Breakdown of heterogeneous materials

Abstract

We discuss the threshold activated extremal dynamics that is prevalent in the breakdown processes in heterogeneous materials. We model such systems by an elastic spring network with random breaking thresholds assigned to the springs. Results are obtained from molecular dynamics simulation of the system under constant stress and constant strain conditions. We find that the distribution P (m) of the avalanches of size m, caused by the rupturing of the springs till the failure of the network, decays as a power-law: P (m) ∼ m −α , where α can be closely approximated to 5/2. The average avalanche size < m > diverges as < m >∼ (F c − F ) −1/2 close to the stress F c at which the total failure of the network occurs. We study the time evolution of the breakdown process: we find that the bonds rupture randomly over the network at initial times but the rupturing becomes highly correlated at late times to give rise to a well-defined macroscopic crack.

Rigidity percolation control of the brittle-ductile transition in disordered networks

“…Furthermore, such discrete structures have been commonly used in statistical models of fracture [20], as a means to conveniently discretize a material. For example, the random fuse model (RFM) [7,21,22], fiber bundle model (FBM) [23,24] or elastic springs model [7,9,13,25,26] descriptions rely on such lattices in which material disorder is introduced. Despite a wealth of models, few fracture experiments to discriminate between the various models have been performed on disordered lattices [11,12], in part due to the difficulty of creating samples by hand [22].With the advent of laser-cutting technology, we are able to readily produce samples with precise, reproducible properties and thereby perform controlled experiments on the failure behavior of disordered lattices with various connectivities.…”

Mixed-mode translaminar fracture of woven composites using a heterogeneous spring network

“…Overall statistical features of brittle failure of heterogeneous systems in absence of a pre-existing macroscopic crack, such as effect of residual stress on transition from brittle to non-brittle macroscopic response are well reproduced using a spring network with random initial spring length (Curtin and Scher, 1990). Similarly, by using a spring network with random failure threshold, the decay in distribution of avalanche size being a power law and damage initiating randomly under application of macroscopic strain initially but the growth of damage becoming highly correlated resulting in formation of a well defined macroscopic crack can also be simulated (Ray, 2006). Extended to composite materials, the effect of disorder, represented by a fraction of softer springs in the network having the same failure threshold stress, is shown to result in decrease in the load bearing capacity of the composite material (Moukarzel and Duxbury, 1994).…”

Splitting fracture in bovine bone using a porosity-based spring network model

“…The energy emitted during an avalanche is known to be proportional to the square of the avalanche size (e.g. [38]). Let P(E) be the distribution of the energy emitted during an increment.…”

“…using velocity-Verlet algorithm [55], where the friction g dissipates energy [38]. For each increment in the applied downward displacement, after equilibration, if any spring i is stretched beyond its threshold strain e i , it and the torsional springs associated with it are broken.…”

“…Statistical models, like the random spring network model (RSNM), approximate the continuum by a network of springs with statistically distributed characteristics. Thereby, it has been successful in providing an insight into the role of disorder in the fracture behaviour of heterogeneous material systems with no preexisting crack [36], reproducing features like transition from brittle to non-brittle macroscopic response [37], avalanche size distributions [38] and qualitative [39,40] and quantitative [41] features of fracture of composite materials. In the context of bone, simple one-dimensional models of parallel springs with statistically distributed properties have been used to simulate the characteristic quasi-brittle softening seen in tension and bending [42] as well as in compression of cortical bone [43].…”