contact region with partial slip conditions. In this respect, this work demonstrates a new damage‐based fretting fatigue model for the prediction of such a failure process. The model is based on Lemaitre's damage equations for quasi‐brittle material with a damageable micro‐inclusion embedded in an elastic meso‐element. It incorporates the cyclic degradation of the elastic modulus of the drawn steel wire material. The fatigue life model acknowledges the mean stress effect. The constitutive and damage equations are formulated into user material (UMAT) subroutine for integration with Abaqus finite element analysis code. The localized fretting fatigue damage mechanism is simulated with an isolated two‐wire model. The effect of the contact condition with the coefficient of friction of 0.2 and 0.8 on the contact mechanics of the drawn wires is considered. The fretting fatigue mechanism map is established for each simulation case. The simulated results of N0 (no of cycles to initiate damage) and damage variable, D, confirm the fretting fatigue condition as the damage occurs in the slip region of the contact area for both the frictional conditions. The results were found in agreement with the previously establish Ruiz fretting parameter. This study will provide a base for the onward reliability assessment of steel wire ropes. Highlights A damage‐based Lemaitre two‐scale model has been modified for the fretting fatigue mechanism in the steel wire ropes. A unified curve of residual elastic modulus has been established through interrupted fatigue tests for different load ratios. A UMAT Subroutine is developed using ABAQUS software. The response of the damage model has been investigated using different parameters like Damage D, Residual Elastic Modulus E(N), Number of cycles to initiate damage N0, and von Mises stress at the contact region.