Showing papers on "Strain rate published in 1986"

Finite strain calculations of continental deformation .2. comparison with the india-asia collision zone

Abstract: Numerical experiments on a thin viscous sheet model for deformation of continental lithosphere subjected to an indenting boundary condition yield distributions of crustal thickness, of stress and strain rate, and of latitudinal displacements that may be compared with observations in the India-Asia collision zone. A simple indenting boundary condition applied to initially laterally homogeneous sheets obeying a power law rheology produces results that are in broad agreement with the observations, provided that the power law exponent is three or greater and the sheet can support vertically integrated stress differences of 2×1013 (±5 × 1012) N m−1 in regions in front of the indenter. Under these conditions, the calculated deformation shows accommodation of convergence primarily by crustal thickening, to produce a plateau in front of the indenter. Palaeomagnetic data from India and Tibet, and the observed distribution of topography, suggest that much of the post-Eocene convergence of India with Asia has been taken up by deformation within Asia that involved crustal thickening. The principal difference between calculation and observation is the absence from the calculated strain rate fields of east-west extension of the plateau in front of the indenting boundary. The calculations show that once such a plateau is formed, the buoyancy force associated with the crustal thickness contrast inhibits further thickening and the plateau strains at less than half the rate of its immediate surroundings. Seismically determined regional strain rates exhibit a similar distribution, with the Tibetan plateau straining at about one quarter the rate of the Tien Shan and Ningxia-Gansu regions. Calculated principal compressive stress orientations and regional strain rates agree with the seismically determined quantities in the Mongolia-Baikal, Tien Shan, Tibet, and Ningxia-Gansu regions of Asia, to within the uncertainty of the latter. The vertically integrated stresses that are calculated for the viscous sheet are comparable with those that can be supported by a Theologically stratified continental lithosphere obeying laboratory-determined flow laws. We suggest that the thin viscous sheet model, described in this paper and its companion, gives a simple and physically plausible description of the observed deformation in central Asia; in this description the predominant mechanism of accommodation of continental convergence is diffuse crustal thickening, with shear on vertical planes playing a subsidiary role once large crustal thickness contrasts have been established.

Viscosity, granular‐temperature, and stress calculations for shearing assemblies of inelastic, frictional disks

Abstract: Employing nonequilibrium molecular‐dynamics methods the effects of two energy loss mechanisms on viscosity, stress, and granular‐temperature in assemblies of nearly rigid, inelastic frictional disks undergoing steady‐state shearing are calculated. Energy introduced into the system through forced shearing is dissipated by inelastic normal forces or through frictional sliding during collisions resulting in a natural steady‐state kinetic energy density (granular‐temperature) that depends on the density and shear rate of the assembly and on the friction and inelasticity properties of the disks. The calculations show that both the mean deviatoric particle velocity and the effective viscosity of a system of particles with fixed friction and restitution coefficients increase almost linearly with strain rate. Particles with a velocity‐dependent coefficient of restitution show a less rapid increase in both deviatoric velocity and viscosity as strain rate increases. Particles with highly dissipative interactions result in anisotropicpressure and velocity distributions in the assembly, particularly at low densities. At very high densities the pressure also becomes anisotropic due to high contact forces perpendicular to the shearing direction. The mean rotational velocity of the frictional disks is nearly equal to one‐half the shear rate. The calculated ratio of shear stress to normal stress varies significantly with density while the ratio of shear stress to total pressure shows much less variation. The inclusion of surface friction (and thus particle rotation) decreases shear stress at low density but increases shear stress under steady shearing at higher densities.

Finite strain calculations of continental deformation: 1. Method and general results for convergent zones

Abstract: A finite element method is used to calculate stresses and strain rates in a thin viscous sheet, representing the continental lithosphere, that is bordered in one part by an indenting boundary. We calculate solutions for velocity fields, crustal thickness distributions, strain rates, rotation (time-integrated vorticity), and finite strain ellipsoids to show the dependence of these quantities on the controlling parameters: the stress-strain exponent n and the strength of the sheet relative to the gravitational forces (which may be expressed as a dimensionless number: the Argand number Ar). For n > 3 and Ar between 1 and 10 a plateau of thickened crust is formed in front of the indenter. The strain histories of individual elements within the viscous sheet may be quite complex, and the finite strain at the end of deformation may bear no obvious relation to the principal stress orientations during the deformation. The strain rate fields are interpreted in terms of the style of faulting that would be expected in the brittle upper crust if it were coupled to the ductile, but stronger, upper mantle. In general, the length scale of deformation increases with Ar and time since the start of the collision and decreases with n; for Ar ≃ 3, the increase in length scale is accompanied by a change in the style of deformation: from predominantly crustal thickening (with thrust faulting in the brittle layer) to predominantly transcurrent deformation (strike-slip faulting in the brittle layer).

