Experimental study of different modes of block sliding along interface. Part 3. Numerical modeling

This paper completes a series of studies on the patterns of block sliding along interface. It has been shown that in order to model the whole range of crustal block movements, the empirical rate and state friction law must be supplemented with a term that accounts for the appearance of additional shear resistance associated with the dynamic viscosity of the contact between blocks. With this term, the experimentally observed slow slip events can be modeled with good accuracy. A generalization of results of the entire series of studies published in several issues of the journal suggests that both the dynamic and quasi-static modes of sliding along faults are components of a single deformation process. The parameter that governs the formation and evolution of a fault sliding mode is the ratio between the effective values of the fault zone stiffness and rock mass stiffness. Their variation determines the occurrence of a particular sliding mode.     

Experimental study of different modes of block sliding along interface. Part 1. Laboratory experiments

This paper is the first part of an experimental work on studying the formation of different deformation modes of rock discontinuities under laboratory and field conditions. The formation conditions of different sliding modes were studied under laboratory conditions for several types of discontinuities, such as rigid surface contact and cracks filled with quartz sand, talc, and clay. A wide range of shear deformation modes were experimentally reproduced—from dynamic slip with a maximum velocity of tens of mm/s to stable sliding with a velocity of 1 µm/s. The behavior of a crack with a clay-containing gouge drastically changes after its wetting. The larger is the content of clay, the longer is the slip duration. The motion of a block consists of a long phase (~100 s) in which displacement velocity smoothly increases, and a retardation phase of almost the same duration in which displacement velocity decreases down to a few tens of µm/s. The used sensors detected no acoustic emission prior to the beginning of block sliding as well as on all stages of block motion until its full stop. It is shown that slow slip events have all stages typical for stick-slip motion: acceleration, long sliding, retardation, arrest, and quiescence. The conducted laboratory experiments substantiate the earlier statement that all types of deformation processes in the Earth’s crust produce a common range of phenomena.     

Comparison of time dependent fracture in viscoelastic and ductile solids

Effects of two parameters on enhancement of the time-dependent fracture manifested by a slow stable crack propagation that precedes catastrophic failure in ductile materials have been studied. One of these parameters is related to the material ductility (ρ) and the other describes the geometry (roughness) of crack surface and is measured by the degree of fractality represented by the fractal exponent α, or — equivalently — by the Hausdorff fractal dimension D for a self-similar crack. These studies of early stages of ductile fracture are preceded by a brief summary of modeling the phenomenon of delayed fracture in polymeric materials, sometimes referred to as “creep rupture”. Despite different physical mechanisms involved in the preliminary stable crack extension and despite different mathematical representations, a remarkable similarity of the end results pertaining to the two phenomena of slow crack growth that occur either in viscoelastic or ductile media has been demonstrated.     

Mesomechanics of shear resistance along a filled crack

The paper reports on laboratory experiments with the aim of studying the effect of microstructural and macromechanical properties of a crack filled with discrete material on the formation of a sliding mode. It is shown that the spectrum of possible deformation events on the discontinuity is governed by both the macroscopic characteristics of the gouge and its mesoscale structure. The evolution of force bridges which are formed and collapsed in shear along the crack, their length and number fully control the type of deformation—stable sliding, stick-slip, and intermediate modes with low-velocity motion of the crack edges. The variation of the Coulomb strength affects mainly the stress drop value in dynamic failure or a slip event with low displacement velocity and little affects the deformation mode. Consideration is also given to the regularities by which the macroscopic characteristics of contact vary in shear.     

Effect of uniaxial tension and hydrostatic compression on the geometry and morphology of amorphous Fe<Subscript>77</Subscript>Ni<Subscript>1</Subscript>Si<Subscript>9</Subscript>B<Subscript>13</Subscript> alloy ribbon surface

The effect of hydrostatic pressure and uniaxial compression on the relief of an amorphous Fe₇₇Ni₁Si₉B₁₃ alloy ribbon surface was studied using scanning tunneling and atomic-force microscopy. The fracture surfaces of samples were also studied. It is found that both the initial surfaces and the surfaces of samples subjected to hydrostatic compression or tension, as well as fracture surfaces, are fractal or multifractal, but their fractality parameters are different. Hydrostatic pressure decreases the surface roughness and the average fractal dimension of the surface on both sides of the ribbons. The dependence of the surface fractal characteristics on tension is more complex. Prior to the occurrence of a “critical event” on the surface (formation of a deformation band or a through crack), the Hölder index and the half-width of the singularity spectrum decrease. The correlation is discussed between the fractal characteristics of the ribbon surface and those of a fracture surface, and the role of an excess free volume in the initiation of fracture of amorphous alloys is analyzed.     

