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Term Paper on Detection of Structural Cracks

Sambit DasRoll No.:08ME3301

Mechanical Engineering departmentIndian Institute of Technology, Kharagpur

E mail: sambitiitkgp@gmail.com

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 electro-mechanical 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 Electro-mechanical 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 on-line 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 electro-mechanical coupling

behaviour of PZTs. A conceptual explanation of the coupling effecting using an ideal 1-D

system is explained in [5].

Fig. 5 1-D electro-mechanical 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

aluminum-alloy 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- Electro-mechanical 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 usingimpedance-based structural health monitoring techniques, Experimental mechanics, 2006, 46:609-618.

[5] P. Fromme, M. B. Sayir, Experimental detection of cracks at rivets using structural wavepropagation, NDT.net, 5 (6), 2000.