PSI - Issue 59

Serhii Drobyshynets et al. / Procedia Structural Integrity 59 (2024) 601–608 Serhii Drobyshynets et al./ Structural Integrity Procedia 00 (2019) 000 – 000

605

5

In this case E fb,0 = 29930 MPa . The correlation coefficient of equation (6) was 0.896. The limiting minimum modulus of elasticity of steel fibre reinforced concrete at  fb  R fb according to formula (6) was equal to E fb,R = 20651 MPa . Knowing the values of E fb,0 ,, E fb,R and R fb , it is easy to find the limit values (at  fb  R fb ) of the main deformation characteristics of steel fibre reinforced concrete: total deformation - ; elastic deformation - ; plastic deformation - ; elasticity coefficient  fb,R = 0.69. Two parametric points can be distinguished in the concrete deformation diagram representing the crack formation processes under loading. The first parametric point of the deformation process is considered the limit of microfractures, at which the concrete begins to loosen (lower limit of microcrack formation). At the level of the second parametric point  crc R (upper limit of microcrack formation) or when it is exceeded, pseudoplastic deformation and accumulation of microfractures occur in concrete. The limit 0 crc R defines the area of concrete strength under repeated (multi-cycle) loading. It can be assumed that the limit of low-cycle fatigue of concrete will be a stress level equal to the limit  crc R . A short-cycle change in plastic deformation will be observed at such stresses and higher. From the above, it follows that to calculate the parameters of equation (6) it is necessary to know the parameters 0 crc R and  crc R which are found for each type of concrete experimentally by the values of the characteristics of the state of the concrete structure.

 fb /R fb

1

0,8

0,6

0,4

0.2

0

0

20

40

60

 *10 -6

Fig. 2. Dependence of the incremental volume strain of the prism  on the relative load level  fb /R fb .

Fig. 2 shows that at the first stages of loading, the prism volume increment slightly decreased and then increased to the value of  fb /R fb = 0.397. After that, the value of the increment began to decrease sharply and, at  fb /R fb = 0.795 reached zero. Thus, the levels of the parametric points for the studied steel fibre-reinforced concrete can be taken as follows: fb crc R R / 0 =0.40 and fb crc R R /  = 0.80. With some caution, taking into account the above experimental and theoretical data for the studied steel fibre reinforced concrete concerning  crc R , we take it equal to 0.75 fb R =   , , cr b cyc = 23.5 MPa . Under this condition, the coefficient p in formula (4) will be equal to   , , cr fb cyc p  .= 0.75. The value of the coefficient q is found as follows. At  fb = 23.5 MPa using formula (6), we find E fb = 22971 MPa