Computational methodology of damage detection on ...

Int. J. Automotive Composites, Vol. X, No. Y, xxxx

Computational methodology of damage detection on composite cylinders: structural health monitoring for automotive components Ricardo de Medeiros Department of Aeronautical Engineering, São Carlos School of Engineering, University of São Paulo, Av. João Dagnone – 1100, 13573-120, São Carlos, SP, Brazil Fax: +55-16-3373-8346 E-mail: [email protected]

Marcelo Leite Ribeiro Federal University of Santa Catarina, Rua Prudente de Moraes 406, Joinville, Brazil Fax: +55-16-3373-8346 E-mail: [email protected]

Volnei Tita* Department of Aeronautical Engineering, São Carlos School of Engineering, University of São Paulo, Av. João Dagnone – 1100, 13573-120, São Carlos, SP, Brazil Fax: +55-16-3373-8346 E-mail: [email protected] *Corresponding author Abstract: A numerical investigation about the damage effects on the structural response of the composite cylinders damaged by impact loading was performed. Thus, it was proposed a computational methodology, which consists on carrying out four-step finite element (FE) analyses in progressive sequence. Firstly, modal analyses were carried out for the intact structure to determine the natural frequencies and modal shapes. Then, vibration analyses were performed for intact structure to obtain the frequency response function (FRF). After that, impact analyses were performed by using a material model, which is accessed to predict the damage. Based on damaged FE model, vibration analyses, again, were carried out to determine the new FRF. Thus, the results of the damaged structure were combined to intact model results by using a specific metric in order to indicate the damage or not in the composite cylinders. Finally, it was discussed about the advantages and limitations of SHM systems, which use vibration-based methods and piezoelectric sensors.

Copyright © 200x Inderscience Enterprises Ltd.

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R. de Medeiros et al. Keywords: structural health monitoring; laminated composites; finite element analysis; vibration-based method. Reference to this paper should be made as follows: de Medeiros, R., Ribeiro, M.L. and Tita, V. (xxxx) ‘Computational methodology of damage detection on composite cylinders: structural health monitoring for automotive components’, Int. J. Automotive Composites, Vol. X, No. Y, pp.xxx–xxx. Biographical notes: Ricardo de Medeiros is a PhD student at University of São Paulo (Brazil). His area of research is analysis and design of smart composite structures, mainly structural health monitoring. Marcelo Leite Ribeiro is an Assistant Professor of Aerospace Engineering at Federal University of Santa Catarina (Brazil). His area of research is analysis and design of composite structures, mainly damage and failure models. Volnei Tita is an Associate Professor of Aeronautic Engineering at University of São Paulo (Brazil) and the Head of the Aeronautical Structure Group. His area of research is analysis and design of composite structures and he has written over 100 papers in scientific journals and proceedings of conferences. He is the principal investigator at research projects with US Air Force and US Army, as well as coordinator of projects between University of São Paulo (Brazil) and Katholieke Universiteit Leuven (Belgium) and LMT-Cachan (France). This paper is a revised and expanded version of a paper entitled [title] presented at [name, location and date of conference].

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Introduction

The application of composite materials in automotive industry has increased in the last decades, mostly due to composite high stiffness and low weight (Al-Qureshi, 2001). Moreover, there are other positive aspects such as noise reduction, improved styling, and reduction of the parts as well as improvement of assembly processes. By one side, the intrinsic anisotropy of fibre reinforced polymeric materials allows achieve an optimal mechanical performance, regarding the structure geometry and applied loadings. Thus, composite materials can provide lighter structures without loss of safety, which is a very attractive characteristic for mobility industry. However, by other side, the damage mechanisms for composite materials are more complex than for metals. For example, intra-ply failures (e.g., fibre fractures and polymer matrix cracks) and delaminations (separation between plies) can occur, reducing the structural strength (Tita et al., 2008). Also, it is well know how the inspection affects the maintenance costs. Thus, the maintenance programme must be well planned, but predictions of the inspections are hard task, mainly for composite structures. In addition, unexpected loads could affect the structural integrity, changing the original maintenance plan. For example, despite the high strength in fibre direction, out-of-plane loads (due to frontal or lateral impact between two vehicles) could lead to severe damage in a composite structure. Intra-ply failures and delaminations can be caused by low velocity impact. In fact, there are several ways to produce this type of event, such as dropping tool, impact of small debris, etc. as specified by Schoeppner and Abrate (2000). In a metallic structure,

