Structural Health onitoring of Aircraft Structure by ethod of Electroechanical Ipedance Vitalijs PAVELKO, Ilars OZOLINSH, Sergejs KUZNETSOV, Igor PAVELKO Aviation Institute of Riga Technical University, Riga, Latvia Phone: +37 678996, ax: +37 678999; e-ail: vitally_pavelo@hotail.co, ilars_o@inbox.lv, sergei@pars.lv, Igors.Pavelo@rtu.lv Abstract Probles of the electroechanical ipedance (EI) ethod for structural health onitoring of aircraft are analyzed. The piezoceraics transducer EI changes were investigated experientally at the different inds of artificial daages. The -D partial odel of constrained PZT is developed and validated by special test. The soe generalized odel of EI of structural eleent - piezoceraics transducer is constructed for the case when odal properties of syste coponents are nown. The exaple of odel application for effect of crac estiation to dynaics properties and the EI is presented and the effect of a crac in a thin sheet is estiated. Keywords: Structural health onitoring, aircraft, electroechanical ipedance, fatigue crac. Introduction Concept of ipedance is well nown as a paraeter of coplex resistance. Ipedance is a easure of soe structure or aterial resistance when it is subjected by a given forced action. The are different specific types of ipedance (echanical, acoustic, electrical). If soe syste includes two of ore different physical object, then its resistance is called as cobined. In ultrasound non-destructive inspection the concept of electroechanical ipedance was used priary in [-3. Since this tie the electroechanical ipedance (EI) several authors used the EI ethod for structural health onitoring, by coparing the ipedance ethod was used efficiently for daage detecting in different inds of structure [4- and other.. any exaples of application of EI ethod can find in fundaental onographs [,. The effect of structural daage is associated with the changes of dynaic properties of a structure and can be effectively defined at ultrasonic frequencies by identification of EI of syste sensor-structural eleent. any ways of the EI interpretation were proposed. One of the ost perspective is atheatical siulation of echanical ipedance of structural eleent. The siple odels of the EI were developed and used for soe applications [- 4. In structural health onitoring (SH) of aircraft structure that basis on ultrasound nondestructive inspection the concept of electroechanical ipedance (EI) can be effectively used for detection of different types of daages (crac, corrosion, delainating etc.). The effect of structural daage is associated with the changes of dynaic properties of a structure and they cause evolution of different inds of dynaic response of syste that can be easured and analyzed. One of the is EI of syste ultrasound sensor-structural eleent at haronics excitation. Soe probles of the electroechanical ipedance (EI) ethod for structural health onitoring of aircraft are analyzed in this paper. irst of all a lot of experiental data on the effect of different types of daage to the EI was obtained in special tests on the saple with artificial and natural defects. The stable influence of those daages to paraeters of EI was shown. The ey proble of increase of efficiency of EI inspection is developent of acceptable ethods of prediction of effect of daage to the ipedance. any ways of the EI interpretation were proposed. One of the ost perspectives of the to which was focused this
investigation is atheatical siulation of EI of a syste structural eleent-ultrasonic transducer. At both cases the theoretical electroechanical ipedance Z can be estiated by forula ( l) w ( ) w Z = 3 () iωc d 3E 3 where 3 and d 3 is the electroechanical coupling factor and coefficient, transverse to electric field E 3, C is the capacitance of the piezoceraics transducer, ω is the cyclic frequency. ain effect of global or local stiffness degradation is associated with a range w ( l) w ( ) of relative displaceent of tips of ultrasound transducer. It defines the change of natural frequencies and can be estiated by odal analysis of non-daaged and daaged systes. The iaginary part of the electroechanical coupling paraeters defines the effect of daping. The soe new results of EI application are discussed in this paper.. Experiental study.. The effect of local stiffness of a sheet Electroechanical ipedance of piezoelectric sensor structural eleent syste is closely related to the local stiffness of a structural eleent and attenuation properties of syste. Here are presented soe results obtained during experients on EI application for thin walled structure near-field daage detection using piezoelectric active wafer sensors. Two experients were carried out. The first one involved local sensor stiffness increase by constraining the area adjacent to the sensor with two etal bars hold together with the force as shown in ig. (a). Second experient was aied on local sensor stiffness decrease by cutting a slit parallel to the sensor as can be seen in igure (b). 5 8 8 (a) (b) igure. Sensor local stiffness increase (a) and decrease (b) effect on EI experiental The PI Ceraic PIC 5 piezoceraic sensor sized.5xx5 was glued on Al alloy 4-T3 x8x8 plate. Sensor was bonded to the plate surface with the Epoxy Paste
