Session L39: Focus Session: Deformation and Fracture

Strain localization as a mechanism for dynamic weakening in amorphous solids

Solids such as foams, colloids, amorphous metals and granular fault gouge are composed of particles in closely-packed, non-crystalline configurations, and small-scale mechanisms for deformation in these materials are less well-understood than those in liquids or crystals. I will discuss a mesoscopic model for these disordered solids, the theory of Shear Transformation Zones (STZs), and show that it captures macroscopic features seen in experiments as well as interesting internal dynamics such as shear banding. An important component of this model is the effective temperature, which describes the statistical distributions of particle configurations and governs plastic deformation. Shear banding occurs due to a ``frozen''-time instability in the effective temperature field, and one can determine a condition for shear banding based on the initial conditions alone. I will discuss how the STZ formulation can be used as a continuum model for fault gouge and includes a mechanism by which the system can dynamically weaken.   

What is the structure of a polymer glass after plastic deformation?

We aim to study the effect of plastic deformation on the structure of a glassy polymer. Using neutrons scattering on a large range of length scales, and comparing samples deformed below and above Tg, we show that: 1) The deformation is extremely homogeneous (or affine) for length scales above the entanglement distance 2) The crossover length scale between affine and non affine deeformation is about half the one of the entanglements, and is independent of temperature below the glass transition 3) The arrangement of the polymer chain is distorded by plastic deformation at the atomic scale We then discuss these results and compare them to the results of the simulation of Hoy and Robbins (J. Polym. Sci., 44 (2006), 3487). As a conclusion we see that the entanglements are respopnsible for the very homogeneous deformations, forcing the individual plastic events to propagate in the sample following the tension of the chains. Thus we conclude that the physics of the plastic deformation of polymer glasses are very different from the one of other glasses.   

Depinning transition in failure of disordered brittle materials

Crack propagation is the fundamental process leading to material failure. However, its dynamics is far from being fully understood. In this work, we investigate both experimentally and theoretically the growth velocity $v$ of a crack propagating in brittle materials in the limit of low velocities compared to the sound speed. The variations of $v$ with respect to the external loading $K_I$ are carefully measured on two kinds of brittle rocks over various orders of magnitude. The crack dynamics is shown to display two regimes, well described by a sub-critical creep law $v \sim e^{-\frac{c}{(K_I-K_0)^{\mu}}}$ with $\mu \simeq 1$ for $K_IK_c$. We show that these variations, as well as the value of the exponents $\mu$ and $\theta$, can be explained extending the theoretical framework of Linear Elastic Fracture Mechanics to inhomogeneous media. In particular, these two regimes are shown to be reminiscent of the dynamical critical transition underlying the failure of disordered brittle materials.   

Role of microstructural heterogeneities on rupture of polycrystalline materials

Grain boundary networks are the dominant heterogeneity in many polycrystalline materials, and their performance may be dramatically improved by increasing the fraction of boundaries which have either low grain boundary misorientation or which 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 special percolating grain or grain boundary structures can be engineered. Nevertheless, grain boundary network correlations constrain the extent to which property improvements can be achieved. A common deleterious effect is that degraded boundaries have a tendency to cluster in linear chains leading to unexpected reductions in performance. After an introduction to the area, scaling laws and the results of large scale simulations of percolation, critical manifolds and rupture in polycrystals will be presented. In particular, deleterious effects due to grain boundary correlations will be elucidated and strategies for their mitigation will be discussed.   

Phase field modeling of liquid metal embrittlement

Liquid metal embrittlement (LME) is a phenomenon whereby a liquid metal in contact with another, higher-melting-point polycrystalline metal, rapidly penetrates from the surface along grain boundaries. This phenomenon is known to be greatly accelerated by the application of tensile stress, resulting in the rapid propagation of intergranular cracks in normally ductile materials. Although this phenomenon has been known for a long time, it still lacks a convincing physical explanation. In particular, the relationship of LME to conventional fracture mechanics remains unclear. We investigate LME using a phenomenological three-order-parameter phase field model that describes both the short scale physics of crystal decohesion and macroscopic linear elasticity. The model reproduces expected macroscopic properties for well separated crack surfaces and additionally introduces short scale modifications for liquid layer thicknesses in the nanometric range, which depend on the interfacial and grain boundary energy as well as elastic effects. The results shed light on the relative importance of capillary phenomena and stress in the kinetics of LME.   

Atomistic simulation studies of plastic deformation and dislocation patterning as a function of temperature

The mechanical properties of crystalline solids depend sensitively on the mechanisms controlling dislocation nucleation, motion, and patterning. To explore the role of thermal activation in these processes, we carry out atomistic Monte Carlo simulation studies of plastic deformation of 2-d single crystals at a range of temperatures. We find that at intermediate temperature, dislocations readily coalesce to form tilt boundaries, while at high temperature, the defects remain disordered in a gas-like phase, suggesting the possibility of an order-disorder phase transition. Conversely, near $T=0$, dislocation mobility is too low to produce patterning on short time scales, again producing disordered structures. We study also the response of a polycrystalline solid under pure compression and look at the resulting distribution of stresses. We find that the defect-rich grain boundary regions bear higher stresses than those in the bulk, in agreement with Mughrabi's two-component composite theory. Results are compared with recent experiments by L. E. Levine et al.   