Comment [t1]: Author: If a previous version of your paper has originally been presented at a conference please complete the statement to this effect or delete if not applicable.

Computational methodology of damage detection on composite cylinders

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the damage caused by collisions can be detected due to plastic deformations. However, for composite structures, it is much more complicated (Ballère et al., 2009); because there are many invisible damages (e.g., delaminations) and the failure mechanisms are dependent on the geometry, laminate thickness, stacking sequence of plies, energy level and boundary conditions (ASTM, 2007). Therefore, several investigations about impacted composite flat plates have been conducted by different researchers (Xiao, 2007; Tita et al., 2008; Khalili et al., 2011), but only few studies have been performed in order to analyse the impact event on curved composite structures (Ballère et al., 2009; Kobayashi and Kawahara, 2012; Ribeiro et al., 2012a, 2012b, 2012c). Considering the scenario previously addressed, the structural health monitoring (SHM) techniques arise as a viable alternative to reduce the inspections and to optimise the structural maintenance programme, carrying out the repair only where and when is really necessary. According to Kessler et al. (2002), SHM has been approached in the literature as the acquisition, validation and analysis of technical data to facilitate lifecycle management decision. For composite structures, it is possible to manufacture a critical automotive component with piezoelectric (PZT) sensors in order to detect and measure the damage during the life time of the vehicle. This is very strategic, because, damage can be often related to a modification of physical parameters such as mass, stiffness or damping of the structure. Thus, some vibration-based methods have been developed to be applied on SHM systems by using PZT sensors. The application of modal analysis is one of the most used approaches, and it is based on the frequency response function (FRF) for detecting damage in structures as observed, in the past, by Cawley and Adams (1979). Therefore, some methods were created to assess the vibration response of the structure in order to detect, localise and quantify the damage as shown in the review written by Farrar and Doebling (1997). These methods have used the differences in natural frequencies and mode shapes between undamaged (intact) and damaged structure due to modifications of the structural stiffness, mass and damping. However, the greatest challenge is related to the damage sensitivity. Thus, modal and/or vibration-based techniques are often considered global methods. In spite of this consideration, some researchers have investigated life in service and system reliability via SHM systems, which use vibration-based methods to detect, localise and quantify the structural damage as shown by Hickman et al. (1991), Pandey et al. (1991), Wallaschek et al. (2002), Manson et al. (2003a; 2003b), Worden et al. (2003), Balageas et al. (2006), Adams (2007), Raghavan and Cesnik (2007), Fan and Qiao (2011), Medeiros et al. (2012, 2013a, 2013b, 2013c) and Sartorato et al. (2013). It is important to highlight that the most of the works were focus on flat beams and plates. Therefore, it is possible to figure out that SHM systems could be used to help the automotive companies in order to design better composite components and to improve the maintenance programmes of these structures, mainly for cylindrical geometries. As it can be observed, curved or cylindrical structures are very commonly found in automotive products, such as springs, exterior body panels, instrument panels, interior trim panels, door panel, air induction system and etc. Thus, in this paper, it is performed a computational investigation via finite element method (FEM) regarding the damage effects on the structural response of filament winding composite cylinders damaged by impact loading. Also, a piezoelectric (PZT) sensor has been used in order to obtain the dynamic behaviour of the FE model. Hence, firstly, undamaged cylinders made of composite material (resin epoxy and carbon fibre) were investigated by using modal

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Comment [t3]: Author: Please confirm if this citation pertains to 2012a, 2012b or both. Reference entries: Medeiros, R., Moreno, M.E., Marques, F.D. and Tita, V. (2012a) ‘Effective properties evaluation for smart composite materials’, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 34, pp.362–370. Medeiros, R., Sartorato, M., Ribeiro, M.L., Vandepitte, D. and Tita, V. (2012b) ‘Numerical and experimental analyses about SHM metrics using piezoelectric materials’, International Conference on Noise and Vibration Engineering – ISMA, Leuven, Belgium.

