New probabilistic lifetime approaches for coarse grained Ni-base superalloys supplement current deterministic gas turbine component design philosophies; in order to reduce safety factors and push design limits. The models are based on statistical distributions of parameters, which determine the fatigue behavior under high temperature conditions. In the following paper, Low Cycle Fatigue (LCF) test data of several material batches of polycrystalline Ni-base superalloy René80 with different grain sizes and orientation distribution (random and textured) is presented and evaluated. The textured batch, i.e., with preferential grain orientation, showed higher LCF life. Three approaches to probabilistic crack initiation life modeling are presented. One is based on Weibull distributed crack initiation life while the other two approaches are based on probabilistic Schmid factors. In order to create a realistic Schmid factor distribution, polycrystalline finite element models of the specimens were generated using Voronoi tessellations and the local mechanical behavior investigated in dependence of different grain sizes and statistically distributed grain orientations. All models were first calibrated with test data of the material with random grain orientation and then used to predict the LCF life of the material with preferential grain orientation. By considering the local multiaxiality and resulting inhomogeneous shear stress distributions, as well as grain interaction through polycrystalline Finite Element Analysis (FEA) simulation, the best consistencies between predicted and observed crack initiation lives could be achieved.
Abstract. In the present work, theoretical approaches, based on grain orientation dependent Young's modulus and Schmid factor are used to describe the influence of local grain orientation on crack initiation behaviour of the coarse grained nickel base superalloy René80. Especially for strongly anisotropic crystal structures with large grain size, such as the investigated material, the local elastic properties must be taken into account for assessment of fatigue crack initiation. With an extension of Schmid's law, the resulting shear stress amplitude, which triggers local cyclic plastic deformation, can be calculated depending on local Young`s modulus and Schmid factor. A Monte Carlo simulation with 100,000 samples shows how random grain orientation affects these parameters. Furthermore, the product of Young`s modulus and Schmid factor (called E•m) is used as a parameter to determine how grain orientation influences resulting shear stress amplitude for given total strain amplitude. In addition to the theoretical work using that approach, this model is also validated using isothermal LCF experiments by determining local grain orientation influence on the crack initiation site using SEM-EBSD analyses.
Mechanical components that are exposed to cyclic mechanical loading fail at loads that are well below the ultimate tensile strength. This process is known as fatigue. The failure time, that is the time when a first crack forms, is highly random. In this work we review some recent developments in the modelling of probabilistic failure times, understood as the time to the formation of a fatigue crack.We also discuss the how probabilistic models can be used in shape design with the design intent of optimizing the component's reliability. We give review a recent existence result for optimal shapes and we discuss continuous and discrete shape derivatives. Another application is optimal service scheduling. The mathematical fields involved range from reliability statistics over stochastic point processes, multiscale modeling, PDEs on variable geometries, shape optimization and numerical analysis to operations research.
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