Brittle fracture in a periodic structure with internal potential energy. Spontaneous crack propagation

Abstract

Spontaneous brittle fracture is studied based on the model of a body, recently introduced by two of the authors, where only the prospective crack path is specified as a discrete set of alternating initially stretched and compressed bonds. In such a structure, a bridged crack destroying initially stretched bonds may propagate under a certain level of the internal energy without external sources. The general analytical solution with the crack speed-energy relation is presented in terms of the crack-related dynamic Green's function. For anisotropic chains and lattices considered earlier in quasi-statics, the dynamic problems are examined and discussed in detail. The crack speed is found to grow unboundedly as the energy approaches its upper limit. The steady-state sub-and supersonic regimes found analytically are confirmed by numerical simulations. In addition, irregular growth, clustering and crack speed oscillation modes are detected at a lower bound of the internal energy. It is observed, in numerical simulations, that the spontaneous fracture can occur in the form of a pure bridged, partially bridged or fully open crack depending on the internal energy level.

Dynamic fracture of a discrete media under moving load

“…The major question is whether the analytical approach proposed in [48], and developed later for several configurations and load conditions in [1,45,47], may be utilised in the case of the moving load where only a transient regime has been realised, and the steady-state regime is only developed within a region distant from the load and the external boundaries. We are particularly interested in the following questions:…”

“…We assume that appropriate radiation conditions at infinity are prescribed. We extensively use the method developed by Slepyan and his co-authors [1,36,45,47,48].…”

“…Moreover, for the fast propagating crack, a branching phenomenon appears as a result of possible irregular breakage of the links [24]. Other phenomena recently discovered and explained include clustering and forerunning regimes, as observed in differing lattice structures [1,14,36,37]. Recently, the lattice structure approach has been used to model the complex phenomenon of hydraulic fracture [23].…”

How a dissimilar-chain system is splitting: Quasi-static, subsonic and supersonic regimes

“…Such an extraordinary mode can exist in any case where the required energy can be delivered to the crack tip, in particular, in a stressed lattice ( Slepyan, 2002, pp. 405-406, Buehler and Gao, 2006, and Ayzenberg-Stepanenko et al, 2014. The peculiarity of the regime under consideration is that the energy transfers from the remote forces, and the supersonic energy delivery channel initially absent is opening with the splitting.…”

“…The dynamic splitting of a strip of two identical chains was considered analytically and numerically in Marder and Gross (1995) (the splitting under a constant load). Mishuris et al (2009Mishuris et al ( , 2014, Ayzenberg-Stepanenko et al (2014) and Slepyan et al (2010) studied the splitting under a sinusoidal wave and in the presence of internal energy. The dynamical extraction of a single chain from a discrete lattice was examined in Mishuris et al (2008).…”