Ein Zuverlässigkeitsmodell für Titan-Aluminide zur Anwendung im Rahmen von multidisziplinären Optimierungen von Niederdruckturbinenschaufeln C. Dresbach, T. Becker, S. Reh, J. Wischek, S. Zur, C. Buske, T. Schmidt DLR e.V. R. Tiefers Access e.V. Werkstoff-Kolloquium 2017 05.12.2017 > WSK 2017 > C. Dresbach > 05.12.2017 DLR.de • Folie 1
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Ein Zuverlässigkeitsmodell für Titan-Aluminide zur ...€¦ · zur Anwendung im Rahmen von multidisziplinären Optimierungen von Niederdruckturbinenschaufeln . C. Dresbach, T. Becker,
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Ein Zuverlässigkeitsmodell für Titan-Aluminide zur Anwendung im Rahmen von multidisziplinären Optimierungen von Niederdruckturbinenschaufeln C. Dresbach, T. Becker, S. Reh, J. Wischek, S. Zur, C. Buske, T. Schmidt DLR e.V. R. Tiefers Access e.V. Werkstoff-Kolloquium 2017 05.12.2017
Fully automated process chain for multidisciplinary optimization (MDO) of a low pressure turbine blade made of γ-TiAl considering: - Aerodynamic - Castability - Structural mechanics - Reliability
Reduced size effect • Introducing a scaling exponent α after
Padgett1995* and Curtin2000**
• Uniaxial stress state • Constant stresses
• Needed enhancement of the model • multiaxial stress state • non-constant stresses • mesh independent
𝑃𝑃f = 1 − exp −𝑉𝑉𝑉𝑉0
𝛼𝛼 𝜎𝜎𝜎𝜎0
𝑚𝑚
mit 𝛼𝛼 = [0, 1]
modified size effect
* Padgett et al. (1995). Weibull Analysis of the Strength of Carbon Fibers Using Linear and Power Law Models for the Length Effect, Journal of Composite Materials 29, 14: 1873-1884
** Curtin, W. A. (2000). Tensile Strength of Fiber-Reinforced Composites: III. Beyond the Traditional Weibull Model for Fiber Strengths, Journal of Composite Materials 34, 15: 1301-1332
Normal stress criteria based on Weibull’s Weakest Link theory
• Principle of Independent Action (PIA)* model based on the principle stresses σj = [σ1, σ2, σ3 ]
• Normal Stress Averaging Method (NSA)* model based on an equivalent normal stress
* original model is described in: Nemeth et al., Lifetime Reliability Prediction of Ceramic Structures Under Transient Thermomechanical Loads, NASA/TP—2005-212505
Modified normal stress criteria based on Weibull’s Weakest Link theory
• Modified Principle of Independent Action (PIA)* model based on the principle stresses σj = [σ1, σ2, σ3 ]
• Modified Normal Stress Averaging Method (NSA)* model based on an equivalent normal stress
* original model is described in: Nemeth et al., Lifetime Reliability Prediction of Ceramic Structures Under Transient Thermomechanical Loads, NASA/TP—2005-212505
n := no of elements, nodes or integration points <σ> := σ for σ > 0 and <σ> := 0 for σ < 0
• Interfaces to the results of FE programs: • ANSYS • PERMAS • CALCULIX
• Element based reliability analysis and node based element integrations are possible with • Classical failure criteria for brittle fracture • Modified failure criteria with scalable size effect
• Lifetime consumption models for creep and fatigue loading
𝑝𝑝s,int = exp −𝑔𝑔 𝝈𝝈int 𝑉𝑉int with An integration degree of 5 with 15 integration points or a degree of 7 with 84 integration points per element are used (Williams et al., 2014).
A Gauss quadrature with an integration degree of 4 with 64 integration points per element is used.
• As-cast flat samples with high aspect ratios (like real LPT blades) with different stress concentrations: • Simple flat sample without notch (R0) • Flat sample with side notches of R=6mm (R6) • Flat sample with side notches of R=10mm (R10)
• Tensile tests for strength evaluation • Finite element model considering the real
geometry • Identifying the parameters using ARS method
in OptiSLang® • Good agreement using the adopted model
• As-cast flat samples with high aspect ratios (like real LPT blades) with different stress concentrations: • Simple flat sample without notch (R0) • Flat sample with side notches of R=6mm (R6) • Flat sample with side notches of R=10mm (R10)
• Tensile tests for strength evaluation • Finite element model considering the real
geometry • Identifying the parameters using ARS method
in OptiSLang® • Good agreement using the adopted model • Bad agreement using classical models
• As-cast flat samples with high aspect ratios (like real LPT blades) with different stress concentrations: • Simple flat sample without notch (R0) • Flat sample with side notches of R=6mm (R6) • Flat sample with side notches of R=10mm (R10)
• Tensile tests for strength evaluation • Finite element model considering the real
geometry • Identifying the parameters using ARS method
in OptiSLang® • Good agreement using the adopted model • Bad agreement using classical models • Fatigue parameters for R=0.1 & N=1e+6 were
• Cast Titanium-Aluminide shows a size effect in strength, which is smaller than the classical size effect for brittle materials
• Two classical reliability models were adopted to rebuild a scalable size effect
• The models were implemented in reliability assessment tool called HYPRA
• The model parameters were identified by an finite element based inverse parameter identification process
• It was possible to increase the efficiency and the reliability of a low pressure turbine blade using an automated multidisciplinary optimization toolbox
The authors kindly thank … • T. Becker, S. Sabet, K. Wilkinghoff and E. Breitbarth for assisting and
discussions relating the reliability model and the software development. • R. Nodeh-Farahani, U. Fuchs, D. Lütz and T. Merzouk for designing the
testing equipment and performing the mechanical experiments.
The study is founded by the German Federal Ministry of Economics and Technology embedded in the LuFo project TATT under founding code 20T1112B.
For further reading … • C. Dresbach et al., A Stochastic Reliability Model for Application in a Multidisciplinary Optimization of a Low
Pressure Turbine Blade Made of Titanium Aluminide. LAJSS (13), 2016, 2316-2332 • C. Buske et al., Distributed Multidisciplinary Optimization of a Turbine Blade Regarding Performance,
Reliability and Castability, ASME Turbo Expo 2016 • Wei-Sheng Lei, A generalized weakest-link model for size effect on strength of quasi-brittle materials, J