* Robotics Laboratory, Department of Mechanical Engineering, National Institute of Technology, Rourkela-769008, Odisha, India, E-mail:dayalparhi@yahoo.com; manoj1986nitr@gmail.com; mechchinu@gmail.com

Vol. 4 • No. 1 • 2012 • ISSN: 0975-3176 • pp. 27-42

© International Science Press: IndiaI J A A I E S

DIAGNOSIS OF CRACKS IN STRUCTURES USING FEA ANALYSIS

D. R. Parhi, Manoj Kumar Muni and Chinmaya Sahu

Abstract: This study is an investigation of location and orientation of crack in beam like structures. The analysis hasbeen done by using finite element method with the help of ANSYS workbench and CATIA V5. A beam with crack atdifferent locations and without crack considered for the experiment. At different crack location, natural frequenciesand mode shapes have been determined. It has been noticed that when the crack depth increases natural frequencydecreases and also there is a deviation in the mode shape. So by considering the drops in natural frequencies andchanges in mode shapes the location and nature of crack can be detected.

INTRODUCTION

Cracks in structures takes place due to certain reasons such as mechanical defects, faults from the manufacturingprocess. Because of the occurrence of cracks in the structures may lead to change the whole behavior of theelement and consequently decreases its safety. Also the presence of crack indicates fatigue problem. So thedetection or identification of cracks in the structures is a relevant issue. According to Rytter [1] there are fourdifferent levels of damage detection in a structure can be attained, they are

• Level 1: detection of the existence of damage

• Level 2:level 1 + damage location

• Level 3: level 2 + damage quantification

• Level 4: level 3 + prediction of the remaining service life

Skrinar [2] replaced each crack by a linear rotational spring with connecting two adjacent elastic parts tofind the presence of crack by taking the stiffness and geometrical stiffness matrices into account. Owolabi et al.[3] used two sets of aluminium beams with each set consisted of seven beams, the first set had fixed ends andthe second set was simply supported for the experiment. In order to detect, quantify and determine the extent ofcrack and locations they used the technique which depends upon the measured changes in the first three naturalfrequencies and the corresponding amplitudes of the measured acceleration frequency response functions. Rezaeeet al. [4] considered a nonlinear model for the fatigue crack and used perturbation method for solving thegoverning equation of motion of the cracked beam. They derived there is a change in damping takes place dueto the change in crack parameters, geometric dimensions and mechanical properties of the cracked beam. OrhanSadettin [5] has studied the free and forced vibration analysis of a cracked beam was performed in order toidentify the crack in a cantilever beam. Single and two-edge cracks were evaluated. Dynamic response of theforced vibration better describes changes in crack depth and location than the free vibration in which the differencebetween natural frequencies corresponding to a change in crack depth and location only is a minor effect. Nahviand Jabbari [6] have developed an analytical, as well as experimental approach to the crack detection in cantileverbeams by vibration analysis. An experimental setup is designed in which a cracked cantilever beam is excited

