# Fatigue Life Assessment in Bainitic Steels Based on The Cumulative Strain Energy Density
## 1 Introduction  
Diminishing fuel consumptions and mandatory lower CO\({}_{2}\) emissions are both pushing the automotive industry to weight reduction in the design of cars and increasing the use of railway transportation of goods and people. Therefore, to achieve those goals, recently advanced high-strength steels are currently being used to reduce components' thicknesses in the automotive industry and to produce improved railway rails and crossings.  
In fact, carbide-free bainitic steels are an example of these new materials which show an excellent combination of strength, ductility and toughness that satisfies demands of high-strength steels in various industrial applications [1, 2]. Moreover, bainite covers some different microstructures, from the classical upper and lower bainite to the carbide-free structures found in lower carbon steels [3], and is produced from the transformation of austenite at temperatures below the pearlite range and above the martensite starting temperature [4]. In the production of bainitic steel, it is paramount that perlite and ferrite regions be pushed as far to the right as possible on the continuous cooling transition diagram to allow for bainitic formation, and alloying elements such as nickel, molybdenum, manganese and chromium are selected for this purpose [4]. Besides, the high silicon content of 1.3 wt% suppresses theformation of brittle cementite from austenite during bainitic transformation [5], and the addition of Al alloying element also decreases hydrogen embrittlement [2]. Similar to Si, Al suppresses cementite precipitation [6] and consequently produces a carbide-free bainitic microstructure--referring to the absence of cementite in between bainitic ferrite laths [5], which improves the toughness and rolling contact fatigue (RCF) resistance of the steels, also crucial for sustainable material design [5].  
Concerning the loadings, automotive components and railway rails are being subjected to very complex and demanding loadings, requiring suitable bainitic steels with high yield strength to avoid severe plastic deformation, high toughness, strain hardening capability, and wear resistance, and improved RCF properties [7] in order to avoid, as much as possible, the nucleation and growth of fatigue cracks. Moreover, dynamic cyclic loadings are frequently applied; hence, low-cycle and high-cycle fatigue regimes are worth investigating [8; 9], since improved fatigue life has a significant effect on safety, reliability and profitability. Additionally, fatigue crack growth rates in bainitic steels are revealed to be lower than in traditional pearlitic rail steels [10].  
Therefore, the influence of Mn content in the cyclic mechanical properties of bainitic steels is of great importance to developing durable components. In this paper, three high-strength bainitic steels were studied. Elastic and plastic strain energy densities were calculated during the entire life of the specimens tested under fully reversed strain-controlled conditions and were associated with the resilience and fatigue toughness of the tested materials. Finally, fatigue life was evaluated by means of a cumulative strain energy density model and the predictions were compared to those obtained via the well-known SWT and Liu criteria.