Ein Zuverlässigkeitsmodell für Titan-Aluminide zur ...€¦ · zur Anwendung im Rahmen von...

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

Goal

Fully automated process chain for multidisciplinary optimization (MDO) of a low pressure turbine blade made of γ-TiAl considering: - Aerodynamic - Castability - Structural mechanics - Reliability


Titanium Aluminide Turbine Toolbox (TATT) (LuFo IV, 2012-2017)

DLR BT Structural mechanics

DLR WF Reliability

DLR SC Fully automated

process chain

DLR AT Aerodynamic

Access Castability

Outline of this talk

• γ-Titanium-Aluminide

• Experimental Results

• Modified Failure Criterion

• Parameter Identification

• Multidisciplinary Optimization of a LPT Blade


Titanium Aluminide Turbine Toolbox (TATT) (LuFo IV, 2012-2017)

DLR BT Structural mechanics

DLR WF Reliability

DLR SC Fully automated

process chain

DLR AT Aerodynamic

Access Castability


γ−Titanium−Aluminide

• (New) material class for low pressure turbine (LPT) blades in jet engines

• Good resistance against oxidation and corrosion • High specific modulus and strength at temperatures up

to 850°C • Low density (3.9 – 4.3g/cm3) direct weight reduction

of 50% compared to Nickel blades lower centrifugal forces lower disk weight less fuel consumption

• Low ductility and toughness at room temperature are critical for reliable design

Source: Access e.V.

Source: MTU Aero Engines


γ−Titanium−Aluminide

Investigated material • Ti-48Al-2Cr-2Nb (GE 48-2-2) • Processed by investment casting followed by hot

isostatic pressing • Intermetallic alloy (not pure metallic bonding) of

Ti and Al consisting of … • the hexagonal α2 (Ti3Al) Phase • and the tetragonal γ (TiAl) Phase

• Duplex microstructure of… • globular γ grain • α2 / γ lamellar grains

α2 (Ti3Al) γ (TiAl)

Ti Al


Experimental Results

Results of tensile test show… • a small amount of plasticity (1%) • significant scatter in initial yield stress

and strength


Experimental Results

Results of tensile test show… • a small amount of plasticity (1%) • significant scatter in initial yield stress

and strength • a size effect in strength (the bigger the

sample the smaller the strength), which is smaller than predicted by the weakest link theory for brittle materials

