Roland Mücke

A constitutive model for anisotropic materials based on Neuber’s rule

Phenomenological approaches to fatigue damage prediction often rely on the assessment of local stress–strain concentrations in structural components. To avoid complex plastic analysis in fatigue assessment, approximate constitutive models have been developed to evaluate the local inelastic response of the material and which allow for an adequate lifetime prediction in a competitive time. One of these approximate methods is the Neuber rule, which has originally been elaborated for the uniaxial loading state of isotropic materials. This paper addresses an approximate method for multiaxial loading of anisotropic materials. The proposed approach is based on a tensorial formulation of the Ramberg–Osgood equation and a generalization of the uniaxial Neuber hypothesis by assuming the equivalence of the deviatoric strain energy density for the elastic and inelastic solution in the notch region. After a decomposition of the stress tensor into a normalized direction tensor and a stress invariant, a nonlinear expression is obtained which can be iterated for the unknown inelastic stress state. It is shown that the proposed anisotropic Neuber rule includes the multiaxial isotropic and the classical uniaxial formulation as special cases. Furthermore, aspects of parameter identification are discussed for directionally solidified Nickel-based superalloys with transverse isotropic properties and single crystal materials with cubic anisotropy. Two numerical examples demonstrate the applicability of the proposed approach.

A lifetime prediction procedure for anisotropic materials

In the paper the well-known strain- and stress-based approach to cyclic fatigue assessment of isotropic materials is extended towards anisotropic structures. The methodology is considered in detail for transverse isotropy, as it occurs in directionally solidified materials. Some remarks on cubic anisotropy for single-crystal applications are given as well. Using a modified HILL approach to describe the anisotropic failure surface, the HILL parameters, which are a function of the actual loading, are expressed in terms of the parameters of the failure laws for independent material axes. Finally, the procedure is verified by experiments in additional directions showing that the experimental results fit well the results of computational anisotropic failure assessment. Copyright

Probabilistic Lifetime Prediction of Thermal Barrier Coating Systems Depending on Manufacturing Scatter

The assessment of Bondcoat/Thermal barrier coating systems is an inherent part of the lifing process of gas turbine component. On the one hand, coatings are considered in the constitutive modelling — e.g. in the thermal model and for the prediction of eigenfrequencies of gas turbine blades. On the other hand, the influence of the coating system on the lifetime of the part (target cyclic life and target operation hours) needs to be assessed. This paper addresses the prediction of coating lifetime. Lifing models of Bondcoat/Thermal barrier coating systems (BC/TBC) are commonly built using isothermal furnace cyclic tests (FCT). The lifetime of the BC/TBC under such test conditions has been shown to depend on multiple coating parameters like TBC thickness, TBC porosity, BC thickness, BC roughness, and also on testing temperature. For example, the TBC life (defined as time to partial TBC spallation) is reduced with increasing temperature, with increasing TBC thickness and decreasing porosity and BC roughness. When operating in a gas turbine (GT), the TBC surface temperature and the BC temperature depend on engine operating conditions, heat transfer of combustion gas and cooling air, coating microstructure and thickness. For instance, a TBC with high porosity typically demonstrates a lower thermal conductivity than that with low porosity. For otherwise same boundary conditions, the BC temperature will decrease with increasing TBC porosity and increasing TBC thickness. The benefit of having a high coating porosity observed in FCT is further amplified by its impact on reducing the BC temperature in GT operation. To the contrary, the positive impact of a reduced TBC thickness observed in FCT is reduced by its negative impact on an increased BC temperature during GT operation. Taking these effects into account a probabilistic lifing model is proposed based on Monte Carlo simulations. Using this model the impact of the manufacturing scatter on the BC/TBC life can be assessed, and enables improved manufacturing by focusing on those parameters that are most critical for coating lifetime.Copyright

A Mathematical Framework for Cyclic Life Prediction of Directionally Solidified Nickel Superalloys

Modern gas turbines utilize single crystal (SX) and directionally solidified (DS) nickel superalloys which hold a higher cyclic life resistance and an improved creep rupture strength compared to their conventionally cast (CC) version. Both, SX and DS materials feature a significant direction dependence of material properties, which needs to be considered in the constitutive and lifing models. In this context, the paper presents a mathematical framework of cyclic life prediction. Although the method is developed for DS nickel alloys with transverse isotropic material behaviour, a generalisation to common orthotropic materials inclu¬ding SX is straightforward. The proposed procedure is validated by two examples. Moreover, an application to turbine components is shown.

A Viscoplastic Modeling Approach for MCrAlY Protective Coatings for Gas Turbine Applications

MCrAlY coatings are applied in industrial gas turbines and aircraft engines to protect surfaces of hot gas exposed components from oxidation and corrosion at elevated temperature. Apart from oxidation resistance, coatings have to withstand cracking caused by cyclic deformation since coating cracks might propagate into the substrate material and thus limit the lifetime of the parts. In this context, the prediction of the coating maximum stress and strain range during cyclic loading is important for the lifetime analysis of coated components. Analyzing the state of stress in the coating requires the application of viscoplastic material models. A coupled full-scale cyclic analysis of substrate and coating, however, is very expensive because of the different flow characteristics of both materials. Therefore, this paper proposes an uncoupled modeling approach which consists of a full-scale cyclic analysis of the component without coating and a fast post-processing procedure based on a node-by-node integration of the coating constitutive model. This paper presents different aspects of the coating viscoplastic behavior and their computational modeling. The uncoupled analysis is explained in detail and a validation of the procedure is addressed. Finally, the application of the uncoupled modeling approach to a coated turbine blade exposed to a complex engine start-up and shut-down procedure is shown.© 2008 ASME