Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session H32: Focus Session: Tribophysics -- Fracture and Plasticity |
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Sponsoring Units: GSNP DMP Chair: Bernd Gotsmann, IBM Zurich Room: E142 |
Tuesday, March 16, 2010 8:00AM - 8:12AM |
H32.00001: Fractal geometry of fracture patterns in rocks simulated with a stochastic Laplacian growth model Alejandra Aguilar-Hernandez, Guillermo Ramirez-Santiago We investigate the fractal properties of 2D-patterns generated from a stochastic two-dimensional Laplacian growth model (SLGM) and 2D-patterns obtained from rock's fracture binary images. The SLGM is defined in terms of a conformal nonlinear mapping that depends on two parameters. One of them $a$ ($0< a < 1$) defines the form of the object, a strike or a bump, that attaches to the cluster that at the end generates the patterns. It was found that the pattern's fractal dimension and roughness exponent values depend on $a$. A detailed analysis of the patterns structures indicates that the fractal dimensions of capacity, information, and correlation, decrease monotonically as $a$ increases. When $a \stackrel{<}{\approx} 1$ the values of these fractal dimensions become closer to each other, suggesting that the patterns are self-similar. In addition, analyzes of the scaling of the patterns roughness exponent for $a=0.9$, suggests a self-affine structure. For this value of $a$, the roughness exponent values are found to be in a range that is characteristic of rock's fractures. [Preview Abstract] |
Tuesday, March 16, 2010 8:12AM - 8:24AM |
H32.00002: Event Scaling in Granular Stick-Slip Failures Karen Daniels, Kate Foco, Karin Dahmen Intermittent failure events in many systems can be characterized by scaling relations relating sizes and durations of individual events. We perform experiments on a sheared granular material which exhibits stick-slip behavior, and compare with predictions from a recent mean-field model. Our experiments are performed in a quasi-2D photoelastic granular material which is sheared via a spring moving at constant velocity. We characterize changes in the duration and size of stick-slip events as a function of packing fraction. We observe that the plate velocity $v(t)$ takes a universal shape during individual events of different sizes, as expected for systems with scaling. [Preview Abstract] |
Tuesday, March 16, 2010 8:24AM - 8:36AM |
H32.00003: Scaling of Stick-Slip Instabilities in Granular Materials Eric Daub, Paul Johnson We investigate stick-slip instabilities in sheared granular materials. This problem involves a broad range of length scales, from individual grain contacts up through larger scale frictional interfaces. Due to this range of length scales, constitutive models for deformation and fracture in granular materials must capture the essential physics at a given scale and efficiently transmit that information to larger scales. In this study, we look at the mechanisms of deformation and constraints on constitutive laws for granular materials using laboratory stick-slip data. We examine the effect of varying the applied normal stress and external shearing rate on the dynamics of stick-slip, including recurrence times, slip magnitudes, dilation and compaction of the material, and dynamic changes in the material properties. By determining the aspects of stick-slip that scale, we can develop models that are applicable to systems under a wide range of conditions at many different scales. Many engineering applications and geophysical systems require scaling from the laboratory to systems at significantly larger scales, and we explore the implications of our results for the multi-scale problem of dynamic earthquake faulting. [Preview Abstract] |
Tuesday, March 16, 2010 8:36AM - 8:48AM |
H32.00004: The precursory fault width formation of large earthquakes Fumihide Takeda, Makoto Takeo We collect earthquake (EQ) events for a region of about 5 degree mesh from a focus catalog of Japan with a regionally dependent magnitude window of M $\ge $ 3-3.5. The time history of the events draws a zigzagged trajectory in a five dimensional space of EQ epicenter, focal depth (DEP), inter-event interval (INT), and magnitude (MAG). Its components are the time series of the EQ source parameters for which time is the chronological event index. Each series has long-term memory and evidence of deterministic chaos. We thus use physical wavelets (P-Ws) to find the process producing large EQs. The P-Ws convert the moving-average of each series, its first and second order differences at any interval into the displacement, velocity and acceleration (A) in selective frequency region, respectively. The process starts with two unique different triple phase couplings of A on source parameters DEP, INT, and MAG, precursory to every large EQ's (M $>$ about 6) throughout Japan. Each coupling then creates a linear DEP variation (W) on its series, which becomes comparable to the fault width of large EQ's. It suggests that the variation exerts the corresponding shear stress on a local plane in Earth's crust to form the fault plane of width W, rupturing a large EQ. [Preview Abstract] |
Tuesday, March 16, 2010 8:48AM - 9:00AM |
