Role Of Normal Stresses Research Articles

Transient and Steady‐State Friction in Non‐Isobaric Conditions

AbstractThe frictional properties of faults control the initiation and propagation of earthquakes and the associated hazards. Although the ambient temperature and instantaneous slip velocity controls on friction in isobaric conditions are increasingly well understood, the role of normal stress on steady‐state and transient frictional behaviors remains elusive. The friction coefficient of rocks exhibits a strong dependence on normal stress at typical crustal depths. Furthermore, rapid changes in normal stress cause a direct effect on friction followed by an evolutionary response. Here, we derive a constitutive friction law that consistently explains the yield strength of rocks from atmospheric pressure to gigapascals while capturing the transient behavior following perturbations in normal stress. The model explains the frictional strength of a variety of sedimentary, metamorphic, and igneous rocks and the slip‐dependent response upon normal stress steps of Westerly granite bare contact and synthetic gouges made of quartz and a mixture of quartz and smectite. The nonlinear normal stress dependence of the frictional resistance may originate from the distribution of asperities that control the real area of contact. The direct and transient effects may be important for induced seismicity by hydraulic fracturing or for naturally occurring normal stress perturbations within fault zones in the brittle crust.

Molecular dynamics of shear banding flow in associative polymers solutions: effect of sticker groups location

Non-equilibrium molecular dynamics are used in a coarse-grained scale to simulate the simple shear flow of telechelic and non-telechelic associative polymer solutions. The work includes the study of inception of flow and stress relaxation in transient flows and the constitutive curve at steady state. The instabilities (plateau stress, stress maxima) and the formation of bands with different velocity gradient and concentration depend on the location of the hydrophobic sites (sticker sites, SS) in the chain. Results allow to shed light on the origin of banded flow within the transient state, related to depletion of bridges between aggregates. This situation induces instabilities in the velocity profiles and concentration inhomogeneities along the velocity gradient during the stress overshoot. As the steady state is reached, instabilities disappear for systems where the SS are in the middle of the chain. The conformation relaxation occurs during a time scale larger than that of the stress, but this is not sufficient condition for the presence of banded flow in telechelic polymer solutions, as it holds in polymer melts. The difference in concentration among the bands suggests the existence of a shear-gradient concentration coupling mechanism under banded flow conditions, such as spatial non-homogeneities in the network density, induces chain diffusivity in the gradient direction and increasing normal stresses, especially in telechelic chains. The role of normal stresses on the flow-concentration coupling instability is analyzed in detail.

Strength evolution of simulated carbonate-bearing faults: The role of normal stress and slip velocity

A great number of earthquakes occur within thick carbonate sequences in the shallow crust. At the same time, carbonate fault rocks exhumed from a depth < 6 km (i.e., from seismogenic depths) exhibit the coexistence of structures related to brittle (i.e., cataclasis) and ductile deformation processes (i.e., pressure-solution and granular plasticity). We performed friction experiments on water-saturated simulated carbonate-bearing faults for a wide range of normal stresses (from 5 to 120 MPa) and slip velocities (from 0.3 to 100 μm/s). At high normal stresses (σn > 20 MPa) fault gouges undergo strain-weakening, that is more pronounced at slow slip velocities, and causes a significant reduction of frictional strength, from μ = 0.7 to μ = 0.47. Microstructural analysis show that fault gouge weakening is driven by deformation accommodated by cataclasis and pressure-insensitive deformation processes (pressure solution and granular plasticity) that become more efficient at slow slip velocity. The reduction in frictional strength caused by strain weakening behaviour promoted by the activation of pressure-insensitive deformation might play a significant role in carbonate-bearing faults mechanics.

Systematic assessment of the static stress triggering hypothesis using interearthquake time statistics

AbstractA likely source of earthquake clustering is static stress transfer between individual events. Previous attempts to quantify the role of static stress for earthquake triggering generally considered only the stress changes caused by large events and often discarded data uncertainties. We conducted a robust twofold empirical test of the static stress change hypothesis by accounting for all events of magnitude M ≥ 2.5 and their location and focal mechanism uncertainties provided by catalogs for Southern California between 1981 and 2010, first after resolving the focal plane ambiguity and second after randomly choosing one of the two nodal planes. For both cases, we find compelling evidence supporting the static triggering with stronger evidence after resolving the focal plane ambiguity above significantly small (about 10 Pa) but consistently observed stress thresholds. The evidence for the static triggering hypothesis is robust with respect to the choice of the friction coefficient, Skempton's coefficient, and magnitude threshold. Weak correlations between the Coulomb index (fraction of earthquakes that received positive Coulomb stress change) and the coefficient of friction indicate that the role of normal stress in triggering is rather limited. Last but not the least, we determined that the characteristic time for the loss of the stress change memory of a single event is nearly independent of the amplitude of the Coulomb stress change and varies between ~95 and ~180 days implying that forecasts based on static stress changes will have poor predictive skills beyond times that are larger than a few hundred days on average.