HYSOL EA 939. Sensor ipedance was easured by the Cypher instruents(c) C6 device. The testing haronic frequency range was -4 Hz and 4 saples recorded. The diensions of constrain steel bars were x6, 5x6, x6. Holding force agnitude equalled 5N. The slit size started fro 5 to 4 and was cut fro the sensor central axis syetrically to both sides. Stiffness variation described changes the ipedance resonance frequencies and aplitudes as can be seen in igure and 3. In the pictures the first resonance band fro 35 to 365 Hz is shown. igure. The first resonance of a constrained sensor (local stiffness increase) igure 3. The first resonance of sensor with decreasing local stiffness or the chosen band the resonance frequency fro the daage length can be seen in igure 4. As can be seen there is a close correlation between the daage size and resonance frequency.
.. The effect of holes igure 4. Local stiffness effects on the first resonance frequency Results of easureent are saved in Cypher electronics (C6) files and text files (in folder ipedance). The effect of specific artificial daage of a plate (holes) to EI was investigated. The syste of the 4 diaeter holes were drilled in the Al4-T3 sheet 8x5 near a PZT PIC 5 x8x3 in series of hole s nubering (igure 5,a). After each drilling the EI was easured by Cypher electronics C6 instruent. On the right-hand side of igure (b) the effect of 4 holes near PZT is deonstrated. The soothed real part of EI relative increent R in frequency range close to resonance is used as a paraeter of holes influence. R = Re Z Re Z, () where Z un Z is current and initial electroechanical ipedance respectively. It is seen that paraeter onotonically increases in entioned range of frequency, if a nuber of holes increases. 8 4 7 3 6 5 a) b) igure 5. The schee of holes in a plate near PZT (a) and soothed real part of EI relative increasing in frequency band near resonance (b)
.3. Electroechanical ipedance for SH of a bolt-joint There are any benefits of high preload of bolts. Very iportant feature of preloaded boltjoints is the high fatigue strength. Decrease of preload results the decrease of fatigue strength of bolt-joint. Therefore, preload of bolts can serve as the ey paraeter of technical state of the bolt-joint in the onitoring syste. The brief review of recent research in this area is presented in the article [7. The nuts or washers were equipped by piezo-sensors and preload-ei correlation was established. The siple theoretical odel also was developed. In igure 6 the part of the frae 7 of the i-8 helicopter tail bea is shown. The ain function of this frae is the tail bea joining with the bea of tail propeller. It is realized by a bolt-joint. Three bolts nubered by,,3 are seen in igure 6. It is seen the pitch of bolts is no unifor here: the distance between and bolts is ore than between and 3 ones. On the surface of the frae near bolts three piezoceraics transducers Pz 7(InSensor) 6.35x6.35x were glued by Electrically Conductive Adhesive EPO-TEK EE9-4 and they are nubered by T, T and T 3. The bolt-joint was preloaded by creation of the axial force in the bolt shan. This operation was done by a wrench with control of the torque. The axial preload in cross-section of a bolt is equal 3 N that corresponds to stress about Pa. igure 6. The fragent of the frae 7 of the i-8 helicopter tail bea with three piezoceraics transducers near bolts The progra of test contained consequential changes of each bolt preload to 4 and 8 N (8 and 6% of axial preload) and EI easureent of each transducer. The real part relative increent () was selected as a paraeter for estiation of preload effect. Results of test is presented in igures 7-9. It is seen one general tendency: the relative increent of real part of EI in resonance frequency band increases as a result of loosing of bolt preload. There are presented soothed function with the span 5. The ost significant it is for the nearest transducer fro weaened bolt. or exaple, the axiu of EI increent of the transducer T is equal.64 and.36 for 8% and 6% of noinal preload (4 and 8 N). These paraeters of others transducers are uch less and are not ore than.3. Siilar tendencies are observed for the transducers T and T 3. Easy see also the axius
for all transducers at 6% of noinal preload are scattered in range.-.5 that presuably due to the individual properties of sensors and their coupling with the frae. igure 7. The relative increent of real part of EI of the transducer T in resonance frequency band as a result of loosing of bolt preload. igure 8. The relative increent of real part of EI of the transducer T in resonance frequency band as a result of loosing of bolt preload.