H32.00005: Pinch-off and Fracture of Bubble Rafts Chin-Chang Kuo, Michael Arciniaga, Michael Dennin The breaking dynamics of a bubble raft bridge between two walls which are pulled apart is studied experimentally. Unlike the pinch-off of liquids, various deformation types can be observed in this complex fluid system. We find that a large ratio between the initial width and length of the bubble raft bridge leads to a solid-like ripping of the foam layer, whereas the deformation tends to have a liquid-like pinch-off behavior for smaller ratios. Furthermore, the bubble size distribution, crystallization and the pulling velocity can have a significant effect on the bridge breaking. In particular, for a highly ordered and uniform bubble composition with a fast pulling velocity, the fracture occurs in the early stage of the pinch-off, which demonstrates an intermediate state between solid-like and liquid-like breaking. We will report on critical pulling speeds for fracture and scaling exponents for pinch-off. [Preview Abstract] |
Tuesday, March 16, 2010 9:00AM - 9:12AM |
H32.00006: Propagation of a crack front in presence of a controlled disorder Julien Chopin, Alexis Pr\'evost, Arezki Boudaoud, Mokhtar Adda-Bedia A interfacial front (wetting contact line, crack front, magnetic domain wall, ...) propagating in a heterogeneous landscape exhibits morphological and dynamical properties whose understanding remains imperfect. We designed an experiment where a crack front propagates at the interface of a quartz plate and an elastomer (PDMS). The quartz plate, initially covered by a nanometric layer of chromium, is patterned by holes of few tens of microns spatially modulating the fracture energy of the materials. An optimal control of the heterogeneities is achieved by optical lithography techniques allowing to investigate the statistical properties of the crack front. In particular we studied the dependence of the roughness exponent of fronts with the average speed of propagation. [Preview Abstract] |
Tuesday, March 16, 2010 9:12AM - 9:48AM |
H32.00007: Failure of disordered materials as a depinning transition Invited Speaker: Laurent Ponson 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 far-from-equilibrium propagation of a crack within a disordered brittle material. At first, we focus on the average dynamics of a crack, and study the variations of its growth velocity $v$ with respect to the external driving force $G$ [1]. Carefully measured on a brittle rock, these variations are shown to display two regimes: above a given threshold $G_c$, the velocity evolves as a power law $v \sim (G- G_c)^{0.8}$, while at low driving force, its variations are well described by a sub-critical creep law, characteristic of a thermally activated crack propagation. Extending the continuum theory of Fracture Mechanics to inhomogeneous media, we show that this behavior is reminiscent of a dynamical critical transition: critical failure occurs when the driving force is sufficiently large to depin the crack front from the material heterogeneities. Another way to reveal such a transition is to investigate the fluctuations of crack velocity [2]. Considering a crack at the heterogeneous interface between two elastic solids, we predict that its propagation occurs through sudden jumps, with power law distributed sizes and durations. These predictions compare quantitatively well with recent direct observations of interfacial crack propagation [3]. Such an interpretation of material failure opens new perspectives in the field of Engineering and Applied Science that will be finally discussed. \\[4pt] [1] L. Ponson, Depinning transition in failure of inhomogeneous brittle materials, Phys. Rev. Lett. {\bf 103}, 055501 (2009). \\[0pt] [2] D. Bonamy, S. Santucci and L. Ponson, Crackling dynamics in material failure as a signature of a self-organized dynamic phase transition, Phys. Rev. Lett. {\bf 101}, 045501 (2008). \\[0pt] [3] K.J. M{\aa}l{\o}y, S. Santucci, J. Schmittbuhl and R. Toussaint, Local waiting time fluctuations along a randomly pinned crack front, Phys. Rev. Lett. {\bf 96}, 045501 (2006). [Preview Abstract] |
Tuesday, March 16, 2010 9:48AM - 10:00AM |
H32.00008: Extending the Scaling Laws of Plasticity Georgios Tsekenis, Karin Dahmen Crystalline materials are known to deform in an intermittent way with avalanches. Power laws govern the statistics of the avalanche sizes, energies and times between avalanches. In this work we are studying the universal aspects of plasticity and dislocation dynamics. We employ a discrete dislocation dynamics simulation, which allows us to reproduce the distributions of avalanche sizes and energies of previous works. In addition, our model accounts for time explicitly. Thus we are able to extract distributions of dislocation slip avalanche durations and interevent times, which compare quite well with the experimental findings. We are also able to extract the power spectra of the dislocation activity that exhibit power law behavior as well. Furthermore, finite stress rate forces avalanches to occur concurrently in time and/or space and appears to lead to similar effects as previously studied for spin systems driven by an increasing magnetic field. The study of larger system sizes and slower stress rates and comparison to new experiments will give us deeper insight into the problem of plasticity as a nonequilibrium critical phenomenon. [Preview Abstract] |
Tuesday, March 16, 2010 10:00AM - 10:12AM |
