PSI - Issue 28

Liudmila Igusheva et al. / Procedia Structural Integrity 28 (2020) 1303–1309 L. Igusheva, Y. Petrov / Structural Integrity Procedia 00 (2019) 000–000

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When the wave is reflected from the stress-free end of the rod, when the original compressive stresses become tensile, a spall fracture can occur. But as the experiment showed, in the presence of other material around the rod, even when the wave passes directly through the rod, there are tensile stresses that can lead to the fracture of the rod. Therefore, rods in various media can be fractured not only as a result of the reflection of waves from the free boundary (open fracture), but also as a result of the trailing stage of the propagation of a direct initially compression wave. This effect was detected in numerical calculations and described by Igusheva, 2019. Threshold pulses were studied, namely the threshold amplitudes of the force perturbing the rod, at which the rod is fractured. Threshold pulses are those that have the smallest fracture amplitude for a fixed duration (Smirnov, 2006). To study the dependence of the threshold amplitude on the duration of the impact, an incubation time fracture criterion was used, taking into account the impulse characteristics of the stress field and structural features of the material to predict the conditions for initiating brittle rod fracture under the action of an applied dynamic shock load. The incubation time criterion was proposed (Petrov and Utkin, 1989; Petrov, 1991; Petrov and Morozov 1994; Petrov et al., 2010). In the case of initially "intact" material, the criteria can be written as follows

t

( )      c s ds

(4)

t

where  is the incubation time corresponding to the sample,

c  is the critical value of the stress in the sample (these

are set values, they can be found experimentally for each sample). For a viscoelastic model, the calculated graph of the dependence of the threshold failure amplitude duration of the impact  for the case when the coefficient of resistance of the medium 0 b  is shown in Fig. 4.in this case, the fracture will occur as a result of the reflection of the wave from the free boundary of the rod, so there is a spall phenomenon. * P on the

Fig. 4. Dependence of the threshold amplitude of fracture on the duration of exposure in the absence of the environment, viscoelastic model.

The graph of a similar dependence for a viscoelastic model for the case when the coefficient of resistance of the medium is different from zero is shown in Fig. 5. Non-monotonic character of the curve is due to the fact that the failure occurs at different points in time. It turns out that with short pulses, the fracture in the rod occurs even when the wave passes through the rod directly, and with an increase in the duration of the impact, there is a spall fracture of the rod. A similar effect was found by Igusheva, 2019 for a model that does not take viscosity into account.