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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coalescence. The incubation time is regarded as a material parameter to be evaluated from available dynamic fracture experiments for a given material. 2.1. Incubation time fracture model According to the incubation time model fracture at point and fracture time ∗ is controlled by the following inequality: 1 ∫ 1 ∗ ∗ − ∫ ( ′ , ′ ) ′ ′ ≥ − (1), where ( , ) is a time-dependent tearing stress, is ultimate stress for the studied material and stands for the incubation time. Criterion (1) also contains linear size parameter , which was firstly introduced by Neuber (1937), Novogilov (1969). This parameter is treated as the fracture process zone size, coinciding with the minimal distance the crack tip can travel. The linear size can be calculated using the formula = 2 2 2 ⁄ , where where is the critical stress intensity factor for the studied material. In the case of stationary crack or intact sample we calculate fracture time as well as critical amplitudes of external loads according to the incubation time approach (1)-(2), which is known as an effective tool to predict characteristics of fracture in both homogenous and non-homogenous materials (Petrov et al (2010), Bragov et al (2012)). The fracture criterion (1) can be simplified to perform analysis of crack growth initiation due to dynamic loads when bodies with cracks are considered: 1 ∫ ( ′ ) ≥ ∗ ∗ − (2). For relatively slow loads criterion (2) is equivalent to criterion ≥ , but cannot be used to simulate the crack propagation process due to possible lack of stress intensity factor dominance in case of moving cracks (Ma and Freund (1986)). 2.2. Analysis of crack initiation under pulse loads Consider an elastic plane with a semi-infinite cut = 0, ≤ 0 . If material behavior is described using shear modulus and elastic wave speeds 1 and 2 , the deformed state is defined by the following system of equations: 2 2 + 2 2 = 1 12 2 2 2 2 + 2 2 = 1 22 2 2 (3), where and are the Helmholz decomposition potentials and horizontal and vertical displacements ( , ) can be (4). The crack faces are supposed to be loaded with a time-dependent normal pressure ( ) and the plane is stress-free for < 0 . Thus, the following boundary conditions and initial conditions are applied: obtained according to formulas = + , = −