Modeling for Damaged-based Fatigue Life Assessment of Steel Wire Ropes

Abstract

This thesis presents the development of fatigue model based on damage mechanics approach. The model has been developed using the two-scale Lemaitre model for quasi-brittle material considering the plasticity at the microscale and elasticity on the mesoscale. The residual Young’s modulus of the drawn steel wire is considered in the damage model. Material properties of the drawn steel wire have been found out using tensile testing. These properties include the yield strength, ultimate tensile strength, modulus of elasticity. The fatigue testing of the drawn wire has been done to find out the residual Young’s modulus by doing quasi static test after certain load block cycles. The residual Young’s modulus for different stress levels and load ratios are combined to form unified curve. The S-N curve for the drawn steel wire are formed after recording the number of cycles to fracture at different stress levels for typical load ratio R=0.1. another relation between the life parameter and number of cycles to failure is established. The life parameter encompasses the amplitude and mean stresses at different tests. The two curves help in determining the residual Young’s modulus at each material point in the FE environment subjected to different amplitude stress and mean stresses which further input in the damage model to find the damage at each loading cycle. A computational framework has been developed for the implementation of the model in Abaqus FEA software. The damage model considering the residual Young’s modulus along with newly introduced load cycle block procedure were implemented through user defined UMAT subroutine. The model is used to study the fretting damage characteristics as predicted by the model. The cross-wire model consists of two elastic wires pressing each other at angle equivalent to the lay angle of wire rope. the cross-wire model is validated through comparison of the analytical and FE contact pressure distribution. The boundary conditions were selected in order to induce two different slipping regimes (partial slipping and gross slipping regimes) at the contact region. The gross slipping conditions includes the contact load of 25 N, 50 N and 100 N with the application of bulk load of 1 kN, 2 kN and 3 kN using the coefficient of friction of 0.2. The partial slipping condition include 100 N contact load with bulk load of 1 kN, 600 N and 200 N using the coefficient of friction of 0.8. The simulation results reveal that surface damage occurs in the slipping region in both the conditions. In the gross slip conditions, damage occurs in the central portion ranges from (-0.4 mm - -0.25mm) at left side of contact center to (-0.45mm – 0.38 mm) exists on both vi sides of the contact center and in the partial slip conditions it is the annulus region which damaged. In 200 N bulk load case the extreme edges got damaged due to the reduction of tangential load however in 600 N bulk load case the annulus region approaches toward the center due to increase of the tangential load. The damage initiation strongly depends on the residual Young’s modulus. The damage initiated starts where the residual Young’s modulus is minimum. The damaged area resembles the experimental morphologies of the wires fretting against each other inside the wire rope. The UMAT Subroutine is implemented on wire rope as fretting fatigue phenomenon is prominent due to presence of micro slippage between the outer and central wire. Similarly stress concentration also exist at the contact region between the central and outer wires. Two frictional conditions were considered to study the characteristics of damage in relative two different slip conditions. The cross-sectional view of critical section where damage is maximum is investigated. The von Mises stress distribution of the cross-section along with damage initiation and propagation with the passage of cycle is obtained for two coefficients of friction i.e. 0.2 and 0.8. The damage initiation occurs at the contact region where von Mises stresses are higher and progress in the surrounding region until the whole core wire damaged. The model indicates that damage is more localized in high frictional conditions relative to the lower frictional condition. The longitudinal distribution of the damage reaches critical value is 2.5 times less in higher friction case. The damage rate of the critical elements in the contact region is linear in the beginning and then reduces in the lateral stages of damage evolution due to reduction in stresses. The contact pressures are found to reduce at higher rate of 48.3 % for the lower frictional condition, while it reduces to the 37.2 % at higher frictional condition at the most critical element. The dependence of residual modulus is also observed as the damage occurs in the region where the residual modulus is minimum. The residual Young’s modulus decreased to 2.54 % in higher coefficient of friction case and to 95 % at one of the critical elements in lower coefficient of friction case at the central node of the contact. The fretting fatigue damage model is validated through mechanics of deformation of steel wire rope and experimental findings. The fretting mechanism is also conformed with Ruiz Criterion which is used to identify the potential area of crack nucleation