Fluctuation-based fracture mechanics of heterogeneous materials

We present results of a hybrid analytical-simulation investigation of the fracture resistance of heterogeneous materials. We show that bond-energy fluctuations sampled by Monte Carlo simulations in the semigrand canonical ensemble provide a means to rationalize the complexity of heterogeneous fracture processes, encompassing probability and percolation theories of fracture. For a number of random and textured model materials, we derive upper and lower bounds of fracture resistance and link bond fracture fluctuations to statistical descriptors of heterogeneity, such as two-point correlation functions, to identify the origin of toughening mechanisms. This includes a shift from short- to long-range interactions of bond fracture processes in random systems to the transition from critical to subcritical bond fracture percolation in textured materials and the activation of toughness reserves at compliant interfaces. Induced by elastic mismatch, they connect to a number of disparate experimental observations, including toughening of brittle solids by deformable polymers or organics in, e.g., gas shale, nacre; stress-induced transformational toughening in ceramics; and toughening of sparse elastic networks in hydrogels, to name a few

Adsorption of selenium wires in silicalite-1 zeolite: a first order transition in a microporous system

peer reviewedA tight binding grand canonical Monte Carlo simulation of the adsorption of selenium in silicalite-1 zeolite is presented. The calculated adsorption-desorption isotherms exhibit characteristic features of a first order transition, unexpected for adsorption in a microporous system with pore size of the order of 0.5 to 0.6 nm. We analyze this behavior as a result of the favored twofold coordinated chain structure of selenium that grows inside the complex three-dimensional microchannel network of silicalite. This analysis is confirmed by simpler calculations of a lattice gas-type mode

Topological Origin of Fracture Toughening in Complex Solids: the Viewpoint of Rigidity Theory

In order to design tougher materials, it is crucial to understand the relationship between their composition and their resistance to fracture. To this end, we investigate the fracture toughness of usual sodium silicate glasses (NS) and complex calcium--silicate--hydrates (CSH), the binding phase of cement. Their atomistic structure is described in the framework of the topological constraints theory, or rigidity theory. We report an analogous rigidity transition, driven by pressure in NS and by composition in CSH. Relying both on simulated and available experimental results, we show that optimally constrained isostatic systems show improved fracture toughness. The flexible to stressed--rigid transition is shown to be correlated to a ductile-to-brittle transition, with a local minimum of the brittleness for isostatic system. This fracture toughening arises from a reversible molecular network, allowing optimal stress relaxation and crack blunting behaviors. This opens the way to the discovery of high-performance materials, designed at the molecular scale

Mesoscale Structure and Mechanics of C-S-H

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