Showing papers on "Slip (materials science) published in 1983"

Micromechanics of Crystals and Polycrystals

Abstract: Publisher Summary This chapter focuses on micromechanics of crystals and polycrystals. In Section II of the chapter, a brief outline of only some of the important features of the micromechanics of crystalline plasticity is given. The discussion is confined to plastic flow caused by dislocation slip, and face-centered-cubic crystals are used in the examples of dislocation mechanisms. Particular attention is paid to kinematics and to the phenomenology of strain hardening, because these are shown to play dominant roles in macroscopic response. In Section III, constitutive laws for elastic-plastic crystals are developed. The framework draws heavily on Hill's analysis of the mechanics of elasticplastic crystals, but the theory is extended by incorporating the possibility of deviations from the Schmid rule of a critical resolved shear stress for slip. Deviations from the Schmid rule are motivated by micromechanical models for dislocation motion and are shown to lead to deviations from the “normality flow rule” of continuum plasticity. The implications of these “non-Schmid effects” regarding the stability of plastic flow are brought out via some examples of models for kinks bands and shear bands in Section IV. In Section IV some examples of analyses of elastic-plastic deformation in crystals are discussed. The chapter concludes with some suggestions for fruitful research. These involve extensions of the theory to finite-strain rate-dependent polycrystalline models.

A dislocation model of strain accumulation and release at a subduction zone

Abstract: Strain accumulation and release at a subduction zone are attributed to stick slip on the main thrust zone and steady aseismic slip on the remainder of the plate interface. This process can be described as a superposition of steady state subduction and a repetitive cycle of slip on the main thrust zone, consisting of steady normal slip at the plate convergence rate plus occasional thrust events that recover the accumulated normal slip. Because steady state subduction does not contribute to the deformation at the free surface, deformation observed there is completely equivalent to that produced by the slip cycle alone. The response to that slip is simply the response of a particular earth model to embedded dislocations. For a purely elastic earth model, the deformation cycle consists of a coseismic offset followed by a linear-in-time recovery to the initial value during the interval between earthquakes. For an elastic-viscoelastic earth model (elastic lithosphere over a viscoelastic asthenosphere), the postearthquake recovery is not linear in time. Records of local uplift as a function of time indicate that the long-term postseimic recovery is approximately linear, suggesting that elastic earth models are adequate to describe the deformation cycle. However, the deformation predicted for amore » simple elastic half-space earth does not reproduce the deformation observed along the subduction zones in Japna at all well if stick slip is restricted to the main thrust zone. As recognized earlier by Shimazaki, Seno, and Kato, the uplift profiles could be explained if stick slips were postulated to extend along the plate interface beyond the main thrust zone to a depth of perhaps 100 km, but independent evidence suggests that stick slip at such depths if unlikely.« less

A specific barrier model for the quantitative description of inhomogeneous faulting and the prediction of strong ground motion. Part II. Applications of the model

Abstract: We construct an earthquake source model which provides a complete description of acceleration power spectra of direct body waves. The model is a specific form of the barrier model proposed by Aki et al. (1977). According to this specific barrier model, the fault surface is visualized as composed of an aggregate of circular cracks which represent areas of localized slip, and the strong motion is assumed to be generated by the stationary occurrence of these localized ruptures as the rupture front propagates. The acceleration power spectra of direct S waves are described by their peak value P and an effective bandwidth Δ f. P scales proportionally to the width of the causative fault and to the square of local stress drop which is proportional to the ratio of maximum slip over the barrier interval. Δ f is specified by the corner frequency and a cutoff frequency which presumably originates from fault nonelasticity and is considered to be inversely proportional to the cohesive zone size. From these spectra and an estimate of the duration of faulting, measures of strong motion intensity such as rms and maximum acceleration can be inferred. Results of the application of the model to strong motion observations of various events are reported in Part II.

Some surprising features of the plastic deformation of body-centered cubic metals and alloys

Abstract: The metals which have the bcc structure at and below room temperature include iron, refractory metals of Groups VA and VIA, and alkali metals. Experimental and theoretical investigations of deformation behavior carried out in the last twenty years are reviewed. Attention is concentrated mainly on low temperature properties where many anomalous features have been discovered. The phenomena discussed include slip asymmetry, failure of the Schmid law of critical resolved shear stress, the observation of anomalous slip in very pure metals and alloys, solution softening, and the ductile-brittle transition.

