Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session P14: Focus Session: Friction, Fracture and Deformation Across Length Scales II: Plasticity and Rupture |
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Sponsoring Units: DMP GSNP DCOMP Chair: Robin Selinger, Kent State University Room: D227 |
Wednesday, March 23, 2011 8:00AM - 8:12AM |
P14.00001: Scaling theory of continuum dislocation dynamics in two and three dimensions Yong S. Chen, Woosong Choi, Stefanos Papanikolaou, James P. Sethna When crystalline materials deform plastically, complex dislocation structures have been observed experimentally.\footnote{P. Hahner et al., Phys. Rev. Lett. 81, 2470, 1998.} We provide a continuum plasticity theory to study the emergent self-similar morphologies.\footnote{Y.S.Chen et al., Phys. Rev. Lett. 105, 105501, 2010.} We analyze the self-similarity in terms of critical exponents for correlation functions of dislocation density, crystalline orientation and plastic distortion, and explore the connection to the power spectrum of the total free energy. In two and three dimensions, we apply anisotropic loadings, and observe little anisotropy in the critical properties. We explore the addition of quenched disorders to our continuum theory, to investigate the relation between dynamics (plasticity avalanches) and static dislocation morphologies. [Preview Abstract] |
Wednesday, March 23, 2011 8:12AM - 8:24AM |
P14.00002: Saddle node scaling on approach to dislocation nucleation Akanksha Garg, Asad Hasan, Craig Maloney We study the process of dislocation nucleation in a perfect 2D hexagonal crystal under nano-indentation loading in a numerical model using energy minimization techniques and analysis of the energy eigenmodes. The nucleation event takes the form of a saddle-node catastrophe and is governed by associated scaling laws. In particular, on approach to nucleation, a single energy eigenmode descends through the spectrum and its eigenvalue vanishes as the square root of the distance to the nucleation point. The velocity of the system shows the same scaling behavior, and its normal mode decomposition demonstrates that it is dominated by the critical mode responsible for nucleation. [Preview Abstract] |
Wednesday, March 23, 2011 8:24AM - 8:36AM |
P14.00003: Dislocation dynamics at zero temperature and at finite temperature: analytics and simulations Karin Dahmen, Georgios Tsekenis, Pak Yuen Chan, Thomas Fehm, Jonathan Dantzig, Nigel Goldenfeld, Jonathan Uhl Crystalline materials are known to deform in an intermittent way with avalanches. Power laws govern the statistics of the avalanches. In this work we are studying plasticity as a member of the universality class of depinning phase transition. Results from our Discrete Dislocation Dynamics simulations agree with analytical mean field predictions for distributions of avalanche sizes, durations, power spectra, and avalanche shapes. Results from phase field crystal simulations agree with analytical predictions for the depinning phase transition at finite temperature. Both numerics and analytics indicate that the dynamics of edge dislocations in sheared crystals belong to the mean field universality class of depinning transitions, both at zero temperature and at finite temperature. [Preview Abstract] |
Wednesday, March 23, 2011 8:36AM - 9:12AM |
P14.00004: Size Matters: size-dependent strength and nucleation-governed deformation mechanisms in nano-scale Cu pillars Invited Speaker: Uniaxial compression and tension tests on single crystalline micro and nanopillars have revealed a strong size effect. For face-centered cubic metals, this size effect is characterized by a power-law: where $n$ is between .5 - .7. The majority of these micro-mechanical tests have been performed on pillars produced by the focused-ion-beam (FIB), a process known to introduce surface damage into the material and to limit the smallest attained pillar diameter to $\sim $150nm while maintaining its shape integrity. In order to overcome these detriments, we developed a new technique combining electroplating and electron beam lithography to create single crystalline Cu nano-pillars with diameters down to 50 nm. We find the mechanical response of these samples to exhibit the same power-law strengthening behavior as other fcc metals down to the diameter of 100nm, as revealed by \textit{in-situ} uniaxial compression and tension tests conducted in a custom-built in-situ mechanical deformation instrument, SEMentor. TEM investigations of the microstructure of pillars produced by the FIB and by electroplating show similar initial dislocation densities of $\sim$10$^{14}$ m$^{-2}$ implying that size-dependent strength at the nano-scale is a strong function of initial microstructure and not of fabrication method. We examine the limits of this power-law trend down to diameters of 50nm, as at these small sizes, deformation behavior has been theoretically predicted to change due to the activation of surface dislocation sources and the increasing influence of the surface stress. Furthermore, we find that these single crystalline Cu nano-pillars show a remarkable strain-rate dependence that increases with decreasing diameter further revealing the thermally activated nature of dislocation sources and corresponding changes in activation volume. HRTEM investigations of post-mortem structures will be presented in the context of dislocation-based phenomenological modeling. [Preview Abstract] |
Wednesday, March 23, 2011 9:12AM - 9:24AM |
