PSI - Issue 39

556 5 Formula (11) yields the following maximum condition: ( ∗ ) = ( ∗ − ) , which means that for the case of a minimal pulse duration the SIF value should exceed the static during the time period. The fracture time can be calculated using formula (12) and ∗ and ∗ − values are marked with squares in figure 1. ∗ = 1 3 ( + + 2√ 2 − ∙ + 2 ) (12). For the considered threshold case (pulse with duration ) maximal fracture delay takes place and ( ∗ ) < . This way, according to the incubation time fracture condition (2) the starting SIF value ( ∗ ) can be both higher or lower than the static ultimate SIF value . Moreover, fracture can occur after the loading pulse ended meaning that facture delay takes place. These conclusions seem to be counterintuitive, however the discussed effects were indeed observed in experiments on crack initiation due to pulse loading (Kalthoff and Shockey (1977)). Yuri Petrov et al. / Procedia Structural Integrity 39 (2022) 552–559 Yuri Petrov/ Structural Integrity Procedia 00 (2019) 000 – 000

Fig. 1. Stress intensity factor history with marked fracture times.

3. Analogy with oscillator failure Let’s consider mass on an elastic spring with stiffness and force ( ) applied to the mass. The mass deflection is described by function ( ) , which satisfies the following balance equation, initial conditions and a critical deflection fracture condition: