Location of delaminations in curved laminated panels

Accepted Manuscript Location of Delaminations in Curved Laminated Panels A. Muc, A. Stawiarski PII: DOI: Reference:

S0263-8223(15)00574-7 http://dx.doi.org/10.1016/j.compstruct.2015.07.030 COST 6609

To appear in:

Composite Structures

Received Date: Accepted Date:

10 June 2015 10 July 2015

Please cite this article as: Muc, A., Stawiarski, A., Location of Delaminations in Curved Laminated Panels, Composite Structures (2015), doi: http://dx.doi.org/10.1016/j.compstruct.2015.07.030

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LOCATION OF DELAMINATIONS IN CURVED LAMINATED PANELS A. Muc and A. Stawiarski Institute of Machine Design Cracow University of Technology Kraków, Poland e-mail: [email protected]

Abstract In the present study the Structural Health Monitoring (SHM) area of science was applied to several levels of analysis: 1, confirmation the existence of damage, 2, determination of the size, location and orientation of the defect, 3, assessment the severity of the damage, 4, controlling the growth of damage and prognosis of service life of construction. The wave propagation in the panel/plate with local delamination was analyzed both numerically and experimentally. The excitation signal was generated by one actuator or more actuators to analyze the effectiveness of the method. Data from PZT sensors were collected by the analyzer and then signals were converted to digital ones with the use of MATLAB package. Based on collected data from different sensors and comparison with wave propagation model of intact structures it is possible to determine localization, size and orientation of defect using the proposed damage index. Experimental analysis has been compared with numerical results both for plates and flat cylindrical panels. In the next step of our analysis we considered optimal design of the location and number of piezoelectric sensors and actuators to characterize their influence on the structural dynamic response.

1. Introduction The dynamic development of the contemporary technology caused a profound change in the design methods of the engineering structures. Continuously improvement of the existence production processes as well as application of the new methods affect on the dissemination of the composite materials as an alternative solution for typical materials. The safety and reliability of the structures mostly depend on effectiveness of the monitoring methods. The necessity of permanent monitoring the state of the structures and prognosis of the service life, as well as the economical aspects associated with optimal utilization of the machines and limitation of the maintenance time brought about the development of the Structural Health Monitoring (SHM) methods and systems. During the past two decades, extensive researches have been conducted in the area of vibrational based damage detection methods. The number of non-destructive inspection technics grows and depend on engineering application [1,2,3]. A basic assumption of SHM systems has been presented by Worden et al. [4,5]. A literature review which summarize the methods of data acquisition, signal processing, feature extraction and data fusion techniques can be found in Refs. [6,7,8,9]. In spite of many commercially used SHM systems and methods, most of the popular damage detection techniques do not give complete satisfaction because of their limitation. However only few methods can be applied in different type constructions made of various materials. One of the most efficient of them is the guided wave propagation method which is the subject of interest for researchers both in time and frequency domain for three decades. A classification of dynamic-based SHM techniques as a relationship between interrogation frequency and damage size was presented by Gopalakrishnan et al. [10]. A several techniques of inspection have been developed in time domain. Jeong et al. [11] presented a time reversal