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analyses (MA) via FEM in order to determine the natural frequencies and the mode shapes. Second, vibration analyses were performed by using dynamic implicit methods for calculating the FRF of intact structures. After that, damage analyses of the FE model were carried out for low energy impact load. During the impact simulations, damage mechanisms were evaluated by a material model developed by Ribeiro et al. (2012a), which was implemented as a FORTRAN subroutine (UMAT – User Material subroutine for implicit integration analyses) and linked to the ABAQUSTM software. Based on damaged structure finite element (FE) model, numerical vibration analyses were performed. Thus, these results were combined to undamaged (intact) model results by using a specific metric in order to detect the damage in the structure. Finally, there is a discussion about the advantages and limitations of SHM systems, which use vibrationbased methods and PZT sensors.

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SHM via vibration-based method

SHM via vibration-based method consists on establishing differences in the modal properties of a structure by using dynamic response data before and after damage. The basic premise in vibration-based method is that damage changes the stiffness, mass, or energy dissipation properties of a structure. Thus, these changes may modify the dynamic response of the damaged structure. However, one of the most important aspects of vibration-based method is that damage consists on a local phenomenon and may not significantly influence the lower-frequency response of the structure. The usage of FRF is a good alternative for SHM systems, because structural FRFs may be sensitive to the damages in the component made of composite material. In fact, this sensitivity depends on different aspects, such as the size and the location of the damage, as well as the analysed mode shape. Thus, one strategy in order to improve the quantification of this sensitivity is to calculate a damage indicator as a metric. In this work, after a deeply investigation, it has been used the metric developed by Mickens et al. (2003). This damage indicator was used to quantify the difference in the FRF responses (H) between intact (undamaged) and damaged structures as follow:

⎛ Hi − Hd y ( f ) = abs ⎜ ⎜ Hi ⎝

⎞ ⎟, ⎟ ⎠

(1)

where the superscripts i and d denote the intact and damage structures, respectively, and the vertical bars represent the magnitude of the function. The damage indicator D is obtained by computing the mean of y(f) in the interest frequency range: D=

1 f 2 − f1

f2

∫ y( f )df ,

(2)

f1

where f1 is the lower frequency, and f2 is the upper frequency in the range of interest. For discrete sampling, equation (2) can be written as: D=

Δf f 2 − f1

n

∑ y ( f ), i

i

(3)

Computational methodology of damage detection on composite cylinders

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where ∆f is the frequency increment between measured points. Hence, equation (3) is a damage indicator, which provides a normalised measure of the damage in the structure. Thus, considering a SHM system by using piezoelectric (PZT) sensors, it is possible to obtain the FRFs of the intact and damaged structures. After that, not only the damage can be identified, but also the amount of the damage in a structure can be quantified by calculating the variable D.

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Composite cylinder and PZT sensor

The FE model is a cylinder made of composite material with a PZT sensor (piezoelectric wafer) attached on the outer surface (Figure 1). The composite cylinders are made of fourteen layers of epoxy resin reinforced by carbon fibres with stacking sequence equal [90/60/–60/90/60/–60/90]s. The cylinder geometries consist on outer diameter of 163.7 mm, length of 150 mm and total thickness of 3.4 mm. The piezoelectric wafer geometries consist on length of 50.8 mm, width of 25.4 mm and thickness of 0.5 mm (MIDÉTM QP10n). The properties of composite material, which was used to manufacture the cylinders, were provided by Ribeiro et al. (2012a) and by Tita et al. (2008) (Table 1). The PZT properties were calculated as given by Medeiros (2012a, 2012b) (Table 2). Figure 1

