Failure analysis of composite structures by thermography

143 Pages·2016·12.23 MB·English

by  Przemysław Daniel Pastuszak

Failure analysis of composite structures by
thermography

Analiza uszkodzeń struktur kompozytowych
metodą termografii

Author: Mgr inż. Przemysław Daniel Pastuszak
Supervisor: Prof. dr hab. inż. Aleksander Muc

Cracow 2015
The author was a holder of a scholarship within the project "Doctus - Małopolska
scholarships fund for PhD students" co-financed by the European Union under the European
Social Fund.

Autor był stypendystą w ramach projektu „Doctus – Małopolski fundusz stypendialny
dla doktorantów” współfinansowanego ze środków Unii Europejskiej w ramach
Europejskiego Funduszu Społecznego.

2
Contents
NOMENCLATURE ................................................................................................................. 6
ACRONYMS ............................................................................................................................ 9
1. INTRODUCTION .......................................................................................................... 11
1.1. MOTIVATION .............................................................................................................. 11
1.2. RESEARCH OBJECTIVES .............................................................................................. 12
1.3. THESIS 12
1.4. SCOPE OF THE WORK .................................................................................................. 12
1.5. ORGANISATION .......................................................................................................... 12
2. STATE OF THE ART AND THE LITERATURE SURVEY .................................... 13
2.1. FUNDAMENTAL INFORMATION ON COMPOSITE MATERIALS ........................................ 13
2.1.1. Introduction .................................................................................................. 13
2.1.2. Governing elastic relations for composite structures ................................... 17
2.1.3. Heat transfer ................................................................................................. 21
2.1.3.1. Thermal boundary conditions ....................................................... 24
2.1.3.2. General thermo-elastic formulations for orthotropic composites. 25
2.1.4. Failure modes of composite materials ......................................................... 26
2.1.4.1. Failure criteria .............................................................................. 27
2.1.4.2. Modelling of structural damage ................................................... 28
2.1.5. Destructive and non-destructive tests .......................................................... 28
2.2. INFRARED THERMOGRAPHY (IRT) ............................................................................. 31
2.2.1. Introduction .................................................................................................. 31
2.2.2. Infrared Thermography in the repertoire of NDT methods ......................... 31
2.2.3. Fundamental Concepts of non-contact temperature measurements ............. 33
2.2.3.1. History of IRT .............................................................................. 34
2.2.3.2. Blackbody and Planck’s Law ....................................................... 35
2.2.3.3. Wien’s Law .................................................................................. 36
2.2.3.4. Reflection, absorption and transmission ...................................... 37
2.2.3.5. Emissivity ..................................................................................... 38
2.2.3.6. Factors affecting IRT measurements ............................................ 41
2.2.4. Infrared Thermography for TNDT&E ......................................................... 44
2.2.4.1. Pulsed Thermography .................................................................. 48
2.2.4.2. Lock-in Thermography ................................................................ 48
2.2.4.3. Vibrothermography ...................................................................... 50
2.2.4.4. Pulse Phase Thermography .......................................................... 51
2.2.4.5. Thermal contrast ........................................................................... 51
2.2.4.6. Determining of the thermal properties ......................................... 52
2.2.4.7. Defects detection and characterisation ......................................... 53
2.2.5. Applications of IRT ..................................................................................... 55
3. NUMERICAL ANALYSIS ............................................................................................ 57
3.1. INTRODUCTION ........................................................................................................... 57
3.2. DESCRIPTION OF FE MODELS ..................................................................................... 58
3.2.1. Meshing ........................................................................................................ 60
3.2.2. Initial and boundary conditions ................................................................... 64
3
3.2.3. Heat load ...................................................................................................... 64
3.2.4. Thermal and mechanical properties of investigated constituents ................ 65
3.3. RESULTS..................................................................................................................... 67
3.3.1. Comparison of simulations for selected meshes .......................................... 67
3.3.2. Parametric thermographic analysis .............................................................. 70
3.3.2.1. Influence of supplied energy ........................................................ 70
3.3.2.2. Effects of delamination size and location .................................... 73
3.3.2.3. Effects of a defect’s material properties ....................................... 76
3.4. SUMMARY AND DISCUSSION ....................................................................................... 78
4. EXPERIMENTAL STUDIES ........................................................................................ 80
4.1. INTRODUCTION ........................................................................................................... 80
4.2. MANUFACTURING OF COMPOSITE MULTILAYERED STRUCTURES ................................ 80
4.2.1. Introduction .................................................................................................. 80
4.2.2. Manufacturing methods ............................................................................... 81
4.2.3. Configurations of the examined specimens ................................................. 84
4.2.4. Corrective treatments of emissivity ............................................................. 85
4.3. TEST STATION ............................................................................................................ 86
4.3.1. Software for AIRT analysis ......................................................................... 89
4.3.2. Test conditions ............................................................................................. 92
4.3.3. Experimental procedure of AIRT tests ........................................................ 93
4.4. RESULTS..................................................................................................................... 94
4.4.1. Detection of defects ..................................................................................... 94
4.4.2. Effects of delamination thickness ................................................................ 97
4.4.3. Uniform heating of curved composite structures ......................................... 99
4.4.4. Deformation of the specimens ................................................................... 102
4.4.5. Effects of the damage growth .................................................................... 104
4.5. NOVEL APPROACH TO AIRT: COOLING DOWN THERMOGRAPHY (CDT) .................. 106
4.5.1. Introduction ................................................................................................ 106
4.5.2. Description of the experiment .................................................................... 106
4.5.3. Results and discussion ............................................................................... 107
4.6. SUMMARY AND DISCUSSION ..................................................................................... 109
5. CONCLUSIONS AND FUTURE WORKS ................................................................ 110
5.1. CONCLUSIONS .......................................................................................................... 110
5.2. RECOMMENDATIONS FOR FUTURE RESEARCH ........................................................... 111
6. STRESZCZENIE .......................................................................................................... 112
6.1. WSTĘP 112
6.2. CEL, TEZA I ZAKRES PRACY ...................................................................................... 113
6.2.1. Cel pracy .................................................................................................... 113
6.2.2. Teza pracy .................................................................................................. 113
6.2.3. Zakres pracy ............................................................................................... 113
6.3. STAN WIEDZY I ANALIZA LITERATURY ..................................................................... 114
6.3.1. Termografia w podczerwieni ..................................................................... 115
6.4. OBLICZENIA NUMERYCZNE ...................................................................................... 116
6.4.1. Opis modeli numerycznych ....................................................................... 116
6.4.2. Wyniki ........................................................................................................ 118
4
6.5. BADANIA DOŚWIADCZALNE ..................................................................................... 122
6.5.1. Opis stanowiska badawczego i próbek ...................................................... 122
6.5.2. Wyniki i dyskusja ...................................................................................... 124
6.6. WNIOSKI I KIERUNKI DALSZYCH PRAC ...................................................................... 126
6.6.1. Wnioski ...................................................................................................... 126
6.6.2. Kierunki dalszych prac .............................................................................. 126
ABSTRACT .......................................................................................................................... 127
ACKNOWLEDGEMENTS ................................................................................................. 128
LITERATURE ..................................................................................................................... 129
LIST OF FIGURES ............................................................................................................. 139
LIST OF TABLES ............................................................................................................... 143

