# Creep-Fatigue Behavior and Life Prediction of Medium-Si-Mo Ductile Iron
## 1 Introduction  
In recent years, the increasing demand for higher power output and fuel efficiency in internal combustion engines has led to more severe operating conditions for exhaust components. Repeated engine starts and shutdowns coupled with the exhaust manifold's self-constraint induce plastic strain in the manifold, causing fatigue damage [1, 2, 3, 4]. Furthermore, prolonged exposure to high temperatures results in creep relaxation, causing creep damage. The synergistic effect of these two damage mechanisms under harsh high-temperature operating conditions can easily lead to localized failure of the exhaust manifold. Therefore, to accurately assess the service life duration of exhaust components, a comprehensive understanding of the material's mechanical behavior and lifetime characteristics is essential [5].  
Nodular cast iron (also known as ductile cast iron) is the most widely used material in the design and manufacture of exhaust systems. In practice, extensive studies have been conducted on the low-cycle fatigue behavior and microscopic mechanisms of various types of ductile iron [6, 7, 8, 9, 10, 11]. [PERSON] et al. [12] conducted low-cycle fatigue (LCF) tests on high-strength compacted graphite cast iron at multiple temperatures. Through systematicanalysis of cyclic characteristics and comparative evaluation of extensive fatigue data, they developed a life prediction methodology for this material by integrating energy-based approaches with damage mechanism analysis. [PERSON] et al. [13] elucidated the effect of notches on the fatigue life of ductile iron by analyzing the combined influence of the microstructure and stress triaxiality. Based on this mechanistic understanding, the author proposed a modified Manson-Coffin-Basquin equation incorporating triaxiality effects. [PERSON] et al. [14] focused on comparative analysis of low-cycle mechanical behavior and fatigue life at elevated temperatures with varying silicon molybdenum contents. [PERSON] et al. [15] suggested that the traditional Manson-Coffin criterion is insufficiently accurate for predicting non-isothermal thermal fatigue in silicon molybdenum ductile iron and proposed that the energy dissipation method is more suitable. However, their study raised the unresolved question of whether creep damage can be characterized by energy dissipation. It is evident that the majority of ductile cast iron research has primarily focused on investigating fatigue behavior and lifetime characteristics, while studies examining fatigue performance under combined creep-fatigue conditions remain relatively scarce.  
This study focused on medium-silicon molybdenum ductile iron (QTRSi4 Mo) as its research subject. QTRSi4 Mo is a critical material for manufacturing exhaust components used in internal combustion engines. Its exceptional properties, including high strength, oxidation resistance, and growth resistance [16; 17], enable exhaust manifolds to operate at temperatures exceeding 700 \({}^{\circ}\)C [18; 19]. Compared to conventional ferritic ductile iron, it exhibits superior strength and deformation resistance. In this research, low-cycle fatigue (LCF) testing was performed on specimens of the target material across multiple temperature conditions, with comprehensive characterization and analysis of its fatigue behavior. On this basis, hold time was incorporated into the fatigue tests and combined with creep test data to investigate creep-fatigue interaction behavior. The existing literature has demonstrated the superiority of strain-based or energy-based approaches to fatigue life assessment [20]. Building on the energy methods, this study integrated the inelastic strain energy density dissipation method with the net tensile hysteresis energy method to characterize creep-fatigue damage, enabling the prediction of the material's comprehensive lifetime under corresponding operating conditions. This research provides valuable support for the durable design and life prediction of exhaust components of internal combustion engines.