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3D Ultrasonic Wave Simulations for
Structural Health Monitoring
Cara A.C. Leckey
Nondestructive Evaluation
Sciences Branch
NASA Langley Research Center
Mark Hinders and Corey Miller
Nondestructive Evaluation Laboratory
College of William &Mary
12th International Symposium on Nondestructive Characterization of MaterialsVirginia Tech, Blacksburg, VA, USA
June 19-24, 2011
Overview• Lamb waves
– Structural health monitoring (SHM)
• Numerical modeling
– Elastodynamic finite integration technique (EFIT)
– 3D Simulations
• Comparison to experiment
• Anisotropic EFIT for composites
6/27/2011
Overview• Lamb waves
– Structural health monitoring (SHM)
• Numerical modeling
– Elastodynamic finite integration technique (EFIT)
– 3D Simulations
• Comparison to experiment
• Anisotropic EFIT for composites
6/27/2011
Lamb Waves• Guided ultrasonic waves:
– Created due to boundaries
– Interaction of coupled L and SV with boundaries leads to various modes
– A and S Lamb wave modes are created in isotropic plates
– Waves are dispersive: group and phase velocity depends on frequency-thickness
• Useful for interrogating plate-like materials– Detect damage before failure of key components
4
Symmetric Lamb wave mode
Antisymmetric Lamb wave mode
6/27/2011
Lamb Waves for SHM• Active interrogation method
• Propagate long distances in plates/pipes
– Tens of meters [Leonard and Hinders 2005]
– Leads to fewer sensors
• Lightweight mounted or embedded sensors
– Piezoelectric wafer sensors [Giurgiutiu and Cuc 2005]
– Macro fiber composite (MFC) piezoceramic fiber-matrix transducer [Collet et al. 2011]
• Ideal cases: Extent of damage can be found from mode arrival time changes [Bingham and Hinders 2009]
• Need to understand Lamb wave interaction with flaws to optimize techniques MFC
Image from www.smart-material.com
Piezo wafers
Image from www.steminc.com
6/27/2011
Overview• Lamb waves
– Structural health monitoring (SHM)
• Numerical modeling
– Elastodynamic finite integration technique (EFIT)
– 3D Simulations
• Comparison to experiment
• Anisotropic EFIT for composites
6/27/2011
Numerical Methods: FIT
• Until recently most elastic wave simulations were 2D
• FIT, FD, FEM
• Finite Integration Technique benefits
– Straight-forward equations
– Implemented in any programming language
• Parallelize for cluster computing
– Simple to incorporate boundary conditions
– Staggered grid means good stability
– Can handle large simulation spaces
6/27/2011 7
Elastodynamic FIT• Start with isotropic equations of motion:
• Discretization yields 9 equations [Fellinger 1995]
– Stability conditions define spatial and time steps
8
Parallel Processing
• Finite integration code is parallel– MPI, 1D virtual topology
• Runs on computing clusters
6/27/2011 9
Each
processor has
entire width
and depth
Stress and velocity information is passed between processors
EFIT: Lamb Waves• Dispersion curves for aircraft grade aluminum
– Group and phase velocity:
• EFIT result: 1.56 MHz mm• Higher MHz mm regions
– Complicated scattering
6/27/2011
dk
dcg
kcp
S0
A0
S1
A1
S2
A2
S0
A0
S1
A1
S2 A2S3
A3
S3
A3
Overview• Lamb waves
– Structural health monitoring (SHM)
• Numerical modeling
– Elastodynamic finite integration technique (EFIT)
– 3D Simulations
• Comparison to experiment
• Anisotropic EFIT for composites
6/27/2011
EFIT: Lamb Waves• Comparison to well-defined experiment
– Aircraft grade aluminum, 3.154 mm
– 5-cycle, 2.15 MHz incident wave
– 6.78 MHz-mm, 8 modes
– Flaw shape, 3D critical to capture wave behavior
– Simulation provide insight and can optimize techniques/design
12
Transmitting transducer
Receivingtransducer
6/27/2011
EFIT: Lamb Waves• 3D output: Visualizing data for useful analysis
Experimental data
Denoisedexperimental
data
EFIT A-scan
t1 t2 t3
EFIT: Lamb Waves• 1400 CPU hours per simulation (~45 wall-clock hours)
• Spatial step λ/15 (0.097 mm), time step 10 ns
• Four chosen transmitter positions
14
99.0 mm
Transmitter Position 1• 2.7 mm deep void, 85% material loss
• 0.98 MHz-mm, expect 2 modes beneath void
6/27/2011 15
S0
A0
S1
A1
S2
A2
S0
A0
S1
A1
S2 A2
S3
A3
S3
A3
Transmitter Position 1• Based on EFIT: expect 6 modes and later high amplitude S0 and A0
• Creation of low phase velocity waves in thinned region
• White lines are regions beneath void
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(a) 27 µs (b) 36 µs
(c) 45 µs (d) 54 µs
(e) 63 µs (f) 71 µs
Experimental data with expected arrival times based on EFIT indicated for flawed plate:
S2 & low amplitude
A0/S0 A2
S1, A3
Highamplitude
A0/S0
High amplitude edge reflections enter at this point
a) Clean plate denoised
b) Flawed plate denoised
Transmitter Position 2• Investigate spatial limit of scattering effects
• 1.87 mm deep void, 59 % material loss
• White lines represent region parallel to flaw
6/27/2011 17
Tomographic flaw reconstruction created with experimental data
EFIT output directly beneath the void
Overview• Lamb waves
– Structural health monitoring (SHM)
• Numerical modeling
– Elastodynamic finite integration technique (EFIT)
– 3D Simulations
• Comparison to experiment
• Anisotropic EFIT for composites
6/27/2011
• Start with macro mechanical behavior – include anisotropy• Recall isotropic case:
• Anisotropic:
• General case: triclinic, 21 elastic constants• Additional nonzero stiffness matrix elements must be included
EFIT for Composites
6/27/2011
EFIT for Composites• Move towards composite materials for
aerospace applications– Composite crew module, commercial aircraft
• Scale of simulation for ultrasonic SHM detection techniques:– Macro mechanical behavior
• Homogeneous at scale of fiber/matrix in each ply
• Anisotropic
– Delamination at interface, microcracking?
– Micromechanic behavior (micron scale)
• Inhomogeneous at scale of fiber/matrix
• Isotropic
– Fiber breakage, microcracking?
Composite crew module
Image from www.nasa.gov
~50% composite
Image from www.boeing.com
~20% composite
Image from www.airbus.com
MacroscaleMicroscale
Anisotropic EFIT• Additional elastic constants lead to increased complexity
– Example: single stress term for anisotropic EFIT
Example of EFIT output for a homogeneous anisotropic medium
Conclusions & Future Work
• 3D EFIT provided an understanding of experimental data
• 2D simulations would not capture these effects
• EFIT simulations provide tool for optimizing ultrasonic SHM techniques
• Custom computational tools can be expanded to account for additional physics
• Future work: – Further develop and validate anisotropic code
– Incorporate multiple layers (plies)
– Built-up composite structures
– Optimize SHM techniques
226/27/2011