This study deals with the numerical estimation of the fatigue life represented in the form of strength-life (S-N, or Wöhler) curves of metals with different crystallographic structures, namely body-centered cubic (BCC) and face-centered cubic (FCC). Their life curves are determined by analyzing the initiation of a short crack under the influence of microstructure and subsequent growth of the long crack, respectively. Micro-models containing microstructures of the materials are set up by using the finite element method (FEM) and are applied in combination with the Tanaka-Mura (TM) equation in order to estimate the number of cycles required for the crack initiation. The long crack growth analysis is conducted using the Paris law. The study shows that the crystallographic structure is not the predominant factor that determines the shape and position of the fatigue life curve in the S-N diagram, but it is rather the material parameter known as the critical resolved shear stress (CRSS). Even though it is an FCC material, the investigated austenitic stainless steel AISI 304 shows an untypically high fatigue limit (208 MPa), which is higher than the fatigue limit of the BCC vanadium-based micro-alloyed forging steel AISI 1141 (152 MPa).

For most engineering alloys, the long fatigue crack growth under a certain stress level can be described by the Paris law. The law provides a correlation between the fatigue crack growth rate (FCGR or da/dN), the range of stress intensity factor (ΔK), and the material constants C and m. A well-established test procedure is typically used to determine the Paris law constants C and m, considering standard specimens, notched and pre-cracked. Definition of all the details necessary to obtain feasible and comparable Paris law constants are covered by standards. However, these cost-expensive tests can be replaced by appropriate numerical calculations. In this respect, this paper deals with the numerical determination of Paris law constants for carbon steel using a two-scale model. A micro-model containing the microstructure of a material is generated using the Finite Element Method (FEM) to calculate the fatigue crack growth rate at a crack tip. The model is based on the Tanaka-Mura equation. On the other side, a macro-model serves for the calculation of the stress intensity factor. The analysis yields a relationship between the crack growth rates and the stress intensity factors for defined crack lengths which is then used to determine the Paris law constants.