Showing papers on "Creep published in 1970"
TL;DR: In this article, the steady state deformation of dunite and peridotite was investigated in solid pressure media in the presence and absence of externally released H 2 O. The steady state data were best fit by a power creep equation with the stress exponent, n ≃ 2.4 and 4.8 and the creep activation energy, Q ≃ 80 and 120 Kcal/mole, respectively.
Abstract: Deformation experiments on dunite and peridotite, both in the presence and absence of externally released H 2 O, have been carried out in solid pressure media apparatus in the confining pressure range 5 to 30 kb, temperature interval 300°C to 1400 ° C at constant strain rates ranging from 10 −3 to 10 −8 /sec. At the lower temperatures and higher rates, olivine deforms by plastic flow on the system T = (110), t = [001], the slip systems changing with increasing temperature and decreasing strain rate through {0kl} [100] to (010) [100]. At a strain rate of 10 −3 /sec, polygonization (dislocation climb) is first observed at about 1000 ° C and recrystallization first appears at about 1050 ° C; these temperatures decrease by about 50 ° C with a ten-fold reduction in strain rate. Preliminary mechanical results indicate that steady state deformation takes place only in the temperature-strain rate range in which the diffusion controlled processes of polygonization and recrystallization are important or dominant. The steady state data are best fit by a power creep equation with the stress exponent, n ≃ 2.4 and 4.8 and the creep activation energy, Q ≃ 80 and 120 Kcal/mole for deformation in the presence and absence of externally released H 2 O, respectively. Extrapolation of the equation for the dunite deformed dry to a representative geological strain rate of 10 −14 /sec gives shear stresses in the range 100 bars to 1 bar and effective viscosities from 10 23 to 10 20 poise for the temperature interval 1000 ° C to 2000 ° C. The estimated variation in shear stress over most of the upper mantle, where T/Tm (the ratio of ambient to melting temperature) is greater than 0.75, is about 6 to 15 bars, and in viscosity in the range 10 20 to 10 21 poise. These inferences are in accord with estimates based on other geophysical observations, and our results suggest that flow in the upper mantle may be governed primarily by a non-linear creep law.
565 citations
TL;DR: In this paper, it was shown that at stresses greater than about 10−2 bar creep in the earth's mantle is caused by dislocation motion rather than by the mass transport of atoms through diffusion from one grain boundary to another.
Abstract: In this paper we show that it is probable that at stresses greater than about 10−2 bar creep in the earth's mantle is caused by dislocation motion rather than by the mass transport of atoms through diffusion from one grain boundary to another. The latter process leads to Nabarro-Herring creep. Only at very low stresses (<10−2 bar) should Nabarro-Herring creep be dominant. Dislocation creep equations (which are nonlinear in stress) are used to estimate the ‘effective viscosity,’ at a constant creep rate of 10−16 sec−1, of the moon, Mars, and the mantles of Venus and the earth. The effective viscosity of the mantles of Venus and the earth diminishes with increasing depth, goes through a minimum, and then increases continuously up to the mantle-core boundary. The effective viscosity in the lower mantle is much smaller than estimates derived from the Nabarro-Herring creep equation. The effective viscosity in the deep interior of the moon is approximately constant and does not increase appreciable with depth. The effective viscosity of Mars is intermediate in behavior between that of the earth and of the moon.
478 citations
TL;DR: An empirical expression for the observed creep curves is developed and deviations from classical viscoelasticity theory noted and a four parameter Maxwell-Kelvin fluid model is proposed and fitted to the creep data.
328 citations
TL;DR: In this article, a model for grain boundary sliding is developed in which sliding occurs by the movement of dislocations along, or adjacent to, the boundary by a combination of climb and glide.
Abstract: A model for grain boundary sliding is developed in which sliding occurs by the movement of dislocations along, or adjacent to, the boundary by a combination of climb and glide. Under these conditions the strain rate due to sliding is proportional to [sgrave]2/d, where [sgrave] is the applied stress and d is the average grain diameter. It is shown that reports in theliterature of enhanced creep rates at low stresses and/or small grain sizes may be explained by assuming that the various deformation mechanisms, including sliding, operate independently.
310 citations
01 Jan 1970-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this paper, it was shown that the deformation mode is a function of strain rate at 1400°F and tensile deformation occurs by the shear of the γ and γ′ phases bya/2 superlattice pairs.
