PSI - Issue 28

Nikita Kazarinov et al. / Procedia Structural Integrity 28 (2020) 2168–2173

2171

N. Kazarinov e al/ Structural Integrity Procedi 00 (2020) 000–000

4

! = _ 0! √2 * 6 ! = 0! (1 + )√ 2 √2

(9),

where = 3 − 4 and = 2(1 + ) ⁄ . This way, motion and failure of the virtual oscillator described by the following system: 7 ̈ + 7 = ( , ) (0) = ̇(0) = 0 ( ) ≥ ! ⇔ (10).

Fig. 2. Scheme of modelling of experimental data from Ravi-Chandar and Knauss (1984). Numerical solution of the differential equation in (9) and application of fracture condition ( ∗ ) = ! allows one to evaluate fracture time ∗ and corresponding dynamic stress intensity factor 0 * ( ∗ ) for different loading rates (different amplitudes of the loading pulse ). Expression for 0 * ( ) is the following (Petrov and Morozov (1994)): 0 * ( ) = 2 M 2⁄3 ( )−( − 6 ) 2⁄3 ( − 6 )O 3 6 (11). In formula (11) 6 is the loading pulse rise time ( 6 equals 25 µ s for the considered case) and = 4 3 F 53 − 33 5 √ 5 j , 5 − shear wave velocity for Homalite-100. Fig. 3 shows comparison of experimental data from Ravi-Chandar and Knauss (1984) with the obtained results using the oscillator model. Each point of the numerically obtained 0 * ( ∗ ) corresponds to a single loading pulse amplitude , which changes in a range from 1 MPa to 15 MPa to simulate loading rates reported in Ravi-Chandar and Knauss (1984). The best fit with the experimental data is obtained for the parameter equaling 4.8 mm, which is close to the thickness of the tested samples.