PSI - Issue 52

Vitalijs Pavelko et al. / Procedia Structural Integrity 52 (2024) 382–390 Vitalijs Pavelko/ Structural Integrity Procedia 00 (2019) 000 – 000 The likelihood function ( , ) was calculated for the mean ∈ [50,80] and the standard deviation ∈ [5,15] with the same increment 0.1 for both parameters. There is only a single maximum of the likelihood function in given area of parameters’ change. In Fig.8 there are showed 3D view and top view of the likelihood function a) and b) respectively. Maximum of this function corresponds to the couple of estimates ̂ = 70.1 MPa and ̂ = 10.1 MPa. In the Fig.8,c) the normal distribution cumulative function corresponds to those estimates. It also shows the points of the lower branch of the experimental cumulative distribution function, built directly from the test data. 389 8

a)

b)

c)

Figure 8. Likelihood function: a) 3D view; b) top view; c) function of normal distribution of PET fatigue strength

5. Discussion and conclusions. At present, the static and fatigue strength is usually estimated indirectly, using a critical load or deformation of the host structure, corresponding to a sharp change in electromechanical impedance. Such an assessment of the strength does not allow a direct assessment of strength in terms of stress and comparison with the manufacturer's information and does not allow an assessment of the true resistance to destruction of PET in the embedded state. There is also practically no information about statistical parameters of strength, which are very important for assessing the reliability of PET as part of a SHM system. Here is done analysis of stress state and strength of piezoelectrical transducer in-built to structural component which subjected by static or cyclic load. All results and conclusions are applicable for thin PET of rectangular shape. The data of the fatigue test of reinforced Al-alloy panel and FEA results were used. It is shown that stress state of constrained PET is non-homogenies, and the type of loading can be defined as the combination tension-bending. The estimates of parameters of normal distribution of fatigue strength of PET in-build to structure. It is seen that the estimate of mean 70.1 MPa and standard deviation 10.1 MPa. This estimate of a mean is much more than static strength of PET at pure tension, declared in specification of material. There is other information confirming a higher level of strength of PET in a constrained state. At the static tension the square 7x7 mm PZT installed to 1 mm thickness Al alloy sample was loaded in tension under strain control Bin Lin et al. (20). Minimal changes occurred to the impedance signature until the value of 3000 / was exceeded. This strain corresponds to nominal stress 210 MPa. The FEA shows that direct stress in middle cross-section of transducer at realistic value of unknown parameters of problem is equal to 0.507 of the stress in host component of this sample. It means that the static strength of this piezoceramic transducer is more than 106 MPa. In the fatigue test the S_N curve was obtained for the host component and there is not any fault in impedance measurement. So, there is possible to estimate approximately the low boundary of fatigue strength of PET by multiplying the fatigue strength of the host component to 0.507. The static and fatigue test of PIC 151 transducer is described in the Pavelko I. (2010). All sizes, technology, and scheme of loading are the same here as in FEA (Fig.2). The first crack of PET obtained at stress of host sheet 175