Hot spots in an athermal system

We study experimentally the dynamical heterogeneities occurring at slow shear, in a model amorphous glassy material, i.e., a 3D granular packing. The deformation field is resolved spatially by using a diffusive wave spectroscopy technique. The heterogeneities show up as localized regions of strong deformations spanning a mesoscopic size of about 10 grains and called the "hot spots." The spatial clustering of hot spots is linked to the subsequent emergence of shear bands. Quantitatively, their appearance is associated with the macroscopic plastic deformation, and their rate of occurrence gives a physical meaning to the concept of "fluidity," recently used to describe the local and nonlocal rheology of soft glassy materials.     

MD investigation of the collective carbon atom behavior of a (17, 0) zigzag single wall carbon nanotube under axial tensile strain

The collective dynamic behavior of carbon atoms of a (17, 0) zigzag single wall carbon nanotube is investigated under tensile strains by molecular dynamics (MD) simulations. The “slip vector” parameter is used to study the collective motion of a group of atoms and the deformation behavior in three different directions (axial, radial, and tangential) of a (17, 0) carbon nanotube. The variations of radial slip vectors indicate almost all carbon atoms of the (17, 0) carbon nanotube will stay on the cylindrical surface before the yielding of the single wall carbon nanotube (SWNT). Furthermore, the tangential vectors show kinking deformation for the (17, 0) zigzag tube only rarely appears when the crack occurs. Non-symmetrical deformation around a carbon atom along the axial direction also can be found. The variations in the slip vector values of each atom display a symmetrical crack along the horizontal direction and normal to the tube axis. Chain-like structures with 3–4 atoms can be observed, with the number of chain-like structures decreasing before the breakage of the SWNT. The mechanical properties and dynamic behavior of a (17, 0) zigzag SWNT under tensile strain are also compared with that of a (10, 10) armchair tube in our previous study (Weng et al. 2009).     

Flory theory of polymeric fractals - intersection,saturation and condensation

We consider swelling effects of polymeric fractals, recently introduced by Cates, by usual simple Flory arguments for the free energy. The Flory arguments can be formulated to give a unified view for all polymers, linear, branched, or percolation clusters, as long they are of fractal connectivity.If the size of solvent molecules, being fractals themselves, is comparable to the given cluster, new values of the fractal dimensions can be found. The upper critical dimension is reduced. This is due to usual screening of the excluded volume. By standing overlap and repulsive energies of fractals of different fractal dimensions we find condensation to non-fractal objects depending on the value of the fracton dimension. A melt of polymeric fractals of the same fractal dimension and the same size becomes compact if the spectral dimension exceeds a “critical” value.These considerations are of relevance concerning recent experiments, considering static and dynamic properties of mixtures of microgels and linear polymers of different or equal sizes.     

Thermodynamically stable fractal-like domain structures in magnetic films

A fractal-like structure of the domain boundaries was revealed in “overcritical” uniaxial Permalloy magnetic films. The fractal dimension of domain boundaries at the film surfaces was determined as a function of the film thickness. It is shown that the phase transition between the two possible types of fractal-like structures is accompanied by a jump in fractal dimension.

     

A simple model for friction detachment at an interface of finite size mimicking Fineberg’s experiments on uneven loading

This work presents a model and simulation results for the friction detachment of a finite sized interface, following previous results on the phenomenon by Ben-David and Fineberg, namely “experiments demonstrating that the ratio of shear to normal force needed to move contacting bodies can, instead, vary systematically with controllable changes in the external loading configuration”. In particular, we extend a previous one-dimensional simulation model by Bar-Sinai with colleagues to a quasi 2D model to allow for a tilting of one of the contacting blocks. While Bar-Sinai with colleagues postulate that the presence of “slow fronts” of detachment (an order of magnitude lower than the usual Rayleigh fronts as in crack propagation) is due to a strengthening term in the friction law, which is not always measured in unlubricated contacts, we find slow fronts also with a purely weakening law.     