Novel plastic processes in nanoindented stepped Au surfaces

While much work has been done recently on defect nucleation during plastic processes, mechanical properties of real surfaces have been seldom studied atomistically. Defect nucleation is well known to be critical in the mechanical behaviour of materials [1]. But the role that surface defects play on the earliest stages of plasticity still needs to be elucidated. We approach realistic surfaces by using vicinal surfaces with a high step density. Nanoindentations with AFM and atomistic simulations have been performed on the Au(788) surface [2]. Force vs penetration curves show a hertzian initial stage and a later incipient plastic regime when dislocations are nucleated. Between these two regimes we report a novel one, in which dislocations nucleate at the steps but no pop-ins are visible. This novel regime is to a large extent reversible in the sense that defects disappear when the tip is retracted [2]. Heterogeneous dislocation nucleation is catalyzed by the presence of the surface steps. \newline [1] J. Li, MRS Bulletin, 32, (2007), 151. \newline [2] V. Navarro et al. Submitted   

Hysteresis in Kinking Nonlinear Elastic Solids and the Preisach-Mayergoyz Model

We show that the stress-induced, dislocation-based, elastic hysteric loops of kinking nonlinear elastic solids -- polycrystalline cobalt, Ti3SiC2 and a 10 vol. {\%} porous Ti2AlC - obey the scalar Preisach-Mayergoyz phenomenological model because they exhibit wipe-out and congruency, two necessary and sufficient tenets of the model. We also present experimental proof of the applicability of the model for the prediction of the response of these materials to complex stress histories.   

Strain Relaxation through Structural Phase Transition in Ultrathin Films of FCC Metals

We report a computational analysis of atomistic mechanisms of relaxation of biaxially applied tensile strain over a broad range of strain levels, $\varepsilon $, in freestanding ultra-thin Cu films based on isothermal-isostrain large-scale molecular-dynamics simulations. Our analysis reveals that for $\varepsilon \quad <$ 10{\%}, plastic deformation occurs through ductile void growth and dislocation nucleation and glide from the thin-film surfaces. For $\varepsilon \quad \ge $ 10{\%}, strain relaxation is dominated by the nucleation of a high density of dislocations at the film's surface, leading to a martensitic transformation of the thin film from an fcc to a hcp lattice structure. The hcp phase nucleates at the surface of the thin film and propagates into the film due to the glide of dislocations; in this process, the relative atomic slips have magnitudes identical to those observed in Bain transformations. Furthermore, mechanical analysis according to generalized stability criteria shows that the observed phase transition is consistent with the onset of a shearing instability of the thin film.   

Mechanical Properties and Fracture of Electrophoretically Deposited CdSe Nanocrystal Films

The fracture, strain, and stress of electrophoretically deposited (EPD) CdSe nanocrystal films are studied as a function of the film thickness, nanocrystal size, and drying method$. $Fracture results from the film stress that develops with the loss of residual solvent after EPD, when the film exceeds a threshold thickness. Generational crack formation and a preferred direction for film drying are observed in real time. The elastic modulus and hardness of films of 3.2 nm CdSe nanocrystals are $\sim $10 GPa and 450 MPa by nanoindentation. Furthermore, after particle cross-linking and partial ligand removal, the films exhibit compaction of the nanocrystal cores suggesting these films have polymeric features that can be attributed to the organic ligands and granular characteristics due to the inorganic cores. The toughness of the thin films is determined to be $\sim $1000-1400 J/m$^{2}$ for channel cracks in 3.2 nm nanocrystal films; the toughness values would be lower for a (likely) sublinear dependence of stress on strain. This work was supported primarily by the MRSEC Program of the NSF under Award No. DMR-0213574 and by NYSTAR. Nanoindentation studies at the Oak Ridge National Laboratory SHaRE User Center were sponsored under DE-AC05-00OR22725.   

Current-induced Stabilization of Surface Morphology in Stressed Solids

We report results on the surface morphological evolution of a conducting crystalline solid under the simultaneous action of an electric field and mechanical stress based on a fully nonlinear model and combining linear stability theory with self-consistent dynamical numerical simulations. Surface diffusional anisotropy is taken into account in the analysis. We address the morphological response of a planar surface for a stress that acts on the solid uniaxially and parallel to the applied electric field, which is directed parallel to the surface plane. For a given stress level, our linear stability analysis predicts three regimes of surface morphological response at weak, moderate, and strong electric fields, respectively. Our key theoretical findings are in agreement with our numerical simulation results. Most importantly, we find that a sufficiently strong electric field, through surface electromigration, can stabilize the surface morphology of the stressed solid against crack-like surface instabilities.   

Potts-Percolation Model of Solids

We study a statistical mechanics model of a solid. Neighboring atoms are connected by Hookian ``springs''. If the energy of a ``spring'' is larger than a threshold, the ``spring'' is more likely to fail, while if the energy is lower than the threshold the spring is more likely to be alive. The phase diagram and thermodynamic quantities, free energy, numbers of bonds and clusters etc, are determined using renormalization-group and Monte-Carlo techniques.   

Statistical Mechanics with Spatial Resolution: a bottom-up approach to nonuniform deformation

The development of theoretical framework connecting pure atomistic simulations to the constitutive macroscopic behavior of a system undergoing nonuniform deformations has been very challenging. Here I report a new formalism that embeds the traditional principles of statistical mechanics with spatial resolution, applied to deformation of crystals. A ``stationary deformation path'' is derived for discrete lattice points. This new atomistic representation of deformation is linked to continuum description of deformed crystalline space through a statistical distribution function whose spatial variation obeys a Liouville-like equation. The formulation is applied to describe local/nonuniform deformations. Dislocations are shown to be represented by an independent-acting nonlocal strain field in nonequilibrium conditions. Continuum equations like Kroner's relation for dislocations are rederived. The formulation can be used in analyzing deformation mechanisms associated with defects involving heterogeneous fields at the nanoscale and macroscale, and in studying nanoscale processes where nonlocality is important.