28 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu

by a hammer and the response is obtained using an accelerometer attached to the beam. To avoid non-linearity,it is assumed that the crack is always open. To identify the crack, contours of the normalized frequency in termsof the normalized crack depth and location are plotted. Bakhary et al. [7] have applied artificial neural network(ANN) for damage detection. In his investigation an ANN model was created by applying Rosenblueth’s pointestimate method verified by Monte Carlo simulation, the statistics of the stiffness parameters were estimated.The probability of damage existence (PDE) was then calculated based on the probability density function of theexistence of undamaged and damaged states. Kisa et al. [8] Presents a novel numerical technique applicable toanalyze the free vibration analysis of uniform and stepped cracked beams with circular cross section. In thisapproach in which the finite element and component mode synthesis methods are used together, the beam isdetached into parts from the crack section. These substructures are joined by using the flexibility matricestaking into account the interaction forces derived by virtue of fracture mechanics theory as the inverse of thecompliance matrix found with the appropriate stress intensity factors and strain energy release rate expressions.To reveal the accuracy and effectiveness of the offered method, a number of numerical examples are given forfree vibration analysis of beams with transverse non-propagating open cracks. Numerical results showing goodagreement with the results of other available studies, address the effects of the location and depth of the crackson the natural frequencies and mode shapes of the cracked beams. Modal characteristics of a cracked beam canbe employed in the crack recognition process. Loutridis et al. [9] present a new method for crack detection inbeams based on instantaneous frequency and empirical mode decomposition. The dynamic behavior of acantilever beam with a breathing crack under harmonic excitation is investigated both theoretically andexperimentally. Mazanoglu et al. [10] have followed an energy-based method for vibration identification ofnon-uniform Euler-Bernoulli beams having open cracks. They considered the change in strain at the crackedbeam and estimated the distribution of energy and the stress field due to angular displacement of beam.Chasalevris and Papadopoulos. [11] have studied the dynamic behaviour of a cracked beam with two transversesurface cracks. Each crack is characterised by its depth, position and relative angle. A local compliancematrix of two degrees of freedom, bending in the horizontal and the vertical planes is used to model therotating transverse crack in the shaft and is calculated based on the available expressions of the stress intensityfactors and the associated expressions for the strain energy release rates. Dharmaraju et al. [12] have usedEuler–Bernoulli beam element in the finite element modeling. The transverse surface crack is considered toremain open. The crack has been modeled by a local compliance matrix of four degrees of freedom. Thiscompliance matrix contains diagonal and off-diagonal terms. A harmonic force of known amplitude andfrequency is used to dynamically excite the beam. Ruotolo et al. [13] has investigated forced response of acantilever beam with a crack that fully opens or closes, to determine depth and location of the crack. In theirstudy, left end of the beam is cantilevered and right end is free. The harmonic sine force was applied on thefree end of the beam. Vibration amplitude of the free end of the beam was taken into consideration. It wasshown that vibration amplitude changes, when depth and location of the crack change. Baris Binici. [14] hasproposed a new method is to obtain the Eigen frequencies and mode shapes of beams containing multiplecracks and subjected to axial force. Cracks are assumed to introduce local flexibility changes and are modeledas rotational springs. The method uses one set of end conditions as initial parameters for determining themode shape functions. Satisfying the continuity and jump conditions at crack locations, mode shape functionsof the remaining parts are determined. Other set of boundary conditions yields a second-order determinantthat needs to be solved for its roots. As the static case is approached, the roots of the characteristic equationgive the buckling load of the structure.

THEORETICAL FIGURE OF BEAM

Diagnosis of Cracks in Structures using FEA Analysis 29

DEVELOPMENT OF MODEL IN CATIA V5

Models of cantilever beam have been developed by using CATIA V5 with different crack size and at differentcrack location. Crack depth varied from 0.5mm to 3.0mm with an interval of 0.5mm. Similarly crack locationwas carried from 50mm to 700mm from fixed end with an interval of 50mm. The section of cantilever beam andthe developed model in CATIA have been shown in the fig.2. and fig.3. respectively. The crack profile with adepth of 0.5mm has been shown in fig. 4. Fig. 5. shows the definition of pocket operation for creation of crackof depth 1.0mm. In the similar way other models of cantilever with a crack at different location and at differentposition from the fixed end have been developed.

STEPS

SKETCHER

Figure 1: Cantilever Beam with Dimensions

Figure 2: Section of Cantilever Beam

PAD DEFINITION

Figure 3: Developed Model of Cantilever Beam

30 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu

Figure 4: Profile of Crack having CrackDepth of 0.5mm

Figure 5: Pocket Definition

PROCEDURE FOR ANALYSIS

• Modal analysis is selected from the analysis systems available in the work bench

Figure 6: Analysis System

Diagnosis of Cracks in Structures using FEA Analysis 31

• In the “Outline of schematic” of engineering data, structural steel is selected.