Deformation behavior of tetramethyl-p-silphenylenesiloxane (TMPS)-dimethylsiloxane (DMS) block copolymer spherulitic films

A study of the morphology of uniaxially drawn spherulites of TMPS-DMS block copolymers with TMPS contents ranging from 90 to 30 wt % was made especially by electron and optical microscopy. For the entire range of polymer compositions, the copolymers, like the TMPS homopolymer, form negatively birefringent spherulites when crystallized from solution, or from the supercooled melt. A banded spherulitic morphology is observed. The deformability of copolymer spherulites increases as the DMS amorphous component increases. The DMS component coexists with, but is physically excluded from the ordered TMPS “crystalline” phase. In samples having the higher TMPS compositions, deformation occurs through crack formation, mechanical slip, tilting and/or twisting of the lamellae that help comprise the spherulites. At high DMS contents this “soft” component is undoubtedly responsible for the flexible character of these copolymers. Sample clarity also increases with DMS content as the crystallinity decreases.     

Frictional shear cracks

We discuss crack propagation along the interface between two dissimilar materials. The crack edge separates two states of the interface, “stick” and “slip.” In the slip region, we assume that the shear stress is proportional to the sliding velocity; i.e., the linear viscous friction law is valid. In this picture, the static friction appears as the tile Griffith threshold for crack propagation. We calculate the crack velocity as a function of the applied shear stress and find that the main dissipation comes from the macroscopic region and is mainly due to the friction at the interface. The relevance of our results to recent experiments, Baumberger et al., Phys. Rev. Lett. 88, 075509 (2002), is discussed.     

FCC Rolling Textures Reviewed in the Light of Quantitative Comparisons between Simulated and Experimental Textures

The crystallographic texture of metallic materials has a very strong effect on the properties of the materials. In the present article, we look at the rolling textures of fcc metals and alloys, where the classical problem is the existence of two different types of texture, the “copper-type texture” and the “brass-type texture.” The type of texture developed is determined by the stacking fault energy of the material, the rolling temperature and the strain rate of the rolling process. Recent texture simulations by the present authors provide the basis for a renewed discussion of the whole field of fcc rolling texture. We simulate the texture development with a model which allows us to vary the strength of the interaction between the grains and to vary the scheme for the calculation of the lattice rotation in the individual grains (type CL/MA or PR/PSA). For the deformation pattern we focus on {111}<110> slip without or with deformation twinning, but we also consider slip on other slip planes and slip by partial dislocations. We consistently make quantitative comparison of the simulation results and the experimental textures by means of a scalar correlation factor. We find that the development of the copper-type texture is best simulated with {111}<110> slip combined with type CL/PR lattice rotation and relatively strong interaction between the grains — but not with the full-constraint Taylor model and neither with the classical relaxed-constraint models. The development of the brass-type texture is best simulated with {111}<110> slip combined with PR/PSA lattice rotation and weak interaction between the grains. The possible volume effect of deformation twins on the formation of the brass-type texture is a controversial question which we discuss on the basis of our simulations as seen together with other investigations.     

Fracture features of granite under various deformation conditions

Fracture mechanisms of dry and water-saturated granite samples and slip (displacement) along a ready fault have been studied by measuring acoustic emission signals. It has been found that disperse defect formation is observed in dry samples under mechanical load, then localization occurs, and a fracture source is formed, whose development results in macrofault formation. In water saturated samples, chaotic defect formation occurs in the entire volume, which leads to a high degree of material damage. At the closing deformation stage, several fault source zones are formed in which main cracks develop. In the case of slip along a ready fault, stoppers at crack edges are broken.     

A mathematical model of Panin’s prefracture zones and stability of subcritical cracks

Basic concept underlying Griffith’s theory of fracture of solids was that, similar to liquids, solids possess surface energy and, in order to propagate a crack by increasing its surface area, the corresponding surface energy must be compensated through the externally added or internally released energy. This assumption works well for brittle solids, but is not sufficient for quasi-brittle and ductile solids. Some new forms of energy components must be incorporated into the energy balance equation, from which the input of energy needed to propagate the crack and subsequently the stress at the onset of fracture can be determined. The additional energy that significantly dominates over the surface energy is the irreversible energy dissipated by the way of the plastic strains that precede the leading edge of a moving crack. For stationary cracks the additional terms within the energy balance equation were introduced by Irwin and Orowan. An extension of these concepts is found in the experimental work of V. Panin, who has shown that the irreversible deformation is primarily confined to the prefracture zones associated with a stationary or a slowly growing crack. The present study is based on the structured cohesive crack model equipped with the “unit step growth” or “fracture quantum”. This model is capable to encompass all the essential issues such as stability of subcritical cracks, quantization of the fracture process and fractal geometry of crack surfaces, and incorporate them into one consistent theoretical representation.     

