Maximum Resolved Shear Stress Research Articles

Glide mechanisms in b.c.c. crystals: An investigation of the case of α-iron through multislip and latent hardening tests

Multislip and latent hardening tensile tests are performed on α-iron single crystals at room temperature, in order to check the assumption of crystallographic glide restricted to the {110} planes and the {112} asymmetric planes. The evidence of a macroscopic glide either following higher indexed planes or the maximum resolved shear stress plane (referred as “non-crystallographic glide”) is interpreted, through a theoretical approach of multislip situations—in terms of mechanics of continuous media and of plasticity theory—as colinear glide on a {110}-{112} neighbouring planes pair. The observed hardening behaviour allows to interpret the influence of the axis orientation on the preferred slip mode. The latent hardening tests are performed according to the assumption of glide on {110} and {112} planes. The experimental results are not consistent with a description of plastic flow resulting from four non crystallographic slip systems only defined by the 〈111〉 slip direction. A hardening law, prevously derived from tests on f.c.c. crystals, is extended in the simplest way in order to analyze the latent hardening tests results and to represent the main features of the observed plastic behaviour of the α-iron crystals.

The influence of surface stress on the shapes of ion bombarded surface asperities

In recent years considerable effort has been devoted to the observation and interpretation of microasperities which emerge on surfaces under ion bombardment. The ultimate morphologies discussed up to now have been either the right circular cone or the right pyramid. Both have been supposed essentially to owe their forms to the ion erosion process alone. In this article we examine the influence of self stress (surface tension) on morphological evolution and show that it can contribute to the development of the distorted tapered forms observed in some recent scanning electron microscopy (SEM) studies. The self stress concept is applied to a microcrystal which is assumed, for generality, to have originally had the form of an oblique cone. Cone angles and surface tension values appropriate to argon bombarded copper indicate that the stress within the ⦅111⦆ planes (i.e. the slip planes) can exceed the critical shear stress at about 1 μm or less, from the apex. Onset of deformation by slip is probable if the crystal orientation is such that there is anisotropy amongst the resolved shear stresses and the maximum resolved shear stress is aligned with the slip direction. This theory is supported by observations in which we find that cones respond to an intense ultrasonic field by bending plastically. The bent forms are identical to those reported for unvibrated cones, thus lending credence to the above interpretation of spontaneous bending.

Stress asymmetries in the deformation behaviour of niobium single crystals

Niobium single crystals of varying orientations have been tested in tension and compression and in alternating tension-compression cycles in the temperature range 77 K-room temperature. Crystals of high purity with centre-triangle orientations deformed in both tension and compression by slip on the (1̄01) plane or on the glane of maximum resolved shear stress (mrss) at temperatures above ~200 K and on the anomalous (01̄1) plane at low temperatures. There was no detectable flow stress asymmetry for these crystals at room temperature, but deformation in compression became progressively harder than deformation in tension as the temperature was lowered and the assymmetry at 77 K_was about 15% of the actual flow stress. High purity crystals with orientations near [011]deformed by (2̄11) slip in both tension and compression at room temperature and the flow stress in tension was measurably higher than that in compression. This asymmetry was reversed at lower temperatures and slip traces were then too fine to be visible even under Nomarski contrast but some evidence was found that slip in tension deviated from (2̄11) towards (1̄01). Some experiments were undertaken also on two less pure crystals with orientations near the [011]-[1̄11]edge of the unit triangle. Here coarse (2̄11) slip traces were observed at room temperature and 228 K and the stress in tension was consistently higher than that in compression; catastrophic local flow occurred at 77 K and quantitative measurements could not be made. The results are discussed in terms of existing models of the deformation of b.c.c. metals.

Mechanical Tests of Fresh Ice Core (Abstract only)

Uniaxial compression tests (UCT) under constant cross-head speed and simple shear tests (SST) under constant load have been carried out in a snow cave at -16°C on ice cores within at most one month of extraction from depths of 235, 504, 708, and 896 m at Dye-3, Greenland, as part of the Greenland Ice Sheet Program (GISP), in order to improve understanding of flow behavior. UCT specimens had their stress axis at 45° from the core axis and SST specimens had their shear parallel to the horizontal plane of the core, so that in both cases maximum resolved shear stress was in the horizontal plane of the ice sheet.Fracture stresses in UCT had characteristic values for each depth corresponding to core quality. When effective strain-rate was plotted against effective shear stress on a double logarithmic plot, (1) data from the same depth fell on the same straight line for both tests, (2) for a given stress, strainrate varied with core-depth by less than half an order of magnitude, and (3) the stress exponent lay between 2 and 2.5, significantly less than the 3 to 4 reported for polycrystalline ice.Values extrapolated from the present data agree quite well with those deduced from bore-hole tilting measurements at Byrd station, Antarctica, and Camp Century, Greenland.