Figure 7: Material Type and Properties

• In the geometry tab, the CATIA V5 model is imported (Right Click -> Import geometry).

Figure 8: Imported Geometry

32 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu

• In the meshing sizing option is added.

Figure 9: Mesh Sizing

• Then the Generate Mesh option is selected.

Figure 10: Model Generated after Selecting Generate Mesh Option

• In the delais of sizing the whole imported model is selected (confirmed by clicking APPLY). The size ischanged from default to 1mm.

Figure 11: Meshed Model

Diagnosis of Cracks in Structures using FEA Analysis 33

• In the next step the use of ‘fixed support’ option in made.

Figure 12: Boundary Condition

• After that one face is selected (Confirmed by clicking APPLY tab)

Figure 13: Face Selected for Fixed Support

• Then the ‘solve option’ is selected which shows the modal frequencies.

Figure 14: Solve Option for Analysis

34 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu

• Each modal frequency or the whole modal frequency was selected to evaluate the mode shape.

Figure 15: To Create Mode Shape Results

• This will create all the mode shapes.

Figure 16: Mode Shape Generation

Diagnosis of Cracks in Structures using FEA Analysis 35

SOLUTION

Figure 17: Generated First Mode shape for beam without Crack

Figure 18: Generated second Mode shape for beam without Crack

Figure 19: Generated Third Mode shape for beam without Crack

36 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu

Figure 20: Generated First Mode shape for beam with Crack depth of 0.5mm located at 100mm from fixed end

Figure 21: Generated Second Mode shape for beam with Crack depth of 0.5mm located at 100mm from fixed end

Figure 22: Generated Third Mode shape for beam with Crack depth of 0.5mm located at 100mm from fixed end

Diagnosis of Cracks in Structures using FEA Analysis 37

TABULATION OF FREQUENCIES FOR DIFFERENT MODE SHAPES CONSIDERINGCRACK AND WITHOUT CRACK

Table 1Frequency Without Crack

Mode Frequency without crack(Hz)

1 5.1571

2 32.161

3 90.321

Table 2Frequency When Crack is at 50mm From Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.1527 5.1414 5.126 5.0972 5.0513 4.9702

2 32.144 32.097 32.033 31.916 31.735 31.423

3 90.282 90.203 90.104 89.907 89.611 89.111

Table 3Frequency When Crack is at 100 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.1534 5.1439 5.1309 5.1066 5.0679 4.9988

2 32.154 32.134 32.105 32.055 31.976 31.837

3 90.309 90.302 90.298 90.281 90.256 90.211

Table 4Frequency when Crack is at 150 Mm From Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.154 5.1462 5.1354 5.1155 5.0835 5.025

2 32.159 32.155 32.147 32.135 32.116 32.082

3 90.309 90.299 90.29 90.266 90.228 90.158

Table 5Frequency When Crack is at 200 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.1545 5.1483 5.1394 5.1229 5.0965 5.0489

2 32.161 32.161 32.159 32.159 32.159 32.158

3 90.294 90.243 90.173 90.036 89.817 89.427

38 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu

Table 6Frequency when Crack is at 250 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.155 5.1501 5.1429 5.1297 5.1086 5.0703

2 32.16 32.156 32.148 32.138 32.121 32.092

3 90.282 90.193 90.067 89.83 89.454 88.787

Table 7Frequency When Crack is at 300 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.1554 5.1516 5.146 5.1359 5.1195 5.0921

2 32.157 32.144 32.123 32.089 32.033 31.942

3 90.282 90.19 90.057 89.815 89.431 88.807

Table 8Frequency when Crack is at 350 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.1558 5.1529 5.1486 5.1408 5.1283 5.1077

