3-D FEA Modeling of Ni60Ti40 SMA Beams as Incorporated in Active Chevrons

Transcription

1 3-D FEA Modeling of Ni60Ti40 SMA Beams as Incorporated in Active Chevrons Darren Hartl Luciano Machado Dimitris Lagoudas Texas A&M University ASME Applied Mechanics and Materials Conference June 6, 2007 Austin, TX

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) Undergraduate research assistant Jesse Mooney All FEA analysis performed using ABAQUS research license. Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles

3 Overview Introduction to SMAs Motivation for development of numerical analysis tools Analysis Example: Introduction of Boeing VGC Unified Model Original Form Improvements developed/implemented Analysis Example: Results Experimental characterization Calibration and validation of model Analysis results Conclusions Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles

4 Motivation: Development of Powerful Numerical Analysis Tools (1/2) SMA Torque Tubes SMA More advanced smart structures incorporating active materials being considered (complex/large deformation, inhomogeneous stress, etc) Complex structures require more powerful analysis tools Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles

5 Motivation: Development of Powerful Numerical Analysis Tools (2/2) Legacy Method: Design, Build, Test, Iterate Optimize Preferred Method: Characterize, Analyze Optimize

6 Analysis Example: The Boeing VGC SMA Calkins, Mabe, & Butler, SPIE, 2006 Mabe, Calkins, & Butler, 47th AIAA, 2006 Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles

7 Analysis Problem Determine the mechanical response of the active chevron provided given temperature changes to the SMA beam elements. The Boeing VGC SMA Beams Focus on chevron deflection, especially with regard to the free stream. Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles

8 Analysis Example: Ni60Ti40 Ni60-Ti (wt %) = Ni55-Ti (at %) Boeing chevrons pioneered use in aerospace applications Nickel rich additional precipitates Precipitates lead 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 Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles

9 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 f M s A s A f M 0f M 0s A 0s A 0f SMA Phase Diagram (Schematic) Temperature, T 3 Τ

10 Thermomechanical Characterization (1/2) I I. Plates of various thickness received II. III. ASTM subsized dogbone specimens prepared Thermomechanical loading paths applied III II 4.3mm thick

11 Characterization (2/2) Strain (%) 1.5% 1.0% 0.5% Constant Stress 300 MPa 250 Mpa 200 MPa 150 Mpa 120 MPa 90 Mpa 0.0% Temperature ( C) 1.6% Martensite Max. Trans. Strain 1.2% 0.8% 0.4% 0.0% 1.8mm, Trained Exponential Fit Applied Stress Test Level (MPa) Stress (MPa) C M =300 C A =300 Austenite M f M s A s A f Temperature (ºC)

12 Unified Model: Original Formulation Gibbs Free Energy: t 1 1 G (, T,, ξ ) = : S : : T 2 ρ ρ ( ) ( ξ ) + c T T ln T / T0 s0 T + u 0 + f 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 Evolution Equation: t = ξ where eff ' 3, 0 2 H ξ > eff σ = t r H, ξ < 0 t r ε Hardening Function: Exponential (Sato & Tanaka, 1986) Polynomial (Boyd & Lagoudas, 1995) Cosine (Liang & Rogers, 1990) Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles

13 More General Evolution Equation Implemented t = ξ Original: 3 2 H, ξ > 0 σ = t r H, ξ < 0 t r ε ε t σ 1, σ 2 T Generalized: (Bo/Lagoudas, 1999) 3 cur 2 H ( σ ), ξ > 0 σ = t r, ξ < 0 r ξ ε t σ 1σ2 σ 3 T

14 New Smooth Hardening Function Developed (1/3) Same thermodynamic framework of Unified Model Same implementation scheme Return Mapping Algorithm New Hardening function - Continuous function with continuous derivatives Smooth transitions between elastic phases and phase transformation Original Form: (Polynomial) New Form: (Smooth) df b1ξ + b2 ; ξ > 0 = dξ b3ξ + b4 ; ξ < 0 1 ( n n ( ) ) 1 2 a1 1 + ξ 1 ξ ; ξ > 0 df 2 = dξ 1 ( n n ( ) ) 3 4 a2 1 + ξ 1 ξ ; ξ < 0 2

15 New Smooth Hardening Function (2/3) Conformity with Experimental Results - Pseudoelasticity Experimental Model n 2 n 1 n 4 n 3 Polynomial Smooth Form: (Trained NiTi wire, T=303K)

16 New Smooth Hardening Function (3/3) Conformity with Experimental Results - DSC Experimental DSC Smooth Model Polynomial Heat Rate, W As Sm As BL Af Sm Af BL Temperature, K

17 Simulation of Experiments: Influence of Hardening Function 1-D Loading of 3-D BVP to validate material parameters chosen Model/Experiment Matching Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles

18 Assembly SLOT connectors bolt down SMA beams SLIDE-PLANE connectors prevent beam rotation Contact enforced: SMA beams and chevron (no friction) The FEA Model Laminate Substrate (Elastic) SMA Beams ONLY ONLY ONLY 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 ) Frictionless contact enforced ( X 6) Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles

19 Results of Analysis (1/2) Stress (VM) Contours Deflection Contours Centerline Profile Tip Deflection History

20 Results of Analysis (2/2) Experimental (Photogrammetry) Numerical Analysis Centerline Axis, in Centerline Axis, in Comparison of flight test data with analysis; Take-off condition (Calkins, Butler, Mabe: AIAA ) Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles

21 Conclusions Original Unified Model implementation has been augmented to include new material effects More general evolution equation New hardening function simulating more smooth material response Improved Unified Model used to analyze complex aerostructure Current and Future work: Addition of permanent plastic yield surface Detailed validation Extension to other applications Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles

22 Current Work: Plastic Yield Surface σ 2 Fwd. Trans. Stress (MPa) Martensite Yield Region Path 2 ξ=1 ξ=0 Plastic Yield σ Path 1 Austenite Temperature (ºC) Stress (MPa) Path 2 Path Strain 0% 2% 4% 6% 8% 10%

23 3-D FEA Modeling of Ni60Ti40 SMA Beams as Incorporated in Active Chevrons Darren Hartl Luciano Machado Dimitris Lagoudas Texas A&M University ASME Applied Mechanics and Materials Conference June 6, 2007 Austin, TX

24 Model Calibration Max. Trans. Strain Stress (MPa) 1.6% 1.2% 0.8% 0.4% 0.0% Martensite 1.8mm, Trained Exponential Fit Applied Stress Test Level (MPa) C M =300 C A =300 Austenite M f M s A s A f Temperature (ºC) Parameter E A H cur (σ) 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 * σ VM =0.0135[1-e ] MPa /ºC 14.9MPa/ºC ) MPa /ºC 10.6MPa/ºC )

25 Phase Diagram for Smooth Hardening Function Martensite Stress (MPa) Austenite Temperature (ºC)