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7/30/2019 Termpaper Crack Detection 08ME3301 2
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Term Paper on Detection of Structural Cracks
Sambit DasRoll No.:08ME3301
Mechanical Engineering departmentIndian Institute of Technology, Kharagpur
E mail: [email protected]
1 Introduction
The present study reviews the techniques of detecting structural cracks , the relative advantages of
different techniques and their applicability. Significant research has been done in detecting
structural damage from analysis of changes in dynamic responses. Measurement of modal
parameters like natural frequency, mode shapes and damping is the simplest and most widely
used technique of crack detection [1, 2]. However, modal parameters are not always reliable in
locating cracks when the effects of the damage are localized [1, 3]. In response, researchers have
computed frequency response functions [3] of structural dynamics from fitting modal data with a
finite element model. Recently, with the advent of piezoelectric actuators and sensors, which
allow higher order frequency bandwidths, alternative techniques have emerged like spectral
analysis of electromechanical impedance [4] and scatter in structural wave propagation [5]. Ibriefly discuss the above techniques in the subsequent sections. Fig. 1 shows a commonly
observed hairline crack, while in fig. 2, a microscopic crack is shown, which is difficult to detect.
Fig. 1 Hairline cracks in concrete.

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Fig. 3 Output response for three different conditions (adapted from [2]).
Fig. 4 Total Harmonic Distortion for different conditions (adapted from [2]).
It is given by
2 2 2 2
2 3 4
1
nV V V V THD
V
nV are amplitudes corresponding to nth harmonics.
1V is the fundamental harmonic.

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2.2 Locating cracks from analysis of natural vibration frequencies and mode shapes
Structural cracks generally decrease the stiffness of the structure causing natural frequencies to
decrease. This can be inferred from the spectral analysis of the response from a harmonic sweep
excitation. It has been verified from experiments [1] that the reduction of a particular naturalfrequency depends on the relative position of the crack and the corresponding mode shape. For
instance a crack might be at the node of a particular mode. In this case, the natural frequency
corresponding to that mode would not be affected. However, changes in modal parameters alone
cannot be used to locate structural faults, unless we consider local modes. Local modes occur at
higher frequencies as a result of energy being trapped in local areas of a structure. In the next
section, the information of both modal parameters along with distributed mass, damping and
stiffness parameters are used to detect and locate cracks.
2.3 Locating cracks from changes in structural frequency response function
In structural dynamics, linear vibration of a structure having N degrees of freedom is represented
by
[ ] ( ) [ ] ( ) [ ] ( )M x t C x t K x f t
, where [M], [C] and [K] are N x N inertial, damping and stiffness matrices. The corresponding
frequency response function is obtained by Fourier transform
2[ ] ( ) [ ] ( ) [ ] ( ) ( )
( ) ( ) ( )
M X C X w K X F
X H F
, where ( )H is the impulse response function. A computational approach is illustrated in
[3], for estimating matrices [M], [C] and [K] from curve fitting the FRF (Frequency Response
Function) with measurements obtained from a general modal test as discussed in Section 2.3. If a
crack occurred somewhere in the structure, the DOFs closer to the crack will be affected more
than the DOFs farther away from the crack. Thus by analyzing the DOFs in matrices [M], [C]
and [K], which show maximum deviation from the undamaged specimen, the crack location is
estimated. Generally N, the total number of DOFs is decided by the number of modes which are
most influenced by the fault, but sufficient number of modes have to be used to adequately
represent the structural dynamics. Measurement through FRFs also has additional advantages
over direct parameter estimation like, removal of measurement noise by using frequencydomain averaging methods.
3 Electromechanical impedance method
Piezoceramics offer many advantages over traditional actuators and sensors. They are lighter,
have a higher order bandwidth and can be used as both actuators and sensors. This makes them
suitable for online structural health monitoring. In [4], surface bonded piezoelectric patches were

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used in conjunction with an impedance analyser to detect cracks in a concrete beam. High
frequency excitations over 20 kHz were utilized. Impedance based damage detection works on
the principle that physical changes in structure translates to changes in structural impedance of
the PZTs., which induces changes in electrical impedance due to electromechanical coupling
behaviour of PZTs. A conceptual explanation of the coupling effecting using an ideal 1D
system is explained in [5].
Fig. 5 1D electromechanical coupling (adapted from [4]).
For an angular frequency , the mechanical impedance,A
Z of the PZT patch and
mechanical impedance of the physical structure,s
Z are defined as
( )
( )A
VZ
I
,( )
( )
Os
FZ
x
, where ( )V the harmonic is input voltage, ( )I is the current response, ( )OF is the
harmonic excitation and ( )x , is the velocity response. Finally, the apparent electro
mechanical impedance of the PZT is obtained as
12
23
33 3
( ) tan( )( )
( ) ( )
ET Ex xx A
x xx
A S
wl d Y Z klZ j d Y
s Z Z kl
, where w is PZT width, l is PZT length, s is PZT thickness,3x
d is PZT strain constant,
E
xxY is elastic stiffness, k is wave number and
33
T is permittivity at constant stress. A root
mean square deviation (RMSD) in the impedance signatures of the PZT patches is used as a
damage indicator which is given as
2
1
2
1
( ( ) ( ))
( ( ))
i N
i o i
i
i N
o i
i
Z Z
RMSD
Z

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( )iZ is the impedance signature with damage and ( )o iZ is the impedance signature
without damage.
4 Detection from scatter in structural wave propagation
This technique is used for detecting cracks in boundaries like holes in thin metallic plates.
Transverse structural waves with a narrow low frequency band are used. By using large
wavelengths in comparison with the plate thickness, we enable the theoretical modeling of wave
propagation using thin plate theory. Additionally, structural waves have good dispersive
properties. Structural wave on hitting the hole causes a scatter, which can be experimentally
measured for an undamaged specimen. Theoretical determination is also possible for simple
geometries using thin plate theories. If a crack is present at the boundary, the scatter wave pattern
differs. The lower limit of the excitation frequency is set by the minimum crack length to be
detected. A simple experimental demonstration is provided in [5] for detecting cracks in an
aluminumalloy plate with a hole.
5 Summary
Various techniques of detecting structural cracks have been presented in this term paper. The
importance of not only detecting cracks but also locating them is stressed. Literature survey
revealed that detection using modal parameters is the most widely used, though they are not
reliable enough for locating cracks. For that purpose, changes in inertial, stiffness and damping
matrices of the structure have to be estimated. Finally, two relatively new methods of crack
detection Electromechanical impedance and wave scatter were discussed.
References
[1] O. S. Salawu, Detection of structural damage through changes in frequency: a review,
engineering structures, 19 (9), 1997.
[2] T. J. Meitzler, G. Smith, Crack detection in armor plates using ultrasonic techniques,
American Society for Nondestructive Testing, 2008.
[3] M. A. Mannan, M. H. Richardson, Detection and location of structural cracks using FRF
measurements, IMAC, 1990.
[4] S. Park, S. Ahmad, C.B. Yun, Y. Roh, Multiple crack detection of concrete structures usingimpedancebased structural health monitoring techniques, Experimental mechanics, 2006, 46:609618.
[5] P. Fromme, M. B. Sayir, Experimental detection of cracks at rivets using structural wavepropagation, NDT.net, 5 (6), 2000.