Minimal failure probability for ceramic design via shape control

We consider the probability of failure for components made of brittle mate- rials under one time application of a load as introduced by Weibull and Batdorf - Crosse and more recently studied by NASA and the STAU cooperation as an objective functional in shape optimization and prove the existence of optimal shapes in the class of shapes with a uniform cone property. The corresponding integrand of the objective functional has convexity properties that allow to derive lower-semicontinuity according to Fujii (Opt. Th. Appl. 1988). These properties require less restrictive regularity assumptions for the boundaries and state functions compared to [arXiv:1210.4954]. Thereby, the weak formulation of linear elasticity can be kept for the abstract setting for shape optimization as presented in the book by Haslinger and Maekinen

Probabilistic Analysis of LCF Crack Initiation Life of a Turbine Blade under Thermomechanical Loading

An accurate assessment for fatigue damage as a function of activation and deactivation cycles is vital for the design of many engineering parts. In this paper we extend the probabilistic and local approach to this problem proposed in [1,2] and [3] to the case of non-constant temperature fields and thermomechanical loading. The method has been implemented as a finite element postprocessor and applied to an example case of a gas-turbine blade which is made of a conventionally cast nickel base superalloy.Comment: 8 pages, 3 figure

Effect of local anisotropy on fatigue crack initiation in a coarse grained nickel-base superalloy

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 Ren\'e80. 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 $E\cdot m$) 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.Comment: 8 pages, 8 figure

A Probabilistic Model for LCF

Fatigue life of components or test specimens often exhibit a significant scatter. Furthermore, size effects have a non-negligible influence on fatigue life of parts with different geometries. We present a new probabilistic model for low-cycle fatigue (LCF) in the context of polycrystalline metal. The model takes size effects and inhomogeneous strain fields into account by means of the Poisson point process (PPP). This approach is based on the assumption of independently occurring LCF cracks and the Coffin-Manson-Basquin (CMB) equation. Within the probabilistic model, we give a new and more physical interpretation of the CMB parameters which are in the original approach no material parameters in a strict sense, as they depend on the specimen geometry. Calibration and validation of the proposed model is performed using results of strain controlled LCF tests of specimens with different surface areas. The test specimens are made of the nickel base superalloy RENE 80.Comment: 20 pages, 6 figure

Hohe Bildungsrenditen durch Vermeidung von Arbeitslosigkeit

Bildungsinvestitionen sind für den Einzelnen mit einem höheren Erwerbseinkommen und einem geringeren Arbeitslosigkeitsrisiko im Lebenszyklus verbunden. Eine Analyse auf Basis von Erwerbsbiografien des Sozio-oekonomischen Panels (SOEP) zeigt, dass die private Bildungsrendite, also der persönliche finanzielle Nutzen, unterschätzt wird, wenn man das durch Bildung gesunkene Arbeitslosigkeitsrisiko ignoriert. Die durchschnittlichen privaten und fiskalischen Bildungsrenditen liegen in Deutschland über der Verzinsung auf Investitionen in Realkapital. Bildungsinvestitionen erscheinen sowohl für den Einzelnen als auch für die Gesellschaft sinnvoll. Eine Ausweitung der staatlichen Bildungsfinanzierung würde also aus fiskalpolitischer Sicht Sinn ergeben, wie auch eine stärkere private Beteiligung an den Ausbildungskosten im tertiären Bildungsbereich. Voraussetzung dafür sind geeignete Modelle der Studierendenfinanzierung, etwa durch Stipendien oder Darlehen.Private returns to education, Fiscal returns, Unemployment