H32.00009: Meso-scale harmonic analysis of homogeneous dislocation nucleation. Asad Hasan, Craig Maloney Atomistic computer simulations are performed using empirical potentials to study the process of the nucleation of dislocations in a perfect thin-film under a smooth nano-indenter. In particular, we study the energy eigenvalue spectrum and spatial structure of the energy eigenmodes of \textbf{mesoscale} regions in the crystal on approach to nucleation. We show that: i) the local strain rate diverges along an \textbf{extended} disc-like region ii) the divergence of the strain rate is in accordance with the classical scaling expected from a saddle-node instability corresponding to a \textbf{single} reaction pathway iii) stresses and strains in the crystal are not particular large near the nucleation site at the time of nucleation iv) the stiffness of meso-scale regions provides good predictive capabilities for identifying the core of the embryonic defect and, moreover, allows one to unambiguously define a characteristic length-scale. These observations point to the shortcomings of several recent approaches and highlight the collective nature of homogeneous dislocation nucleation, while at the same time, they show how a quasi-local approach may be useful as a predictor of dislocation nucleation. [Preview Abstract] |
Tuesday, March 16, 2010 10:12AM - 10:24AM |
H32.00010: Bauschinger effect in oriented polymer glasses Ting Ge, Mark O. Robbins The Bauschinger effect in oriented polymer glasses refers to the anisotropic response of the material to deformation. We use molecular simulations to examine the microscopic origin of this effect in both entangled and unentangled systems. Oriented states are obtained by stretching an isotropic state uniaxially to certain prestrains. States of different prestrains are then stretched and compressed along the axis of preorientation. As in experiment, the tensile response is stronger than the compressive one, but we find that the stresses for different prestrains collapse when plotted against the total strain with respect to the isotropic state. Examining conformations of individual chains shows that this collapse reflects a direct correlation between the degree of orientation and the stress. The stress rises with increasing chain orientation, because more local plastic rearrangements are required to maintain chain connectivity. The phenomenon is similar for entangled and unentangled chains, but entanglements force the system to deform affinely leading to a greater degree of orientation. Tensile deformations along directions at an angle $\theta $ to the preorientation are also performed. The response is less anisotropic because the initial strain has a smaller effect on the degree of orientation. [Preview Abstract] |
Tuesday, March 16, 2010 10:24AM - 10:36AM |
H32.00011: Strain Localization in Metallic Glasses: Role of Mechanical Heterogeneity Pavan Valavala, Michael Falk Metallic glasses are a technologically interesting material in large part because their flow behavior near the glass transition temperature makes them optimal for complex manufacturing processes. At lower temperatures, however, these materials tend to accommodate strain in ``shear bands'' resulting in macroscopically brittle behavior undesirable for load bearing applications. In order to better characterize the plastic processes that govern flow in these materials, we analyze spatial changes in local elastic response during molecular dynamics simulations of strain localization in a binary Lennard-Jones (LJ) glass. Isothermal elastic stiffnesses are evaluated at different length scales from equilibrium stress and strain fluctuations for the glass and a LJ crystal. The differences in convergence and variations in the elastic properties measured using stress and strain fluctuation methods are compared for the ordered and disordered systems. The average elastic properties are verified against direct measurements on the atomistic models. Finally, the consequences of mechanical heterogeneity on plastic response and strain localization in the glass will be discussed. [Preview Abstract] |
Tuesday, March 16, 2010 10:36AM - 10:48AM |
H32.00012: Effects of Molecular Architecture on Shear Band Formation and Mode II Fracture of Polymeric Glasses Jared Archer, Alan Lesser Mode II fracture studies were performed at various rates on a series of acrylic polymers and on polycarbonate (PC). The shear banding response of polymethyl methacrylate (PMMA) is shown to be highly sensitive to rate. As the rate increases, shear deformation becomes more localized to the point where Mode II fracture occurs. PC is much less rate dependent with lesser amounts of localization. A new theory is formulated relating orientation in a shear band to intrinsic material properties obtained from true-stress true-strain tests. A kinematic limit for orientation within a shear band is also derived based on entanglement network parameters. [Preview Abstract] |
Tuesday, March 16, 2010 10:48AM - 11:00AM |
H32.00013: Stress enhanced shear yielding in aging polymer glasses Joerg Rottler, Amy Y.-H. Liu The plastic response of polymer glasses is strongly dependent on the thermomechanical history of the material. We determine the molecular level origin of the enhancement of the shear yield stress reported in experiments of polymer glasses that undergo physical aging in the presence of a pre-stress. Molecular dynamics simulations are employed to show that the applied stress does not alter the physical aging rate, but instead induces a highly orientation-dependent mechanical response of the polymer glass. The change in yield stress with respect to polymers that have aged without pre-stress is directly proportional to the orientation of covalent bonds, which is proportional to strain and logarithmic aging time. We observe a pronounced Bauschinger effect, which amplifies or reduces the pressure dependence of shear yielding. Control simulations with a monovalent Lennard-Jones glass offer further evidence that these effects are distinct from other rejuvenation and overaging behavior reported for a broad class of amorphous solids. [Preview Abstract] |
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