method for damage detection and localization in plates. A several modification of this method has been introduced by Sohn et al. [12]. A time-of-flight (TOF) method with techniques of data fusion has been presented by Xu, Yu and Giurgiutiu [13]. A direct comparison of the signals from defected and intact structures has been utilized by Kessler [14] and Giurgiutiu [15]. To describe the state of the structure based on time history data the statistical analysis must be applied to characterize the damage size and type. A variety of parameters and functions summarized by Adams [8] may be used by damage detection and description algorithm. The efficiency of the damage index definition depends on many parameters like size and type of the defect. One of the most effective statistical measure is correlation coefficient [16]. It is one of the most often used both in laboratory experiments [17,18,19] and real structures applications [20,21,22]. Delaminations in composite materials are one of the most danger failure mode results typically from impact damage or manufacturing imperfections. The presence of delamination leads to a reduction in the overall buckling strength of the structure and usually tend to grow rapidly causing a fatal structural failure. The online SHM systems based on Lamb wave propagation are the most efficient techniques for detection such a defect. The waves reflected from the delamination are used in pulse-echo technique of inspection [23,24]. The pitch-catch method needs a several sensors in the analyzed area from which one is an actuator and the response signal from the sensors are taken into account in damage detection consideration [25]. A many researchers are focused to develop the method of delamination detection based on multipoint measuring system [26,27,28]. However it is worth to point out that most of the vibration-based methods, presented in literature, are only applied to simple beam-like, plate or truss structures. A study about the damage in laminated composite cylindrical shells has been carried out only by Krishnamurthy et al. [29] and Muc, Stawiarski [30].A preliminary considerations and numerical results has been presented by Muc and Stawiarski [31,32]. In the present paper we intend to develop an elastic wave-based damage identification technique for laminated composite cylindrical structures. It is essential to understand wave propagation behaviour in multilayered anisotropic media with delaminations. In details, the aim of this study is to evaluate delamination in cylindrical composite panels using guided waves and detect debonding using an inverse algorithm based guided wave signals activated and captured by surface-mounted PZT elements. The analysis is carried out both experimentally and theoretically with the use of the finite element method and the damage index. 2. Finite element modeling of structures with an artificial delamination Nowadays the finite element method is usually applied in the analysis of various engineering problems. The FE ANSYS package was frequently used to evaluate dynamic behaviour of composite structures. In the present study the 3D solid95 finite element type with a 20 nodes was used in modelling a structure. A higher order version of a classical 8node solid element with three degrees of freedom per node allows us to obtain accurate results of the analysis. Delamination, being a debonding of neighbourhood plies in composite laminates, is the most common and danger defect which may originate during fabrication or utilization of a structure under out-of-plane stresses or subjected to transverse impact. In this study from several methods of modelling of delamination the direct model based on non-

merged nodes between lamina on area of the defects was used (Fig. 1) with eight layers of elements in the shell thickness corresponding to eight laminae. A surface contact algorithm was introduced to process the contact problem arising from delamination, primarily relaxing restrictions on two contactable surfaces.

Fig. 1. The finite element model of the delamination An appropriate finite element model of delamination has to satisfy several requirements which have been pointed out by Ye and Su [19]. In the considered case the finite element mesh density features 8 node per wavelength. The time step for dynamic calculation is less than the ratio of the minimum distance of any two adjoining nodes to the maximum wave velocity. An approximation to the stability limit is often introduced as the smallest transit time of a dilatational wave across any element in a FE model: L (1) ∆t ≤ min Cd where Lmin is the smallest element dimension in the FE model and Cd is the dilatational wave speed defined by the effective Lame’s constants [15]. The above mentioned features of finite element model and application of higher order element type allow us to obtain accurate characteristics of guided wave propagation and scattering phenomena. A concentrated force applied to the model of composite cylindrical panel varies with time function and simulate the load generated by real PZT element with 100kHz excitation frequency. The excitation signal was generated by one actuator and the data from the sensors placed after an artificial defected zone was compared with the results from an intact structure. The computed deflections are strongly affected by the value of the shallowness parameter f (see Fig.2):

f = D 4 12( 1− ν12ν 21 ) / Rt )

(2)

and are the smallest for the cylindrical shells (R=D/2). It demonstrates evidently that the excitation amplitude used for the detection of cylindrical panels displacements must be higher than for plated structures.

Total displacement [m]

0

-0.01

Location of the sensor -0.02

-0.03

-0.04

-0.05 0

0.1

0.2

0.3

0.4

0.5

Shallowness parameter f/D

Fig.2 Variations of the displacements with the dimensionless shallowness parameter

3. Experimental set-up

With the PZT actuators and sensors both located on the cylindrical panel, Fig.1, activation and acquisition of ultrasonic wave signals were fulfilled using an active signal generation and data acquisition system, consisting mainly of a signal generation unit, signal amplifier, signal conditioner and signal digitizer. 5-cycle sinusoidal tone bursts enclosed in a Hanning window were generated and applied to the PZT actuator, and the wave signals were captured using the PZT sensor at a sampling rate of 100 kHz (a schematic is shown in Fig.3). The acquisition duration was set to insure that at least the first reflected wave signal from the far end of the structure was captured.

