# Fatigue Life Prediction of Radial Tire Bead Using a Maximum Strain Energy Density Range Method
## 1 Introduction  
As the only contact component between a vehicle and the road, the tire has an important influence on the operating characteristics of a vehicle. The durability of tire performance is one of the most important indicators for evaluating vehicle safety performance. In addition, if the tires have premature fatigue failure from market feedback, it will also affect the reputation and economic benefits of tire manufacturers. In recent years, as the energy crisis has increasingly become a global issue, tire durability problems have been magnified in the tire industry [1]. Therefore, a method to evaluate the durability of a tire is of great importance.  
The finite element analysis method to predict tire performance has been used widely. Many scholars and experts have done a lot of scientific research on tire fatigue simulation. [PERSON] et al. [2] used the cracking energy density (CED) proposed by [PERSON] [3] and virtual crack [PERSON] technology (VCCT) to calculate the energy release rate of the crack. The fatigue life for tires was predicted by using Paris' law. [PERSON] et al. [4] computed local crack driving forces from strain history loads, obtained via the cracking energy density (CED) fatigue predictor with a finite element method, to predict the fatigue life of the components of an off-the-road (OTR) tire. [PERSON] [5] applied a deterministic analysis method to evaluate the fatigue life of the tire [PERSON] on the basis of finite element analysis, and proposed a probabilistic analysis method by the Monte Carlo simulation of test statistics to predict the life. The results are consistent with each other. [PERSON] [6] utilized the finite element method and combined the average response analysis method to explore the influence of the bead reinforcement layer on tire durability. Based on the results, the structure of tire bead for the formula racing tire was optimized and the expected effect was achieved.  
From a survey of the literature, the research on tire durability finite element analysis and prediction methods primarily uses stress, strain, and energy [7, 8], or is combined with fracture mechanics to predict the actual fatigue life [9, 10]. Indoor durability testing hasbeen used to evaluate the durability of a tire; however, this method is still time-consuming. Moreover, even for some ultra-large tires, the size and weight make them unsuitable for drum endurance tests. In order to shorten the development period and improve the quality of tires, it is necessary to develop a reliable and valid approach to predict the fatigue life for the bead region of tires.  
The aim of this paper is to propose a method that applies the finite element method and the fatigue life equation of bead rubber compounds to predict the fatigue life of indoor durability testing of tires. In this process, a new fatigue parameter--maximum strain energy density range--was presented to analyze fatigue characteristics, and a controlling factor of durability for the tire bead was suggested. Compared with experimental results, this method has good correspondence with predicting fatigue life.