Mechanical Tests of Fresh Ice Core (Abstract only)

Uniaxial compression tests (UCT) under constant cross-head speed and simple shear tests (SST) under constant load have been carried out in a snow cave at -16°C on ice cores within at most one month of extraction from depths of 235, 504, 708, and 896 m at Dye-3, Greenland, as part of the Greenland Ice Sheet Program (GISP), in order to improve understanding of flow behavior. UCT specimens had their stress axis at 45° from the core axis and SST specimens had their shear parallel to the horizontal plane of the core, so that in both cases maximum resolved shear stress was in the horizontal plane of the ice sheet. Fracture stresses in UCT had characteristic values for each depth corresponding to core quality. When effective strain-rate was plotted against effective shear stress on a double logarithmic plot, (1) data from the same depth fell on the same straight line for both tests, (2) for a given stress, strainrate varied with core-depth by less than half an order of magnitude, and (3) the stress exponent lay between 2 and 2.5, significantly less than the 3 to 4 reported for polycrystalline ice. Values extrapolated from the present data agree quite well with those deduced from bore-hole tilting measurements at Byrd station, Antarctica, and Camp Century, Greenland.

Deformation of Fe<SUB>3</SUB>Al<SUB>0.8</SUB>Si<SUB>0.2</SUB> with DO<SUB>3</SUB> Structure

The yield stress and slip plane in Fe3Al0.8Si0.2 having the critical ordering temperature of the B2-DO3 transformation Tc=1028 K were investigated at temperatures between 77 and 1100 K with respect to their dependence on temperature and orientation. A peak in the yield stress takes place at 880 K except in the crystal whose maximum resolved shear stress plane coincides with the twinning {112} plane. In the crystals which exhibit the peak in strength, the operative slip plane changes from {110} on which the antiphase boundary energy is lowest (below the peak temperature) to the maximum resolved shear stress plane (above the peak). The peak in strength is attributed to the Stoloff and Davies’ model based on the transition from superdislocations to imperfect dislocations below Tc. In the crystal exhibiting no peak, the yield stress is remarkably higher than that in the crystals exhibiting a peak, at temperatures between 350 and 880 K, where the operative slip plane is the twinning {112}. The yielding is related to the generation of imperfect dislocations.

Deformation of metastable betaTi-15Mo-5Zr alloy single crystals

Deformation modes have been investigated in metastable beta Ti-15Mo-5Zr alloy single crystals using both transmission electron microscopy techniques and multisurface trace analysis. {332} twinning and 〈111〉 crystallographic slip were observed to occur at an initial stage of deformation depending on deformation axis. {332} twinning occurs in a crystal whose tensile axis lies around 〈111〉, while 〈111〉 slip appears in a crystal having the tensile axis in the neighborhood of 〈001〉 to 〈011〉. The twinning system which possesses the maximum resolved shear stress is always operative in both tensile and compressive deformations. Single crystals of this alloy exhibit an asymmetry of the active slip plane and of the yield stress in a manner similar to other bcc metals and dilute alloys.

Electron microscope observation of shear cracks in stainless steel single crystals

Abstract Electron microscope studies have been made of the propagation of shear cracks and the distribution of dislocations in the plastic zone during in situ tensile deformation of stainless steel single crystals. In thin-foil specimens under plane stress conditions, the plastic zone was coplanar with the crack and it represented the slip system of maximum resolved shear stress. The dislocations in the plastic zone were in the form of an inverse pile-up. Contrast analysis has shown that these dislocations were of pure screw type which were extended into two Shockley partials. The crack opening displacement was measured directly by counting the number of dislocations in the plastic zone and it was found to be approximately equal to the foil thickness. These observations are in good agreement with the model of shear cracks proposed by Bilby, Cottrell and Swinden (1963). The size of the plastic zone was much shorter than the value predicted by the theory and possible reasons for this discrepancy are discussed.

Theoretical latent hardening in crystals—II. BCC crystals in tension and compression

T he general latent hardening law of single slip derived in the first paper of this series (H avner, B aker and V ause, 1979) is applied to an analysis of “overshooting” phenomena in bcc crystals in tension and compression. This new law, which predicts anisotropic hardening of latent slip systems, is based upon the simple theory of finite distortional crystal hardening introduced by H avner and S halaby (1977). Because of historical ambiguities regarding identification of the slip plane in bcc metals, parallel analyses are presented corresponding to two separate criteria: (i) slip on {110}, {112} and {123} crystallographic planes only; and (ii) slip on the plane of maximum resolved shear stress containing a 〈111〉 direction. It is established that the new hardening law is a theory of “overshooting” in bcc crystals according to either identification of the slip plane. A qualitative comparison between theoretical results and two experimental papers on Fe crystals is included. The general difficulties in making comparisons with the experimental literature on finite distortional latent hardening are briefly discussed.

