termpaper crack detection 08me3301 2

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  • 7/30/2019 Termpaper Crack Detection 08ME3301 2



    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 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.

  • 7/30/2019 Termpaper Crack Detection 08ME3301 2


  • 7/30/2019 Termpaper Crack Detection 08ME3301 2



    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


    nV V V V THD


    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


    [ ] ( ) [ ] ( ) [ ] ( )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

  • 7/30/2019 Termpaper Crack Detection 08ME3301 2



    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



    ,( )

    ( )




    , 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



    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,


    xxY is elastic stiffness, k is wave number and


    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





    ( ( ) ( ))

    ( ( ))

    i N

    i o i


    i N

    o i


    Z Z



  • 7/30/2019 Termpaper Crack Detection 08ME3301 2



    ( )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.


    [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.