PSI - Issue 42

1042 Yuri Petrov et al. / Procedia Structural Integrity 42 (2022) 1040–1045 Yuri Petrov/ Structural Integrity Procedia 00 (2019) 000–000 3 In (3) MNOP #NQRS corresponds to a case, when fracture occurs right when the loading stops, thus there is no fracture delay and XYONZYPQ# denotes minimal duration needed for a given amplitude for the pulse to be critical. This case corresponds to a maximal fracture delay. In addition to this in (3) 5 = 5 is a critical static force for the oscillator. In figure 1a both ( ) dependencies from (3) are shown. All critical pulses lie in the zone between these two curves and points lying above the upper curve “drop” to this curve since the load ends at the moment of the system failure. Note that due to limitations of the arccos function argument there is a minimal admissible value of the amplitude of a critical pulse _`a = 5 ⁄2 .

Fig. 1. Dependencies of loading pulse duration (a) and load impulse (b) on amplitude for pulses that cause fracture with and without delay. The obtained ( ) curves can be used to investigate impulse = ∙ ( ) for the critical loads. The corresponding ( ) curves are shown in figure 1b. The zero delay ( ) dependence appear to have a minimum point G PdX , PdX H = (0.592 5 , 1.38 5 ⁄ ) providing optimal (in terms of the load force impulse) regime for the oscillator failure when no fracture delay is considered and the system is overloaded. 3. Crack initiation analysis using ITFC 3.1. Incubation time fracture criterion (ITFC) The incubation time fracture criterion was originally proposed in works by Petrov and Utkin (1989) and Petrov (1996). The incubation time fracture model implies that macroscopic fracture event requires specific time – the incubation time – to develop from microscopic fracture processes such as microcracking and defect movement and coalescence. The incubation time is regarded as a material parameter to be evaluated from available dynamic fracture experiments for a given material. The original version of the ITFC is a stress-based condition, however, a simplified SIF-based criterion can be used for the crack onset analysis: 1 k ( l ) ≥ "5 X ∗ X ∗ mn (4),