DIAGNOSIS OF CRACKS IN STRUCTURES USING FEA ANALYSIS

Transcription

1 Vol. 4 No. 0 ISSN: pp. 7-4 IJAAIES International Science Press: India 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 has been done by using finite element method with the help of ANSYS workbench and CATIA V5. A beam with crack at different locations and without crack considered for the experiment. At different crack location, natural frequencies and mode shapes have been determined. It has been noticed that when the crack depth increases natural frequency decreases and also there is a deviation in the mode shape. So by considering the drops in natural frequencies and changes 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 manufacturing process. Because of the occurrence of cracks in the structures may lead to change the whole behavior of the element and consequently decreases its safety. Also the presence of crack indicates fatigue problem. So the detection or identification of cracks in the structures is a relevant issue. According to Rytter [] there are four different levels of damage detection in a structure can be attained, they are Level : detection of the existence of damage Level :level + damage location Level : level + damage quantification Level 4: level + prediction of the remaining service life Skrinar [] replaced each crack by a linear rotational spring with connecting two adjacent elastic parts to find the presence of crack by taking the stiffness and geometrical stiffness matrices into account. Owolabi et al. [] used two sets of aluminium beams with each set consisted of seven beams, the first set had fixed ends and the second set was simply supported for the experiment. In order to detect, quantify and determine the extent of crack and locations they used the technique which depends upon the measured changes in the first three natural frequencies and the corresponding amplitudes of the measured acceleration frequency response functions. Rezaee et al. [4] considered a nonlinear model for the fatigue crack and used perturbation method for solving the governing equation of motion of the cracked beam. They derived there is a change in damping takes place due to the change in crack parameters, geometric dimensions and mechanical properties of the cracked beam. Orhan Sadettin [5] has studied the free and forced vibration analysis of a cracked beam was performed in order to identify the crack in a cantilever beam. Single and two-edge cracks were evaluated. Dynamic response of the forced vibration better describes changes in crack depth and location than the free vibration in which the difference between natural frequencies corresponding to a change in crack depth and location only is a minor effect. Nahvi and Jabbari [6] have developed an analytical, as well as experimental approach to the crack detection in cantilever beams by vibration analysis. An experimental setup is designed in which a cracked cantilever beam is excited * Robotics Laboratory, Department of Mechanical Engineering, National Institute of Technology, Rourkela , Odisha, India, dayalparhi@yahoo.com; manoj986nitr@gmail.com; mechchinu@gmail.com

2 8 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 terms of 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 point estimate 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 the existence of undamaged and damaged states. Kisa et al. [8] Presents a novel numerical technique applicable to analyze the free vibration analysis of uniform and stepped cracked beams with circular cross section. In this approach in which the finite element and component mode synthesis methods are used together, the beam is detached into parts from the crack section. These substructures are joined by using the flexibility matrices taking into account the interaction forces derived by virtue of fracture mechanics theory as the inverse of the compliance 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 for free vibration analysis of beams with transverse non-propagating open cracks. Numerical results showing good agreement with the results of other available studies, address the effects of the location and depth of the cracks on the natural frequencies and mode shapes of the cracked beams. Modal characteristics of a cracked beam can be employed in the crack recognition process. Loutridis et al. [9] present a new method for crack detection in beams based on instantaneous frequency and empirical mode decomposition. The dynamic behavior of a cantilever beam with a breathing crack under harmonic excitation is investigated both theoretically and experimentally. Mazanoglu et al. [0] have followed an energy-based method for vibration identification of non-uniform Euler-Bernoulli beams having open cracks. They considered the change in strain at the cracked beam and estimated the distribution of energy and the stress field due to angular displacement of beam. Chasalevris and Papadopoulos. [] have studied the dynamic behaviour of a cracked beam with two transverse surface cracks. Each crack is characterised by its depth, position and relative angle. A local compliance matrix of two degrees of freedom, bending in the horizontal and the vertical planes is used to model the rotating transverse crack in the shaft and is calculated based on the available expressions of the stress intensity factors and the associated expressions for the strain energy release rates. Dharmaraju et al. [] have used Euler Bernoulli beam element in the finite element modeling. The transverse surface crack is considered to remain open. The crack has been modeled by a local compliance matrix of four degrees of freedom. This compliance matrix contains diagonal and off-diagonal terms. A harmonic force of known amplitude and frequency is used to dynamically excite the beam. Ruotolo et al. [] has investigated forced response of a cantilever beam with a crack that fully opens or closes, to determine depth and location of the crack. In their study, left end of the beam is cantilevered and right end is free. The harmonic sine force was applied on the free end of the beam. Vibration amplitude of the free end of the beam was taken into consideration. It was shown that vibration amplitude changes, when depth and location of the crack change. Baris Binici. [4] has proposed a new method is to obtain the Eigen frequencies and mode shapes of beams containing multiple cracks and subjected to axial force. Cracks are assumed to introduce local flexibility changes and are modeled as rotational springs. The method uses one set of end conditions as initial parameters for determining the mode shape functions. Satisfying the continuity and jump conditions at crack locations, mode shape functions of the remaining parts are determined. Other set of boundary conditions yields a second-order determinant that needs to be solved for its roots. As the static case is approached, the roots of the characteristic equation give the buckling load of the structure. THEORETICAL FIGURE OF BEAM