igure 9. The relative increent of real part of EI of the transducer T 3 in resonance frequency band as a result of loosing of bolt preload. 3. Analytical study and coparison with test results 3.. The electroechanical ipedance of constrained transducer If the ultrasound transducer is constrained, the EI of a syste differs fro this one in free state. Because the typical daages (crac, corrosion) change the local stiffness of structural eleent, the EI of transducer also changes itself. The -D odel of constrained piezoceraics transducer (PZT) was developed and described in [3,4. The siplest type of constrained transducer is shown in igure. δ δ y δ l 3 x igure. Piezoceraics transducer, structural eleent, and glue layer Syste of differential equations for the one-diensional odel of elastic wave propagation is: u t u t = c = c ( ) ( ) x u u x + c ( ) ( + ν ) c ( ) ( + ν ) b δ A b δ A Gδ G δ D Gδ G δ D ( u u ) ( u u ) (3)
where u i, ρ i,e i, G i, A i, b i, δ i are axial displaceent, density, elastic odulus, shear odulus, cross-section area and its width and thicness for each layer (i=,,). Solution was accepted in a standard for of two haronic functions of tie: u iωt iωt ( x,t) = U ( x), u ( x,t) U ( x) e = (4) e inally the theoretical electroechanical ipedance Z can be estiated by forula where 3 b l T ε 3 3 δ ( l) U ( ) U Z = 3 (5) iωc d 3E3 is the electroechanical coupling factor, transverse to electric field, and C = is the capacitance of the piezoceraics transducer, ω is the cyclic frequency. 3.. General odel of EI of conservative elastic syste The dynaic reaction of an elastic linear syste under soe external load can be described as a decoposition of displaceent vector to the natural functions W ( x, y,z) (=,, ) of linear cobination. where ( t) w ( x, y,z,t) W ( x, y,z) θ ( t) = = (6) θ is so called noral function that is a solution of following ordinary differential equation Here ( t) + ω θ ( t) Φ ( t) & θ = (7) = ρ ( x, y,z) W ( x, y,z)dv, ( t) = ( x, y,z,t) W ( x, y,z ) dv W Φ (8) is a generalized ass of a syste and a generalized force respectively associated with ode of natural oscillation. The natural frequency of this ode is ω. w at haronic excitation in surround of natural frequency ω is ainly defined by dynaic properties of this ode. It eans, if ω ω, then The dynaic reaction ( x, y,z,t) w ( x, y,z,t) Φ W ( x, y,z) where Φ = Q ( x, y,z) W ( x, y,z ) ds and ( x, y,z) S W iωt e (9) iωt excitation force. It eans that ( ) ( ) x, y,z,t = Q x, y,z,t e. Q is an aplitude of the haronic
It is the iportant feature of function w( x, y,z,t) that can be effectively used for the EI approxiate estiation. Two views of the syste structural eleent-ultrasound transducer is presented in igure, a. σ T σ ( ) σ T σ l ( ) a) b) igure. The views of the syste structural eleent-ultrasound transducer (a) and the siplified schee of interaction of a transducer with structural eleent (b) The prisatic geoetrical shape of a transducer is accepted. It is assued that the dynaic properties (natural odes and frequencies) both isolated coponents of this syste are nown. The dynaic properties of syste and finally the aplitude of transducer elongation should be estiated. Φ ( ) ( W ) ( x, y,z) ( ) e iωt Φ = ( ) ( W ) ( x, y,z) ( ) e iωt () Here is nuber of transducer ode with natural frequency nearest to frequency of forced load, but is analogical ode of structural eleent. If two linearly elastic systes are relatively constrained, then at the natural vibration of the joined syste with soe natural frequency ω vibration of the each coponent is forced by haronic load of the sae frequency. Obviously this load is dynaic reaction of other coponent. Type, distribution and value of this load is defined by internal constrains. ( i ) ( i ( ) ) ( i ) t = ( x, y,z,t) W Φ ( x, y,z ) ds, S ( i ) ( i ) ( i ) = ( x, y,z) W Φ ( x, y,z ) ds, S ( i ) ( i ) iωt ( ) Φ t = Φ e, ( i ) ( i ( ) ) iωt ( ) x, y,z,t = x, y,z e ( ) ( ( x, y,z) = ) ( x, y,z) If the siplified schee of interaction of a transducer with structural eleent is accepted (igure, b), then ( i ) ( i ) ( x, ) ( i ) x, ( ) i y,z W ( y,z )ds ( i ) W ( i Φ ) bl = () ( ) S i Here W is the increent of th natural ode of i th eleent of syste at base l of transducer. Taing into account the expression () the equation () can be transfored to following for: ( ) ( ) ( ) ( ) = ()
