Showing papers on "Strain rate published in 1974"
TL;DR: In this paper, a flow law of the form e˙ = ƒ(σ) exp (−Q/RT) is obtained, where σ is an empirical function that is not simply proportional to σn for constant n and Q is equal to 125 ± 5 kcal/mol.
Abstract: Gem quality single crystals of dry olivine were plastically deformed in compression at differential stresses between 50 and 1500 bars, with zero confining pressure, and at temperatures between 1428° and 1650°C. When these new data are combined with existing creep data for dry olivine-bearing rock, a flow law of the form e˙ = ƒ(σ) exp (−Q/RT) is obtained, whereƒ(σ) is an empirical function that is not simply proportional to σn for constant n and Q is equal to 125 ± 5 kcal/mol. The flow law covers the stress range 50–10,000 bars and the temperature range 1100°–1700°C and is consistent with all published data to 1 decade in strain rate.
377 citations
TL;DR: In this article, a series of experiments are described, which illustrate the effects of temperature, strain rate and the presence of pore water on the rheological behaviour of Carrara Marble and Solnhofen Limestone.
258 citations
TL;DR: In this paper, a theoretical model for hot working when dynamical recrystallization occurs is presented, which is based on a description of the volume distributions of dislocations, which are produced as a result of the continuous grain growth.
248 citations
TL;DR: In this article, the authors describe the development of dynamic test techniques applicable to testing hard rock under high confining pressures, presents the results of an extensive series of tests on Dresser basalt, and correlates the strength data obtained with a failure criterion which incorporates both temperature and strain rate.
229 citations
TL;DR: In this article, a model was proposed to account for the yield behavior of amorphous glassy polymers, where the critical step in the yield process was envisaged as being the nucleation under stress of small disc-shaped sheared regions (the strain fields of which are analogous to those of dislocation loops) that form with the aid of thermal fluctuations.
Abstract: A model has been proposed to account for the yield behaviour of amorphous glassy polymers. The critical step in the yield process is envisaged as being the nucleation under stress of small disc-shaped sheared regions (the strain fields of which are analogous to those of dislocation loops) that form with the aid of thermal fluctuations. The model explains quantitatively the variation of the yield stress with temperature, strain rate and hydrostatic pressure using only two parameters, the shear modulus of the material which must be determined experimentally and the Burgers vector of the sheared region which is a constant related to the dimensions of the molecular chains making up the polymer. The model is also capable of accounting qualitatively for the marked strain softening that occurs in many glassy polymers after the yield point and for the observed variation of the degree of softening with temperature, strain rate and thermal treatment. Finally it is shown that the visco-elastic deformation a...
158 citations
TL;DR: In this paper, it was shown that bulk compression or dilatation (i.e., an extra strain rate div U) also appears to affect turbulent shear layers, typical values of Reynolds stress being increased by compression and decreased by dilatations.
Abstract: It is now well known that the turbulence structure of thin shear layers can be strongly affected by the application of extra rates of strain in addition to the shear velocity gradient. Examples of such extra strain rates include lateral divergence or convergence, and streamline curvature in the plane of the mean shear. The changes in Reynolds stress are an order of magnitude larger than would be expected from the explicit extra terms in the Reynolds-stress transport equations, and therefore an order of magnitude larger than predicted by conventional calculation methods. In the present paper, one of a series on ‘complex’ turbulent flows, we show that bulk compression or dilatation (i.e. an extra strain rate div U) also appears to affect turbulent shear layers, typical values of Reynolds stress being increased by compression and decreased by dilatation. The fractional change in Reynolds stress is an order of magnitude larger than the fractional change in volume of a fluid element. The physical mechanism is probably analogous to that responsible for the large effects of divergence or convergence in incompressible flow. Because the phenomenon seems to be of great practical importance we discuss it in the context of engineering calculation methods. An empirical correction formula, analogous to those used to allow for divergence or curvature effects, greatly reduces the large discrepancies found between recent experiments on supersonic boundary layers and calculations by conventional extensions of successful incompressible-flow methods.
154 citations
TL;DR: In this paper, the behavior of anisotropic compact bone in tension at a range of strain rates was examined and the modulus of elasticity, breaking stress and breaking strain were found to vary with strain rate.
Abstract: The paper examines the behavior of anisotropic compact bone in tension at a range of strain rates. Specimens of fresh bovine bone were loaded at strain rates between. 001 and 200 sec−1. This bone was shown to exhibit considerable plasticity throughout the range, except when tested in a direction normal to the long axis. The modulus of elasticity, breaking stress and breaking strain were found to vary with strain rate. There is a maximum energy absorbtion capability at a strain rate of .1 sec−1.
131 citations
TL;DR: In this paper, the least square strain is computed from calcite twin lamellae in cylinders of Indiana limestone experimentally shortened from 0 to 8.5 percent at 1.0-kb confining pressure, room temperature, and a constant strain rate of 10 −4 /sec.