Abstract: The creep deformation of Mar-M200 single crystals of various orientations has been studied at a temperature of 1400°F. It was found by a combination of transmission microscopy and analysis of lattice rotations that shear of the γ−γ′ structure occurs by the glide of loosely coupled intrinsic/extrinsic fault pairs with a net Burgers vector ofa . The orientation dependencies of both the rate and extent of primary creep are correlated with the Schmid factors and multiplicity of slip for {111} systems. It is also shown that strain hardening due to intersecting slip is necessary to obtain the transition from primary to steady-state creep. In addition, it was found that the deformation mode is a function of strain rate at 1400°F. In contrast to the observed glide mechanism during creep, tensile deformation occurs by the shear of the γ and γ′ phases bya/2 superlattice pairs.
215 citations
TL;DR: In this paper, the unstable growth of a crack in a large viscoelastic plate is considered, within the framework of continuum mechanics, and a non-linear, first order differential equation is found to describe the time history of the crack size if the stress applied far from the crack is constant.
Abstract: The unstable growth of a crack in a large viscoelastic plate is considered, within the framework of continuum mechanics. Starting from the local stress and deformation fields at the tip of the crack, a non-linear, first order differential equation is found to describe the time history of the crack size if the stress applied far from the crack is constant. The differential equation contains the creep compliance and the intrinsic surface energy of the material. The surface energy concept for viscoelastic materials is clarified. Inertial effects are not considered, but the influence of temperature is included for thermorheologically simple materials.
Initial crack velocities are given as a function of applied load in closed form, as well as a comparison of calculated crack growth history with experiments. Above a certain high stress, crack propagation ensues at high speeds controlled by material inertia while at a lower limit infinite time is required to produce crack growth. Thus an upper and lower limit criterion of the Griffith type exists. For rate insensitive (elastic) materials the two limits coalesce and only the brittle fracture criterion of Griffith exists. The implications of these results for creep fracture in metals and inorganic glasses are examined.
138 citations
TL;DR: The clinical marginal fracture characteristics of three commercial dental amalgams were evaluated and compared with a number of their mechanical properties to determine which properties would relate best to clinical performance, and it was found that compressive strength, tensile strength, Transverse strength, transverse deflection, and flow were ineffective.
Abstract: The clinical marginal fracture characteristics of three commercial dental amalgams were evaluated and compared with a number of their mechanical properties to determine which properties would relate best to clinical performance. It was found that compressive strength, tensile strength, transverse strength, transverse deflection, and flow as determined by ADA Specification No. 1 were ineffective, whereas the rheological properties of dynamic creep, static creep, and slow compressive strength appeared effective in relating to marginal fracture.
137 citations
TL;DR: In this article, the authors evaluated the importance of diffusion-creep processes, especially in the range where the effect of grain-boundary diffusion is expected to predominate and found that at low stresses and elevated temperatures, polycrystalline copper can behave in a Newtonian manner with the primary creep stage of negligible importance.
Abstract: Experiments are described on the deformation of copper, both in the form of long straight wires and in the form of helices, with the aim of evaluating the importance of diffusion-creep processes, especially in the range where the effect of grain-boundary diffusion is expected to predominate. It is established that at low stresses and elevated temperatures, polycrystalline copper can behave in a Newtonian manner with the primary creep stage of negligible importance. Above a specific temperature, which is shown to vary inversely as the logarithm of the grain size, creep rates agree closely with the Nabarro–Herring equation, and the activation energy is identical with that for lattice self-diffusion. Below this temperature the activation energy is found to be near the value expected for grain-boundary self-diffusion, and the creep rate now varies inversely as the cube of the grain size in agreement with the equation derived by Coble (J. Applied Physics, 1963, 34, 1679). Within the range of the presen...
115 citations
TL;DR: In this paper, the dislocation substructure formed during creep of molybdenum single crystals of axial orientation was examined by etch-pitting techniques after creep at 900 psi and 1650°C.
105 citations
TL;DR: In this article, a theoretical and experimental treatment of the strength of unidirectional fiber-reinforced composite loaded in tension in the fiber direction is presented, where the fibers are treated as having variable strength which results in fiber fractures prior to composite failure.
