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NTRODUCTION

MOST engine components are simultaneously subjected to thermal and mechanical boundary conditions, which lead to Thermo-Mechanical Fatigue (TMF). This is characterized by a significant plastic strain (ep) and relatively low number of cycles before failure.[1,2] One example is the diesel engine cylinder head, which for most heavy-duty trucks is casted of Compacted Graphite Iron (CGI) with vermicular graphite morphology.[3] The material is chosen in order to improve thermal conductivity, compared to spheroidal graphite iron, and to concurrently improve the mechanical behavior compared to flake graphite iron.[4,5] The Valve Bridge (VB) areas of a cylinder head are located between EDWIN A. LOPEZ-COVALEDA is with the Metals Science and Technology Group, EEMMeCS Department, Ghent University, Technologiepark 46, 9052 Ghent, Belgium and also with the Metal Processing group of the CRM GROUP, Technologiepark 48 B, 9052 Gent, Belgium. Contact e-mail: [email protected] SEPIDEH GHODRAT is with the Design Engineering Department, Faculty of Industrial Design Engineering, Delft University of Technology, Landbergstraat 15, 2628 CE Delft, The Netherlands. LEO A.I. KESTENS is with the Metals Science and Technology Group, EMMeCS Department, Ghent University and also with the Materials Science and Engineering Department, Delft University of Technology, Delft, The Netherlands. Manuscript submitted January 29, 2019.

METALLURGICAL AND MATERIALS TRANSACTIONS A

the couples of valve bores for exhaust and intake, facing the combustion chamber. In consequence, the areas are under thermal expansion and contraction during every engine start-up and shut-down cycle. Nevertheless, the positive thermal strain is mechanically restricted by the surrounding material leading to compressive stresses. Conversely, during cooling, thermal contraction is restricted, leading to tensile stresses in the VB. The cyclic combination of high-temperature compression and low-temperature tension is also known as Out of Phase (OP)-TMF.[3,6] The OP-TMF condition has been mimicked in laboratory setups, and simulated by numerical models. Examples of the former approach are reported by Collin,[7] Norman et al.[8] using cast iron, and Riedler et al.[9] using aluminum. These researchers studied the effect on the lifetime (Nf) of superimposed High Cycle Fatigue (HCF), associated with combustion cycles, to Low Cycle Fatigue (LCF), associated with engine start-up and shut-down cycles. The main conclusion was the identification of a threshold frequency of HCF significantly reduces the fatigue lifetime. Other researchers have developed numerical models to predict the TMF lifetime of cast irons, although the bonding between graphite and metallic matrix was generally ignored.[10–13] Such research describes cast iron as a matrix containing idealized voids. Pusch et al. [10] used this assumption to develop mathematical models for crack propagation in static and dynamic scenarios based

on measured fracture mechanics parameters. Ghodrat et al.[11,14] assume t