Deformation near a fault termination, part I: A fault in a clay experiment

Strike-slip faults were induced in a 5.5 cm-high clay cake by moving slowly half of the supporting base plate. The strain at 24 sample points near the termination of one of the faults was determined by measuring the preferred orientation of the basal planes of kaolinite crystals with an X-ray pole-figure goniometer and by calculating the strain according to the theory of March (1932). Each observed strain is the result of two consecutive strains. The first strain is due to the compaction of the clay under its own weight before the experiment. It is uniform throughout the clay cake and was sampled at points remote from faults. The second strain is variable and is due to the faulting. In order to separate the two strains and to find the “tectonic” strain alone, a strain with the orientations and magnitudes of the “pretectonic” strain was made, by calculation, to act on a hypothetical body that had first undergone the inverse of the observed strain. The result is the inverse of the “tectonic” strain, converted by an easy calculation into the “tectonic” strain itself. A contoured map of the shear strain (ϵ 2–ϵ 3)/2 shows great similarity with the maximum resolved shear stress distribution found by Chinnery and Petrak (1968) to exist theoretically in a semi-infinite elastic medium at the end of a dislocation surface representing a strike-slip fault. Unstraining the fault and superposing the unstrained configuration on the strained one allowed the construction of the displacement field. It resembles displacement fields determined near several natural strike-slip faults.

Deformation behavior and slip systems of quenched β-CuZn single crystals

The effect of quenching temperature and orientation on the yield stress and slip system at 290 K in quenched β-CuZn single crystals was investigated. The yield stress was remarkably dependent on quenching temperature and showed a maximum value by quenching from around the order-disorder transformation temperature ( T c ) independent of orientation. A {110} slip plane which is the same as that in an annealed crystal was observed in the crystal strengthened by quenching from just above T c in the orientation of χ ≧ +20 ° . but a plane which deviates from {110} to {112} plane in the twinning sense was operative with decreasing χ, where χ is the angle between the primary slip plane {110} in an annealed crystal and the maximum resolved shear stress plane (MRSSP) measured from the {110} toward {112} in the anti-twinning sense. The electron microscope observation and the orientation dependence of the yield stress and slip system in a quenched crystal deformed at 77 K suggest that the observed slip systems at 290 K are associated with the orientation dependence of critical resolved shear stress (CRSS) for {110} 〈111〉 and and {112} 〈111〉 slip systems in the quenched and the annealed crystals.

The Creep of NaCl-Doped Ice Monocrystals

Abstract Monocrystals of ice grown from NaCl solutions (concentration 5 X 10–4 to 10–2 mol/l) have been tested in creep at —10°C by basal glide. The maximum resolved shear stress ranged from 0.6 to 2.5 bar. The resulting creep curves show a deceleration, that is, the creep rate decreases with time. At the highest concentration the creep is essentially transient; the strain tends to a fixed value. This is unlike the behaviour of similarly orientated monocrystals of pure ice or of ice grown from solutions of other dopants so far reported in the literature. The possible causes for this behaviour are discussed and the implications for the mechanical properties of polycrystalline ice, and in particular sea ice and glacier ice, are described.

The Creep of NaCl-Doped Ice Monocrystals

AbstractMonocrystals of ice grown from NaCl solutions (concentration 5 X 10–4 to 10–2 mol/l) have been tested in creep at —10°C by basal glide. The maximum resolved shear stress ranged from 0.6 to 2.5 bar. The resulting creep curves show a deceleration, that is, the creep rate decreases with time. At the highest concentration the creep is essentially transient; the strain tends to a fixed value. This is unlike the behaviour of similarly orientated monocrystals of pure ice or of ice grown from solutions of other dopants so far reported in the literature.The possible causes for this behaviour are discussed and the implications for the mechanical properties of polycrystalline ice, and in particular sea ice and glacier ice, are described.

Twinning Deformation in Single Crystals of Cu-8 at%Al Alloy

Twinning mode and twinning stress in Cu-8 at%Al single crystals have been examined as a function of crystal orientation in the temperature range from −196°C to room temperature. The main results obtained are summarized as follows: (1) Twinning mode strongly depends not only on the crystal orientation but on the deformation temperature. (2) Twins are generally nucleated along the slip planes with the maximum resolved shear stress at the intersections between the twinning planes and the well-developed slip-bands. Those well-developed slip-bands also act as obstacles for the growth of twins. (3) Twins are formed along the cross slip-planes as well as along the conjugate and primary slip-planes at −196°C. (4) The twinning stress depends not only on the prestrain for the twinning but on the twinning mode.The results are discussed with a twinning model proposed by the present authors.