P14.00005: Effect of Inertia and Damping on Avalanche Distributions in Sheared Amorphous Solids K. Michael Salerno, Craig Maloney, Mark O. Robbins Avalanches occur in a variety of contexts from magnets to granular materials. Molecular dynamics simulations of a sheared binary Lennard-Jones glass are used to explore the effect of inertia and damping on avalanche distributions. We find that the energy dissipation rate is one of the key factors in determining the size of an individual avalanche as well as the distribution of avalanche energies. There are three distinct regimes: an overdamped regime where the distribution has an exponential cutoff that varies with dissipation rate, a critical regime where avalanches follow power-law statistics and large events are limited by simulation size, and a run-away regime where inertia leads to a peak at large energies. The same regimes are found for Langevin type viscous damping and Galilean-invariant Kelvin damping. While inertia determines how an avalanche evolves, some properties of the avalanche are predetermined. Weakening of the average shear modulus prior to an avalanche is a good indicator that a large, system-spanning event may occur. [Preview Abstract] |
Wednesday, March 23, 2011 9:24AM - 9:36AM |
P14.00006: Nonclassical Nucleation and Growth of Cohesive Tensile Cracks Joseph Gran, John Rundle, William Klein We analyze the nucleation and growth of cohesive tensile cracks using a Hamiltonian which is written as a functional of the crack separation (offset field). We simulate the nucleation events on a square lattice using a Metropolis Monte Carlo algorithm. Several modes of crack propagation are seen in the simulations. Our results indicate that for certain materials, crack nucleation and growth proceed through the formation and extension of a diffuse ``halo'' surrounding the classical portion of the crack. This is similar to nonclassical nucleation near the spinodal in magnetic systems. Theoretical considerations and numerical calculations strongly suggest that the diffuse halo can be identified with the fracture ``process zone'' seen in laboratory studies of advancing cracks. We are investigating scaling exponents associated with this apparent phase transition. [Preview Abstract] |
Wednesday, March 23, 2011 9:36AM - 9:48AM |
P14.00007: Enhanced Strength via crack friction and Pressure Donald Wiegand, Kevin Ellis, Claire Leppard The effect of pressure on the mechanical response of particulate polymer composites is being studied. Between about 0.1 and 7 MPa for one composite the results indicate that slow crack growth is the dominant failure mode. With continuously creasing strain at low pressures the stress initially increases to a maximum, the compressive strength, then decreases indicating work softening and them becomes approximately constant at a plateau value. Both the compressive strength and the plateau stress increases linearly with pressure but the plateau stress increases with a steeper slope such that at higher pressures work softening is not observed. The results are analyzed in terms of shear cracks with friction between the crack surfaces. The model predicts a threshold stress for crack growth which increases linearly with pressure and further predicts that the compressive strength increases linearly with pressure as observed and with the same slope as the threshold stress. These results clearly indicate that the pressure dependence of the compressive strength is due to the pressure dependence of the threshold stress for crack growth. The changes in the plateau region can also be attributed to frictional effects. [Preview Abstract] |
Wednesday, March 23, 2011 9:48AM - 10:00AM |
P14.00008: Irreversible Damage in Amorphous Silica Cindy Rountree, Damien Vandembroucq, Stephane Roux, Elisabeth Bouchaud Glass touches every aspect of our lives including the glass dishes which we cook with to the storage of nuclear waste. The extensive use of oxide glasses can be attributed to optical transparency, electrical and heat insulation, and large hardness. However, oxide glasses have a major drawback: brittleness. Even small flaws in the structure can lead to the ultimate failure of the material. Recent Atomic Force Microscope experiments and Molecular Dynamics simulations revealed a process zone ahead of the crack tip where damage nucleates, augments, and finally merges with the advancing crack front. Furthermore, when a-SiO$_{2}$ samples are nanoindented, one finds permanent damage under the indenter in the form of densified silica. To shed light on the origin of irreversible deformation in amorphous media, we have expanded our studies to examine what happens to an oxide glass when subjected to shear. MD simulations have been performed in a-SiO$_{2}$ systems which are subject to a shearing force at room temperature. The system was initially isotropic and as long the maximum shear deformation remains under 5{\%} the system remains isotropic upon unloading. However if the system is sheared to a point greater than 5{\%} permanent plastic deformation sets in and the system is no longer isotropic upon unloading. [Preview Abstract] |
Wednesday, March 23, 2011 10:00AM - 10:12AM |
P14.00009: Molecular dynamics study of the contact strengths between clean metallic surfaces with nanoscale asperities Hojin Kim, Alejandro Strachan A fundamental understanding of the mechanical behavior of contacting surfaces with nanoscale asperities including their adhesion and friction is critical for MEMS and other applications. We characterize the tensile strength of contacts formed between various clean Pt surfaces such as commensurate contacts between (001) and (111) surfaces and incommensurate (001) ones by using MD simulations over wide range of asperity size. In cyclic closing and opening, the first contact shows significant plastic deformation, leading to a considerable reduction in the contact area. After few cycles, steady state is achieved both contact size and the pullout force. The strength of bridges in both commensurate and incommensurate contacts exhibits strong size effects. Their strength increases with decreasing size until a length of approximately 5 nm below which weakening is observed. Commensurate contacts are stronger than incommensurate ones but only during the initial contacts, after steady state is achieved commensurate and incommensurate (001) surfaces lead to similar strengths. [Preview Abstract] |