TL;DR: In this paper, the microdynamics of elevated temperature deformation in single and polycrystalline Fe-3 % Si is examined in terms of measured minimum effective stresses, which are obtained through the use of a new experimental technique based upon the response of dislocations to the internal and applied stresses.
01 Jan 1970
TL;DR: In this article, the constitutive equation for creep, shrinkage and thermal expansion of concrete and concrete is derived, which reflects correctly the effect of variable humidity and temperature, including the effects of size, shape and stress distribution.
Abstract: The constitutive equation for creep, shrinkage and thermal expansion, which reflects correctly the effect of variable humidity and temperature, including the effect of size, shape and stress distribution, is derived. Cement paste and concrete are treated as a multi-phase composite material, in which both the static and thermodynamic conditions of equilibrium must be considered.
TL;DR: In this paper, a phenomenological theory of steady state ceep is formuated which explicitly includes the development of an average internal back stress, which is based on the premise that dislocation glide and recovery are separate kinetic processes driven by different components of the applied stress, the effective and internal stress respectively, and it is shown that the predicted applied stress dependence for high temperature creep can be predicted in a straightforward manner from the stress dependence of strain hardening, recovery and glide if the relative magnitudes of the internal and effective stresses are known.
01 Jan 1970
TL;DR: In this article, the activation area for creep deformation is collected and examined in the light of many material and deformation variables, including Boltzmann's constant, temperature, Burgers vector, steady state creep rate, and effective shear stress.
Abstract: The activation areas for creep deformation are collected and examined in the light of many material and deformation variables. The activation area is A
*= (kT/b) (∂ In
$$\dot \in $$
/∂τ*)
T
where k is Boltzmann's constant, T the absolute temperature, b the Burgers vector,
$$\dot \in $$
the steady state creep rate, and τ
* the effective shear stress. It is found that within a factor of 5, there is a general correlation between activation area and stress for all metals, alloys, semiconductors and ionic crystals. A jog-limited dislocation motion with a distribution of jog spacings is suggested as a possible mechanism for this behaviour. Some limitations for the jog mechanism are discussed.
01 Feb 1970-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this article, transmission electron microscopic observations showed that the density of dislocations within subgrains and the subgrain diameter vary with applied stress according to: ϱD∝σAK,D ∝ σA−0.8, where K=1.4 to 2.0.
Abstract: Specimens of 304 stainless steel subjected to different thermomechanical histories develop different internal stresses, σi, and different substructures. Creep rate is uniquely related not to the applied stress, σA, but to the effective stress, σ*=(σA−σi). Values of σ* are determined from experimental results and σi calculated from σi=(σA−σ*). Results show σi increases with the applied stress according to σi∝σA1.7. Transmission electron microscopic observations show that the density of dislocations within subgrains, ϱD, and the subgrain diameter,D, vary with applied stress according to: ϱD∝σAK,D ∝ σA−0.8, whereK=1.4 to 2.0. Subgrain misorientation is independent of creep stress, strain, or temperature. The contributions of these structural variables to the internal stress are discussed.
TL;DR: In this article, the shear within a matrix volume is assumed to be an important process during the creep of composite material reinforced with short rigid fibres, and the rate of elongation of such a composite with certain fibre distributions can be estimated.
Abstract: The shear within a matrix volume is assumed to be an important process during the creep of composite material reinforced with short rigid fibres. The rate of elongation of such a composite with certain fibre distributions can be estimated. The agreement with a few experimental data is reasonably good.
TL;DR: In this article, the authors investigated the effect of tensile creep on the activation energy of magnesium in the range 400-800°K and 1.0-10.0 kg mm−2, respectively.
TL;DR: In this article, a dough of 45.8% water absorption prepared from a medium strength baking flour was used for simple tension testing and the results showed that the dough exhibited linear viscoelastic behavior.
Abstract: Creep and creep recovery tests in simple tension were made on a dough of 45.8% water absorption prepared from a medium strength baking flour. Within the experimental uncertainty, the creep compliance was found to be the same at stresses from about 2 to 3.2 mbar (2000 to 3200 dynes/cm2). Values of the steady-state viscosity and the steady-state compliance derived from the creep data were in close agreement with those from the recovery data; the average values are 1.2 × 108 poise and 2.7 × 10−5 cm2/dyne. These observations show that the dough exhibited linear viscoelastic behavior. They also indicate that no structural changes are produced by stress, over the covered range, and thus that the dough does not behave like a material crosslinked by covalent bonds.
