PSI - Issue 39

Yuri Petrov et al. / Procedia Structural Integrity 39 (2022) 552–559 Yuri Petrov/ Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction When quasistatic loads are discussed the strength of a material with crack-type defects is associated with the value of the stress intensity factor measured at the moment of failure (fracture toughness). This approach also works for the dynamic problems when loading rates are not very high and the load durations are long. However, the SIF-based methods fail in the case of high-rate intense loads, and especially in the case of short load pulses, since many experiments in these cases show unstable and poorly predictable behavior of the critical intensity factor value (dynamic fracture toughness), as well as the critical SIF value dependence on the loading rate and/or time to failure (Petrov and Utkin (1989), Ravi-Chandar and Knauss (1984), Petrov and Sitnikova (2004)). Moreover, in some experiments, dynamic fracture of the material is observed when the local stress field at the point of rupture has already passed its maximum values and has reached the stage of a noticeable decrease (Mikhailova et al. (2017), Berezkin et al. (2000)). This fundamental fracture effect is poorly studied and cannot be explained on the basis of classical approaches and is the main subject of analysis presented in this work. For convenience the concept of the fracture delay is introduced. If, under given boundary and initial conditions, the fracture in the vicinity of the crack tip occurs after the peak of the local tensile force field is passed (it can be expressed, for example, in terms of the current stress intensity factor value), then it is said that the fracture occurs with a delay. The time elapsed from the peak of the local tensile stress to the moment of macroscopic rupture of the material will characterize the magnitude of the fracture delay. It will be further shown that this phenomenon is a fundamental feature of the dynamic fracture process, which manifests itself in threshold situations and is associated with the presence of an incubation preparatory process occurring at a microscopic level during a certain period preceding the macroscopic rupture. In the presented study this phenomenon is examined using the incubation time fracture model. Moreover, a simple mass-spring model is used to investigate the fracture delay phenomenon and to show that samples with cracks may break similarly to oscillator when subjected to short pulse loads. Nomenclature incubation time fracture scale level identifier ( , ) stress in material at point and time stress intensity factor (mode-I) ultimate static stress intensity factor ultimate static stress ∗ fracture time , Helmholz decomposition shear modulus 1 , 2 elastic wave velocities , horizontal and vertical displacements ( ) load applied to crack faces load pulse amplitude load pulse duration mass spring stiffness ( ) mass deflection oscillator eigen frequency critical oscillator mass deflection 2. Incubation time fracture model and crack initiation analysis The incubation time fracture criterion was originally proposed in works by Petrov and Utkin (1989) and Petrov (1991). 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