Geometry of the FE model: composite cylinder with the PZT sensor attached on the outer surface (see online version for colours)

In Table 1, it is noteworthy that for the composite material, the local coordinate system (1-2-3) is defined by the fibre reinforcement, i.e., one-direction is aligned to the reinforcement, two-direction is normal to the reinforcement and three-direction is normal to the plane of the layer. Hence, in the FE model, 0° fibre orientation is aligned to X axis (Figure 1). However, for the piezoelectric transducer, three-direction (local coordinate system) is related to the longitudinal direction of the piezoelectric element, but one- and two-directions are related to the normal direction of the piezoelectric element. Therefore, the polarisation direction is aligned to the three-direction of the PZT sensor. In the FE model, longitudinal direction of the PZT sensor is aligned to Y axis (Figure 1).

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R. de Medeiros et al. Elastic properties and density for the composite material – epoxy resin reinforced by carbon fibres

Table 1

Elastic properties

Values

E11 [GPa]

127

E22 [GPa]

10

G12 = G13 [GPa]

5.44

G23 [GPa]

3.05

υ12 = υ13

0.34

υ23

0.306

Density

Value 3

ρ [kg/m ]

1,580

Source: Tita et al. (2008)

In Table 2, cijeff denotes the elasticity tensor under a constant electric field, eijeff is the piezoelectric coupling tensor and εijeff is the dielectric tensor under a constant strain. The subscript eff expresses effective properties. Table 2

Effective coefficients and density for the smart material – MIDÉTM QP10n

Effective coefficients*

Values

c11eff [GPa]

81.73

c12eff [GPa]

5.23

eff 13

[GPa]

50.06

eff 33

[GPa]

46.35

eff 44

[GPa]

5.91

eff 66

[GPa]

5.63

c c c c

e13eff [C/m2]

–5.24

e15eff [C/m2]

1.13

eff [C/m2] e33

12.85

ε11eff [nF/m]

6.89

eff ε33 [nF/m]

5.73

Smart material density

Value

ρ [kg/m3]

7,400 E

S

Note: *Considering C and ε Source: Medeiros (2012a)

Computational methodology of damage detection on composite cylinders

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Computational methodology: FE models and numerical analyses

The computational methodology proposed in this work consists on carrying out four-step numerical analyses in progressive sequence as shown in Figure 2. As it can be observed, firstly, MA were carried out for the intact structure in order to determine the natural frequencies and modal shapes. Then, vibration analyses, via dynamic implicit algorithm of ABAQUSTM software, were performed for intact structure in order to obtain the FRFi. After that, impact numerical analyses, via dynamic implicit algorithm of ABAQUSTM software, were processed by using a material model (implemented as a UMAT – user material subroutine for dynamic implicit analysis), which is accessed to predict the damage in the composite structure. Based on damaged FE model, vibration analyses, again via dynamic implicit algorithm, were performed to determine the new FRFd. Finally, damage indicators D were calculated by applying the FRFs data in the equation (3). Figure 2

Computational methodology

For the composite cylinder FE models (Figure 3), it was used four node reduced integration shell elements with six degree of freedom (DOF) per node (defined as S4R – ABAQUSTM) even in the impact analyses. In this case, the mesh was refined until eliminating the severe element distortion in order to avoid numerical convergence issues during damage analyses. The composite cylinder was modelled with 19,200 quadrilateral elements with 19,456 nodes. The piezoelectric sensor was modelled by using eight node coupled 3D elements (defined as C3D8E – ABAQUSTM) with four DOF per node, which are three linear displacements and one electric voltage. Therefore, measurement of the electric potential in a specific node on the free surface corresponds to local information under an applied strain. In practice, the free surface of the PZT sensor is covered by an electrode, which ensures a uniform level of induced electric potential in this position (equipotential). The piezoelectric sensor was modelled by using 325 hexahedron elements with 728 nodes. Another important issue of FE model is to ensure the