As a result the natural frequency of the syste structural eleent-ultrasound transducer induced by ode of a transducer and ode of a structural eleent cab be estiated by forula ω ( ) ( ) ( ) ω + W ( ) ( ) [ ( ) ( ) ( ) + ω = (3) It eans if the natural frequency is used as a paraeter of EI for structural health onitoring, then the forula (3) can be used for theoretical prediction of daage effect. Siilar approach can give an estiate of EI agnitude and at the cobining with concept of coplex stiffness it is possible to obtain also an estiate of EI phase. Below the approxiate theory of daage effect to EI is given. If the syste is loaded by a cyclic force generated by piezo-transducer, then the axial force in the cross-section of transducer can be defined by following way. Axial strain of a prisatic transducer is * S = s T + d E = S + d, (4) 3 3 3E 3 * where S is axial strain induced by axial force (echanic part of a strain)in a rectangular cross-section of transducer with the width b and the thicness t, s is the longitudinal elastic copliance of aterial of piezo-transducer. The eber d E 3 3 in (4) is piezoelectric part of a strain. The condition of strain copatibility * w = w + d E l =, (5) 3 3 w * where w is echanic part of axial increent of displaceent, together with asyptotic expression (9) gives equation for interacting axial force definition: This force is: ( ) ( ) = ( ) ( ) + d 3 E 3 l (6) = ( ) ( ) d 3 E 3 l + ( ) ( ) ( ω ω ) (7) inally the estiate of axial increent of displaceent is expressed by forula: w ( ) ( ) ( ) ( ) ( ) d 3E 3l = w ( ) (8) ( ω ω ) + As a result, using forulas () and (8) the EI can be approxiately expressed by forula
Z = iωc 3 ( ) ( ) ( ) ω ω ( ) ( ) [ ( ) + ( ) ( ) ( W ) ω ω ω ω (9) 3.3. Exaple: the thin sheet with a crac a L L c igure. The crac in the thin plate (top) and approxiate siulation of its effect to stiffness (botto) The siple rectangular plate with the central syetric crac is considered (igure top). The vertical sides of a plate are fixed. Two piezoceraics transducers of rectangular shape are glued on the surface of a plate. The dynaics properties and EI of syste,plate transducer are analyzed. In the theoretical analysis the effect of a crac is approxiately estiated by the increasing of elastic copliance of a plate (igure botto) replacing weaens effect of a crac by soe equivalent elastic spring (D odel). The estiation of elastic copliance increasing can be executed by the use of the energetic approach of fracture echanics. This reception has been successfully used earlier for an estiation of influence of a crac on rod and rod syste [3,4. The principle of the reciprocity wors (axwell s theore) is the basis of this concept. It allows to define a copliance of an equivalent elastic spring that causes the increent of integral displaceent of a plate as well as the crac. In case of the general crac this additional copliance δ j corresponded to the generalized force ( -ν ) ( ) ν K + K + K da Q can be defined by forula: δ j = I II III Q j E E S +, () where K I, K II, K III are stress intensity factors of three odes caused by the generalized force Q j ; E is the odule of elasticity and ν is Poisson s ratio; A is area of crac surface. It is assued that there is the plane strain in a surround of crac front. In the considered proble the stress intensity factor (SI) of first ode K I is non-zero only and in this case there is the plane stress. This SI can expressed by forula K I = π cϕ( c / B) = σ πcϕ( c / B), () A where is tension force subjected a plate, φ(c/b) is the correction function of the sizes and for of a plate with a crac. It was obtained nuerically by.isida [8 and with can be approxiated by polynoial function (difference is less than.6%, if λ <. 6 ): ( λ ) B x 3 ϕ = +.48λ +.3554λ +.963λ, () j