2 32.153 32.13 32.092 32.028 31.926 31.769

3 90.294 90.234 90.145 89.983 89.728 89.321

Table 9Frequency when Crack is at 400 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.156 5.154 5.1508 5.1451 5.1359 5.1205

2 32.147 32.116 32.065 31.977 31.834 31.6

3 90.307 90.288 90.26 90.209 90.128 89.994

Table 10Frequency when Crack is at 450 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.1562 5.1548 5.1526 5.1487 5.1423 5.1315

2 32.145 32.109 32.05 31.948 31.784 31.513

3 90.314 90.313 90.313 90.312 90.31 90.309

Diagnosis of Cracks in Structures using FEA Analysis 39

Table 11Frequency when Crack is at 500 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.1566 5.1557 5.154 5.1513 5.1469 5.1391

2 32.147 32.108 32.049 31.944 31.771 31.474

3 90.309 90.289 90.257 90.203 90.113 89.963

Table 12Frequency When Crack is at 550 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.1567 5.1561 5.1551 5.1534 5.1508 5.1463

2 32.148 32.114 32.061 31.969 31.82 31.573

3 90.292 90.225 90.126 89.95 89.668 89.213

Table 13Frequency When Crack is at 600 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.168 5.1564 5.1558 5.1549 5.1533 5.1508

2 32.151 32.124 32.083 32.01 31.893 31.7

3 90.275 90.165 90.005 89.712 89.247 88.51

Table 14Frequency When Crack is at 650 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.1568 5.1567 5.1563 5.1559 5.1551 5.1538

2 32.154 32.136 32.108 32.061 31.983 31.852

3 90.27 90.146 89.972 89.65 89.135 88.292

Table 15Frequency When Crack is at 700 Mm from Fixed End

Mode Frequency (in Hz) with crack depth in mm

0.5 1 1.5 2 2.5 3

1 5.1569 5.1568 5.1566 5.1564 5.1561 5.1556

2 32.157 32.147 32.132 32.105 32.062 31.991

3 96.278 90.179 90.043 89.782 89.361 88.73

40 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu

Figure 23: For First Mode

Figure 24: For Second Mode

Figure 25: For Third Mode

Diagnosis of Cracks in Structures using FEA Analysis 41

DISCUSSION

Discussion is based upon the outputs of ANSYS workbench. Fig.2. shows how the section of the cantileverbeam developed, Fig.3.shows pad definition, Fig.4. is about profile of the crack and Fig.5. tells about pocketdefinition. The steps taken for the analysis by using ANSYS workbench as follows:

1. Modal analysis is selected from the analysis systems available in the work bench and shown in Fig.6.

2. Fig.7. shows, in the “Outline of schematic” of engineering data, structural steel is selected and the valueof density and young’s modulus is defined.

3. The model developed in CATIA is imported in ANSYS Work bench to find out natural frequencies andmode shapes is shown in Fig. 8.

4. Then mesh sizing option is inserted with mesh size of 1mm and then generate mesh option is selectedwhich is shown in Fig. 9. and Fig. 10.

5. Then the whole body is selected to be meshed which is shown in Fig. 11.

6. In the next step boundary condition is applied by selecting fixed support option from support tool barwhich is shown in Fig. 12.

7. After that one face is selected to show this end is fixed end support and shown in Fig. 13.

8. Then the ‘solve option’ is selected which shows the modal frequencies. Each modal frequency or thewhole modal frequency was selected to evaluate the mode shape by selecting create mode shape resultsand shown in Fig. 14. and Fig. 15.

9. Then natural frequencies and mode shapes can seen in the screen by selecting deformation optionswhich is shown in Fig. 16.

