A new approach to estimate stress relaxation in a high strength steel wire using nanoindentation and finite element analysis

High-strength steel wires have been widely employed in the construction for long-span structures. Since highstrength steel wires are susceptible to stress relaxation, the investigation of stress relaxation in cable materials is the most important task. This work intends to use nanoindentation to estimate the relaxation rate of highstrength steel wires, which are sensitive to applied initial stress levels. First, Nanoindentation was conducted at several applied loads and a holding time of 1000 s to determine the relaxation rate during the holding time. Finite element analysis was then used to simulate the nanoindentation process to determine volume fraction of stress levels. Based on the information of volume fraction and relaxation rate from indentation testing, relaxation equations were well constructed, such as RE70% = 0.1603ln(t) + 1.5319, RE60% = 0.1664ln(t) + 1.4370, RE50% = 0.1350ln(t) + 1.3440, and RE40% = 0.1289ln(t) + 1.2395. These relaxation equations were used to estimate the relaxation rate for each stress level of the von Mises stress state underneath the indenter tip. To demonstrate the accuracy of proposed methodology, stress relaxation experiments were then performed at different stress levels of 0.7fu, 0.6fu, 0.5fu, and 0.4fu. All the relative errors for three initial stress cases were less than 5% indicating that relaxation rates from the proposed method are correct and reliable. The results from this study can be used to predict values of relaxation rate of high-strength steel wires subjected to initial applied stress levels using nanoindentation. The novelty of this work is the use of nanoindentation technology in the estimation of the relaxation rate to reduce the time and cost of the experiment.