Strain Direct Mapping by Using Carbon Nanotube Strain Sensor

Transcription

1 TOMODACHI Rice University FinalPresentation (March 18, 016) Strain Direct Mapping by Using Carbon Nanotube Strain Sensor Shuhei Yoshida (University of Tokyo) Supervisor: Professor Bruce Weisman (Department of Chemistry)

2 Can you see material deformation? Q: Which is DANGEROUS deformation?? A B Material deformation Strain What if we could see STRAIN? Both are Structural health monitoring DANGEROUS deformation! Non- destructive Non- contact Simple Ideal strain measurement methods /6

3 Strain- sensing smart skin S 4 method Mechanisms Carbon nanotubes + Polymer Single- walled Carbon nanotubes different wave length Strain- sensing smart skin Fluorescence intensity Strain Peak shift Strain value can be obtained. Strain scanner Scanning material surface Strain map (Picture of material deformation) Wave length Strain 3/6

4 Principle strain maps [µε] Stretch Maximum strain distribution was successfully obtained. Cu plate Applicable to structural health monitoring 4/6

5 Houston 5/6

6 Diversity in research lab. United States Japanese students Japan Why important? Diverse people Diverse ideas Better ideas International students Racially homogeneous society (Ours Others) Language barrier Tolerance for diversity 6/6

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8 Appendix

9 What I have Rice (1) Strain / Stress map () Local work hardening map (3) Theoretical model formulation

10 Theoretical model (1) Observed spectral shift Δν #$%&'(&) = + 7: ; ; : + f θ, φ Δ ν θ, φ, α sin 4 θ cos 7 φ α dθdφ Spectral shift (individual SWNTs) Δν θ, φ, α = Δν <=> (cos 7 β μ sin 7 β) ε Δν #$%&'(&) = Δν <=> 8 (3 μ) ΔE II = hδν = 3 1 <#) LM<,4 NI t ; 1 + μ QRST cos 3θ U ε For (7,6)- (7,5) separation ε = 8 3 μ h 3t ; 1 + ν QRST cos 3θ V,W + cos3θ V,X Δν (V,W) Δν (V,X)

11 Theoretical model () Observed spectra shape 7: : S #$%&'(&) = + + f θ, φ P ν ν ; Δν θ, φ, α sin 4 θ cos 7 φ α dθdφ ; Peak function (individual SWNTs) Gaussian distribution ; P = Aexp ν ν ; Δν θ, φ, α 7 ε = 8 3 μ w 7 h Lorentzian distribution P = A π 1 Γ ν ν ; Δν θ, φ, α Γ 7 3t ; 1 + ν QRST cos3θ V,W + cos 3θ V,X Δν (V,W) Δν (V,X) = 8C I 3 μ Δν (V,W) Δν (V,X) V,W M(V,X) ε = C 7 Δλ #$%&'(&) μ = 3 8C I Δν (V,W) Δν (V,X) C V,W M(V,X) 7 Poisson ratio can be obtained more precisely. Δλ #$%&'(&)

12 Methods Strain Data Fitting Model Theory of Elasticity ε = 1 ν ε I ν ε I cos θ + φ ε 1 Strain ε ε φ Strain Stress Transformation σ gh = E ghij ε ij (Hooke s low) Symmetry of Young s modulus tensor σ II σ 77 σ I7 = φ+ π/ Angle θ E IIII E II77 E III7 E II77 E 7777 E 77I7 E III7 E 77I7 E I7I7 ε ε II ε 77 ε I7 σ ε 1 1 σ Principle Stress (Magnitude) σ I σ = σ II + σ 77 ± 7 (Direction) σ ε φ φ σ 1 ε 1 φ = 1 tanmi Work hardening mapping Elastic deformation Poisson ratio: Constant Work hardening Plastic deformation Poisson ratio: Increase σ II σ 77 σ I7 σ II σ 77 + φ σi7 Stress / Strain map can be made. Initial plastic deformation is detectable. 1/5