The mechanisms of plastic strain accommodation during the high strain rate collapse of corrugated Ni–Al laminate cylinders

The Thick-Walled Cylinder method was used on corrugated Ni–Al reactive laminates to examine how their mesostructures accommodate large strain, high strain rate plastic deformation and to examine the potential for intermetallic reaction initiation due to mechanical stimuli. Three main mesoscale mechanisms of large plastic strain accommodation were observed in addition to the bulk distributed uniform plastic flow: (a) the extrusion of wedge-shaped regions into the interior of the cylinder along planes of easy slip provided by angled layers, (b) the development of trans-layer shear bands in the layers with orientation close to radial and (c) the cooperative buckling of neighbouring layers perpendicular to the radius. These mesoscale mechanisms acted to block the development of periodic patterns of multiple, uniformly distributed, shear bands that have been observed in all previously examined solid homogeneous materials and granular materials. The high-strain plastic flow within the shear bands resulted in the dramatic elongation and fragmentation of Ni and Al layers. The quenched reaction between Al and Ni was observed inside these trans-layer shear bands and in a number of the interfacial extruded wedge-shaped regions. The reaction initiated in these spots did not ignite the bulk of the material, demonstrating that these mesostructured Ni-Al laminates are able to withstand high-strain, high-strain rate deformation without reaction. Numerical simulations of the explosively collapsed samples were performed using the digitized geometry of corrugated laminates and predictions of the final, deformed mesostructures agree with the observed deformation patterns.     

Baikal Ice Cover as a Representative Block Medium for Research in Lithospheric Geodynamics

The paper summarizes the results of long-term field research in the dynamics of the Baikal ice cover as a multiscale block medium similar to the lithosphere in structure, rheology, and seismotectonic features. The analysis covers data on deformation, seismicity, and contact interaction modes as well as on meteorological factors responsible for dynamic fracture of ice plates and strong ice shocks with earthquake-like vibrations. Similarity between seismic features in ice interface zones and zones of tectonic subduction, collision, and shear is discussed. Reasoning from dynamic analogies and similarities of destruction processes in the ice and lithosphere, the research data can help solving fundamental and applied problems, particularly those of earthquake prediction and assessment of contact interactions between lithospheric plates in fault zones.     

Dynamic cracking resistance of metallic materials during rapid propagation of a self-similar crack

A model is proposed to determine the dynamic cracking resistance K _ID of metals and alloys for the case of a rapidly moving fractal or self-affine crack. The values of this characteristic correlate with the fractal dimension D _f of the future contour of a crack surface profile. K _ID is lower or higher than K _IC depending on the fractal dimension.     

高速铁路轮轨滚动噪声的分形描述及分形维估计

提出基于分形分析的轮轨滚动噪声研究方法,研究了不同尺度下轮轨滚动噪声增量的统计特性,证明轮轨滚动噪声具有分形特性,可由分形布朗运动描述。在此基础上,利用分形布朗运动的小波系数方差与分形维的幂律关系估计了轮轨滚动噪声的分形维,并估计了以裂纹扩展为代表的钢轨伤损声发射信号的分形维,对比研究发现:轮轨滚动噪声分形维本身具有随机性,不同车速下的轮轨滚动噪声分形维估计以1.5666为均值随机分布在小于2的小区间内;分形维是轮轨滚动噪声的固有特征,与车速无关,不同车速的轮轨滚动噪声可由统一的分形布朗运动模型描述;裂纹扩展信号与轮轨滚动噪声不同,其分形维估计大于2,不满足分形布朗运动模型的要求,但分形维可作为二者的区别特征。研究提取了轮轨滚动噪声的分形维作为固有特征,为高速轮轨滚动噪声描述及轮轨伤损检测提供了有效的分析方法。      

Exterior dimension of fat fractals

Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which we call the exterior dimension. In addition, it is shown that the exterior dimension is related to the “uncertainty exponent” previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.