5
Nomenclature
Scalars

α absorptivity
a
α thermal diffusivity
d
α thermal expansion
e
g 0
xy membrane tangential deformations of the middle surface in the x-y plane
ε emissivity
ε maximum nominal compressive strain
c
e 0 e 0
x , y membrane deformations of the middle surface in the x and y axis directions
θ fibre orientation in the global coordinate system
k k
x , y curvature change parameters of the mid-plane resulting from bending
k
xy curvature change parameters of the mid-plane resulting from torsion
λ wavelength
υ , υ , υ Poisson's ratios for principal directions of the material
12 23 13
ρ the mass density of the material
ρ artificial defect density
d
ρ reflectivity
r
τ transmissivity
φ the angle of incidence and reflection of the light
D T temperature difference
Φ phase shift
d diameter
d depth of a defect
d
f frequency
h convection heat transfer coefficient
h height of a composite structure
c
h height of a defect
d
l length of the test piece
q convection heat flux
c
q conduction heat flux
k
q radiation heat flux
r
q internal heat generation
w
(cid:1)(cid:2) components of vector heat flux density (i=1,2,3),
(cid:3)
r radius
r radius of curvature
c
r outer radius
o
t time
t time of the analysis
an
t thickness of a composite structure
c
t thickness of a defect
d
6
t time of maximal contrast occurrence
maxC
t duration of the heat pulse
pd
t beginning of the analysis
0
v volume
w out of plane displacement
w width of a composite structure
c
w width of a defect
d
x,y,z global coordinate system
x ,x ,x local coordinate system
1 2 3
A area
A defective area
d
A non-defective area
nd
C absolute thermal contrast
a
C running thermal contrast
r
C standard thermal contrast
s
C maximum absolute thermal contrast
max
C heat capacity at constant pressure
p
D standard defect
s
E energy or Young's modulus
E ,E , E Young's modules in principal directions of the material
1 2 3
E : input energy
in
E : generated internal energy
g
E : output energy
o
E : stored internal energy
int
G , G , G Kirchhoff’s modules for principal directions of the material
12 23 13
G critical energy release rate
c
K critical stress intensity factor
c
Q heat
Q¢ (k) elements of stiffness matrix for kth-layer in global coordinate system
ij
R ultimate tensile strength
R total blackbody spectral radiance (the total amount of radiated energy)
t
S part of the surface of the body
c
S part of the surface in contact with a fluid media
cs
S front (observed) surface
F
S rear (heated) surface
R
S part of the surface exposed to radiation
r
T temperature in [°C]
T ambient temperature
amb
T temperature of defective region of specimen
d
Te temperature of body or surface emitting the radiation
T final temperature of the analysis
fin
T initial temperature of the model or the sample
in
T maximum temperature of front surface
maxF
7
T maximum temperature of rear surface
maxR
T temperature of non-defective region of the specimen
nd
T absolute temperature of a fluid
F
T absolute temperature of a surface
S
T0 temperature of the reference surface
T’ temperature gradient in the thickness direction