c where λ =. B If the thicness t of a plate is constant, then the area of crac surface function of crac half-length c. As a result, the surface integral in () A = tc and it is a c c 4t 4πtB πb δ = K dc λϕ ( λ ) dλ λϕ ( λ ) dλ I EA = EA = EA (3) Relative additional copliance caused by a crac is: c / B δ πb δ = = λϕ ( λ ) dλ δ L, (4) L where δ = is the tensile copliance of the non-craced plate. EA Using expression (4), the relative additional copliance as a function of crac half-length was obtained and presented in igure 3. c / B igure 3. The relative additional copliance of plate as a function of crac half-length Now the approxiate frequency analysis of entioned syste,plate transducer can be executed. The odal properties of both isolated coponents of syste are needed. or free transducer it is necessary to define only first ode because it provides the ost effective possibility to generate Lab wave [. It eans that first natural frequency of transducer in longitudinal direction of the plate (loo at the igure ) is ( ) π E ω =, (4) b ρ
where E and ρ is odule of elasticity and density of transducer aterial respectively, b is the width of transducer (a size to direction of axis x). ( irst ode is ) πx W ( x) = cos and the increent of this function at base b is: b ( ) πx W = cos = (5) b b Generalized ass that corresponds to this ode is: ( ) b b πx ρ btl = ρ lt cos dx = (6) b or second coponent (the plate) the natural frequencies can be defined fro following the frequency equation: [ sin( L ) + δlcos( L )[ sin L sin( L ) + cos( L ) cos L + (7) + cos L sin Lcos L sin L cos L = ( )[ ( ) ( ) Here δ = δ L / ( EA) is relative copliance of the equivalent spring. It is a transcendent equation and its roots should be defined by nuerical ethod. The ode of natural oscillation is: L ( ) C sin x, if x < W ( ) = x (8) L C 3 cos x + sin x, if x > where C = tan L tan L +, C 3 = tan L. As a result ( ) x = C sin x = C ( sin x sin x ) l x W, (9) where x = a, x = a + b. In the nuerical analysis the sizes of a plate and a condition of its supporting have been accepted the sae ones as in experient: х8х4мм, aterial of a plate is the aluiniu alloy 4-Т3. There was accepted that along the short edges the plate was otionlessly fixed that corresponds to constrained effect of claps of the test achine. The longitudinal edges are free fro external forces and any constrains. The longitudinal free oscillations of such structure were analyzed. igure 4 presents soe results of the analysis. Plot of ten natural frequencies as functions of half-length of a crac is shown. It is seen for odes of oscillation at which the unit line of the ode coincides with an axis of a crac, frequency of natural oscillation does not vary. or syetric odes the increase in length of a crac causes decrease in frequency of natural oscillation. irst natural frequency of a free transducer (T): 46. Hz It eans that the EI of syste related with daage of a sheet can be observed in the frequency band - Hz. The closest natural frequency of a plate at non-daaged state less than T is equal to 34.3 Hz and corresponds to 4 th ode of a sheet. The closest natural frequency of a plate at nondaaged state ore than T and affected by crac growth is equal to 67.8 Hz and corresponds to 5 th ode of a sheet. The crac in the iddle cross-section of a plate does not affect to frequency of 5 th ode. Therefore the natural frequency of a syste generated by interaction with this ode is independent fro entioned daage and is non-inforative for