3 Diagnosis of Cracks in Structures using FEA Analysis 9 Figure : Cantilever Beam with Dimensions DEVELOPMENT OF MODEL IN CATIA V5 ls of cantilever beam have been developed by using CATIA V5 with different crack size and at different crack location. Crack depth varied from mm to.0mm with an interval of mm. Similarly crack location was carried from 50mm to 700mm from fixed end with an interval of 50mm. The section of cantilever beam and the developed model in CATIA have been shown in the fig.. and fig.. respectively. The crack profile with a depth of mm has been shown in fig. 4. Fig. 5. shows the definition of pocket operation for creation of crack of depth.0mm. In the similar way other models of cantilever with a crack at different location and at different position from the fixed end have been developed. STEPS SKETCHER Figure : Section of Cantilever Beam PAD DEFINITION Figure : Developed l of Cantilever Beam

4 0 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu Figure 4: Profile of Crack having Crack Depth of mm Figure 5: Pocket Definition PROCEDURE FOR ANALYSIS Modal analysis is selected from the analysis systems available in the work bench Figure 6: Analysis System

5 Diagnosis of Cracks in Structures using FEA Analysis 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

6 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 0: l Generated after Selecting Generate Mesh Option In the delais of sizing the whole imported model is selected (confirmed by clicking APPLY). The size is changed from default to mm. Figure : Meshed l

7 Diagnosis of Cracks in Structures using FEA Analysis In the next step the use of fixed support option in made. Figure : Boundary Condition After that one face is selected (Confirmed by clicking APPLY tab) Figure : Face Selected for Fixed Support Then the solve option is selected which shows the modal frequencies. Figure 4: Solve Option for Analysis

8 4 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu Each modal frequency or the whole modal frequency was selected to evaluate the mode shape. Figure 5: To Create Shape Results This will create all the mode shapes. Figure 6: Shape Generation

9 Diagnosis of Cracks in Structures using FEA Analysis SOLUTION Figure 7: Generated First shape for beam without Crack Figure 8: Generated second shape for beam without Crack Figure 9: Generated Third shape for beam without Crack 5

10 6 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu Figure 0: Generated First shape for beam with Crack depth of mm located at 00mm from fixed end Figure : Generated Second shape for beam with Crack depth of mm located at 00mm from fixed end Figure : Generated Third shape for beam with Crack depth of mm located at 00mm from fixed end

11 7 Diagnosis of Cracks in Structures using FEA Analysis TABULATION OF FREQUENCIES FOR DIFFERENT MODE SHAPES CONSIDERING CRACK AND WITHOUT CRACK Table Frequency Without Crack Frequency without crack(hz) Table Frequency When Crack is at 50mm From Fixed End Table Frequency When Crack is at 00 Mm from Fixed End Table 4 Frequency when Crack is at 50 Mm From Fixed End Table 5 Frequency When Crack is at 00 Mm from Fixed End

12 8 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu Table 6 Frequency when Crack is at 50 Mm from Fixed End Table 7 Frequency When Crack is at 00 Mm from Fixed End Table 8 Frequency when Crack is at 50 Mm from Fixed End Table 9 Frequency when Crack is at 400 Mm from Fixed End Table 0 Frequency when Crack is at 450 Mm from Fixed End

13 9 Diagnosis of Cracks in Structures using FEA Analysis Table Frequency when Crack is at 500 Mm from Fixed End Table Frequency When Crack is at 550 Mm from Fixed End Table Frequency When Crack is at 600 Mm from Fixed End Table 4 Frequency When Crack is at 650 Mm from Fixed End Table 5 Frequency When Crack is at 700 Mm from Fixed End

14 40 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu Figure : For First Figure 4: For Second Figure 5: For Third

