Can Local Stress Enhancement Induce Stability in Fracture Processes? Part I: Apparent Stability

By comparing the evolution of the local and equal load sharing fiber bundle models, we point out the paradoxical result that stresses seem to make the local load sharing model stable when the equal load sharing model is not. We explain this behavior by demonstrating that it is only an apparent stability in the local load sharing model, which originates from a statistical effect due to sample averaging. Even though we use the fiber bundle model to demonstrate the apparent stability, we argue that it is a more general feature of fracture processes.Comment: 7 pages, 8 figure

A Legendre-Fenchel Transform for Molecular Stretching Energies

Single-molecular polymers can be used to analyze to what extent thermodynamics applies when the size of the system is drastically reduced. We have recently verified using molecular-dynamics simulations that isometric and isotensional stretching of a small polymer result in Helmholtz and Gibbs stretching energies, which are not related to a Legendre transform, as they are for sufficiently long polymers. This disparity has also been observed experimentally. Using molecular dynamics simulations of polyethylene-oxide, we document for the first time that the Helmholtz and Gibbs stretching energies can be related by a Legendre-Fenchel transform. This opens up a possibility to apply this transform to other systems which are small in Hill's sense

On the Stability of the Local Load Sharing Fiber Bundle Model

This thesis investigates a generalized history-independent local load sharing (LLS) fiber bundle model for two dimensional interfacial fractures. When the failure threshold of the fibers are assigned according to the cumulative distribution P(x)=1-e^{-x+x_0}, the model displays two distinct regimes separated by a critical transition. For systems with low cutoff x_0, the damage is developing through random weakening of the system, which resembles the equal load sharing (ELS) model. As the cutoff is increased, the behaviour approaches invasion percolation. This localization transition is determined to occur at the critical cutoff x_c=0.6173 ± 0.0005, with a critical exponent beta / nu = 1.5 ± 0.1. The LLS model displays a local stability not seen in the ELS model. By estimating the cutoffs that results in the highest positive slope in the strain curve for a range of lattice sizes, extrapolation to the thermodynamic limit reveals a cutoff that coincides with the critical cutoff, with a correlation length exponent nu = 2. This stability originates in the short-range interaction of the model, which effectively stresses the strong fibers the most. Moreover, the LLS model is shown to be globally more stable than the ELS model when x_0 is approximately less than 0.5. The global stability of the LLS model vanishes around the critical transition. This is related to a change in the distribution of bursts, i.e. the fibers that fails consecutively. For the LLS model, the burst distribution is shown to be consistent with a power law D (delta) ~ delta^{-tau}, with burst exponent tau=2 around the critical transition. Analog to the criticality of the ELS model at x_0=1, lower cutoffs results in higher burst exponents, and cutoffs above x_c gives rise to exponential decay in the burst distribution. The distribution of fatal bursts, which cause the entire bundle to rapture, reveals a drastic change of behaviour around the critical transition. For cutoffs above x_c, far fewer fibers may break before the bundle would undergo catastrophic failure in a force controlled experiment

Stretching, breaking, and dissolution of polymeric nanofibres by computer experiments

Bundles of polymeric materials are ubiquitous and play essential roles in biological systems, and often display remarkable mechanical properties. With the never-ending experimental advances in control and manipulation of molecular properties on the nanometric level follows an increasing demand for a theoretical description that is valid at this scale. This regime of nano-scale bundles of small numbers of molecules has not been investigated much theoretically; here chain–chain interactions, surface effects, entropy, nonlinearities, and thermal fluctuations all play important roles. In my thesis, I present a broad exploration by molecular-dynamics simulations of single chains and bundles under external loading. Stretching and rearrangements of chains are investigated, as well as their breaking and dissolution

Stretching and breaking of PEO nanofibres. A classical force field and ab initio simulation study

