On the strength of the piezoceramic transducer in the system of structural health monitoring

The aim of the presented paper is the more detailed investigation and improvement of pre-stressing technology for the piezoelectrical transducer (PET) protection from degradation at action of extreme overload and longtime variable load in operation. Earlier developed 1D model of embedded PET is verified by the finite element analysis. Using this model, the parametrical assessment of stress state and strength of conventional transducer is done. It is shown that there is specific class of PET for which satisfying solution cannot always be obtained by optimization of parameters of the conventional piezoelectrical transducer (CPET). Therefore, further analysis is focused on the stress state and strength of the pre-stressed piezoelectrical transducer (PPET) it comparison with CPET. The electromechanical impedance (EMI) and its integral indicis are used for assessment of PET operability. Numerical simulation of EMI response to possible damages of PET and the outcome of static and fatigue tests are shown the significantly higher resistance of PPET against operational degradation in comparison with CPET.


Introduction
One of the promising ways to effectively solve the problem of monitoring the technical condition of the structure is the creation of built-in monitoring systems that can continuously automatically monitor the appearance of damage and assess their danger.Such systems must ensure the accuracy and reliability of defect detection.From the point of view of the mathematic statistics, this means that, on the one hand, the probability of missing a defect should be minimized if it exists (error of the first kind), and on the other hand, the probability of a false positive (error of the second kind) should be very small.
Structural health monitoring (SHM) of aircraft can be successful, if together with the requirement of functional efficiency is obeyed also the requirement of own reliability of SHM system.In ultrasonic SHM system the least defended element is a piezoceramics transducer integrated in structure.Conditions of aircraft operation are very complex, but mechanical loading is the most significant factor of operational influence to own properties (strength and lifetime) of PET.The problem of own reliability is especially relevant for PET of large length embedded to the structure in direction of basic load.
Figure 1 shows a piezoceramics 0.5x10x50mm transducer PIC 151 (PI Piezoceramics) installed to the Alalloy panel in direction of basic tension.After 60000 cycles of loading with the alternative stress 150/50 MPa [1] nine fatigue cracks on the surface of the transducer were detected by penetration test.
. So, the problem of strength and fatigue live of transducers is the most relevant.It is known that piezoceramic is the most popular material of piezoelectrical transducer (PET).Piezoceramic materials have a sufficiently high compressive statice strength (about 600 MPa) and compressive fatigue strength [3], and relatively low strength at tension or bending, about 45 and 80 MPa respectively [4].The simplest way to avoid sudden destruction or fatigue damage involves the installation of transducers on compressed or weakly loaded stretched sections of the structure.At the same time, to ensure effective detection of structural damage, transducers must be embedded in a structure that is most often exposed to tensile stresses.In any case, the analysis of loading conditions and the estimation of safety of operational load for piezoceramic transducer are required.The conditions of loss of operability of a typical piezoelectrical transducer (PET) installed on the surface of thin-walled host sample under static and fatigue loads are investigated in [5][6][7][8][9][10].In the paper [11] it is shown the piezoceramic sensors still work well when they are bonded on the host structures with tensile strain up to 4000με by using the optimal adhesive.Another means of PET protection from fatigue is proposed and developed in [1,[12][13][14].It is based on the creation in the transducer of a field of residual compressive stress.
The aim of the presented paper is more detailed investigation and further development of prestressing technology of the piezoelectrical transducer protection from degradation at action of extreme overload and longtime variable load in operation.The main attention is focused to PET of large length and this type transducer PIC151 is used in simulation and in the static and fatigue tests.

1D model of the piezoelectrical transducer interaction with host structure
The main aim of this analysis is to estimate the effect of constraints on stress state and strength of piezoelectric transducer.Some geometrical parameters of the host structure and its material elasticity constants, glue layer thickness and elastic properties, type of load and transducer orientation in respect to direction of main load and other structural parameters define intensity of stress state of PET.The approximate model of constrained PET should be able to adequately response to variation of those structural parameters.
In [1] the simplified 1D model of embedded PET was proposed for estimation of electromechanical impedance of embedded PET.Here this model is adapted for analysis of PET strength.The strip of constant width  2 and thickness  2 is equipped by PET of the length , width  1 and thickness  1 (figure 2).Connection is made by the glue layer of the thickness  0 .All materials are perfectly linearly elastic with elasticity constants, corresponding to actual materials.
The direct stresses on external surfaces are defined by those equations: where Below the model verification is done by comparison with corresponding data obtained by FEA.The elastic properties of materials are presented in table 1. Table 1.Material elastic properties The data of FEA of this option is compared with data predicted by model.Distribution of tensile stress in PET in normalized form which was predicted by model for long (50 mm) and short (10 mm) PET is shoved on the figure 2 by solid curves: blue is for long PET and orange for short PET.
Two configurations of PET supporting used in FEA for verification of a model is done for: 1) All sizes and physical properties of materials are the same as the limiting option of developed model, for which  2 =  1 and the length of supporting strip is equal to .This comparison allows us to estimate the acceptability of basic assumptions of model and corresponding accuracy of prediction.