15 Diagnosis of Cracks in Structures using FEA Analysis 4 DISCUSSION Discussion is based upon the outputs of ANSYS workbench. Fig.. shows how the section of the cantilever beam developed, Fig..shows pad definition, Fig.4. is about profile of the crack and Fig.5. tells about pocket definition. The steps taken for the analysis by using ANSYS workbench as follows:. Modal analysis is selected from the analysis systems available in the work bench and shown in Fig.6.. Fig.7. shows, in the Outline of schematic of engineering data, structural steel is selected and the value of density and young s modulus is defined.. The model developed in CATIA is imported in ANSYS Work bench to find out natural frequencies and mode shapes is shown in Fig Then mesh sizing option is inserted with mesh size of mm and then generate mesh option is selected which is shown in Fig. 9. and Fig Then the whole body is selected to be meshed which is shown in Fig.. 6. In the next step boundary condition is applied by selecting fixed support option from support tool bar which is shown in Fig.. 7. After that one face is selected to show this end is fixed end support and shown in Fig.. 8. Then the solve option is selected which shows the modal frequencies. Each modal frequency or the whole modal frequency was selected to evaluate the mode shape by selecting create mode shape results and shown in Fig. 4. and Fig Then natural frequencies and mode shapes can seen in the screen by selecting deformation options which is shown in Fig. 6. Fig. 7., 8, and 9 show the different mode shapes of vibrating beam having no crack. Fig. 0.,, and show different mode shapes of the beam with crack at 00mm from fixed end. From these it has been noticed that crack has a great influence on mode shapes. Outputs of ANSYS workbench for cantilever beam with different crack location and different crack depth has given in the above tabulation. From these outputs graphs have been plotted by taking crack depth in x-axis and frequency in y-axis and shown in Fig.., Fig. 4. and Fig. 5. for first mode, second mode and third mode of vibration respectively.. From the table given above and from Fig.., Fig. 4. and Fig. 5. 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 it can be observed that there are significant variations in mode shapes at the vicinity of crack location due to presence 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 of crack. It is also observed that with increase in crack depth natural frequency decreases for first mode, second mode and third mode of vibration. The crack depth and crack location of a beam can be predicted by using the values of natural frequencies obtained from ANSYS workbench within a very short time and thereby saving a considerable amount of computational time.

16 4 D. R. Parhi, Manoj Kumar Muni & Chinmaya Sahu References [] Rytter A. (99), Vibration based Inspection of Civil Engineering Structures, Ph.D. thesis. Denmark: Aalborg University. [] Skrinar M. (008), Elastic Beam Finite Element with an Arbitrary Number of Cracks, Finite Elements in Analysis & Design, 45, [] Owolabi, G. M., Swamidas, N. R. S. and Seshadri, R. (00), Crack Detection in Beams using Changes in Frequencies and Amplitudes of Frequency Response Functions, Journal of Sound and Vibration, 65, -. [4] Rezaee Mousa and Hassannejad Reza (00), Free Vibration Analysis of Simply Supported Beam with Breathing Crack using Perturbation Method, Acta Mechanica Solida Sinica,, [5] Orhan, Sadettin (007), Analysis of Free and Forced Vibration of a Cracked Cantilever Beam, NDT&E International, 40, [6] Nahvi, H. and Jabbari, M. (005), Crack Detection in Beams using Experimental l Data and Finite Element l, International Journal of Mechanical Sciences, 47, [7] Bakhary, N., Hao, H. and Deeks, A. J. (007), Damage Detection using Artificial Neural Network with Consideration of Uncertainties, Engineering Structures, 9, [8] Kisa Murat (0), Vibration and Stability of Multi-cracked Beams under Compressive Axial Loading, International Journal of the Physical Sciences, 6, [9] Loutridis, S., Douka, E. and Hadjileontiadis, L. J. (005), Forced Vibration Behavior and Crack Detection of Cracked Beams using Instantaneous Frequency, NDT&E International, 8, [0] Mazanoglu, K., Yesilyurt, I. and Sabuncu, M. (008), Vibration Analysis of Multiple-cracked Non-uniform Beams, Journal of Sound and Vibration, 0, [] Chasalevris Athanasios, C. and Papadopoulos Chris, A. (006), Identification of Multiple Cracks in Beams under Bending, Mechanical Systems and Signal Processing, 0, [] Dharmaraju, N., Tiwari, R. and Talukdar, S. (004), Identification of an Open Crack l in a Beam based on Force Response Measurements, Computers and Structures, 8, [] Ruotolo, R. (996), Harmonic Analysis of the Vibrations of a Cantilevered Beam with a Closing Crack, Computers and Structures, 60, [4] Baris Binici (005), Vibration of Beams with Multiple Open Cracks Subjected to Axial Force, Journal of Sound and Vibration, 87,