Stress calculations for assemblies of inelastic speres in uniform shear

Abstract: Previous work on assemblies of inelastic, frictional disks is extended to three dimensions in a molecular-dynamics study of steady shearing flow of an idealized granular material consisting of equal-sized spherical particles that are smooth but inelastic. Cumulative time and space averages are calculated for several diagnostic quantities including the kinetic and potential energy densities, the R.M.S. (deviatoric) velocity and both the kinetic and potential contributions to each component of the stress tensor. Under steady-state shearing deformation the kinetic-energy-density (granular temperature) generally is found to increase as the solids fraction is decreased and decrease as the binary-collision coefficient-of-restitution is decreased. For constant coefficient-of-restitution interactions the calculated stresses increase generally with the square of the strain rate, with exceptional behavior noted at extremes in solids loadings. The general trends of the calculated stresses and velocities are in substantial agreement with the Lun et al. linearized perturbation of Chapman-Enskog theory for slightly inelastic spheres. However, some significant differences are noted at very low (ν 0.5) solids fractions. A variable coefficient-of-restitution interaction interaction model (decreasing as the impact velocity increases) results in calculated stresses that deviate from the constant coefficient-of-restitution behavior in a manner similar to that predicted by Lun and Savage. The calculated stresses are in rough agreement with experimental measurements; however, the calculated shear-stress to normal-stress ratio for spheres with coefficients of restitution between 0.8 and 0.95 are significantly below experimentally measured values for glass and polystyrene beads in annular shear cell tests. Based on effects seen in two-dimensional calculations, the inclusion of interparticulate friction and particle rotations are expected to significantly reduce the discrepancy.

Earthquakes in the ductile regime

Abstract: Pseudotachylytes from a crustal scale shear zone in Central Australia have developed in a cyclical manner: once developed, an individual pseudotachylyte is deformed in a ductile manner, only to be overprinted at a later stage by a new generation of pseudotachylytes. Such cyclic generation and deformation of pseudotachylyte has been interpreted in the past as representing conditions at the brittleductile transition; a different interpretation, however, is presented here. It is proposed that psuedotachylytes and associated ultramylonites can develop entirely within the ductile regime as ductile instabilities. Such instabilities are different in nature to those previously discussed at length in the geophysical literature but are identical in principle with the instabilities that develop for velocity-weakening frictional behavior in spring-slider systems. At a given strain rate a critical temperature,T c, is defined, at which the transient work hardening equals the product of stress relaxation due to a thermal fluctuation and the heat generated by shearing. A necessary condition for ductile instability at a given strain rate is that the temperature is belowT c; then the rate of change of stress with respect to strain is negative. An additional requirement is that this rate of change exceeds, in magnitude, the effective elastic stiffness of the loading system. Ductile instabilities are marginally possible at geological strain rates in quartzites but are possible at mid-crustal temperatures in other rock types. On the basis of these observations a new interpretation is presented for the base of the seismogenic zone in crustal regions.

On rate sensitivity of f.c.c. metals, instantaneous rate sensitivity and rate sensitivity of strain hardening

Abstract: A n up-to-date approach to the phenomenon of rate sensitivity observed in f.c.c. metals is discussed. It is shown that the rate sensitivity of strain hardening, which so far has been neglected, plays an equal or even dominant role in an estimation of the total rate sensitivity. It is suggested that the presence of the rate sensitivity of strain hardening is developed by the athermal generation of structural defects (dislocations), while at the same time collision and partial annihilation of dislocations occurs with the assistance of thermal activation. These micromechanisms of plastic deformation are capable of developing so-called strain rate and temperature history effects. Some experimental evidence of strain rate history effects, for both polycrystals and monocrystals, are provided in this paper; they are discussed within the framework of instantaneous rate sensitivity versus rate sensitivity of strain hardening. Both rate sensitivities are reviewed within the framework of thermal activation strain rate analysis. Experimental data are provided for aluminium, copper and lead. They conclusively demonstrate the importance of rate sensitivity of strain hardening which is developed by dynamic recovery (annihilation of defects during plastic deformation). Some fundamentals of how to construct constitutive relations have been discussed on the basis that the total flow stress τ is the sum of the effective stress τ∗ and the internal stress τμ. General relations for structural evolution have been analysed, which are able to describe strain rate and temperature history effects. On the basis of earlier results a general relationship for structural evolution has been proposed using the concept of the effective dislocation multiplication coefficient Meff. It is shown that an evolutionary relationship should be of differential type with generation and annihilation terms. Finally, some recommendations are provided as to constitutive modeling and future studies of both instantaneous rate sensitivity and rate sensitivity of strain hardening.

