Session X22: Focus Session: Deformation and Fracture

Crystal strength by direct computation

The art of making materials stronger goes back to medieval and even ancient times. Swords forged from Damascus steels more than 10 centuries ago possessed a unique combination of hardness and flexibility, two qualities that are difficult to attain simultaneously. The skills of metalworking were based on empirical knowledge and were passed from the master smith to his pupils. The science of physical metallurgy came about only in the XX century bringing with it new methods for finding out why some materials are strong while others are not. Soon it was realized that, when it comes to metal strength, it is all about crystal defects -- impurities, dislocations, grain boundaries, etc. - and how they are organized into crystal microstructure. This understanding has since resulted in new effective methods of material processing aiming to modify crystal microstructure in order to affect material's properties, e.g. strength and/or hardness. Remarkably and disappointingly, general understanding that microstructure defines material's response to external loads has not yet resulted in a workable physical theory of metal strength accounting for the realistic complexity of material microstructure. In this presentation I would like to discuss a few tidbits from computational and experimental research in our group at LLNL on crystal defects and their contributions to material strength. My selection of the examples aims to illustrate the major premise of our work that the mechanisms by which the microstructure affects crystal strength are multiple and complex but that there is hope to bring some order to this complexity.   

Modeling of Self-Healing in Materials Reinforced with Nanoporous Fibers.

We report on our group's progress towards continuum rate equation modeling, as well as numerical simulations, of self-healing of fatigue in composites reinforced with glue carrying nanoporous fibers. We conclude that with the proper choice of the material parameters, effects of fatigue can be partially overcome: fracture and degradation of mechanical properties can be delayed.   

Effects of grain boundary constraints on properties of polycrystalline materials

Grain boundary networks are engineered by increasing the fraction of boundaries which have favorable properties. Favorable boundaries have either low grain boundary misorientation or they are special boundaries, such as coincident site lattice boundaries. Significant improvement in properties such as corrosion resistance, critical current in superconductors and mechanical strength and toughness occur, provided percolating grain or grain boundary structures can be engineered. We demonstrate that grain boundary constraints shift percolation thresholds from their uncorrelated values and that the behavior near threshold is also modified. The origin of these behaviors is an enhanced clustering of weak boundaries induced by grain boundary constraints.   

Modeling the Evolution of Subsurface Microstructures During Wear of Metal Single Crystals

Friction can lead to complex mechanical and microstructural evolution near the worn surface, and these changes can impact the properties of the material. Recent results from tribological experiments on nickel single crystals reveal the formation of microstructural features ranging from nanometers (very near the surface) to microns in size. The formation and mechanical response of these zones is sensitive to crystallography, and can dramatically alter the frictional properties of the material itself. We have modeled these phenomena using a combination of dislocation plasticity, microstructure formation, and grain boundary sliding. The loading conditions are adopted from an analysis of static frictional contact. A phenomenological treatment of wear debris and asperity-mediated contact is included to appropriately describe the mechanical mixing that occurs very near the contact interface. We will provide an overview of the experimental evidence, discuss the wear model in detail, and present results for kilocycle wear on nickel single crystals in different crystallographic orientations.   

Spontaneous shear localization in a model brittle solid

A better understanding of the failure of brittle materials is practically important in situations ranging in scale from nano-indentation to earthquake physics. Recent discrete models of this failure focused on geometries such as uniaxial tension or anti-plane strain where creation of free surfaces dominates. They are not appropriate for modeling the formation of shearing systems where frictional sliding of material in intimate contact and plastic deformation are important. We present results on a novel approach which introduces damage directly into particle based simulations. When loaded, the model exhibits a period of bursts of spatially correlated damage accumulation followed by a period of catastrophic weakening during which a geometrically complex through-going fault network forms, strikingly reminiscent of both laboratory experiments and geophysical observations at the field scale. We will discuss: spatial correlations in damage, evolution of the geometry of the fault system, and the dependece on confining pressures.   

Simulations of Nanoscale Mechanical Contacts with Intervening Adsorbates

Molecular simulations are used to investigate the role of intervening adsorbed molecules in nanometer scale mechanical contacts between nominally spherical tips and flat elastic substrates. Previous studies show that atomic scale deviations from the sphere that are present on any tip constructed from discrete atoms can have profound effects on contact areas, adhesive energies, and lateral stiffness. We find that including adsorbed molecules in contacts reduces the variation with tip geometry, but introduces new effects. One is that tip geometry affects the number of atoms that are pushed out of the contact and the resulting pressure distribution. The pressure at the center of the contact may be smaller than at the edge. We also find that the presence of adsorbates influences frictional behavior of contacts. For some cases the frictional force is proportional to area for bare tips and proportional to load when adsorbed molecules are present.   

Rubber Band Recoil

When an initially stretched rubber band is suddenly released at one end, an axialstress front propagating at the celerity of sound separates a free and a stretched domain of the elastic material. As soon as it reaches the clamped end, the front rebounds and a compression front propagates backward. When the length of the compressed area exceeds Euler critical length, a dynamic buckling instability develops. The rebound is analysed using Saint-Venant's theory of impacts and we use a dynamical extension of the Euler-Bernoulli beam equation to obtain a relation between the buckled wavelength, the initial stretching and the rubber band thickness.   

String breaking and the Petersburg Paradox

The Petersburg Paradox(1) provides a simple paradigm for systems that show critical sensitivity to rare events. The breaking strength of filaments, yarns and strings is determined by the presence of defects. In a given sample, the largest defect determines the stress at which failure occurs, and since the defect distribution is a function of sample size, the breaking strength of strings depends on their length. Analogy with the Petersburg paradox suggests that the breaking strength should vary approximately linearly with the logarithm of the length. We have carried out experiments to measure the breaking strength of samples of polyester sewing thread and of monofilament fishing line ranging in length from \textit{1mm} to \textit{1km}. We describe our experiments, present the results, and, compare fits of our data to Weibull and mean field failure statistics and the predictions from analogy with the Petersburg Paradox. 1. I. Todhunter, \textit{A History of Mathematical Theory of Probability}, (Chelsea, New York, 1949)   

Simulations of aging and plastic deformation in polymer glasses

Experiments on a broad class of amorphous glassy materials show that their mechanical behavior strongly depends on the time since vitrification. The slow relaxation of configurational degrees of freedom, or aging, generally increases the material's resistance to applied stress. In this study, we investigate the interplay between aging and plastic deformation in a simple model for polymer glasses by means of molecular dynamics simulations. We determine the macroscopic creep compliance for different loading conditions and aging times and find excellent qualitative agreement with experiments: compliance curves can be shifted to form a universal master curve, and the applied stress can reduce the effective age of the glass (mechanical rejuvenation). We then measure microscopic, local relaxation times and show that they correlate well with the aging characteristics of the macroscopic creep response. In addition, we explore the evolution of several measures of local order during aging and discuss their role in the mechanical behavior.   

Deformation mechanism of silver nanowires

Silver is the metal which exhibits the highest electrical and thermal conductivity, and has potential applications in electronics, photonics and catalysis. Silver nanowires could serve as interconnects between electronic circuits, catalysts in chemical reactions, or substrates for surface-enhanced Raman spectroscopy. Understanding how their mechanical properties are affected by their structure (size, cross-section geometry) is essential for their integration in nanodevices. Recently, silver nanowires have been synthesized in aqueous solution without surfactant or catalyst. These nanowires were characterized by Atomic Force Microscopy (AFM) and have a diameter ranging from 20 to 40 nm. Their deformation mechanism was studied by AFM nanoindentation and the results were correlated with atomistic simulations of silver nanowires with a pentagonal cross section.