Nucleation and growth of strike slip faults in granite

Abstract: Fractures within granodiorite of the central Sierra Nevada, California, were studied to elucidate the mechanics of faulting in crystalline rocks, with emphasis on the nucleation of new fault surfaces and their subsequent propagation and growth. Within the study area the fractures form a single, subparallel array which strikes N50°–70°E and dips steeply to the south. Some of these fractures are identified as joints because displacements across the fracture surfaces exhibit dilation but no slip. The joints are filled with undeformed minerals, including epidote and chlorite. Other fractures are identified as small faults because they display left-lateral strike slip separations of up to 2 m. Slickensides, developed on fault surfaces, plunge 0°–20° to the east. The faults occur parallel to, and in the same outcrop with, the joints. The faults are filled with epidote, chlorite, and quartz, which exhibit textural evidence of shear deformation. These observations indicate that the strike slip faults nucleated on earlier formed, mineral-filled joints. Secondary, dilational fractures propagated from near the ends of some small faults contemporaneously with the left-lateral slip on the faults. These fractures trend 25°±10° from the fault planes, parallel to the direction of inferred local maximum compressive stress. The faults did not propagate into intact rock in their own planes as shear fractures. Rather, adjacent faults were linked together by secondary, dilational fractures. Extensive secondary fracturing between faults produced larger fault zones that accommodate 10–100 m of left-lateral slip. As deformation progressed, faulting evolved from relatively short, closely spaced faults to longer, more widely spaced fault zones.

Nonlinear strain buildup and the earthquake cycle on the San Andreas Fault

Abstract: Two contrasting models of the earthquake deformation cycle on strike slip faults predict significant temporal declines in shear strain rate near the fault, accompanied by a progressive broadening of the zone of deformation adjacent to it. In the thin lithosphere model, transient deformation results from flow in the asthenosphere due to stress relaxation following faulting through most or all of the lithosphere. For an earth model with a thick elastic lithosphere (plate thickness » depth of seismic slip), transient motions are due to postearthquake aseisrnic slip below the coseismic fault plane. Data from the San Andreas fault indicate a long-term temporal decrease in strain rate that persists for at least 30 years and may extend through the entire earthquake cycle. Observations support a cycle-long rate decrease and a temporal spreading of the deformation profile only if movement cycles on the northern and southern locked sections of the fault are basically similar. If so, the usually lower strain rates and broader deformation zone currently observed on the southern San Andreas represent a later evolutionary stage of the northern locked section, where a great earthquake is a more recent occurrence. Although the data allow some extreme models to be discarded, no sufficiently strong constraints exist to decide between the thin and thick lithosphere models. Regardless of the appropriate model the geodetic observations themselves indicate that strain buildup is sufficiently nonlinear to cause significant departures from recurrence estimates based on linear strain accumulation and the time-predictable model.

Constitutive relations for fault slip and earthquake instabilities

Abstract: Constitutive relations for fault slip are described and adopted as a basis for analyzing slip motion and its instability in the form of earthquakes on crustal faults. The constitutive relations discussed include simple rate-independent slip-weakening models, in which shear strength degrades with ongoing slip to a residual frictional strength, and also more realistic but as yet less extensively applied slip-rate and surface-state-dependent relations. For the latter the state of the surface is characterized by one or more variables that evolve with ongoing slip, seeking values consistent with the current slip rate. Models of crustal faults range from simple, single-degree-of-freedom spring-slider systems to more complex continuous systems that incorporate nonuniform slip and locked patches on faults of depth-dependent constitutive properties within elastic lithospheric plates that may be coupled to a viscoelastic asthenosphere.

The 1979 Homestead Valley Earthquake Sequence, California: Control of Aftershocks and Postseismic Deformation