Material E, MPa
Poisson ratio Al2024-T3 7100 0.33 PIC 151 6700 0.34 Hysol930.3A2232 0.42 2) Sizes of PET, the thickness of glue layer and the thickness of host structure as also physical properties of materials are the same as the limiting option of developed model, but host structure sizes in plane are much more.There are accepted: the width  2 = 80 and the length of a strip is equal to  = 300.This comparison allows us to estimate the additional effect of actual sizes of host structure to stress state of PET.
Results of comparison are presented in figure 3. Note that for configuration 1 of PET the data of FEA is shown at boundary condition: normal displacement of low surface of a strip is equal to 0 (the bending of a strip is excluded).
The main conclusion of this paragraph: The predicted stresses by 1D model are close to obtained in FEA and the model can be used for parametrical analysis of effect of geometrical and mechanical properties to stress in piezoceramics transducer.
The 1D model is used below for parametric analysis of stress state of PET as embedded sensitive component of SHM system.

Properties of embedded PET stress state
The 1D model is used below for parametric analysis of stress state of PET as embedded sensitive component of SHM system.The PET of rectangular shape is considered at action of external force in direction of the length.The length is a unique parameter, the effect of which variation is analyzed at fixed other parameters.There are obtained next important conclusions: 1) At least beginning from the length/ thickness ratio 60, the normalized stresses in the middle zone of PET is practically independent from value of this ratio (from length of PET) and for considered example is equal to 0.65.For the length/ thickness ratio 100, this zone consists of about 70% of PET length.2) Taking in attention of previous feature, it can be concluded the trend of large length PET to multiple cracking at static overload and cyclic loading.
3) The reducing of PET length may be used for prevention of its destruction in operation.Note that the ability of this means is restricted and practically loss at decreasing of the thickness of glue layer.The thickness of glue layer presented in normalized form as ratio to the thickness of transducer also is important parameter of influence: 1) For PET of the length/ thickness ratio 60 and more the effect of thickness is non-significant for maximal direct stress.2) Maximal stress in short PET this effect is significant, and it can be used for decreasing of operational load of PET and increasing of its lifetime.The effect of thickness of host structure is also significant.If the host structure is plane and flexible, then its tension is accompanied by concavity of deformed surface and less intensive stress of PET, than in case of thicker host structure.
General conclusion of parametrical analysis: the stress of PET can be decreased by variation of geometrical parameters of connection PET/host structure and by rational choice of PET location.But those possibilities are limited.
The alternative means of PET protection from destruction at overload and fatigue degradation is discussed below.

General description of pre-stressed PET
There was note below that in compression the piezoceramics have a high strength (more than 600 MPa).Therefore, the resistance to static and fatigue failure of piezoceramics can be increased by creating a compound in which the PET is subjected by residual compressive stress (figure 4).This compound can be manufactured by the glue joint of PET 2 to the surface of the overlap 1 in its stretched state.After the period of glue hardening, the overlap must be unloaded, and the pre-stressed PET can be installed to the host structure 3.

Some details of the pre-stressed PET structure and experimental technology
The basic component of the pre-stressed PET is Al-alloy overlap of 1 mm thickness and width 10 mm.The overlap should be satisfied to two conditions.First, two cables must pass through the overlap 1, going to the contactors of PET.Second, the axial deformation of overlap must be quasi-homogenius for providing of homogenity of residual stress state of PET.Both conditions will be approximatly satisfied, if the overlap is perforated by a system of periodic holes.Therefore, the 7 holes with a diameter of 4 mm were drilled with the step of 10 mm.Two views of this device for manufacturing pre-stressed PET are shown in figure 5.For controlled pre-stretching of the overlap, the special device was made [1].The technological ends of the overlap are clamped in the grips with tightening screws.This displacement is fixed by an indicator.Thus, the required tensile stresses are created in the overlap.On the overlay, stretched to  ≈ 210MPa a PET with pre-soldered wires is glued.After the glue hardening, the pad with the PET is removed from the device and the technological ends cut off.

