Sebastian Schmitz

Optimal Reliability in Design for Fatigue Life

The failure of a component often is the result of a degradation process that originates with the formation of a crack. Fatigue describes the crack formation in the material under cyclic loading. Activation and deactivation operations of technical units are important examples in engineering where fatigue and especially low-cycle fatigue (LCF) play an essential role. A significant scatter in fatigue life for many materials results in the necessity of advanced probabilistic models for fatigue. Moreover, optimization of reliability is of vital interest in engineering, where with respect to fatigue the cost functionals are motivated by the predicted probability for the integrity of the component after a certain number of load cycles. The natural mathematical language to model failure, here understood as crack initiation, is the language of spatio-temporal point processes and their first failure times. This translates the problem of optimal reliability in the framework of shape optimization. The cost functionals derived in this way for realistic optimal reliability problems are too singular to be

Risk Estimation for LCF Crack Initiation

H^1

Probabilistic LCF Risk Evaluation of a Turbine Vane by Combined Size Effect and Notch Support Modeling

-lower semi-continuous as many damage mechanisms, like LCF, lead to crack initiation as a function of the stress at the components surface. Realistic crack formation models therefore impose a new challenge to the theory of shape optimization. In this work, we have to modify the existence proof of optimal shapes, for the case of sufficiently smooth shapes using elliptic regularity, uniform Schauder estimates and compactness of strong solutions via the Arzela-Ascoli theorem. This result applies to a variety of crack initiation models and in particular applies to a recent probabilistic model for LCF.

Minimal Failure Probability for Ceramic Design Via Shape Control

An accurate risk assessment for fatigue damage is of vital importance for the design and service of todays turbomachinery components. We present an approach for quantifying the probability of crack initiation due to surface driven low-cycle fatigue (LCF). This approach is based on the theory of failure-time processes and takes inhomogeneous stress fields and size effects into account. The method has been implemented as a finite-element postprocessor which uses quadrature formulae of higher order. Results of applying this new approach to an example case of a gas-turbine compressor disk are discussed.

A probabilistic model for LCF

A probabilistic risk assessment for low cycle fatigue (LCF) based on the so-called size effect has been applied on gas-turbine design in recent years. In contrast, notch support modeling for LCF which intends to consider the change in stress below the surface of critical LCF regions is known and applied for decades. Turbomachinery components often show sharp stress gradients and very localized critical regions for LCF crack initiations so that a life prediction should also consider notch and size effects. The basic concept of a combined probabilistic model that includes both, size effect and notch support, is presented. In many cases it can improve LCF life predictions significantly, in particular compared to \textit{E-N} curve predictions of standard specimens where no notch support and size effect is considered. Here, an application of such a combined model is shown for a turbine vane.

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

We consider the probability of failure for components made of brittle materials under one time application of a load, as introduced by Weibull and Batdorf-Crosse. These models have been applied to the design of ceramic heat shields of space shuttles and to ceramic components of the combustion chamber in gas turbines, for example. In this paper, we introduce the probability of failure as an objective functional in shape optimization. We study the convexity and the lower semi-continuity properties of such objective functionals and prove the existence of optimal shapes in the class of shapes with a uniform cone property. We also shortly comment on shape derivatives and optimality conditions.