Wednesday, March 23, 2011 10:12AM - 10:24AM |
P14.00010: Friction and Sliding of Polystyrene Micro Spheres in the Presence and Absence of Capillary Adhesion Iyam Lynch, Jacqueline Krim Quartz crystal microbalance (QCM) response to varying load geometries, particularly micro particles, is a rapidly growing field of research.\footnote{Dybwad, G.L. J. Appl. Phys. \textbf{1985}, 58, 2789}$^,$\footnote{Dultsev, F.N. et al. Langmuir \textbf{2000}, 16, 5036.} This no doubt is due to its varied applications involving the study of textiles, DNA and viruses$^{3}$, micro adhesion$^{2,3}$, micro sorting$^{3}$, and friction. There are many challenges that must be overcome in this field. One major difficulty is capillary adhesion, which is difficult to quantify. We have created an experiment to greatly reduce the impact of capillary adhesion by employing the shaking motion of a 5MHz QCM to eject micro spheres (15$\mu $m) from its surface, which subsequently land on the surface of a nearby 8 MHz QCM. The experiment is performed in a vacuum chamber to include different environments such as air, vacuum, and dry nitrogen. During the experiment we monitor the behavior of the unloaded QCM by measuring the change in frequency and quality factor as a result of the newly landed spheres. Particle motion and dynamics are observed using a microscope with a camera attached. [Preview Abstract] |
Wednesday, March 23, 2011 10:24AM - 10:36AM |
P14.00011: Cooperative adhesion and friction of compliant nanohairs Ali Dhinojwala, Liehui Ge, Lijie Ci, Anubha Goyal, Pulickel Ajayan, L. Mahadevan The adhesion and friction behavior of soft materials, including compliant brushes and hairs, depends on the temporal and spatial evolution of the interfaces in contact. For compliant nanofibrous materials, the actual contact area of individual fibers make with surfaces depends on the preload applied upon contact. Using in-situ microscopy observations of preloaded nanotube hairs, we show how nanotubes make cooperative contact with a surface by buckling and conforming to the surface topography. The overall adhesion of compliant nanohairs increases with increasing preload as nanotubes deform and continuously add new side-wall contacts with the surface. Electrical resistance measurements indicate significant hysteresis in the relative contact area. Contact area increases with preload (or stress) and decreases suddenly during unloading, consistent with strong adhesion observed for these complaint nanohairs. [Preview Abstract] |
Wednesday, March 23, 2011 10:36AM - 10:48AM |
P14.00012: The effect of Coulombic friction on spatial displacement statistics Andreas Menzel, Nigel Goldenfeld We study the effect of Coulombic (dry) friction on the spatial displacement statistics of one-dimensional stochastic motions. In other words, one of the simplest forms of nonlinear friction is added to the Fokker-Planck equation for conventional viscous Brownian motion, and its consequences are investigated. First, we find the eigenfunctions to the problem that includes the velocity component only. This problem can be mapped on the case of a quantum mechanical harmonic oscillator in the presence of a delta potential. Then we show numerically that a crossover from exponential to Gaussian displacement statistics results from the Coulombic frictional contribution. A transient regime of multiscaling is identified for the spatial distribution function. Our results are important for the interpretation of recent experiments in the field of soft matter physics: it turns out that, for practical purposes, higher order moments of the spatial distribution function must be determined to identify the presence of effective Coulombic frictional forces. [Preview Abstract] |
Wednesday, March 23, 2011 10:48AM - 11:00AM |
P14.00013: Understanding frictional duality and bi-duality: Sb-nanoparticles on HOPG Jan Brndiar, Robert Turansky, Ivan Stich We have simulated [1] the behavior of motion of Sb$_{n}$ nanoparticles on HOPG with the quest to elucidate the experimentally observed frictional bi-duality [2]. The first duality was observed for clean Sb-nanoparticles deposited under UHV conditions. Both frictionless and ``normal'' behavior was observed. Another dual behavior was found for Sb-nanoparticles exposed to ambient conditions, both scaling linearly with contact area. The vanishing friction branch is due to incommensurability of the Sb-HOPG. The non-vanishing friction branch can be accounted for by contaminants due to imperfect UHV, such as water, hydrocarbons, oxygen, etc., including small Sb$_{n}$ clusters. The large friction forces after exposition to ambient conditions result from presence of mobile oxidized multiasperities. The simulations allow for quantitative estimates of impurity concentrations and understanding of the molecular mobility. \\[4pt] [1] J. Brndiar et al. submitted (2010). \\[0pt] [2] D. Dietzel et al. Phys.Rev.Lett. \textbf{101}, 125505 (2008), Phys.Rev. \textbf{B 82}, 035401 (2010). [Preview Abstract] |
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