Direction dependence of fracture compliance induced by slickensides

The effect of a fracture on seismic wave propagation can be represented in terms of the normal and shear fracture compliance. In many studies, fractures are assumed to have no preferential orientation for slip along the fracture plane. However, examination of fractures found in recovered cores or in exposed outcrops shows irregularities, such as hackles or slickensides, which are formed in the direction of joint/fault propagation. These irregularities, represented as sawtooth ridges, can be expected to facilitate movement in a particular direction more than the opposite direction, in a way that depends on the height and shape of the irregularities. As a result, fractured rocks should exhibit a different compliance for shear in one direction compared with shear in the opposite orientation. We used numerical modeling to offer a critical assessment of this phenomenon by directly calculating the change in normal and shear compliance in the presence of hackles. The effect of the geometry of the hackles, the friction coefficient between fracture surfaces, and the role of normal stresses on the ratio of normal-to-shear fracture compliance were evaluated.

Heterogeneity and the Role of Normal Stresses during the Extensional Thinning of Non-Brownian Shear-Thickening Fluids

We contrast the extensional and shear dynamics of non-Brownian suspensions as a function of particle concentration. We show that the thinning rate selected during the viscoelastic pinch-off of a liquid bridge is related to the shear rate at which normal stresses become positive, which differs from the shear rate at the onset of shear thickening. By tracking particles, we demonstrate that the extensional flow is heterogeneous, with local variations of the volume fraction consistent with self-dilution. This nonuniform structure is the cause of the buckling of the threads formed after breakup.

Aerodynamic coefficients of a spinning sphere in a rarefied-gas flow

A three-dimensional rarefied-gas flow past a spinning sphere in the transitional and near-continuum flow regimes is studied numerically. The rarefaction and compressibility effects on the lateral (Magnus) force and the aerodynamic torque exerted on the sphere are investigated for the first time. The coefficients of the drag force, the Magnus force, and the aerodynamic torque are found for Mach numbers ranging from 0.1 to 2 and Knudsen numbers ranging from 0.05 to 20. In the transitional regime, at a certain Knudsen number depending on the Mach number the Magnus force direction changes. This change is attributable to the increase in the role of normal stresses and the decrease in the contribution of the shear stresses to the Magnus force with decrease in the Knudsen number. A semi-empirical formula for the calculation of the Magnus force coefficient in the transitional flow regime is proposed.

Curvilinear flows of noncolloidal suspensions: The role of normal stresses

The role of normal stresses in causing particle migration and macroscopic spatial variation of the particle volume fraction φ in a mixture of rigid neutrally buoyant spherical particles suspended in Newtonian fluid is examined for curvilinear shear flows. The problem is studied for monodisperse noncolloidal Stokes-flow suspensions, i.e., for conditions of low-Reynolds-number flow and infinite Péclet number, Pe=O(ηγ̇a3/kT), where η is the suspending fluid viscosity, γ̇ is the shear rate, a is the particle radius, and kT is the thermal energy. Wide-gap Couette, parallel-plate torsional, and cone-and-plate torsional flows are studied. The entire φ dependence of the compressive shear-induced normal stresses is captured by a “normal stress viscosity” ηn(φ), which vanishes (as φ2) at φ=0 and diverges at maximum packing in the same fashion as does the shear viscosity ηs(φ). Anisotropy of the normal stresses arising from the presence of the particles is modeled as independent of φ, so that ratios of any two particle contributions to the bulk normal stress components are constants, Σ22p/Σ11p=λ2 and Σ33p/Σ11p=λ3; the standard convention of (1,2,3) denoting the (flow, gradient, vorticity) directions is used so that, for example, Σ11p is the normal component of the particle stress Σp in the flow direction. Predictions for the steady and unsteady flows are presented to demonstrate the influence of variation of the normal stress anisotropy parameters λ2 and λ3, the rheological functions ηs and ηn, and the sedimentation hindrance function used to represent the resistance to relative motions of the phases during migration. Comparison with available experimental data shows that a single set of parameters for the rheological model is able to describe all qualitative features of the observed migrations in the flows considered.

Theory and application of microindentation in studies of glide and cracking in single crystals of elemental and compound semiconductors

The microhardness of Si (MP 1688 K), GaP (1623 K), GaAs (1510 K) and InP (1327 K) single crystals was determined by indentation (Vicker's hardness, VHN) of low-index facets at loads of 5–100g at 296–673 K, complementing earlier work on Ge and InSb. In the brittle range, extending up to about 0.35 Tmelt (K), cracking occurred preferentially along the diagonals of the indentations, and was observed at all loads, with the possible exception of the lowest (5 g) in the case of InP at 289 K. At higher temperatures the relative orientations of crack and slip traces on the crystal surface, as observed by SEM, suggested that cracks nucleated preferentially at the slip-band intersection, as was also noted by Hirsch et al. (Phil. Mag.3 (1985) 759) in GaAs above 600 K. As earlier in Ge, the VHN was found to depend on the load, L, as Lp, and on the indentation diameter, d, as dn, with p = 1/2 and n = 2, as required by the model of indentation plasticity of Banerjee and Feltham [4, 5], but higher p and n values were found if chipping at the indentation edges was evident. The effect was related to the resulting decrease in indentation diameter due to the work lost, through chipping, by the indenter. Above about 0.35 Tmelt (K), relaxation of the dislocation structures entails a decrease of p and n; both parameters tend to zero as T → Tmelt. Shear and tensile stresses seem to co-operate in the process of plastic deformation, the role of normal stresses, acting across slip planes, predominating in the ‘brittle’ range.