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mechanical coupling between the composite cylinder and the PZT sensor. In order to have an ideal perfect bonding, the nodes on the bottom surface of the transducer is mechanically coupled to the ones on the top surface of the composite cylinder by using the ‘TIE’ tool in ABAQUSTM (Figure 3). Figure 3

Meshes of the FE model; boundary conditions for MA and DIA (before and after impact) (see online version for colours)

Once guaranteed mechanical coupling, it was necessary to define suitable boundary conditions for obtaining the electric potential in the PZT sensor. In fact, the dielectric properties of the MIDÉ QP10n provide homogeneous distribution of the induced electrical charges on the free surface of the transducer. Thus, all the nodes of the piezoelectric transducer surface attached to the composite cylinder were considered electrically grounded. And, the grounding nodes were assumed to have the potential equal to zero at any stage of strain. The purpose of grounding was to define a reference value for the induced voltages on the nodes of the free surface, which were measured. Thus, all nodes of the piezoelectric wafer free surface should respect to the equipotential condition.

4.1 MA (first analyses) As shown by the methodology (Figure 2), the first numerical simulations consist on performing MA via FEM. Two lines of nodes in the cylinder FE model, which are in opposite position of the PZT sensor, have been restricted for all DOF (Ux = Uy = Uz = URx = URy = URz = 0 – Figure 3) considering a future experimental setup, which will be carried out by the authors. MA were performed by using the eigenvalue solution in order to obtain the natural frequencies (Table 3) and the respective modal shapes of the intact structure (Figure 4). For these analyses, the frequency range from 0 to 1,000 Hz was considered, and the results were used to evaluate the natural frequencies obtained via dynamic implicit analyses (DIA).

Computational methodology of damage detection on composite cylinders Figure 4

Mode shapes for the first six natural frequencies via modal analysis (see online version for colours)

(a)

(b)

(c)

(d)

(e)

(f)

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Table 3

Natural frequencies for intact composite cylinder with PZT sensor via modal analysis

Mode Frequency [Hz] Figure 4

f1

f2

f3

f4

f5

f6

105.66

194.31

293.02

526.50

616.86

949.17

(a)

(b)

(c)

(d)

(e)

(f)

4.2 Vibration analyses of intact structure (second analyses) The second numerical simulations consist on carrying out DIA via FEM in order to obtain the FRFs for undamaged cylinder. The same boundary conditions (described previously for MA) were applied on the FE model. In addition, an impulse loading was applied on the surface of the cylinder close to the piezoelectric wafer (Figure 3), simulating the excitation of a hammer at the ‘loading’ point. Thus, for these analyses, the input signal is a transverse force of amplitude equal 1 N localised in a specific node of the FE model. The frequency of the force is applied in a range from 0 to 1,000 Hz, considering size step of 1.0 Hz for the numerical solution. Based on the input (impact of hammer) and output signals (acceleration of a specific node and PZT sensor measurement), fast Fourier transform (FFT) was applied in order to obtain the FRFs for the PZT sensor (H12) and for a specific node (H13 – simulating the position of an accelerometer) as shown by the Figure 3. Table 4 compares the natural frequency for intact structure by using MA and DIA. It is important to notice that the differences are not greater than 2.21%. Table 4

Natural frequencies for intact composite cylinder: MA vs. DIA Mode

f1

f2

f3

f4

f5

f6

MA

Frequency [Hz]

105.66

194.31

293.02

526.50

616.86

949.17

DIA-H12

Frequency [Hz]

108.0

197.0

297.0

532.1

622.1

950.1

DIA-H13

Frequency [Hz]

107.0

197.0

297.0

531.1

622.1

950.1

Δ* – Modal vs. DIA-H12

2.21%

1.38%

1.36%

1.06%

0.85%

0.10%

Δ* – Modal vs. DIA-H13

1.27%

1.38%

1.36%

0.87%

0.85%

0.10%

Note: *Δ = [(MA – DIA)/MA]