Abstract: The coseismic slip and geometry of the March 15, 1979, Homestead Valley, California, earthquake sequence are well constrained by precise horizontal and vertical geodetic observations and by data from a dense local seismic network. These observations indicate 0.52±0.10 m of right-lateral slip and 0.17±0.04 m of reverse slip on a buried vertical 6-km-long and 5-km-deep fault and yield a mean static stress drop of 7.2±1.3 MPa. The largest shock had MS = 5.6. Observations of the ground rupture revealed up to 0.1 m of right-lateral slip on two mapped faults that are subparallel to the modeled seismic slip plane. In the 1.9 years since the earthquakes, geodetic network displacements indicate that an additional 60±10 mm of postseismic creep took place. The rate of postseismic shear strain (0.53±0.13 μrad/yr) measured within a 30×30-km network centered on the principal events was anomalously high compared to its preearthquake value and the postseismic rate in the adjacent network. This transient cannot be explained by postseismic slip on the seismic fault but rather indicates that broadscale release of strain followed the earthquake sequence. We have calculated the postearthquake stress field caused by the modeled coseismic slip. We assume that failure is promoted when the sum of the shear stress plus 0.75 times the faultopening stress increases. Most aftershocks concentrate at points where the stresses are enhanced by 0.3 MPa (3 bars) or more; aftershocks are nearly absent where postearthquake stresses decrease by 0.3–0.5 MPa. Isolated off-fault clusters of aftershocks that locate at one fault length from the rupture plane are explainable by this hypothesis. We find that ground rupture and postseismic creep take place where near-surface stresses are calculated to increase within the preexisting fault zones. Two patches that extend 4 km from both ends of the seismic fault exhibited neither aftershocks nor measurable postseismic creep. The sensitivity of aftershocks and ground rupture to changes in stress that are less than 5% of the earthquake stress drop demonstrates that the region around the earthquakes was within a few percent of its failure threshold before the main shocks. The preearthquake stress field and the stress required for failure must also have been nearly uniform.

Reflection of elastic waves from periodically stratified media with interfacial slip

Abstract: A periodically stratified elastic medium can be replaced by an equivalent homogeneous transverse isotropic medium in the long wavelength limit. The case of a homogeneous medium with equally spaced parallel interfaces along which there is imperfect bonding is a special instance of such a medium. Slowness surfaces are derived for all plane wave modes through the equivalent medium and reflection coefficients for a half-space of such a medium are found. The slowness surface for the SH mode is an ellipsoid. The exact solution for the reflection of SH-waves from a half-space with parallel slip interfaces is found following the matrix method of K. Gilbert applied to elastic waves. Explicit results are derived and in the long wavelength limit, shown to approach the results for waves in the equivalent homogeneous medium. Under certain conditions, a half-space of a medium with parallel slip interfaces has a reflection coefficient independent of the angle of incidence and thus acts like an acoustic reducing mirror. The method for the reflection of P- and SV-waves is fully outlined, and reflection coefficients are shown for a particular example. The solution requires finding the eigenvalues of a 4 × 4 transfer matrix, each eigenvalue being associated with a particular wave. At higher frequencies, unexpected eigenvalues are found corresponding to refracted waves for which shear and compressional parameters are completely coupled. The two eigenvalues corresponding to the transmitted wavefield give amplitude decay perpendicular to the stratification along with up- and downgoing phase propagation in some other direction. Much of this work was performed while the author was at the Department of Geophysics and Planetary Sciences, Tel-Aviv University, Ramat-Aviv, Israel. The author is grateful for illuminating discussions with K. Helbig and K. Gilbert.

Shear wave polarization anisotropy in the upper mantle beneath Honshu, Japan

Abstract: Shear wave polarization anisotropy in the wedge portion of the upper mantle between a subducting plate and the earth's surface is investigated using three-component seismograms of intermediate depth and deep earthquakes recorded at 14 local stations in Honshu, Japan Eighty nine high-quality seismograms were selected from a period of 3 years The data used in this study are restricted such that incidence angles are smaller than the critical angle of 30° to the earth's surface in order to avoid phase shifts in the shear wave train To find directions of the maximum and minimum velocities in split shear waves, where shear waves are resolved into two phases with the maximum time separation, each set of the two horizontal component seismograms is rotated in the horizontal plane The split shear waves thus obtained are again recombined after the correction of anisotropy, and the anisotropy-corrected particle motion is compared with the focal mechanism for a cross-check of the observed anisotropy Directions of the maximum axes are plotted on azimuthincidence angle stereograms at each station The stereograms and the cross sections of seismic ray paths show that (1) the anisotropic material is distributed at intermediate location between earthquake sources and receiving stations, and (2) the anisotropic region is separated into two parts: one in the north of the present study area with the polarization of the maximum velocity shear wave trending 0° to 30° from the north (north anisotropy) and the other in the south with it trending 90° to 120° (south anisotropy) The maximum time delays between the two shear waves along a vertical seismic ray is about l s for both the anisotropic regions The horizontal extent of the anisotropic area in the north is 50 km at depths of 50 to 150 km perhaps prevalent in west Honshu However, the depth of anisotropic material is not well constrained because of insufficient coverage of seismic ray paths and angles If we assume the vertical extent of the anisotropic material to be 100 km, the maximum velocity contrast would be 4% If we adopt a crack alignment model, for the observed anisotropy, cracks are inferred to be distributed vertically trending 0° to 30° in the north and 90° to 120° in the south If we assume an olivine alignment model, olivine crystals are inferred to be aligned in the north with the a axis of the slip direction trending 0° to 30° and the slip plane normal to the b axis being vertical and in the south anisotropy with the axis trending 90° to 120° and the slip plane being horizontal

