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

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Overview• Lamb waves

– Structural health monitoring (SHM)

• Numerical modeling

– Elastodynamic finite integration technique (EFIT)

– 3D Simulations

• Comparison to experiment

• Anisotropic EFIT for composites

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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

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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

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Overview• Lamb waves

– Structural health monitoring (SHM)

• Numerical modeling

– Elastodynamic finite integration technique (EFIT)

– 3D Simulations

• Comparison to experiment

• Anisotropic EFIT for composites

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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

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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

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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

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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

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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

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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

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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

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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

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• 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

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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

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QUESTIONS ?

Thanks to:

Dr. Matt Rogge, NASA LaRC