Characterization and 3-D Modeling of Ni60Ti SMA for Actuation of a Variable Geometry Jet Engine Chevron

Transcription

1 Characterization and 3-D Modeling of Ni60Ti SMA for Actuation of a Variable Geometry Jet Engine Chevron Darren Hartl Dimitris Lagoudas Texas A&M University SPIE Smart Structures and Materials/NDE Conference 2007

2 Acknowledgments The Boeing Company, for their support of this work. Special thanks to James Mabe and Frederick Tad Calkins National Defense Science and Engineering Grant (NDSEG) Material and Structures Lab staff, for providing a productive testing atmosphere All FEA analysis performed using ABAQUS research license.

3 Overview Introduction Experimental Characterization Calibration and Validation of Model Finite Element Analysis of Variable Geometry Chevron (VGC) Conclusions

4 Introduction-The Boeing VGC SMA Calkins, Mabe, & Butler, SPIE, 2006 Mabe, Calkins, & Butler, 47th AIAA, 2006

5 Introduction - Ni60Ti40 Ni60-Ti (wt %) = Ni55-Ti (at %) Boeing chevrons pioneered use in aerospace applications Nickel rich additional precipitates Leads to the following attributes: Thermomechanical stability Transformation temperatures set by heat treatments No initial cold work required to promote the shape memory effect complex shapes Mabe, Ruggeri, & Calkins, Int l Conf Shape Memory & Superelast., 2006; Clingman, Calkins, & Smith, SPIE, 2003

6 Introduction SMA Behavior Stress σ Martensite (Detwinned) 1 3 C M C A 1 σ σ ε 2 A to M d 2 f s M t to M d M d to A Austenite ε Martensite (Twinned) A to M t ε M 0f M 0s A 0s A 0f SMA Phase Diagram (Schematic) Temperature, T 3 Τ

7 Thermomechanical Characterization (1) I I. Plates of various thickness received II. III. ASTM subsized dogbone specimens prepared Thermomechanical loading paths applied III II 4.3mm thick

8 Thermomechanical Characterization (2) 2.5% 300 Mpa Strain (%) 2.0% III.a. Untrained material specimens tested (generation of plastic strains evident) 200 Mpa 1.5% III.b. Material trained (stabilized) 120 MPa 1.0% III.c. Testing repeated for trained specimens (model parameters calibrated) 0.5% -0.1% Temperature ( C) 1.5% Strain (%) 3.0% 2.5% Effective Strain (%) Constant Stress 300 MPa 250 Mpa 200 MPa 150 Mpa 120 MPa 90 Mpa 2.0% 100 Cycles, 1.5% 1.0% 300MPa 0.5% 1.0% 0.5% 0.0% % Surface Temperature ( C) Temperature ( C)

9 Calibration of the Unified Model (1) UNIFIED MODEL proposed by Bo/Lagoudas/Qidwai; implemented in ABAQUS here modified to account for variable transformation strain includes the following three key attributes: Gibbs Free Energy: (Includes elastic terms) t 1 1 G (, T,, ξ ) = : S : : T 2 ρ ρ ( ) ( ξ ) + c T T ln T / T0 s0 T + u 0 + f Thermoelastic Stress/Strain: te G = ρ = S : + T E A, E M ν α A,α M Evolution Equation: (Relates internal state variable and observable quantity, i.e. strain) t eff ' 3 cur 2 H ξ > eff σ = t cur H ξ < t, 0 where H cur (σ) = ξ, 0 ε

10 Calibration of the Unified Model (2) Kuhn-Tucker Conditions: (Defines transformation surfaces) ξ 0, Φ 0, Φ ξ = 0 ξ 0, Φ 0, Φ where ξ = 0 π Y = 0, ξ > 0 Φ = π Y = 0, ξ < 0 & G π = ρ ξ Transformation Surfaces: 1 : : : α df > Φ = ± S + [ T + ] + ρ s0 T ρ u0 Y = 0, ξ 0 2 dξ < ρ ρ s 0A, ρ s M 0 M s, M f A s, A f Example transformation surface for cosine hardening: (forward transformation) M 1 M a 1 ξ = cosa ( T M f ) T 1 M + S HC 2

11 Model Calibration: Trained Material Max. Trans. Stress Stress (MPa) 2.0% 1.8% 1.6% 1.4% 1.2% 1.0% 0.8% 0.6% 0.4% 0.2% 0.0% Exponential Fit: H = H max [1-e C σ eff ] H max = 1.5% C = -7.0e Applied Constant Stress (MPa) Martensite Constant Stress 300 MPa 250 Mpa 200 MPa 150 Mpa 120 MPa 90 Mpa 1.8mm, Trained Exponential Fit C M =300 C A =300 Austenite M f M s A s A f Temperature (ºC) Parameter E A H ρ s 0 A ρ s 0 M 90GPA 47GPa E M 0.33 ν α A, α M M s M f 10.0E-6/ºC 34ºC -17ºC A s 23ºC A f 57ºC ( C A =300 ( C M =300 Value -7.0E-9* σ VM =0.015[1-e ] 0.300MPa /ºC 14.9MPa/ºC ) 0.212MPa /ºC 10.6MPa/ºC )

12 Simulation of Experiments Strain (%) 1.6% 1.4% 1.2% 1.0% 0.8% 0.6% 0.4% 0.2% 0.0% Temperature ( C) 1-D Loading of 3-D BVP to validate material parameters chosen 90 Mpa 90 MPa - Analysis 200 MPa 200 MPa - Analysis Model/Experiment Matching

13 The FEA Model (1) Chevron Substrate Laminate structure Linearly elastic Node triangular shell (STRI65) elements used Constrained along forward edge SMA Curved Beam 3 instances used SMA material behavior - UMAT 2100 Quadratic brick elements w/ reduced integration (C3D20R) used (6 thru thick) Fastened to chevron via ABAQUS connector elements

14 The FEA Model (2) Assembly SLOT connectors used to bolt down SMA beams SLIDE-PLANE connectors used to prevent beam rotation Contact enforced between SMA beam edge nodes and chevron elements (no friction) Loading Steps 1. Clamp beams (T<A s ) 2. Heat beams (T>A f ) 3. Cool (M f <T<M s ) 4. Heat beams (T>A f ) ONLY Frictionless contact enforced ( X 6) ONLY ONLY

15 Results of Analysis (1) 1) Initial Condition 2) Clamp SMA beams (T<A s ) Von Mises (MPa) 3) SMA beams heated (T>A f ) 4) SMA beams cooled (M f <T<M s )

16 Results of Analysis (2) Deflection Contours Tip Immersion Time History Centerline Profile

17 Results of Analysis (3) Experimental (Photogrammetry) Numerical Analysis Centerline Axis, in Centerline Axis, in Comparison of flight test data with analysis; Take-off condition (Calkins, Butler, Mabe: AIAA )

18 Conclusions Ni60-Ti (wt %) SMA has been characterized for use as an actuator Unified Model (as implemented in ABAQUS) has been successfully calibrated using the experimental data BVP consisting of the Boeing VGC has been analyzed using the calibrated model Future work: Detailed validation Extension to other applications

19 Use of Analysis Tools for Modeling of VGC Actuation Cycles Legacy Method: Design, Build, Test, Iterate Optimize Preferred Method: Characterize, Analyze Optimize