its detection. The next natural frequency of a plate at non-daaged state ore than T and affected by crac growth is equal to.4 Hz and corresponds to 6 th ode of a sheet. The nuerical analysis using (3) and the estiates of dynaic properties of coponents gave the estiates of natural frequencies of a syste in narrow band close to first natural frequency of a transducer. As it should suppose the natural frequencies of a syste practically coincide with they of a plate. igure 4. The natural frequencies of the plate as functions of half-length of a crac 3.4. Coparison with test results Ipedance of the piezoceraics transducer PIC5.5xx5 installed to surface of the Al saple described above was easured during fatigue test at the stage of crac growing. The ipedance easureent device C6 of Cypher was used in frequency band Hz- Hz. Soe results are presented in igure 5, 6 and 7. Three resonance frequencies were observed in frequency band 8- Hz. irst of the was fixed in range 8-88 Hz (igure 5). It is seen the resonance frequency corresponded to iniu of EI agnitude has a tendency of decreasing, if fatigue crac length increases. Second and third resonance frequencies in range 34-4 Hz (igure 6) and 7-8 Hz (igure 7) respectively have the sae tendency of changing as a function of the crac length. It can be concluded that the estiated frequency and trends of EI qualitatively consistent with the results obtained in the experient. However, there are significant deviations fro the prediction. irst of all, experientally defined frequencies are slightly lower in coparison with the theory. ainly this is due to the proxiity of the one-diensional odel of a plate with daage (crac), as well as with the idealization of conditions. EA shows that even flat natural odes significantly ore coplex and their nuber is a lot ore than is predicted by the one-diensional odel. Although the frequencies of the appropriate odes are close enough to theory. Especially the elastic copliance of supports can greatly affect the odal characteristics of elastic syste, as shown, for exaple, in [9. A significant factor is the
attenuation of ultrasonic signal at its propagation. The developed odel is not taen into account the effect of this factor. igure 5. agnitude of EI of syste in narrow frequency band lower than the first natural frequency of transducer igure 6. agnitude of EI of syste in narrow frequency band close to the first natural frequency of transducer
igure 7. agnitude of EI of syste in narrow frequency band higher than the first natural frequency of transducer 4. Conclusions The effect of structural daage is associated with the changes of dynaic properties of a structure and can be effectively defined at ultrasonic frequencies by identification of EI of syste sensor-structural eleent. The developed -D odel of constrained PZT can be used for analysis of the elastic and geoetrical paraeters effect to properties of piezoceraics transducer, and for structural health onitoring of eleent with possible daage. The ey proble of increase of efficiency of EI inspection is developent of acceptable ethods of prediction of effect of daage to the ipedance. The siple ethod of estiation was developed. This ethod uses the effect of natural frequency changing as a result of PZT and structural eleent coupling. The effect of a crac is approxiately estiated as a function of elastic copliance of a plate using the energetic approach of fracture echanics. The odel of constrained piezoceraics transducer can be also used for creation of a type of prestressed one protected fro effect of echanical fatigue and environental degradation. Acnowledgeent. The research leading to these results has received funding fro the European Counity's Seventh raewor Progra [P7/7-3 under grant agreeent n 9. The authors are grateful to European Coission for financial support and all partners for scientific and technological collaboration. References. Liang, C., Sun,.P. and Rogers, C.A. Coupled electro-echanical analysis of adaptive aterial syste-deterination of the actuator power consuption and syste energy transfer. Journal of Intelligent aterial Systes and Structures, 5, pp., 994.. Sun,.P., Liang, C. and Rogers, C.A. Experiental odal testing using piezoceraic patches as collocated sensors-actuators. Proceeding of the 994 SE Spring Conference and Exhibits, Baltiore, I, June 6 8, 994.
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