4.3 Impact analyses (third analyses) The third numerical simulations are related to the investigation of how the damage evolves in composite cylinders under impact loads (via DIA). In this work, it was considered that the composite cylinders were damaged by impact loading of a drop tower apparatus [Figure 5(a)]. Thus, a certain mass is dropped from a certain height, hitting the test coupon (composite cylinder), which is simply supported by the basis of the drop tower [Figure 5(b)]. In order to simulate the impact test, the present work uses a new damage model proposed by Ribeiro et al. (2012a) for composite materials, which was computational implemented as a FORTRAN Subroutine (UMAT) and linked to the FE dynamic implicit algorithms (ABAQUSTM). The used material model is simple to be implemented and has a low computational cost. Also, the model parameters are easy to be obtained as shown by Ribeiro et al. (2012a). Two lines of nodes in the cylinder FE model, which are in

Computational methodology of damage detection on composite cylinders

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opposite position of the impact point, have been restricted as simply supported [Ux = Uy = Uz = 0 – Figure 6(a)] to simulate the boundary conditions imposed by the experimental setup [Figure 5(b)]. The aluminium round impactor (diameter of 16 mm) was modelled by using discrete rigid triangular elements (defined as R3D3 – ABAQUSTM) and the mass of 3.24 Kg was applied in the mass point as shown by Figure 6(b). The impactor was modelled by using 1,308 triangular elements with 656 nodes. Moreover, all rotations (Rx, Ry, Rz) as well as the Ux and Uy displacements were restricted, and initial velocity of 4.35 m/s was applied in the impactor [Figure 6(a)]. Figure 5

(a) Experimental set-up of the impact test (b) Test coupon on the basis of the drop tower (see online version for colours)

(a) Figure 6

(b)

(a) Boundary conditions for impact DIA (b) Impactor mesh (see online version for colours)

(a)

(b)

The contact between the impactor and the composite cylinder was modelled by hard contact algorithm for normal interactions and by penalty method for tangential behaviour. Considering the ABAQUSTM software, the friction coefficient was set 0.3 for the tangential contact algorithm. Other important issue in simulating of the impact on composite filament winding cylinders consists of the dissipation of the impact energy.

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Part of the impact energy is dissipated by irreversible process as damage (intra-ply failures and delamination) and other part is dissipated by damping effects. However, damping in composite materials are dependent on several factors, such as fibre volume fraction, composite lay-up, environmental factors, force magnitude, etc. (Zabaras and Pervez, 1990). Also, the structure geometry has an important influence on the impact response. ABAQUSTM provides the Rayleigh’s model for direct integration dynamic analysis in order to simulate damping effects (Simulia, 2010). Thus, the Rayleigh model was used in order to simulate the damping effects in the structure by using a linear combination of mass and stiffness system matrices. In Figure 7(a), it is possible to observe the Displacement vs. time result, considering Rayleigh damping parameter α equal 0.1. Regarding the FE model, the maximum displacement is around 16 mm at 10.0 ms. In this work, the damage model evaluates fibre and matrix damage for normal and shear stresses. Considering the cylinder layup and impact energy level, all layers had matrix damaged due to shear and/or normal stresses. Regarding the fibre damage, only two internal layers had shown this damage mode. In the Ribeiro et al. (2012), it is possible to find more details about the damage model. Furthermore, Figure 7(b) only shows the damage zone in the first layer (outer layer of the cylinder) in the final step of the numerical simulation. It is very important to mention that this damaged model was used in the fourth analyses, i.e., vibration analyses of the damaged structure with the material properties reduced in the red zone. Figure 7

DIA results, (a) displacement vs. time (b) damaged zone in the outer layer (see online version for colours)

0 4

5

6

7

8

9

10

11

12

13

14

15

16

-0,002

Comment [t5]: Author: Please confirm if this citation pertains to 2012a, 2012b, 2012c or all. Reference entries: Ribeiro, M.L., Tita, V. and Vandepitte, D. (2012a) ‘A new damage model for composite laminates’, Composite Structures, Vol. 94, No. 2, pp.635–642. Ribeiro, M.L., Martins, T.H.P., Sartorato, M., Ferreira, G.F.O., Tita, V. and Vandepitte, D. (2012b) ‘Experimental analysis of low energy impact in filament winding cylinders’, International Journal of Vehicle Structures & Systems, Vol. 4, pp.118–122.