Fig. 17., 18, and 19 show the different mode shapes of vibrating beam having no crack. Fig. 20., 21, and 22show different mode shapes of the beam with crack at 100mm from fixed end. From these it has been noticedthat crack has a great influence on mode shapes. Outputs of ANSYS workbench for cantilever beam withdifferent crack location and different crack depth has given in the above tabulation. From these outputs graphshave been plotted by taking crack depth in x-axis and frequency in y-axis and shown in Fig. 23., Fig. 24. andFig. 25. for first mode, second mode and third mode of vibration respectively.. From the table given above andfrom Fig. 23., Fig. 24. and Fig. 25. it can be noticed that with increase in crack depth (at a certain crack location)frequency of vibration decreases for first mode, second mode and third mode of vibration. From these figures itcan be observed that there are significant variations in mode shapes at the vicinity of crack location due topresence of crack.

CONCLUSION

From the results and discussions the following conclusions have been drawn

• There is a change in natural frequencies and mode shapes of the vibrating beam in the presence ofcrack.

• It is also observed that with increase in crack depth natural frequency decreases for first mode, secondmode and third mode of vibration.

• The crack depth and crack location of a beam can be predicted by using the values of natural frequenciesobtained from ANSYS workbench within a very short time and thereby saving a considerable amountof computational time.

42 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu

References

[1] Rytter A. (1993), ‘Vibration based Inspection of Civil Engineering Structures’, Ph.D. thesis. Denmark: Aalborg University.

[2] Skrinar M. (2008), ‘Elastic Beam Finite Element with an Arbitrary Number of Cracks’, Finite Elements in Analysis &Design, 45, 181-189.

[3] Owolabi, G. M., Swamidas, N. R. S. and Seshadri, R. (2003), ‘Crack Detection in Beams using Changes in Frequenciesand Amplitudes of Frequency Response Functions’, Journal of Sound and Vibration, 265, 1-22.

[4] Rezaee Mousa and Hassannejad Reza (2010), ‘Free Vibration Analysis of Simply Supported Beam with Breathing Crackusing Perturbation Method’, Acta Mechanica Solida Sinica, 23, 459-470.

[5] Orhan, Sadettin (2007), ‘Analysis of Free and Forced Vibration of a Cracked Cantilever Beam’, NDT&E International,40, 443-450.

[6] Nahvi, H. and Jabbari, M. (2005), ‘Crack Detection in Beams using Experimental Model Data and Finite Element Model’,International Journal of Mechanical Sciences, 47, 1477-1497.

[7] Bakhary, N., Hao, H. and Deeks, A. J. (2007), ‘Damage Detection using Artificial Neural Network with Consideration ofUncertainties’, Engineering Structures, 29, 2806-2815.

[8] Kisa Murat (2011), ‘Vibration and Stability of Multi-cracked Beams under Compressive Axial Loading’, InternationalJournal of the Physical Sciences, 6, 2681-2696.

[9] Loutridis, S., Douka, E. and Hadjileontiadis, L. J. (2005), ‘Forced Vibration Behavior and Crack Detection of CrackedBeams using Instantaneous Frequency’, NDT&E International, 38, 411-419.

[10] Mazanoglu, K., Yesilyurt, I. and Sabuncu, M. (2008), ‘Vibration Analysis of Multiple-cracked Non-uniform Beams’,Journal of Sound and Vibration, 320, 977-989.

[11] Chasalevris Athanasios, C. and Papadopoulos Chris, A. (2006), ‘ Identification of Multiple Cracks in Beams under Bending’,Mechanical Systems and Signal Processing, 20, 1631-1673.

[12] Dharmaraju, N., Tiwari, R. and Talukdar, S. (2004), ‘Identification of an Open Crack Model in a Beam based on Force–Response Measurements’, Computers and Structures, 82, 167–179.

[13] Ruotolo, R. (1996), ‘Harmonic Analysis of the Vibrations of a Cantilevered Beam with a Closing Crack’, Computers andStructures, 60, 1057–1074.

[14] Baris Binici (2005), ‘Vibration of Beams with Multiple Open Cracks Subjected to Axial Force’, Journal of Sound andVibration, 287, 277–295.