TL;DR: In this article, a stress exponent, n, of 1.5 was found for scandia-doped zirconia and two regimes, with n=1 and 6, were found for the yttria-dope ZrO2-6 mol% Sc2O3 (grain size ∼2 μm).
Abstract: Compression creep measurements at constant load on ZrO2-6 mol% Sc2O3 (grain size ∼1 μm), ZrO2-6 mol% Y2O3 (grain size ∼17 μm), and heat-treated ZrO2-6 mol% Sc2O3 (grain size ∼2 μm) yield activation energies of 89, 86, and 74 kcal/mol, respectively. The creep rates are linearly proportional to the inverse square of the grain size of the material. A stress exponent, n, of 1.5 was found for the scandia-doped zirconia and two regimes, with n=1 and 6, were found for the yttria-doped zirconia. These data, supported by metallographic evidence, are interpreted as showing that n=1 is associated with cation diffusion control of creep, n=6 with local propagation of inter-crystalline cracks, and n=1.5 with a transition region.
DOI•
01 Jan 1970TL;DR: In this paper, the effect of alloying additions, slip line topography, and dislocation structure on the temperature dependence of flow stress has been studied with respect to the effect on the slip line.
Abstract: The temperature dependence of the ordinary flow stress, the microplastic yield stress, and the transient creep responses ofγ′ have been studied with respect to the effect of alloying additions, slip line topography, and dislocation structure. The increase observed in the flow stress with increase in temperature may be attributed to a change in the mechanism controlling the flow stress. An exhaustion hardening process at low temperatures appears to be supplanted by a debris hardening process at high temperatures. This transition arises from an increased propensity for {100} slip as the temperature is raised. Solute additions affect the temperature dependence of the flow stress probably by altering the tendency for {100} slip.
TL;DR: In this paper, it is suggested that transient creep at high temperatures arises principally as a result of the dispersal of entanglements by the climb mechanism, with a rate constant that depends on stress and temperature in the same way as does the secondary creep rate.
Abstract: It is suggested that transient creep at high temperatures arises principally as a result of the dispersal of entanglements by the climb mechanism. The dispersal of the entanglements is assumed to follow a unimolecular reaction kinetics with a rate constant that depends on stress and temperature in the same way as does the secondary creep rate. The analysis shows that the strain (e) versus time (t) relation can be represented by e=e 0 +e. 3 t+ β−1 K [1- exp (−K e 3 t)] , where e0 is the instantaneous strain on loading, e 3 , the secondary creep rate, K e 3 the rate constant, and β the ratio of initial to secondary creep rate. The experimental creep data on several b.c.c. and f.c.c. metals and alloys correlate quite well with the proposed mechanism. The constants β and K were found to be independent of temperature and stress. The proposed formulation becomes inapplicable for correlating creep data in polycrystals at low stresses because of the significant contribution of grain-boundary sliding to the total creep at these stress levels.
TL;DR: In this article, the authors tested polycrystalline magnesium oxide in compressive creep at a temperature of 1200°C and under initial applied stresses of 3.44 × 108−13.76 × 108 dynes/cm2.
TL;DR: In this paper, the authors demonstrate the influence of antimony on the grain-boundary cavitation processes involved in creep rupture and conclude that the enhanced cavitation in antimonial copper can be attributed to the reduction in interfacial energies.
Abstract: Antimony has been shown previously to reduce the interfacial energy of copper by adsorbing at interfaces and this paper demonstrates the influence which the phenomenon has on the grain-boundary cavitation processes involved in creep rupture. Copper of two different grain sizes and a copper–0·3 at.-% antimony alloy have been creep-tested to rupture in vacuum at ∼ 0·5 Tm . Antimony was found to increase the minimum creep rate but to lower the rupture ductility. Counts of the number of cavitated boundaries showed that antimony accelerated both bubble- and wedge-type cavitation in copper more than it accelerated the creep rate. It is concluded that the enhanced cavitation in antimonial copper can be ascribed to the reduction in interfacial energies. Some tests on copper-oxygen alloys showed a similar association between poor rupture ductility and interface adsorption.
TL;DR: In this paper, the activation volume for diffusion or steady-state creep at high temperature (> 0.5Tm) is estimated for all crystalline solids if the crystal structure, valence, entropy of melting, and volume change on melting are known.