Internal Oxidation of Ag-In Alloys: Stress Relief and the Influence of Imposed Strain,

Abstract: The kinetics of internal oxidation of silver-indium alloys containing 3.5, 5.9, and 9.8 at.% In in air at temperatures 773 to 973 K were established by TGA with no load applied to the specimens. Silver nodules free of oxide particles were observed to form at the surface during internal oxidation. The volume of these silver nodules was comparable to the total volume increase caused by internal oxidation. The alloys were also creep tested during oxidation in air at creep rates varying from 10−7 to 5×10−5 s−1 at 773, 873, and 973 K. The parabolic rate constants kp for the internal oxidation of the solute were determined from the measured widths of the internal oxidation zones. A small increase in kp was observed with increased strain rate. The large volume change associated with internal oxide formation resulted in a stress gradient between the stress-free surface and the internal oxidation front which is under a high compressive stress. Stress relief occurred by transport of silver to the surface. A Nabarro-Herring creep type mechanism based on lattice diffusion of Ag cannot account for the high rate of silver transport to the surface. Pipe-diffusion controlled creep is proposed as the mechanism of stress accommodation by silver diffusion.

The effect of the relationship between punch velocity and particle size on the compaction behaviour of materials with varying deformation mechanisms.

Abstract: The effect of punch velocity over the range 0.033-300 mm s-1 on the compaction properties of lactose, microcrystalline cellulose and a drug substance (a phthalazine derivative) for a range of particle sizes has been studied using the yield pressure derived from the Heckel relationship and a strain rate sensitivity index (SRS index), as the criteria to describe their behaviour. For lactose, a material which deforms by a mixed mechanism of particle fracture and plastic deformation at the contact points, the yield pressure increased and the SRS index decreased as particle size decreased, due to a reduction in the amount of fragmentation of the particles. For microcrystalline cellulose, a material which is known to deform plastically, the yield pressure and the SRS index were independent of particle size. For the phthalazine derivative the yield pressure increased as particle size decreased; however the SRS index reduced from 41% to zero, indicating that the deformation mechanism was changing from plastic flow to brittle behaviour. This decrease in the SRS index has been explained in terms of the relative amounts of strain-hardened material produced as milling severity increased, resulting in an increasing resistance to deformation and thus an apparent increase in brittle behaviour as particle size decreased.

Geodetic measurement of deformation in the central Mojave Desert, California

Abstract: Data from triangulation and trilateration surveys made during 1934-1982 are used to calculate shear strain rates in the central Mojave Desert of California. For the region between the Helendale and Camp Rock faults the shear strain rate was determined to be 0.16 + or - 0.03 microstrain/yr, with maximum right-lateral shear strain occurring on a plane oriented N41 deg W + or - 5 deg. If this deformation is due to right-lateral motion across the northwest trending local faults, the average shear straining corresponds to a relative displacement of 6.7 + or - 1.3 mm/yr across this portion of the network, accounting for about 12 percent of the predicted 56 mm/yr of relative motion between the North Atlantic and Pacific plates. From the Camp Rock fault eastward across the network there is a transition from significant to very low strain rates. Examination of nine focal mechanisms and their relation to the local geology and the strain data suggests that most of the long-term displacement occurs on the major northwest trending faults oriented nearly along the direction of relative motion between the North American and Pacific plates. Secondary faulting, controlled by a Coulomb-Anderson failure mechanism or by slip on preexisting faults can account for the occurrence of earthquakes on faults of other orientations.

Effect of material rate sensitivity on failure modes in the Charpy V-notch test

Abstract: For the C harpy V-notch test the influence of strain rate on competing failure mechanisms is analyzed numerically. The nucleation and growth of micro-voids is represented in terms of an elastic-viscoplastic constitutive model, which describes the mechanism of ductile fracture by void coalescence. Failure by cleavage is assumed to occur if the maximum principal tensile stress exceeds a certain critical value. Attention is focused on the temperature regime where the transition in fracture mode between cleavage and ductile rupture takes place. In the analyses the temperature is taken as constant and the effect of inertia is neglected, so that time dependence enters only through the material strain rate sensitivity. The material model is found to reproduce the experimentally observed change in failure mode from predominantly ductile fracture at low strain rates, to cleavage fracture at high strain rates. The numerical results show that in the transition regime, the porosity in the notch tip region plays a role in the fracture process even when failure occurs by cleavage. Once the transition of failure mode from cleavage to ductile rupture has occurred, the energy absorbed at low rates is greater than that absorbed at high rates.