Simulation of functional properties of PET.
There are possible various options of PET damage at loading of host structure: static destruction at overload, fatigue crack of PET, partial debonding, electrods fracture etc.There may be also different position and size of damage.Therefore for a damage identification the simulation of electromechanical impedance of embedded PET is very important.
Many EMI models have been developed [13][14][15][16][17][18][19][20][21][22].A new type of the EMI model and its application for aircraft structural health monitoring (SHM) was developed in articles [23].There was obtained an expression of the EMI common to any dimension of models (1D, 2D, 3D), and invariant in respect of details of structure and its loading.The modal analysis of the system "host structure -PET" dynamic response is the basic tool of this model.The final EMI equation is: where  For estimation of EMI the modal analysis of system 'PET-host structure' should be made.Using the COMSOL Multiphysics software the modal analysis was performed and information on 400 modes of considered electromechanical system is obtained in the frequency band 120-260 kHz.Different types of damage was simulated.Several of them are presented below in comparison with test data.

Experimental study: static strength and fatigue lifetime of conventional and prestressed PET.
On the Al alloy carrier-strip with the dimensions of the working part 1x15x230mm (total length 300mm), one conventional (CPET) and one prestressed (PPET) transducer were glued.The static test program provided for a gradual slow increase in the load with stops after each stress increment in the cross-section of the sample by 50 MPa to measure EMI and response on the Lamb's wave.The main outcome of static test: 1) For CPET • EMI magnitude of all initial stages of load including 150 MPa practically coincide one to others.
• Next increment of stress to 200 MPa causes intensive increment of EMI magnitude.
• At stress of 350 MPa the full destruction of PET in cross-section of connecting point of a cable with upper electrode is fixed.2) For PPET • EMI magnitude of at all stages of load in average coincide one to others.
• Beginning from stress 250 MPa the partial progressive debonding of PET is observed.The cyclic test of the same type of the host-sample equipped by two PET was performed on the Instron 8800 test machine.The program of fatigue test provides multilevel cyclic loading at frequency 10 Hz and parameters of load and duration of test at each level those are presented in the table 2. Periodically the test was stopped for EMI measurement and response on the Lamb's wave.2) PPET saved its operability during all test (total 5 million cycles), although beginning 4.2 million cycles the growth of partial debonding of PPET was observed.

