Influence of fracture criteria on dynamic fracture propagation in a discrete chain

Abstract

The extent to which time-dependent fracture criteria affect the dynamic behavior of fracture in a discrete structure is discussed in this work. The simplest case of a semi-infinite isotropic chain of oscillators has been studied. Two history-dependent criteria are compared to the classical one of threshold elongation for linear bonds. The results show that steadystate regimes can be reached in the low subsonic crack speed range where it is impossible according to the classical criterion. Repercussions in terms of load and crack opening versus velocity are explained in detail. A strong qualitative influence of history-dependent criteria is observed at low subsonic crack velocities, especially in relation to achievable steady-state propagation regimes. Keywords

Wave transmission across surface interfaces in lattice structures

“…In the same time discrete models can describe in all details the material behaviour in the vicinity of crack tips, changes in geometry and other geometrical singularities, see, e.g. Mishuris et al (2007Mishuris et al ( , 2009 ;Slepyan (2002); Sharma (2015aSharma ( , 2017c; Porubov and Andrianov (2013); Porubov et al (2018); Gorbushin et al (2018), where the efficiency of discrete lattice models is demonstrated. As an example, we recently provided the comparison of the surface wave propagation within the Gurtin-Murdoch model and the lattice dynamics which shows similarities in dispersion relations for both models after some re-scaling, see Eremeyev and Sharma (2019).…”

Dynamic fracture of a discrete media under moving load

“…Additionally, Slepyan's approach allowed to study the consequences of application of different dynamic fracture conditions, e.g. the incubation time criterion [15], for the discrete mechanical systems [16].…”

Alternating Strain Regimes for Failure Propagation in Flexural Systems

“…In this representation, the function L + (L − ) is analytic in the upper (lower) half of the complex plane defined by k. Then, (21) can be written in the form of the Wiener-Hopf equation…”

“…Different fracture criteria, independent of or dependent on time, can also produce a variety of fracture patterns within lattice systems and can affect the existence of admissible steady-state fracture regimes. The impact of time dependent fracture criteria on the failure of one-dimensional mass-spring chains has been investigated in [21].…”