Effect of anisotropy on the coefficient of sliding friction in Schistose rocks

Foliated schist samples were sawcut at 45° to th cylinder axis and tested at 500 bars confining pressure, 25°C, and 10 −4sec −1 shortening rate, to examine the effect of anisotropy on the coefficient of sliding friction (μ). Cylinders were cored from sample blocks in a variety of orientations to produce sawcut-to-foliation (STF) angles ranging from 0° to 180° in 15° increments. The variation of μ with foliation orientation is sinusoidal. Maximum values of μ occur when the foliation is parallel to principal stress planes ( STF = 30°−45° and 105°−120°; τ = 0), and minimum values of μ correspond to planes of maximum resolved shear stress ( STF = 75° and 165°, τ = τ). Sliding-surface damage and gouge development vary inversely with μ. Surface damage results from the interaction of asperities with the sawcut surface, and failure and cataclasis of asperities produces gouge. Precursor events visible on force-time records, and partial loading tests terminated before megascopic sliding, indicate that surface damage and gouge are generated before megascopic sliding on the sawcut. Apparently, high resolved shear stress produces slip along the foliation prior to sliding on the sawcut. Foliation slip generates gouge at the sawcut interface; and the effect of the gouge is to lower μ.

Influence of normal stress on yielding behaviour in Fe -3 ·2% Si alloy single crystals

Specimens of Fe-3·2 wt% Si alloy single crystals of various orientations, both with 18 ppm C and decarburized, have been deformed in compression (\(\dot \varepsilon \) ∼ 10−4 s−1) at different temperatures between 125 K and 293 K. It has been found that the magnitude of CRSS, the choice of the slip planes and the shape of the stress-strain curves depend on the angle between the compression axis and the Burgers vector (angleξ). The stress normal to the maximum resolved shear stress plane is strongly altered on changing the angleξ. The discussion of the obtained experimental results seems to indicate that the normal stress influences the structure of screw dislocation core and subsequently the dislocation mobility.

Slip planes and asymmetric slip in fatigue of iron single crystals

Abstract Slip planes in iron single crystals are identified and the relative critical resolved shear stresses for slip on those planes are estimated from the results of torsional fatigue experiments. The torsional mode of fatigue is uniquely suited for these purposes because, generally, two different slip systems operate in a given region of maximum resolved shear stress. One slip system can be identified with one sense of shear and the other slip system with the opposite sense of shear. This effect is due to asymmetry of slip on certain planes. Slip is found to occur on {110}, {112} and {123} planes and to be asymmetric on {112} and {123} planes. The relative critical resolved shear stresses are ranked from tests on a number of different orientations.

Burgers Vector of Dislocations Generated by Small Stresses in Copper Crystals

In an x-ray topography study of the deformation of copper, the dislocations which were generated during the beginning stage of deformation were determined by the external geometry of the crystal in addition to the usual requirements of the maximum resolved shear stress.

Resolved shear stress in elastically anisotropic polycrystals

Kneer’s analysis was used to calculate the fraction of a tensile stress applied along the rolling or transverse direction, which is resolved as a shear stress on the various slip systems of an α titanium crystallite as a function of crystallite orientation. The crystallite was assumed to be imbedded in a sheet for which the crystallite orientation distribution had been previously determined. The maximum resolved shear stress was found to increase in the order\(\left\{ {10\bar 10} \right\} - \left\langle {1\bar 210} \right\rangle \),\(\left\{ {10\bar 11} \right\} - \left\langle {1\bar 210} \right\rangle \),\(\left\{ {0001} \right\} - \left\langle {1\bar 210} \right\rangle \) in the ratio 1∶1.04∶1.17 for the material studied. This seems to be a direct consequence of single crystal anisotropy, and should be relatively insensitive to changes in crystallite orientation distribution. For a given slip system, the maximum resolved shear stress was found to be higher for a tensile stress applied along the rolling direction than for an equivalent stress along the transverse direction in the ratio 1.04∶1 for the material studied. This is a result of the type of preferred orientation present, which is typical for titanium sheet continuously rolled in the α phase.

Plane of Crack Propagation in Stress Corrosion Fracture in Copper Beryllium

Abstract Single crystals of a copper-beryllium alloy of two axial orientations ([111] and [110]) strained in tension showed slip on (111/ planes. The same crystals, stressed in tension and exposed to an ammonia atmosphere, failed in a transcrystalline mode. In crystals of [111] orientation cracks propagated on (123) planes. Calculations show that in these crystals, the maximum resolved shear stress on the (111) slip planes is produced when the crack propagates on the (123) plane. In crystals of the [110] axial orientation, the cracks propagated on (110) planes. Again calculations show that the maximum resolved shear stress on the (111) slip planes is produced when the crack propagates on the (110) plane. These results indicate that crack propagation occurred on planes which would result in the maximum plastic deformation on the available slip system.