Early prediction of macrocrack location in concrete, rocks and other granular composite materials

Abstract

Heterogeneous quasibrittle composites like concrete, ceramics and rocks comprise grains held together by bonds. The question on whether or not the path of the crack that leads to failure can be predicted from known microstructural features, viz. bond connectivity, size, fracture surface energy and strength, remains open. Many fracture criteria exist. The most widely used are based on a postulated stress and/or energy extremal. Since force and energy share common transmission paths, their flow bottleneck may be the precursory failure mechanism to reconcile these optimality criteria in one unified framework. We explore this in the framework of network flow theory, using microstructural data from 3D discrete element models of concrete under uniaxial tension. We find the force and energy bottlenecks emerge in the same path and provide an early and accurate prediction of the ultimate macrocrack path $${\mathcal {C}}$$ C . Relative to all feasible crack paths, the Griffith’s fracture surface energy and the Francfort–Marigo energy functional are minimum in $${\mathcal {C}}$$ C ; likewise for the critical strain energy density if bonds are uniformly sized. Redundancies in transmission paths govern prefailure dynamics, and predispose $${\mathcal {C}}$$ C to cascading failure during which the concomitant energy release rate and normal (Rankine) stress become maximum along $${\mathcal {C}}$$ C .

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“…Interestingly, Li and co-workers also observed particle clusters in the mesoregime of gas/solid-particle flow systems, and conjectured that these emerge from particles tending to minimize their potential energy, while the gas tries to choose a path of least resistance through the particle layers 29 – 31 . Analogously, in the systems studied here, damage favors the path of least resistance to failure – the path that forms the common boundaries of kinematic clusters 13 , 14 .…”

“…Some are preferred over others. Experimental studies into the transmission of force and energy in natural and synthetic granular media (e.g., sand, photoelastic disk assemblies) and associated discrete element simulations have shown that the mesoregime of PFR is governed by the coupled evolution of two dominant mechanisms 13 – 15 , 32 , 33 . The first comprises the preferred paths for force transmission (mechanism A): a set of system-spanning paths that can transmit the highest force flow along direct and shortest possible routes through the system.…”

“…Following this analogy to road networks, grain contact networks similarly give rise to emergent flow bottlenecks. Prior network flow studies have shown that these sites, which are highly prone to congestion, ultimately become the preferred paths for damage in the failure regime 13 , 14 . Counter to intuition, however, the bottlenecks do not generally coincide with the location of damage sites in the nascent stages of PFR, which is when ideally predictions should be made to allow enough time to enact mitigative measures.…”

“…(c) The principles of mesoscience. To account for the compromise-in-competition among preferred transmission paths and simultaneously ‘jump scale’—from laboratory to field—we integrate the network flow approach 13 , 14 with the principles of mesoscience (Table 1 , Fig. 2 ).…”

“…(f) Establishing a connection to first principles fracture and failure mechanics for granular solids. Relative motions at the grain-grain level were used to study the coevolution of force and damage propagation in a network flow analysis – with explicit connections to the most popular fracture criteria, starting with Griffith’s theory for crack propagation 13 , 14 . The emerging flow bottlenecks for force and energy, proven to be the paths of least resistance to failure, were found to deliver an accurate and early prediction of the location of shear bands and macrocracks that ultimately develop in the failure regime.…”