PSI - Issue 42

Yuri Petrov et al. / Procedia Structural Integrity 42 (2022) 1040–1045 Yuri Petrov/ Structural Integrity Procedia 00 (2019) 000–000 However, when short pulse loads are applied the whole SIF-based approach can fall apart, since fracture delay can take place: fracture can occur when local stresses are dropping falling far beneath the "# values (Kalthoff and D.A. Shockey (1977)). This effect is fundamental for proper understanding of the dynamic fracture phenomenon, however it is poorly studied experimentally, since threshold loads are needed for this effect to take place. If a rectangular load pulse with amplitude and duration is considered, then minimal sufficient amplitude for the fracture to take place for a fixed duration is called a threshold amplitude and threshold pulse duration is defined in a similar manner. In this work we show that the ITFC approach is able to process the fracture delay cases and to evaluate threshold pulse loads for the cracked specimens. Additionally, we show that the dynamic fracture process has similarities with the linear oscillator failure exhibiting inertial behavior. We use a simple mass-spring model to investigate conditions for the fracture delay in a simple inertial system. The linear oscillator-like systems have been used to investigate dynamic fracture and the dynamic fracture inertia term has already appeared in literature (Goldman et al. (2010)), however it has never been mentioned in connection with the fracture delay phenomenon. In this paper we use available analytical formulas for the crack problem and for the linear oscillator to formally calibrate the linear oscillator model so that it could describe the crack onset when short pulse loads are applied. 2. Linear oscillator failure due to application of pulse loads 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 failure condition: . . + = ( ) (0) = ̇(0) = 0 ( ) ≥ 5 ⇔ (1). Problem (1) can be solved for a rectangular force pulse, when ( ) = [ ( ) − ( − )], where and are the pulse amplitude and duration correspondingly and ( ) is Heaviside step function. The solution of problem (1) is the following: ( ) = @ (1 − cos( )), ≤ GcosG ( − )H − cos( )H, > (2), where = J ⁄ is the oscillator eigen frequency. If the system failure is considered and fracture time is denoted by ∗ , equation ( ∗ ) = 5 , one can investigate two distinguishing cases: fracture with zero delay ( ∗ ≤ ) and fracture with delay ( ∗ > ). Proper analysis of these two situations using (2) and system failure condition ( ∗ ) = 5 renders two dependencies of critical load pulse duration on the load amplitude : MNOP #NQRS = 1 V1 − 5 W XYONZYPQ# = 1 [ − 2 V 5 2 W^ (3). 1041 2