Abstract: It is shown that the activation volume for diffusion or steady‐state creep at high temperature (>0.5Tm) can be estimated for all crystalline solids if the crystal structure, valence, entropy of melting, and volume change on melting are known. The calculated results agree well with the available experimental data for metals and compounds. Calculations performed for a number of crystalline materials show that the activation volume is a function of the crystal structure and that negative activation volumes are obtained for those materials that contract on melting. These results suggest that diffusion in the solid state occurs by a mechanism similar to the ``relaxion'' mechanism as originally proposed by Nachtrieb and Handler. In our proposed model the thermally activated process in diffusion involves the cooperative formation of a liquid‐like cluster of atoms surrounding a vacant lattice site. Such a model predicts negative activation volumes and satisfactorily explains the influence of different crystal str...
01 Jan 1970
TL;DR: In this paper, the authors surveyed the Ti-Al-Sn-Zr system with emphasis on 1000°F creep strength and retention of ductility (stability) after creep exposure, and found that Ti-6Al-2Sn-4Zr-2Mo is the creep/density optimized stable alloy.
Abstract: The Ti-Al-Sn-Zr system is surveyed with emphasis on 1000°F creep strength and retention of ductility (“stability”) after creep exposure. “Stability” is assured if Ti-6Al-2Sn-2Zr is found to be the creep/density optimized stable alloy. The alloying behavior of Ti is consistent with a “metallic bonding valence” of four and an “alloy structure valence” of 1.5. Covalent bonding between Ti and Al is confirmed. This substantially precludes blocking Al embrittlement through dilution of alpha soluble additions of elements from groups IV B , V B and VI B . Ti-6Al-2Sn-4Zr-2Mo is shown to have good hot strength and creep resistance. Between about 850° and 1050°F, Ti-6Al-2Sn-4Zr-2Mo obeys a creep rate equation of the general form for small strains and strain rates.
TL;DR: In this paper, the authors examined the forms of such plots and the ambiguities which arise near transitions from one regime to another and noted that ranges of temperature, stress and grain size commonly used are inadequate and serious errors in interpreting the results of creep tests will continue to be made until a better understanding of the interaction of the basic processes is developed, so as to enable the positions of transitions to be predicted.
Abstract: Attempts to identify the mechanisms operating during creep are often made by examining plots which yield apparent activation energies, or the stress or grain size-dependences of creep-rate The forms of such plots are here examined and the ambiguities which arise near transitions from one regime to another are noted The ranges of temperature, stress and grain size commonly used are inadequate and serious errors in interpreting the results of creep tests will continue to be made until a better understanding of the interaction of the basic processes is developed, so as to enable the positions of transitions to be predicted
TL;DR: In this paper, a new theory based on Charles's theory of the subcritical growth of pre-existing cracks in the specimen by stress-aided corrosion is put forward, which is a successful explanation of new experiments on the creep of Pennant sandstone and Carrara marble under uniaxial compression at room temperature.
Abstract: Scholz's theory of brittle creep is rejected. A new theory based on Charles's theory of the subcritical growth of pre-existing cracks in the specimen by stress-aided corrosion is put forward. It is a successful explanation of new experiments on the creep of Pennant sandstone and Carrara marble under uniaxial compression at room temperature.
TL;DR: In this paper, the authors used differential (step-stress) creep tests and constant axial strain-rate tests on two frozen soils, Sault Ste. Marie clay and saturated Ottawa sand.
Abstract: Soil strength, defined in terms of the stress to cause a stated strain-rate, was studied using differential (step-stress) creep tests and constant axial strain-rate tests on two frozen soils, Sault Ste. Marie clay and saturated Ottawa sand. Incremental increases in mean stress, with deviatoric stress constant produce measurable changes in secondary creep rates. Plots of a stress term versus the logarithm of creep rates give straight lines. The linear relationship indicates that creep rate increases exponentially with increases in stress difference and decreases exponentially with increase in the mean stress. The temperature effect on creep behavior is described by an exponential function of the reciprocal of temperature. For a specific creep rate and temperature, several stress circles give a Mohr-Coulomb envelope. The angle of internal friction evaluated for the sand-ice samples falls in the range of values expected for dry sand and appears to be independent of creep rate and temperature. The cohesion is dependent on creep rate.