-0,004

Ribeiro, M.L., Martins, T., Vandepitte, D. and Tita, V. (2012c) ‘Progressive failure analysis of low energy impact in carbon fiber filament winding cylinders’, 10th World Congress on Computational Mechanics – WCCM, São Paulo, Brazil.

Displacment [m]

-0,006 -0,008 -0,01 -0,012 -0,014 -0,016 -0,018 Time [ms]

(a)

(b)

4.4 Vibration analyses of damaged structure (fourth analyses) The fourth numerical simulations consist on performing DIA for damaged composite cylinder, obtained from the damage analyses under impact loading (third analyses). Thus, an impulse loading was applied close to the PZT sensor as shown by the second analyses. The input signal was a transverse force of amplitude equal 1 N localised in a node of the FE model (Figure 3). The frequency of the force was applied in a range from 0 to 1,000 Hz, considering size steps of 1.0 Hz for numerical solution. Thus, again, two lines of nodes in the cylinder FE model, which are in opposite position of the PZT sensor, have been restricted for all DOF (Ux = Uy = Uz = URx = URy = URz = 0 – Figure 3), considering a future experimental setup, which will be carried out by the authors.

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Computational methodology of damage detection on composite cylinders

Table 5 shows the comparison between the frequencies obtained via DIA for intact and damaged structure by using PZT sensor (H12) or via a specific node of FE model (H13 – Figure 3). Table 5

Natural frequencies for intact and damaged composite cylinder via PZT sensor Mode

f1

f2

f3

f4

f5

f6

Intact H12

Frequency [Hz]

108.0

197.0

297.0

532.1

622.1

950.1

Intact H13

Frequency [Hz]

107.0

197.0

297.0

531.1

622.1

950.1

Damaged H12

Frequency [Hz]

107.0

197.0

296.0

531.1

621.1

946.1

Damaged H13

Frequency [Hz]

108.0

197.0

297.0

531.1

621.1

946.1

Δ*: intact vs. damaged H12

0.93%

0.0%

0.34%

0.19%

0.16%

0.42%

Δ*: intact vs. damaged H13

0.93%

0.0%

0.0%

0.0%

0.16%

0.42%

Note: *[Δ = (Hi – Hd)/Hi]

Figure 8 shows the magnitude log-scale plot of the electric potential calculated from 0 Hz to 1,000 Hz frequency range. Six resonance peaks are well distinguished. As confirmed by Table 5, there are small frequency changes that it is a typical behaviour when the damage caused by impact is localised [as shown by numerical simulation – Figure 7(b)]. Thus, the identification of the damage is much more complicated. Figure 8

FRF of the composite cylinder by using PZT sensor: undamaged vs. damaged (see online version for colours)

Figure 9 shows the magnitude log-scale plot of the acceleration calculated from 0 Hz to 1,000 Hz frequency range. Again, it is possible to observe that there are small frequency differences between undamaged and damaged FRFs as observed at Table 5. Also, it can be observed that the frequency shift is often larger for higher modes. Thus, it is very strategic to calculate the damage indicator D as recommended by equation (3) for lower frequencies.