13 Strain [µε] Strain Min Strain Max

14 Local work hardening map Colored region show damaged part Local work hardening

15 Strain gage rosettes ε (7) ε (4) Consisting of 3 strain gage with different angle ε (I) = ε I + ε 7 ε (7) = ε I + ε 7 ε (4) = ε I + ε 7 + ε I ε 7 + ε I ε 7 + ε I ε 7 cos θ cos θ + π 3 cos θ + π 3 ε (I) ε I ε 7 = ε (I) + ε (7) + ε (4) 3 ± 3 Principle strain can be determined based on 3 data with different angle. ε I ε ε 7 ε ε 4 ε I 7 Problems Low accuracy (small # of data) Space is necessary (larger than SWNTs) Difficulties on deciding 0 of angle Stiffness & thermal conductivity of materials could be altered locally. These can be solved by using SWNTs strain sensor. θ = 1 tanmi 3 ε 4 ε (7) ε (I) ε 7 ε (4)

16 Single- walled carbon nanotubes SWNTs (n, m) Rolling up graphene sheet into cylindrical shape Quasi- 1D structure different van Hove singularity Various optical properties Various superior properties Chirality and electronic structure (n m) mod 3 = 0 Metal (n m) mod 3 0 Semiconductor

17 Semiconducting SWNT Optical property of SWNTs conduction c 1 c 1 Energy 0 E 11 emission E absorption -1 v 1 - v -3-4 valence Density of Electronic States

18 Measurement setup

19 SWNT dispersed polymer films 100 µm IR fluorescence microscopy images

20 Deformation of materials Elastic deformation Plastic deformation Tensile strength Fracture strength Nominal stress Yield point Work hardening = Level of plastic deformation Dislocation density increase Young s modulus ~0. % Permanent strain Nominal strain Fracture elongation

21 Mohr s circle γ <=> ε 1 γ ε ε ε I + ε 7 ε = ε I + ε 7 ε = 1 ν ε 7 + γ 7 + ε I ε ν φ ε 11 = ε I ε 7 cos θ + φ cos θ + φ ε 7 = νε I 7 ε ε 1 ε 1 ε Equivalent ε 1 ε φ ε I7 ε = ε II ε 7I ε (Strain tensor) 77 εx = εx ε εi x = 0 ε εi = 0 ε I ε = ε II + ε 77 ± 7 φ = 1 tanmi Strain state diagonalization ε ε 1 ε I7 ε II ε 77 ε 11 ε 1 ε 11 ε II ε 77 ε 1 7 ε ε I7 ε

22 Dynamic measurement Viscoelasticity of polymer film Strain response delay in cycle test Voigt model σ ; σ σ = const. t ε t = σ ; E 1 exp E η t σ = σ & + σ ( ε = ε & = ε ( σ & = Eσ & = Eε σ ( = ηε ( = ηε σ = Eε + ηε Input force σ = σ ; f(t) ε t = f ε = L MI L f L ε Strain response delay can be eliminated.

23 Levenberg Marquardt algorithm Problem: Finding least squares Idea < S β = y g f x g, β 7 gƒi f x g, β ; + δ f x g, β ; + J g δ J g = f x g, β ; β < S β ; + δ y g f x g, β ; + J g δ 7 gƒi Solution J T J δ = J T y f β ; J T J + λdiag J T J δ = J T y f β ; β ; : Initial guess of optimization parameter Moving from β to β + δ Jacobian matrix = y f β ; Jδ 7 same as ( differential = 0 ) One of the most used, typical & fast optimization algorithms Finding best δ Levenberg- Marquardt algorithm λ: Damping factor (Adjustable) make the calculation faster.

24 Peak deconvolution Levenberg Maquardt algorithm Optimized solution depends on initial assumption Problem: Inappropriate fitting curve could appear. Solution: Polynomial fitting curves ( Analytically solved) Before After

25 Annealing methods Initial value Local optimized solution Initial value Optimized solution Levenberg Maquardt algorithm Optimized solution depends on initial assumption Problem: Inappropriate fitting curve could appear. Solution: (1) Random initial value () Find the most optimized one (Annealing methods)

26 Future applications (1) Structural health monitoring () Application for nano- micro mechanical structures

27 Remained issues (1) Material optimizations Degradation resistance Good adhesion with substrates Cost performance Spray technique () System optimizations Data precision Data acquisition speed up Data processing speed up