Discussion of the research outcomes
The use of non-direct approach of damage identification is related with some uncertaintity because different damages can cause the same EMI reponse.Therefore the combinaite method of damage identification and reconstruction of process of damage is used.It includes three steps:1) aprior estimation of types of possible damage, 2) selection of realistic options those are in accordance with current measurement of EMI of PET, 3) final selection of the most likelyhood option of damage development using information on the final NDT of PET.For CPET of large length aprior types of damage are:1) only crack of piezoceramic, 2) crack of piezoceramics together with glue layer, 3) crack of piezoceramics thogether with glue layer and electrod (figure 6), 4) destruction of PET caused by stress concentration in the soldering point of cable to electrods.At next step of analysis using wide simulation, the damage type 3 is the most perspective for description of destruction process.The crack at one quarter of PET length from soldered end provides the satisfied correspondance with test data.At third step of identification of the damage development the most likelyhood option of this process can be done using the shape of CPETafter test end and all cracks detection by penetration method (figure 7).Four cracks were indicated and damage development is not contradicy to the following scenario.During loading interval from stress 150MPa to 200 MPa the crack 1 (figure 7) ocurres in PET including piezoceramics, glue layer and electrods.Only this event explains the shift (in average) of the EMI curve in the figure 6.After this cracking approximalely one quarter part of PET remains active and the occurrence of cracks 2 and 3 (in non-active part of PET) at further loading does not change of EMI.The full collapse of CPET causes by the crack 4 which is result of the stress concentration in the soldering point of cable to electrods.
PPET saves its owm operability during of all test, but loading at stress more than 250 MPa the progressive debonding of PET and chenging of its measurement properties.
The integrated estimation two type of damage indeses are considered: 1) Root mean square deviation RMSD), and 2) Correlation coefficient deviation CCD).
The RMSD index is defined by the following equation: Here () is the current realization of some component of EMI that changing should be estimated,  0 (  ) signifies this EMI signature in the initial (unloaded) state, N is the number of sample points in the frequency band of interest.The CCD index is defined by the following equation:  = 1 −  = 1 − ((),  0 ())    0 (7) where  is the correlation coefficient that indicates the statistical relationship between two signals () and 0() of the EMI component.
Comparison of CPET and PPET at static loading is made using RMSD and CCD indeces and analysis results are presented below in figure 8. RMSD value at the host structure (HS) stress 350 MPa in graph is parcially cutted, and it is equal 136.The index RMSD of EMI magnitude of CPET complitly corresponds to the scenario describled above.At initial steps of loading, including the step 150 MPa, RMSD remain small.Next increasing of the host structure load (stress 200 MPa) causes sharp increment of index caused by the crack 1 (figure 7).Its value is saved at the two next steps and at the last step 350 MPa the full loss of operability of CPET caused by the crack 4 (figure 7).RMSD index fot PPET is small during all test and effect of partial debonding is expressed weakly.The response of CCD index is adequate but is low sensetive for both CPET and PPET.
At fatigue test the RMSD index of EMI magnitude reliably indicates full collapse of CPET at 4.64•10 6 cycles (figure 9, a).Note that the value of RMSD index in the graph is presented by the truncated column and its corresponding height is equal to 17.3.Degradation of CPET beginning from 4.2•10 6 cycles is expressed non-clearly.In respect of PPET this index indicates the save of complete operability to test end at 5•10 6 cycles, but the partial debonding of PPET is expressed non-clearly.
Similar outcomes also give the fatigue test analysis by using the CCD index (figure 9, b).Outcome of experimental study allows to estimate the static strength and fatigue lifetime of nonprotected piezoceramic transducer PIC 151 0.5×10×50 mm which is embedded in the stretched HS in direction of the longest size (50 mm) of PET.Static test shows that the first crack of transducer is observed at the tension stress of in cross-section of HS that is more than 150 MPa.The 1D model and FEA shows that the corresponding average tension stress in PET is equal to 0.65 of HS stress.So, the first destruction of embedded PET is corresponding to more than 97.5 MPa in the cross-section of PET.It is much more that declared by manufacturer for the free tension test.The durability of PET can be ensured by rational design of SHM systems (selection of the type and size of the converter, the optimal position of its installation, the choice of the type of glue and the thickness of the adhesive layer).The simplified 1D model of embedded PET that proposed here and verified by the finite element analysis can be convenient tool for fast estimation of PET in SHM system, at least, in the initial stage of system designing.However, within the framework of project restrictions, the desired solution cannot always be obtained by optimization of parameters of the conventional PET.
A radical solution to the problem of protecting PET from destruction is the preliminary creation of residual stresses in PET in the direction of the main tensile force of the monitored host structure.The technology of protection of large length PET is developed and realized, and efficiency of proposal is demonstrated in this paper.EMI technology is applied for assessment of structural health of embedded PET.The comparison of conventional and pre-stressed PET is performed by using simulation of embedded PETs and they static and cyclic tests for estimation static strength and fatigue lifetime.The three-steps procedure of PET degradation history reconstruction provides a way of estimating PET operational properties.Outcome of this research shows that for considered type of PZT transducer in typical operational conditions of Al-structure the pre-stressing technology provides the save of operability of PET at possible overloads and at longtime action of cyclic load.
It is shown that there are specific problems of PPET.Particularly, the weak place of PPET is the trend of debonding in the finite zone of glue layer which is caused by increased stiffness of PET.

Figure 1 .
Figure 1.PET view after fatigue test and cracks detecting by penetration test.

Figure 5 .Figure 4 .
Figure 5. Device for manufacturing of pre-stressed PET

Figure 7 .
Figure 7. Shape of CPET after static test

Figure 8 .
Figure 8.Effect of static loading to EMI magnitude RMSD a) and CCD b) indices

The strip is considered as the host structure and outside of zone of PET location is uniformly loaded by
constant tensile stress   = .
33  11 ) is the electromechanical coupling coefficient,  11 is the component of mechanical compliance at zero field,  33 is the dielectric constant at zero stress, and  31 is the induced strain coefficient, i.e., mechanical strain per unit electric field,  and ′ are the elasticity modulus, and  and ′ are the Poisson ratios of transverse isotropic material of PZT,  =  33 /ℎ is the capacitance,  and ℎ are the electrodes area and the thickness of PZT,   = This model was effectively used for damage identification of PET at analysis of test data in experimental study of this research.Two options of PET embedded to host structure (the thinwalled plate) are simulated: conventional PET and pre-stressed PET.

Table 2 .
Parameters of cyclic load The main outcome of the fatigue test: 1) Complete destruction of CPET after 0.14 million cycles at 150/50 MPa (4.64 million cycles since the start of testing).