PSI - Issue 42

Yuri Petrov et al. / Procedia Structural Integrity 42 (2022) 1040–1045 Yuri Petrov/ Structural Integrity Procedia 00 (2019) 000–000 where is the incubation time, ∗ is the fracture time and "5 is a static ultimate SIF value. 3.2. Crack initiation analysis 4

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In this paper the crack initiation analysis is based on experiments on crack instability due to pulse loads described in Kalthoff and D.A. Shockey (1977). In this work polycarbonate samples with penny-shaped cracks were tested using rectangular pressure pulses with duration 2.8 . The authors report that fracture took place at a decreasing stage of the ( ) function and thus one can conclude that the fracture delay took place. Despite the fact that in Kalthoff and D.A. Shockey (1977) penny-shaped cracks are discussed, we consider the semi-infinite crack and plane strain approximations to be applicable due to shortness of the load and length of the considered cracks. The polycarbonate properties used for the calculations are listed in table 1.

Table 1. Polycarbonate material properties. Material property Value Critical stress intensity factor, "# √ 3.08 Longitudinal wave velocity, * , / 2264 Transversal wave velocity, . , / 1250 Incubation time, ,

5e-6 – from fitting of experimental points by the threshold ( ) curve. Consider an elastic plane with a semi-infinite cut = ±0, ≤ 0 . If elastic wave speeds in the material are denoted by p and . , the deformed state is defined by a following system of equations: . . + . . = 1 p. . . . . + . . = 1 .. . . (5), where and are the Helmholz decomposition potentials and horizontal and vertical displacements ( , ) can be (6). 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: qS F Sr±t, qut = 0 S F Sr±t, qut = ( ) | Xvt = | Xvt = 0 (7). If a rectangular pressure pulse ( ) = H ( ) − ( − )J is applied to the crack faces, the following formula for the stress intensity factor holds: ( ) = ∙ ∙ H√ − √ − J, = 4N1⁄ N p N1 − . , = . p ⁄ (8). obtained according to formulas = + , = −