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R. de Medeiros et al. FRF of the composite cylinder by using a node of the FE model: undamaged vs. damaged (see online version for colours)

4.5 Damage metric The damage indicator ‘D’ values for intact and damaged composite cylinder are given in Table 6. These values are obtained by a PZT sensor (H12) and by a specific node of the FE model, which represents an accelerometer (H13). It is verified that D(a, b) indicates the point a of input force and the point b of output signal as shown by Figure 3. Table 6

Damage indicator (metric) results for the composite cylinder

Damage indicator

Intact

Damaged

D(1, 2)

0.0

0.8266

D(1, 3)

0.0

0.7039

It is important to notice that, in case of no damage, the response of the intact and damage structure are the same and as the damage indicator represents the difference between intact and damaged structure, this value ‘D’ is equal to zero. It was observed that the damage indicator D(1, 2) is greater than D(1, 3). This difference can be explain due to the sensor position, i.e., as the equation (1) has considered the difference of amplitudes, the piezoelectric transducer position is more susceptible to show vibration amplitudes higher than ones for a specific node, which simulates an accelerometer position (Figure 3). Moreover, the damage indicator values may provide a prediction of the damage severity, because the difference of amplitudes can be influenced by the degradation material properties due to the impact event. Hence, the more critical value for ‘D’ could be associated to a design criterion.

Computational methodology of damage detection on composite cylinders

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Conclusions

A damage identification numerical study was shown for cylinders made of epoxy resin reinforced by carbon fibre damaged by low velocity impact via vibration-based method and piezoelectric sensor. Therefore, it was proposed a computational methodology, which consists on performing four-step different numerical analyses in progressive sequence: MA for intact structure; vibration analyses for intact structure; impact analyses and vibration analyses for damaged structure. After that, it was calculated a damage indicator based on the results provided by numerical analyses. Regarding the MA for intact structure, it was determined the natural frequency and the mode shape of the intact structure. Thus, it is possible to define the frequency range for the next analyses. Considering the vibration analyses for intact structure, it was obtained the mechanical behaviour in function of time, after that, it was applied the FFT to determine the FRF of the structure without damage. According to impact analyses, material damage model was used in order to predict the damage evolution during an impact test created by a drop tower apparatus. Based on the damaged structure FE model, it was determined the FRF by using vibration analyses, again. The numerical results demonstrated the usefulness of vibration-based method by using piezoelectric sensor in detection of damage caused through low velocity impact loading. This methodology has the advantage to be easily implemented and has low cost. Also, it can be provide the global behaviour of the overall condition of the system as well as local information on structural health condition and do not require direct human accessibility to the structure. On the other hand, there are some limitations, as the methodology is a difference between the data of the intact and damaged structure, if the data show noise, this difference can be considered as damage. For example, the comparison between FRFs from intact and damaged structure confirmed that the localised damage promoted small influence on the lower frequencies. Therefore, it is concluded that the identification of the damage cannot be based on the difference of natural frequencies for intact and damaged structure. Thus, a damage indicator is strongly recommended. In this work, it was shown that the damage metric developed by Mickens et al. (2003) is a good option not only to identify the damage, but also to provide a prediction of the damage severity. However, even using damage metrics, SHM systems based on vibration methods provide little information about the location and extension of the damage, unless large quantities of sensors are employed. And, this will probably increase the cost and the weight of the component. Finally, it is possible to conclude that there is a great future perspective for the application of vibration-based methods by using PZT sensors on SHM systems for composite structures in the automotive industry. In the future works, the authors will show the methodology by using experimental methods in order to evaluate better the potentialities of the numerical analyses carried out in this paper.

Acknowledgements The authors would like to thank Sao Paulo Research Foundation (FAPESP – process number: 2012/01047-8), as well as, Coordination for the Improvement of the Higher Level Personnel (CAPES process number: 011214/2013-09), National Council for Scientific and Technological Development (CNPq process number: 135652/2009-0 and

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208137/2012-2) and FAPEMIG for partially funding the present research work through the INCT-EIE. The authors would like to thank Prof. Reginaldo Teixeira Coelho (EESC-USP) for the ABAQUSTM license.

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Computational methodology of damage detection on composite cylinders

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