Tensors
α components of thermal expansion tensor in the local coordinate system
mn
a ' components of linear coefficients of thermal expansion tensor in the global
ij
coordinate system
ε components of the strain tensor in the local coordinate system
ij
e¢
components of total strain tensor in the global coordinate system
ij
λ components of thermal conductivity tensor in the local coordinate system
ij
σ components of the stress tensor in the local coordinate system
ij
s ¢
components of stress tensor in the global coordinate system
ij
s T components of the thermal stress tensor in the local coordinate system
ij
C components of stiffness tensor in the local coordinate system
ijkl
J components of second order transformation tensor in the local coordinate
ij
system
P components of second order transformation tensor
ij
Q components of stiffness tensor in the local coordinate system
ij
Q' components of stiffness tensor for plane strain state in the global coordinate
ij
system
S components of compliance tensor in the local coordinate system
ijkl

Constants
σ Stefan-Boltzmann’s constant, σ = 5.6697 x 10-8 [W/m2K4]
c speed of light, c = 2.9979 x 108 [m/s]
b Wien's displacement constant, b = 2.8977729(17)×10−3 [mK]
W W
h universal (or Planck’s) constant, h = 6.6256 x 10-34 [Js]
pc pc
k Boltzmann constant, k = 1.38064852(79) x10-23 [J/K]
B B

8
Acronyms
2D: Two-dimensional
3D: Three-dimensional
AIRT: Active Infrared Thermography
AOI: Area of Interest
APDL: ANSYS Parametric Design Language
CDT: Cooling Down Thermography
CFRP: Carbon Fibre Reinforced Plastic
CM: Composite Material
CMC: Ceramic Matrix Composite
CMOS: Complementary Metal Oxide Semiconductor
BC: Boundary Conditions
DFT: Discrete Fourier Transform
EM: Electromagnetic
FDM: Finite Difference Method
FEM: Finite Element Method
FFT: Fast Fourier Transform
FOV: Field of View
FPA: Focal Plane Array
FPF: First Play Failure
FT: Flash Thermography
FT: Fourier Transform
FWHM: Full-width at half-maximum
GFRP: Glass Fibre Reinforced Plastic
GUI: Graphical User Interface
IFOV: Instantaneous Field of View
IR: Infrared
IRT: Infrared Thermography
LOI: Line of interest, temperature profile
LPT: Long Pulse Thermography
LT: Lock-In Thermography
LWIR: Long-wavelength infrared
MMC: Metal Matrix Composite
MRTD: Minimum Resolvable Temperature Difference
NDT: Non-Destructive Testing
PIRT: Passive Infrared Thermography
PMC: Polymer Matrix Composite
PT: Pulsed Thermography
PPT: Pulsed Phase Thermography
PTFE: Polytetrafluoroethylene (also known as Teflon or Tarflen)
SH: Step Heating
SNR: Signal-to-Noise Ratio
TBC Thermal Boundary Conditions
9
TLC: Thermochromic Liquid Crystals
TNDT&E: Thermal Non-Destructive Testing and Evaluation
TPs: Thermographic Phosphors
TSA: Thermal Stress Analysis
TSR: Thermographic Signal Reconstruction
VT: Vibro Thermography

10