Earthquake frequency distribution and the mechanics of faulting

Abstract: The level of intraplate seismicity in Japan generally shows a positive correlation with the density of Quaternary faulting. In southwest Japan, where intraplate seismicity is concentrated on land, rates of seismic moment release ( M˙0) are similar when calculated from either the 400-year historical record of seismicity or geologically determined slip rates of Quaternary faults. A data set of 18 earthquakes with seismic moments (M0) ranging from ∼0.01 to 3×1027 dyn cm shows a relationship between rupture lengthl and M0(log M0 = 23.5+1.94 · log l). When seismic moment on each Quaternary fault is assumed to occur in discrete events every T = M0/ M˙0g years (where M0 is estimated for a rupture extended over the entire fault length, and M˙0g is proportional to the slip rate of each Quaternary fault), the moment frequency distribution of earthquakes (log N =A − B · log M0) predicted from the geologic record is virtually identical to that seen with the 400-year record of seismicity. In contrast, if it is assumed that earthquakes on each fault occur according to the Gutenberg-Richter relation, we obtain poor agreement with the observed seismicity. Thus, while regional seismicity satisfies the relation log N =A − B · log M0 (or equivalently, log N = a − b · log M, where M is magnitude), it appears that seismicity on individual faults does not. This further implies that the primary factor that leads to the magnitude frequency distribution in regional seismicity studies is the relative distribution of the slip rates and lengths of preexisting faults.

On the No-Slip Boundary Condition of Hydrodynamics *

Abstract: The slip velocity measured experimentally in flow through capillaries of sufficiently small diameters, with solid surfaces made repellent to the liquid, is examined. An answer to the question that whether the slip occurs directly on the surface of the solid or there exists a gap between the solid and liquid surfaces is sought. The slip velocity, when the molecules move directly on the solid surface, can be obtained as the product of the gradient of the chemical potential and the mobility coefficient. However, comparison with experiment provides values too high for the surface diffusion coefficient. This suggests that slip does not occur directly over the solid surface but over a gap. Such a gap is generated when the liquid and the solid have different natures (one of them hydrophobic and the other hydrophilic), and may be increased in thickness by the release of the gas entrained in the flowing liquid and/or the desorption of the soluble gas.

Local bond stress-slip relationships of deformed bars under generalized excitations : experimental results and analytical model

Abstract: This report covers integrated experimental and analytical investigations that permit predicting analytically the local bond stress-slip relationship of deformed reinforcing bars subjected to generalized excitations, such as may occur during the response of reinforced concrete (RIC) structures to severe earthquake ground motions.

Slip resistance testing of shoes — new developments

Abstract: This paper describes research being undertaken to develop a more realistic test for measuring the slip resistance of complete shoe soles and thus determine the effectiveness of sole patterns as well as sole materials and floor surfaces. The frictional forces between shoe and ground have been measured in normal walking using a force platform and photographic techniques used to record human slipping experiments. This has led to the development of an experimental test which reproduces slip conditions in walking as closely as possible. Using this test it has been found that slip severity depends on how friction changes as the shoe moves. Furthermore, it seems that a single measurement of friction may not be sufficient to completely predict the slip resistance of a shoe sole. Further work is necessary to understand the complex nature of slip resistance between shoe sole and ground.

