The prediction of damage mechanisms, such as fatigue in e.g. piping, requires the consideration of the microstructure because crack initiation starts at the grain level. Therefore, it is important to know the local strain/stress state, which due to the misorientation of neighboring grains, can reach significantly higher values than the nominal (macroscopic) ones. A finite element model for the calculation of stresses and strains as well as the formation of crack networks, based on the measured anisotropic microstructure of austenitic stainless steel, was developed at Paul Scherrer Institut (PSI). This mesoscale model (SNF) uses the sizes and crystallographic orientations of the grains, measured with 2- or 3-dimensional electron backscatter diffraction (EBSD) to generate a representative volume element (RVE) of the material. The anisotropic elastic properties and the anisotropic plastic behavior of each single crystal of the RVE, defined through the evolution of shear deformation in the slip plane with the highest Schmid factor, is considered. The corresponding single crystal properties have been preliminary determined by a standard tensile test followed by an inverse analysis procedure (Levenberg-Marquardt algorithm).
The SNF code uses a four-parameter damage model for crack initiation and growth and is based on the accumulated inelastic hysteresis energy. Besides the calculation of local stresses and strains in the microstructure, this model allows the calculation of high (HCF) and low cycle fatigue (LCF) lifetime and to perform sensitivity studies, e.g. to analyze the influence of grain sizes and orientation or multiaxial loading on the stress-strain curves.
The local strains in the microstructure, calculated by the SNF model, were validated by the crystal plasticity finite element (CPFEM) code CAPSUL and by measurements with a digital image correlation system (DIC). Good agreement between strains evaluated with these three different methods was observed up to nominal strains of about 4%. The analyses have shown that local strains can be up to a factor 2 higher than the applied global strain.
Furthermore, aspects such as the influence of 2D or 3D EBSD data and the approximation with corresponding columnar, synthetic or real grain geometries with finite elements (FE) on the accuracy of the calculated strains are also discussed.