## 1 Introduction  
Wheels are critical parts for the safety and reliability of land vehicles. They are subjected to cyclic loads in service, which can generate fatigue phenomena in the most stressed points, leading to cracks, nucleation, and development until failure if the component is not properly designed. For that reason, wheels are usually tested by manufacturers or independent laboratories to assess their durability according to industrial standards [1]. Both in the automotive and in the off-highway industry, some test standards have been defined by technical organizations such as, for example, EUWA (Association of European Wheel Manufacturers [2]) and SAE (Society of Automotive Engineers [3]). Generally, test standards target specific vehicle applications, but they are mainly based on two kinds of tests: the dynamic radial fatigue test and the dynamic cornering fatigue test. The former is used to assess the fatigue strength of the rim component by pushing the type and wheel assembly against a rotating drum at a certain radial load [4] (Figure 1a). The latter simulates the effects of lateral loads, which arise in service, during vehicle turning, on the wheel disc by submitting it to a rotating bending moment [5] (Figure 1b). A further test, which combines both radial and lateral load conditions, has been developed through a remarkable work by LBF-Germany [6, 7]. It is known as the biaxial fatigue test and is mainly used in the automotive industry. All these tests are usually conducted at constant amplitude loads, which are calculated multiplying the wheel rated load, specified by the vehicle manufacturer, by an accelerated test factor. This factor depends on both the vehicle application and the test standard of reference, but it is generally included in a value range between 1.3 and 2.5 [8]. It is important to reduce fatigue test times, however, this can lead to a situation where the test load is too high for the durability of tyres or even test machine fixtures. For example, a premature wear of the tyre can make it impossible to finish the test in reasonable time and with acceptable cost. That is the reason why, for many years, researchers have been trying to develop analytical and numerical models, based on the finite element method analysis (FEA), to simulate fatigue test conditions and assess wheel durability, reducing or avoiding physical tests [5; 9; 10; 11; 12]. Alternative approaches to predict the fatigue life of structural components are based on strain acquisitions, by means of proper sensors, during field tests of vehicles in real working conditions. Similarly, forces and moments acting on wheels can be acquired through special devices such as wheel force transducers (WFT) [13] and can then converted to stresses and strains by FEA. Data recorded can be analyzed, in a time or frequency domain [14; 15; 16], to estimate the fatigue life of the component in case the standard durability tests are not feasible. In any of the alternative methods, reliable fatigue properties of the material are fundamental for an accurate evaluation of the durability of the components, as pointed out in [13; 14]. For that reason, the material properties should also consider the effect of the production process on the surface condition from the point of view of roughness, residual stresses, and potential local work hardening induced by plastic deformations. Some of these aspects are highlighted, for example, in [17; 18; 19; 20] for an automotive wheel disc and in [21] for an automotive wheel rim. The topic of properly designing against fatigue is essential for the reliability and safety of vehicles, especially considering the increasing request of reducing their fuel and energy consumption. To achieve this target, in fact, designers have continuously been working on the weight reduction of components [22]. This underlines the importance of improving the knowledge of fatigue-related phenomena, which are still the main cause of failure for structural components in the modern industry.