Fig.3 Schematic diagram of experimental set-up The cylindrical composite panel was made of 8 layers and had the following geometrical parameters: L=298 [mm], R=92 [mm], t=1.8 [mm]. The cylindrical panel was made of glass

woven roving having the following properties: Elong=Ecircumf=13.14 [GPa], G=9.68 [GPa], ν=0.25,ρ=1100 [kg/cm3]. The single local square delamination (Fig. 3) having the size 10 [mm] and being in the middle of the laminated structure was introduced between fourth and fifth layers. The circular PZT element electrodes, measuring 10 mm in diameter and 1 mm in thickness, were surface-mounted on the specimen. One PZT element served as the actuator and the others as sensors. It is obvious that any observations of waves is strongly dependent both on the locations of the actuator/s and sensors. To analyze deeper those effects at the beginning let us consider the actuator and sensors configuration in the form presented in Fig. 4. Various localization of the sensors are taken into account to determine the influence zone of delamination on wave propagation path.

Fig. 4. Top view of delaminated cylindrical panel with 10 mm square delamination and the assumed actuator and sensor configuration. Each PZT disk in the configuration (Fig.4) is chosen following an optimal criterion introduced by Kessler et al. [20], to minimise the geometric effect and consequently avoid uneven wave propagation: RPZT =

v wave  1   n +  , n = 0 ,1,2 ,... f  2

(3)

where RPZT is the radius of the PZT disk; vwave and f are the wave velocity (circa 6000 m/s in quasi-isotropic laminates) and frequency. Based on the above equation diverse transducer networks can be conveniently customized to different geometries and boundary conditions. The sensor network configuration can be also determined measuring the difference in ToF (Time-of-flight) between the incident wave signal and the damage reflection captured by sensors – Ref. [15].

4. Damage Index

While one PZT element functioned as the actuator to activate wave signals (Fig.4) , the others functioned as sensors to capture the wave signals. For each individual sensing path it is possible to define damage index Ik where the index k corresponds to the number of the path. It is assumed that the k-th path between the sensor and actuator is surrounded by the ellipse (the assumed damage area) having the major and minor semi-axis denoted by the a and b, respectively. The values a and b are chosen in the arbitrary way, i.e. a can be greater, lower or equal to the distance between the sensor and actuator, and b
scaling parameter, β, that can be designated as the reciprocal of eccentricity, ε, i.e. ε=1/ β = 1− b 2 / a 2 . For the k-th path the estimation of probability of the presence of damage is defined in the following way:

I k ( x , y ) = (1− λ k )

β − rk β −1

(4)

where:  Rc (x , y , xak , yak , xsk , ysk ) if Rc ( x , y ,xak , yak , xsk , ysk ) < β rk =  if Rc (x , y , xak , yak , xsk , ysk )≥ β β

(5) 2

2

2

( x − xak ) + ( y − yak ) + ( x − xsk ) + ( y − y sk )

Rc ( x, y, xak , yak , xsk , ysk ) =

2

( xak − xsk ) 2 + ( yak − y sk ) 2

Rc denotes the ratio of the sum of distances from the grid (x,y) to the actuator (xa,ya) and to the sensor (xs,ys) to the distance between the actuator and the sensor. λk is the correlation coefficient between the present signals and the reference signals from the k-th sensing path: N

λk =

C xy σx ⋅σ y

∑( x − µ i

=

x

)( yi − µ y )

i =1 N

∑( x − µ i

2

x

) ⋅

i =1

(6)

N

∑( y − µ i

2

y

)

i =1

i denotes the number of the grid, and Cxy is a covariance, µ are mean values, whereas σ are standard deviations. Assuming that there are K sensing paths for damage identification from the sensor network, estimation of the presence of damage at position (x, y) in the monitoring area can be written as:

DI ( x , y ) =

1 K ∑ Pk (x , y ) K k =1

(7)

As it will be demonstrated later the above definition is not convenient for arbitrary network of sensing paths. Therefore, we propose to introduce also the damage index in the following way: K

DI ( x , y ) = ∏ Pk ( x , y )

(8)

k =1

Let us note that for each individual sensing path the semi-axis length of the ellipse encircling the sensing path can be different and in this way the optimal scaling parameters may be introduced independently for each of the ellipses. However, in the present analysis, the scaling parameter, β, was set at 1.15.