𝑃𝑃f = 1 − exp −𝑉𝑉𝑉𝑉0

𝜎𝜎𝜎𝜎0

𝑚𝑚

𝜎𝜎0 charaterictic strength 𝑚𝑚 Weibull modulus 𝑉𝑉0 Reference Volume

classical size effect


Modified Failure Criterion

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


Modified Failure Criterion Multiaxial Extension

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

multiaxial stresses

𝑃𝑃f = 1 − exp −� 𝑔𝑔 𝝈𝝈 d𝑉𝑉𝑉𝑉

𝑔𝑔 𝝈𝝈 = �𝜎𝜎j𝜎𝜎0

𝑚𝑚1𝑉𝑉0

3

j=1

𝑔𝑔 𝝈𝝈 = (2𝑚𝑚 + 1)𝜎𝜎n𝜎𝜎0

𝑚𝑚 1𝑉𝑉0

with 𝜎𝜎n𝑚𝑚 =2𝜋𝜋� 𝜎𝜎n𝑚𝑚 sin 𝛼𝛼 d𝛽𝛽d𝛼𝛼

𝜋𝜋2�

0


Modified Failure Criterion Multiaxial Extension

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

multiaxial stresses non-constant stress distribution, mesh independent

𝑃𝑃f = 1 − exp −� 𝑔𝑔 𝝈𝝈 d𝑉𝑉𝑉𝑉

𝑔𝑔 𝝈𝝈 = �𝜎𝜎j𝜎𝜎0

𝑚𝑚 𝑉𝑉eff,j𝑉𝑉0

𝛼𝛼 1𝑉𝑉eff,j

3

j=1

𝑉𝑉eff,j = �𝜎𝜎j,i𝜎𝜎max

𝑚𝑚

𝑉𝑉i

𝑛𝑛

i=1

with

𝑔𝑔 𝝈𝝈 = (2𝑚𝑚 + 1)𝜎𝜎n𝜎𝜎0

𝑚𝑚 𝑉𝑉eff𝑉𝑉0

𝛼𝛼 1𝑉𝑉eff

𝑉𝑉eff = �𝜎𝜎n𝑚𝑚i

max (𝜎𝜎n𝑚𝑚)𝑉𝑉i

𝑛𝑛

i=1

with 𝜎𝜎n𝑚𝑚 =2𝜋𝜋� 𝜎𝜎n𝑚𝑚 sin 𝛼𝛼 d𝛽𝛽d𝛼𝛼

𝜋𝜋2�

0


Modified Failure Criterion Reliability Postprocessor

• Python based postprocessor tool

• 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

• Vtk export of the results for visualization

HYbridPRobabilisticAnalysis


Modified Failure Criterion Reliability Postprocessor

Realization of volume integration

Evaluation of element mean stresses Element integration based based on nodal stresses

𝑝𝑝s,elem = exp −𝑔𝑔 𝝈𝝈s,elem 𝑉𝑉elem

𝑃𝑃f,comp = 1 − exp −� 𝑔𝑔 𝜎𝜎 d𝑉𝑉𝑉𝑉

= 1 − �𝑝𝑝s,elem(𝑖𝑖)l

i=1

𝑝𝑝s,elem = exp − � det 𝐽𝐽(𝑠𝑠, 𝑡𝑡, 𝑟𝑟) 𝑔𝑔 𝝈𝝈int(𝑠𝑠, 𝑡𝑡, 𝑟𝑟) d𝑠𝑠d𝑡𝑡d𝑟𝑟1

−1

𝑝𝑝s,elem = �𝑝𝑝s,int(j)p

j=1

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.

Hexaeder

Tetraeder


Parameter Identification

• 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

NSA

σ0 = 381.7 m = 28.1 α = 0.74

R6 R10 R0

min 𝐹𝐹exp 𝜎𝜎n − 𝐹𝐹sim 𝜎𝜎n

http://www.google.de/url?sa=i&rct=j&q=&esrc=s&source=imgres&cd=&cad=rja&uact=8&ved=0ahUKEwiK3sWVjeHXAhUHExoKHQiTDuoQjRwIBw&url=http://www.cadfem.ch/meldungen/article/jetzt-anmelden-kostenfreie-webinare-zum-thema-optislang.html&psig=AOvVaw3wnhafio0o3V32QspEz5ZX&ust=1511952782393050

Rm = 371 ± 12

σeqv






in OptiSLang® • Good agreement using the adopted model • Bad agreement using classical models

R6 R10 R0








in OptiSLang® • Good agreement using the adopted model • Bad agreement using classical models • Fatigue parameters for R=0.1 & N=1e+6 were

also be estimated

σ0 = 331.5 m = 28.1 α = 0.74

PIA

R10




Multidisciplinary Optimization of a LPT Blade The multidisciplinary optimization toolbox 1. Generation of different

blade geometries using genetic algorithms

2. Check for geometric restrictions related to castability

3. Performing of a) CFD simulation b) FEM simulation c) Reliability calculation

4. Using the multidisciplinary objective for building new members


Multidisciplinary Optimization of a LPT Blade Comparison of initial member and a member in the Pareto front

Pf = 1.0 η = 90.2%

Initial Member

pf

1e+00

1e-04

1e-02

1e-06 MDO

η = 90.8% Pf = 1.8e-4

pf

1e+00

1e-04

1e-02

1e-06

Increase of efficiency and reliability at the same time!

MDO Member


Summary

• 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

Initial Design Optimized Design


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

Mater Sci (2018) 53:1227–1245

http://www.bmwi.de/

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