PSI - Issue 42

1044 Yuri Petrov et al. / Procedia Structural Integrity 42 (2022) 1040–1045 Yuri Petrov/ Structural Integrity Procedia 00 (2019) 000–000 5 Note that all the roots in (8) and other formulas are supposed to be multiplied by a Heaviside function with an identical argument. If we substitute (8) into condition (4) we obtain an expression linking fracture time ∗ and pulse duration : 3 2 "5 H( ∗ ) w⁄. − ( ∗ − ) w⁄. − ( ∗ − ) w⁄. + ( ∗ − − ) w⁄. J = 1 (9). If we consider a zero-delay case, we should substitute ∗ = into (9) to obtain expression which connects and for this particular overloaded situation. However, in order to process the threshold case, one should firstly calculate maximal fracture time _∗ Rq = 1 3 T + + 2N . + + . U (10), and then substitute it into (9). This way, we can numerically construct two ( ) dependencies similar to those for the oscillator case (figure 1). These curves for the polycarbonate are shown in figure 2. Note that the lower threshold curve is used to calibrate the model and to evaluate the incubation time value = 5 .

Fig. 2. Dependencies of loading pulse duration on pulse amplitude for polycarbonate samples (Kalthoff and D.A. Shockey (1977)). The obtained ( ) curves can be used to calculate impulse ( ) = ⋅ ( ) of the critical loads for the zero-delay and threshold scenarios. The corresponding ( ) dependencies are shown in figure 3a. The upper ( ) curve appears to have a minimum analogously to the oscillator problem and this minimum can be used to calibrate the oscillator and to attribute a virtual oscillator for the particular crack initiation problem that would describe the crack initiation process. It is impossible to calculate independently the virtual oscillator mass and stiffness, however, the corresponding virtual oscillator eigen frequency can be obtained: = 403.8 . Figure 3b shows the ( ) curves for the constructed virtual oscillator. This way, there are obvious similarities between the crack initiation due to pulse loading and the oscillator failure when similar loads are applied.