The first part of the work is devoted to the theoretical (numerical) analysis only and it deals with the analysis of damage indexes for rectangular plates having a single square delamination. The observed wave component is associated with the transmitted fundamental Lamb waves. In estimating the probability of the presence of damage in the monitoring area, different networks of sensing paths were established and their performance was investigated. Typical images of damage are shown in Fig.5. The damage indexes were analysed for the increasing number of actuators. The positions of sensors/actuators were numbered consecutively, counterclockwise, starting from the lower, left corner (the number 1). For one actuator (the number 1) the highest probabilities were reached for the paths: A1-S8 (I8=0.22) and A1-S9 (I9=0.44), A1-S10 (I10=0.11), others are very low. The damage index expressed by Eq (7) is demonstrated in the second column of plots presented in Fig.5, whereas the third column is referred to Eq.(8). As it may be observed with the increasing number of actuators the damage indexes are concentrated around the area of the square delaminations. The best description of damage occurs for five actuators. It is worth to emphasize that that the multiplication of probabilities – Eq. (8) leads to better results than their sum – Eq. (7). The identified areas may be enlarged when the larger scaling parameter than 1.15 is used. It will enlarge the affected zone, making the diagnostic algorithm conservative. One actuator A1

Two actuators A1, A13

Three actuators A1, A3, A13

Four actuators A1, A3, A13, A14

Five actuators A1, A3, A5, A13, A14

Fig. 5 The probability of the presence of damage: a) for one actuator – Eq. (4), b) the sum of probabilities – Eq. (7), c) the multiplication of probabilities – Eq. (8). It is interesting to mention also that for the analysed structure it is possible to find the minimal number of sensors and actuators required for the analysis. It was found that the identical contours of the probabilistic damages index to those plotted in Fig.5 b and Fig. 5c could be obtained for 5 sensors only (i.e. S7-S11) instead of 15 sensors. 5. Cylindrical panel – a comparison of experimental results.

A photograph of the composite cylindrical panel with the active sensor network installed is presented in Fig. 6. Lamb wave signals from the selected sensing paths (Fig. 7) were captured experimentally in both the reference and present states (before and after the artificial damage was introduced).

Fig.6 The composite cylindrical panel with the active sensor network installed. The current network configuration is presented in Fig. 4 A noticeable decrease in the amplitude of the transmitted mode between the two states was observed for the signals from sensing path (the sensor 4). This decrease was attributed to the fact that this sensing path passed directly through the damage, and was seriously impaired by the damage. In contrast, no such a phenomenon was evident for the signals from sensing path S1 for the reason that this sensing path was located relatively distant from the damage, and was only slightly impaired by the damage.

Fig.7. Captured Lamb wave signals from different sensing paths (compare with Fig.4) The estimated probability of damage is presented in Fig.8. Similarly as for composite plates the better estimation of the damage contour is obtained with the use of the multiplication of probabilities for sensitivity paths.

a) the sum of probabilities – Eq. (7)

b) the multiplication of probabilities – Eq. (8)

Fig. 8 The probability of the presence of damage for cylindrical panels

In our opinion, the similarity of the results is a consequence of the deformation analogy for plates and cylindrical panels – Fig. 2. Both for plates and cylindrical panels the cross-section of the probabilistic damage index has almost identical forms – Fig.9.

a) plate f/D=0.0

b)cylindrical shell f/D=0.33

Fig.9 The comparison of the cross-sections of damage indexes for plates and shells. 6. Concluding Remarks

Presented results show the effectiveness of proposed damage detection method based on wave propagation comparison for intact and defected structures. The numerical results presented in this paper and previous research has been qualitatively confirmed by the experiment. The direct comparison of the dynamic response of the intact and benchmark structure can be applied to localize and size assessment of the structural failure. It is worth to point out that the greatest difference between response signals not always indicates the position of the delamination centre. For different size and orientation of the defect it is much more possible to detect the boundary of the defect what has been shown in numerical and experimental results. The accurate and efficient damage detection requires the careful analysis and optimal design of the location and number of piezoelectric actuators and sensors. The number of the PZT elements used in multipoint measuring system influences on the size of defect which can be detected in the structure. The parameters of the generated signal should also be carefully selected. The effect of the actuation frequency is much more important than the number of the cycles in the excitation signal. The wave propagation analysis can be used in damage detection of composite multilayered plated or cylindrical structures. Optimal design of localization and number of actuators and sensors is possible in damage detection analysis based on wave propagation and damage index References [1] J. Hoła, K. Schabowicz, State-of-the-art non-destructive methods for diagnostic testing of building structures – anticipated development trends, Archives of Civil and Mechanical Engineering 10(3), 2010, pp. 5-8 [2] R. Raišutis, E. Jasiūnienė, R. Šliteris, A. Vladišauskas, The review of non-destructive testing techniques suitable for inspection of the wind turbine blades, Ultrasound Journal Vol.63, No.1, 2008, pp. 26-30

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