Average regional strain due to slip on numerous faults of different orientations

Abstract: If a region is cut by faults with different orientations and if the faults intersect the boundaries of the region of interest, then the average finite (rotational) strain, eij=∂ui/∂xj, is given by eij=∑Mij*/μV where μ is the shear modulus, V is the volume of the region, and ∑Mij* represents the sum of asymmetric moment tensors, Mij*. For each fault, Mij*=M0 uˆ nˆ, where M0 is the scalar seismic moment and u and nˆ are the unit vectors parallel to the slip vector and perpendicular to the fault plane. This result is applicable when the average regional strain occurs primarily by displacements of essentially rigid blocks that together compose the region of interest and hence when both elastic strains and inelastic strains due to folding and bending are small.

Measurements of frictional heating in granite

Abstract: A large (150×150×40 cm) granite sample, sawn diagonally in half to simulate a fault, was deformed in a biaxial rock press at normal stress up to 6.41 MPa. Displacements and local shear stress were monitored along the fault (200×40 cm). Temperature transients as large as 10 m°C were recorded following stick slip events at distances of 0.2 to 1.0 cm from the fault and were related to stress, displacement, and total work. The temperature measurements were used to calculate the heat generated on the fault during slip. Frictional heating was found to be 94±2% of the total work expended in each event, implying a seismic efficiency of 4–8%. When water was injected onto the fault, both fractional stress drop and static frictional stress increased. The efficiency of frictional heating was not lowered by the presence of water. Heat generated during deformation of a 0.15-cm-thick layer of simulated gouge was also measured for sliding rates from 0.09 to 9.1 μm/s. In these gouge experiments, temperature rises were less than 0.1°C and were proportional to sliding rate.

Decoupling approximation to the evaluation of earthquake-induced plastic slip in earth dams

Abstract: SUMMARY Newmark's sliding block analysis for evaluating earthquake-induced permanent displacements of earth dams and slopes did not consider the effects of elastic dynamic response. Makdisi and Seed extended the analysis to include such effects, using the simpfying assumption that the computation of dynamic response and plastic slip can be decoupled. This paper examines the error introduced by this assumption, using three idealized lumped-mass models for a dam. Both sinusoidal and synthetic earthquake motions are employed. When the predominant frequency of the input motion lies in the proximity of the fundamental frequency of the dam, the slip based upon the decoupling assumption exceeds the exact value. This error decreases as the threshold acceleration required to initiate slip and the damping in the soil increase. For practical application, the error should seldom exceed 20 per cent.

Anelastic response of the earth to a dip slip earthquake

Abstract: The deformation induced by a vertical dip slip earthquake is examined using a variety of rheologic models. In this way the complications of dipping faults are avoided, and the phenomenon of transient peripheral warping is clearly revealed. A thrust fault dipping at 30 deg is investigated, and the important effects of dip and the existence of a slab on the asymmetry of strain pulses propagated into the overthrust and subducted lithosphere are demonstrated. One of the signal results of the study is the essential similarity of the strain patterns for Newtonian and non-Newtonian flow laws: the two rheologies give nearly identical strain field geometries. The principal difference between the two, which is readily observable, is in their time evolution. Relaxation in non-Newtonian rheologies tends to be initially fast, then slow at times that are late in comparison with relaxation in a Newtonian rheology. The possibility of simply recalling the time dependence of a Newtonian solution to obtain an approximate solution to a non-Newtonian problem is demonstrated.

A micromechanical theory of grain-size dependence in metal plasticity

Abstract: T he effect of grain-size on the elastoplastic behavior of metals is investigated from the micromechanics standpoint. First, based on the observations that dislocation pile-ups, formation of cell structures, and other inelastic activities influenced by the presence of grain boundary actually take place transcrystallinely, a grain-size dependent constitutive equation is proposed for the slip deformation of slip systems. By means of a modified Hill's self-consistent relation the local stress of a grain is calculated, and used in conjunction with this constitutive equation to evaluate the plastic strain of each constituent grain. The grain-size effect on the plastic flow of polycrystals then can be determined by an averaging process. To check the validity of the proposed theory it was finally applied to predict the stress-strain curves and flow stresses of a copper at various grain-sizes. The obtained results were found to be in good agreement with experimental data.

Rhombohedral Twinning in Alumina

Abstract: Alumina single crystals were deformed in compression along the c axes at temperatures of 625 to 1373 K. Large scale deformation by rhombohedral twinning was observed at a constant resolved shear stress of only 12.6 MPa between about 900 and 1373 K. Below 900 K, the twinning stress for specimens with ground surfaces rose rapidly to 227 MPa at 625 K. A model for twin growth in the absence of dislocation slip is proposed.