PSI - Issue 59

M. Levchenko et al. / Procedia Structural Integrity 59 (2024) 724–730 M. Levchenko et al. / Structural Integrity Procedia 00 (2019) 000 – 000

728

5

(a) (c) Fig. 2 Mesh structure and electric potential distribution for (a) a whole model, (b) vicinity of the crack, (c) scale. (b)

It is assumed that the upper part of the region is made of piezoelectric material PZT-4, the lower part is piezoelectric PZT-5. The properties of these materials in the system of SI units are given by known matrices of stiffness, piezoelectric and dielectric constants, namely

9 11 139 10 c   , 15 13,4 e  , 31 9 11 121 10 c   , 15 12.3 e  , 31

,

9 33 113 10 c   ,

,

PZT-4:

9

9

74,3 10

25,6 10

12 13 c c   

c  

44

6.98

, 33 13,8 e  ,

,

;

e 

9

9

6 10

5,47 10





d

d

 

 

11

33

PZT-5:

,

,

,

9

9

9

75.4 10

111 10

21.1 10

12 13 c c   

33 c  

c  

44

5.4

, 33 15.8 e  ,

,

.

e 

9

9

8.1 10

7.3 10





d

d

 

 

11

33

It was considered that: - a uniformly distributed normal tensile stress

10 , MPa   is applied to the upper and lower faces of the

bimaterial body; - an electric flux

2 2 10 / d C m   passes through the entire area, which is implemented by setting a uniformly

distributed charge of intensity (

2 2 10 / C m   ) on the upper face;

- zero electric potential is prescribed on the bottom face; We’ll assume further that the crack is filled with air. Then according to the table 1 the electric flux through the crack, in the plane case, is equal approximately 2 0.005 / C m . Let us assume that such electric flux of constant magnitude also occurs in the 3-dimensional case. That is, according to the rules of the FEM Abaqus package, in order to implement the specified electric flux through the crack on its upper face, it is necessary to set a uniformly distributed charge of 2 0.005 / C m , and on the lower one should be uniformly distributed charge 2 0.005 / C m  . For the indicated external factors, the calculation was carried out on the mesh shown in Fig. 2. The colored levels in this figure shows the resulting electric potential distribution. In addition, the following most interesting results can be noted: Crack opening and electric potential jump through the crack were obtained for different cross-sections in the direction of the axis 2 x and are shown in Fig. 3. Lines I and II correspond to 2 0 x  and 2 2 /2 x l  (their values are very near of each other and the correspondent lines almost coinsides). The line III is drawn for the cross-section 2 2 9 /10 x l  , which is situated very near to the face of the body. It follows from this figure that the crack opening increases for the cross-sections approaches to the face 2 2 x l  of the body whilst the jump of the electric potential decreases for these sections. The jumps of the electric potential through the crack are shown in Fig. 4 for the same cross-sections as in Fig.3.