Superplastic flow in fine-grained alumina

Abstract: Dense polycrystalline alumina having an average grain size of 1.6 μm was deformed to true strains of up to 60% in simple uniaxial compression at 1693 K without significant cavitation. A strain rate of ∼2 × 10−4 s−1 was obtained at a uniaxial stress of ∼30 MPa. Such a reasonable flow stress at such high strain rates and a relatively low temperature raises a real possibility of isothermal superplastic forging of alumina ceramics. The mechanism of deformation was identified to be diffusion creep with grain boundaries as the dominant diffusion path. The specimens suffered considerable grain growth during deformation. Part of the grain growth resulted from time and temperature, but the majority was induced by deformation strain.

Strain accumulation in southern California, 1973–1984

Abstract: Repeated surveys of selected lines from five trilateration networks along the San Andreas fault in southern California have been used to deduce the 1973–1984 strain accumulation records at five localities. The secular rate of engineering shear strain accumulation is about 0.3 μrad/yr with the plane of maximum shear parallel to the local strike of the San Andreas fault. The secular rate of accumulation of areal dilatation is negligible. The data were examined to detect evidence for fluctuations in the rate of strain accumulation. For this examination, 19 lines were removed from the data set: four because they exhibited an obvious coseismic offset and 15 others because they contained at least one very anomalous measurement that could reasonably be attributed to a survey blunder. (The incidence of such blunders appears to be one in every 75 measurements.) The remaining data consist of 104 lines with an average of 10 measurements each. Although the strain accumulation plots for the five networks may exhibit marginally significant temporal fluctuations, we are not convinced that those fluctuations are greater than could be attributed to survey error. In particular, we are unable to demonstrate that the 1973–1979 southern California strain anomaly reported by Savage and others is real. Given the uncertainty in the random and systematic errors in measurement, the strain measurements in southern California are marginally consistent with linear-in-time strain accumulation. The strain accumulation plots for the Salton network clearly established that, unlike the deformation reported after the 1940 Imperial Valley earthquake, no acceleration in the shear strain rate has yet been observed following the 1979 Imperial Valley earthquake.

Void growth in shear

Abstract: The growth of an isolated void is analysed for a void contained in a block of material undergoing simple shearing combined with superimposed hydrostatic tension. The evolution of the size, shape and orientation of two- and three-dimensional voids in an incompressible, linearly viscous solid is first discussed. The main problem addressed is the behaviour of a two-dimensional cylindrical void in an incompressible, nonlinearly viscous solid for which the strain rate varies as the stress to a power. The growth rate of the void and its shape evolution are strong functions of the degree of material nonlinearity. Relatively simple approximate formulas are obtained for the dilatation rate of a circular void as well as for the void potential. The constitutive relation of a block of material containing a dilute distribution of circular cylindrical voids is obtained directly using the isolated void potential. The paper concludes with a summary of available results for the dilatation rates of voids and cracks under combinations of shear and hydrostatic tension.

Effects of Strain Rate and Gauge Length on the Failure of Ultra-High Strength Polyethylene Fibers

Abstract: Ultra-high strength polyethylene filaments taken from a single spool of yarn were examined for strain rate and gauge length effects. As noted in previous research, high strength polyethylene exhibits pronounced strain rate effects that may be seen in strength changes, stress-strain behavior, and and topography of the fracture zones. Unlike most polymeric fibers, ultra-high strength polyethylene seems to exhibit no gauge length effects over the range from 10 to 200 mm, holding the strain rate constant. This latter effect, if true in general, would be a substantial advantage for polyethylene fibers, because scaling effects would be minimized.

Dynamic Constitutive Behavior of Concrete

Abstract: A constitutive model for confined and unconfined concrete subjected ro dynamic compression is proposed. This model is based on numer­ ous measurements of the maximum stress and the strain at maximum stress in tests performed at different strain rates. The proposed model distinguishes between the strain rate effects on dry and wet concrete, and compares well with the available test results.

Theoretical study of the dynamic tensile test

Abstract: A numerical investigation of the tensile test using a finite-difference, one-dimensional elasto-viscoplastic code is presented. The influence of strain rate, strain rate sensitivity, and inertia on the development of the axial particle velocity, stress, strain, and strain rate profiles in pure copper is studied. The initial stages of post-uniform deformation and the stabilizing influence of inertia and strain rate sensitivity in this regime are demonstrated. Both inertia and strain rate sensitivity are shown to decrease the rate of unloading of the uniform region of a tensile specimen past the point of instability given by the maximum load criterion. A comparison of numerically predicted and experimentally determined values of the post-uniform elongation is shown.