A finite element study of tessellated thermal stresses around inclusions and their effect on fatigue

Production processes of steel are constantly developing and currently steel industry is able to produce high-quality steels with excellent strength and hardness for demanding applications. However, without expensive fatigue tests, it is difficult to estimate the fatigue strength of these high-quality steels. The fatigue limit of these steels is complex to estimate because of inclusion-induced fatigue fractures. Inclusions in high-purity steels have little influence on easy-to-measure properties like hardness, tensile strength or yield strength, but they tend to control the fatigue strength of these materials. Inclusions in steels act as initial flaws or cracks, from which fatigue fractures can originate. There are various inclusion types found in steel of different shapes, sizes and material properties. The aim of this thesis is to numerically evaluate the effect of the difference in the thermal expansion coefficients between the inclusion and the matrix on fatigue fracture. During steel production processes such as quenching or heat treatment the difference in thermal expansion coefficients may induce tessellated thermal stresses. Other mechanical features studied include, frictional contact between the inclusion and the matrix, and cracking of the inclusion itself. In the theory section of this study basic concepts of linear elastic fracture mechanics and fatigue crack growth are introduced. The effects of inclusions on fatigue limit of high-strength steel and empirical modelling of these effects are reviewed. The properties of inclusions and their effect on the fatigue strength are also described. In the analysis portion of this thesis, finite element models are formulated to enable the computation of stress intensity factor for a crack assumed to initiate on the equatorial plane of a spherical inclusion. The crack is assumed to propagate into the steel matrix. Four inclusion configurations are analyzed: an aluminium oxide inclusion, a pore simulating a sulfide inclusion, a cracked aluminium oxide inclusion, and a duplex inclusion i.e., an aluminium oxide inclusion within a thin sulfide envelope. All the material models used are elastic and the material parameters are taken from the literature. It was discovered that the stress intensity factor values were sensitive to the magnitudes of the tessellated thermal stresses, friction between the inclusion-matrix interface and cracking of the inclusion itself. Increasing thermal misfit, i.e., the thermal expansion coefficient of the inclusion is smaller than that of the steel matrix, and the increasing friction between the inclusion and the matrix reduces the values of stress intensity factor at the crack tip. Furthermore, a cracked inclusion showed higher stress intensity factor values than intact inclusion. The stress intensity factor values for four models from the highest to lowest were: pore, cracked aluminium oxide inclusion, duplex inclusion and intact aluminium oxide inclusion. The sulfide envelope of duplex inclusion reduces tessellated thermal stresses around inclusion leading to higher stress intensity values at the crack tip compared to pure aluminium inclusion