The burgeoning development of nanotechnology is allowing us to construct more and more nano-scale systems in the real world that used to only exist in computer simulations. Among them, nanofibres made of only a few aligned polymeric chains in particular might soon have important roles in nanofabrications as well as in nanomedicine. In this work, we present a broad exploration by computer simulations of elastic and inelastic properties of polyethylene-oxide (PEO) nanofibres under load. We cover the full range from unloaded fibres up to their breaking point, focusing on all features that arise from chain–chain interactions and collective behaviour of the chains. We employ both molecular dynamics (MD) simulations and density functional theory (DF). The classical force field is represented by a minimal reactive force field model, allowing for the breaking of covalent bonds. Density functional (DF) computations provide a benchmark to gauge and validate the empirical force field approach, and offer an intriguing view of the bundle chemical evolution after breaking. Force-field based MD is employed for the systematic investigation of bundles of up to 24 chains, and for a single bundle of 100 chains. Low-temperature results for bundles under moderate loading provide a size-dependent sequence of cross-sections, structures, cohesive energies and elastic properties. A remarkably high Young's modulus on the order of 100 GPa was estimated with DF and MD, explained by the semi-crystalline state of the fibres giving mechanical properties comparable to those of carbon nanotubes and of graphene. Breaking is investigated by simulations with constant strain rate or constant stress. The bundle breaks whenever the potential energy is raised above its metastability range, but also below that limit due to creep activated by thermal fluctuations. A Kramer's-type approximation for the rate of chain breaking is proposed and compared to simulation data

Can Local Stress Enhancement Induce Stability in Fracture Processes? Part II: The Shielding Effect

We use the local load sharing fiber bundle model to demonstrate a shielding effect where strong fibers protect weaker ones. This effect exists due to the local stress enhancement around broken fibers in the local load sharing model, and it is therefore not present in the equal load sharing model. The shielding effect is prominent only after the initial disorder-driven part of the fracture process has finished, and if the fiber bundle has not reached catastrophic failure by this point, then the shielding increases the critical damage of the system, compared to equal load sharing. In this sense, the local stress enhancement may make the fracture process more stable, but at the cost of reduced critical force

Can Local Stress Enhancement Induce Stability in Fracture Processes? Part II: The Shielding Effect

We use the local load sharing fiber bundle model to demonstrate a shielding effect where strong fibers protect weaker ones. This effect exists due to the local stress enhancement around broken fibers in the local load sharing model, and it is therefore not present in the equal load sharing model. The shielding effect is prominent only after the initial disorder-driven part of the fracture process has finished, and if the fiber bundle has not reached catastrophic failure by this point, then the shielding increases the critical damage of the system, compared to equal load sharing. In this sense, the local stress enhancement may make the fracture process more stable, but at the cost of reduced critical force

Computational study of the dissolution of cellulose into single chains: the role of the solvent and agitation

We investigate the dissolution mechanism of cellulose using molecular dynamics simulations in both water and a mixture solvent consisting of water with Na+, OH− and urea. As a first computational study of its kind, we apply periodic external forces that mimic agitation of the suspension. Without the agitation, the bundles do not dissolve, neither in water nor solvent. In the solvent mixture the bundle swells with significant amounts of urea entering the bundle, as well as more water than in the bundles subjected to pure water. We also find that the mixture solution stabilizes cellulose sheets, while in water these immediately collapse into bundles. Under agitation the bundles dissolve more easily in the solvent mixture than in water, where sheets of cellulose remain that are bound together through hydrophobic interactions. Our findings highlight the importance of urea in the solvent, as well as the hydrophobic interactions, and are consistent with experimental results

Can Local Stress Enhancement Induce Stability in Fracture Processes? Part I: Apparent Stability

By comparing the evolution of the local and equal load sharing fiber bundle models, we point out the paradoxical result that stresses seem to make the local load sharing model stable when the equal load sharing model is not. We explain this behavior by demonstrating that it is only an apparent stability in the local load sharing model, which originates from a statistical effect due to sample averaging. Even though we use the fiber bundle model to demonstrate the apparent stability, we argue that it is a more general feature of fracture processes

Computational study of the dissolution of cellulose into single chains: the role of the solvent and agitation

We investigate the dissolution mechanism of cellulose using molecular dynamics simulations in both water and a mixture solvent consisting of water with Na+, OH− and urea. As a first computational study of its kind, we apply periodic external forces that mimic agitation of the suspension. Without the agitation, the bundles do not dissolve, neither in water nor solvent. In the solvent mixture the bundle swells with significant amounts of urea entering the bundle, as well as more water than in the bundles subjected to pure water. We also find that the mixture solution stabilizes cellulose sheets, while in water these immediately collapse into bundles. Under agitation the bundles dissolve more easily in the solvent mixture than in water, where sheets of cellulose remain that are bound together through hydrophobic interactions. Our findings highlight the importance of urea in the solvent, as well as the hydrophobic interactions, and are consistent with experimental results