Abstract: The least-squares strain is computed from calcite twin lamellae in cylinders of Indiana limestone experimentally shortened from 0 to 8.5 percent at 1.0-kb confining pressure, room temperature, and a constant strain rate of 10 −4 /sec. The best fit to the experimental results is obtained by using the inner width of the thick twins and setting the ratio between thin twin width and thick twin width at 0.5. The sum of deviations from the experimental axial strains for the best fitting strain magnitudes is only 0.52 strain in percent. The average accuracy is to within 27 percent of the experimental value. The average angle difference between the experimental and computed principal axes is 6.5°. The calculation technique is considered to be confirmed by these results. Results of the Conel (1962) technique and the version of it modified by Spang and Chappie (1969) are compared to the experimental results. Both techniques produce nearly the same agreement between principal axis directions as the least-squares method does. However, they underestimate the strain magnitudes by factors of 3.6 and 3.0, respectively. The principal axes produced by a numerical dynamic analysis of the data are essentially parallel to the computed principal strain axes.
116 citations
01 Mar 1974
TL;DR: In this paper, a strain energy density function is proposed which is based on a generalized measure of strain, and the function has the form W=(2G/n)IE+BIEm where G, B, n, and m are material constants, and IE is the first invariant of the Lagrangean strain (λan−1)/n.
Abstract: A strain energy density function is proposed which is based on a generalized measure of strain. The function has the form W=(2G/n)IE+BIEm where G, B, n, and m are material constants, and IE is the first invariant of the (generalized) Lagrangean strain (λan−1)/n. The function fits data on natural rubber and on a synthetic rubber in various homogeneous stress fields up to the point of break. The powers n and m are sensibly independent of temperature, while the two moduli G and B depend linearly on temperature, over the range investigated.
106 citations
95 citations
TL;DR: In this paper, the authors measured the yield stress of copper crystals containing a dispersion of SiO2 particles and found that the ratio of the modulus-corrected yield stress at temperatures from 20° to 1050°C, to that at 20°C was strongly temperature-dependent above about 400°C.
Abstract: The yield stress of copper crystals containing a dispersion of SiO2 particles was measured as a function of temperature (20°-1050°C), strain rate, and volume fraction and diameter of the SiO2 particles. The ratio of the modulus-corrected yield stress at temperatures from 20° to 1050°C, to that at 20°C, was found to be strongly temperature-dependent above about 400°C. But the modulus-corrected yield stress at 1050°C was still about half the value at 20°C. Between 600° and 1000°C, the yield stress was found to vary logarithmically with the strain rate. The theoretical analysis of these results will be the subject of another paper.
01 Jul 1974-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
Abstract: The onset of diffuse instability in sheet metals is associated with initially small, but grad-ually increasing, changes in the strain rate,e, and in the ratio of the minor to the major principal strains,p = e2/e1in the plane of the sheet. The hardening and softening contri-butions from such changes have been considered to obtain a condition for partial flow sta-biliity in the neck. The effect of the change ine on the uniaxial stress was determined from measurements of e changes in the neck and from the strain rate sensitivity of the materials. Similar evaluation of the change in the axial stress due to a change in p was made by means of an approximate analysis. The combination of these effects, along with the basic strain hardening of the materials, is used to explain the slowness or the rapid-ity of the process of necking in several materials, exhibiting different normal anisotropy, strain hardening and strain rate hardening behaviors. These results can also be used to explain the size of a diffuse neck and the strain distribution within it. Correlation has also been obtained between necking extensions to failure and the forming limits.
TL;DR: In this article, the authors performed mean velocity and mean turbulent field measurements for the case of a three-dimensional turbulent boundary layer on an axially rotated cylinder model consisting of two parts: a stationary section followed by a spinning afterbody.
Abstract: Mean velocity and mean turbulent field measurements are performed for the case of a three-dimensional turbulent boundary layer on an axially rotated cylinder The cylinder model consists of two parts: a stationary section followed by a spinning afterbody Techniques of hot-wire anemometry are employed, which yield complete mean velocity and turbulence measurements in skewed flows The general behaviour of the three-dimensional boundary layer is first discussed: two asymptotic layers analogous to the two-dimensional wall and defect layers are observed; they are shown to evolve from the equations of mean motion The hypothesis of scalar eddy viscosity is investigated in the light of these results Using conventional length scale assumptions together with the Reynolds stress tensor equations, a prediction of curvature effects in the law of the wall region is developed; a result in the present case is a smaller slope of the semi-logarithmic portion of the law of the wall, No assumptions over and above those necessary for plane, two-dimensional flow are required for this analysis The geometry of the model is such that a rapid change in mean rate of strain occurs along the streamlines From the history of the components of the tensor, it is possible to draw some fundamental conclusions concerning the dynamics of the energy dissipation, diffusion and redistribution processes
TL;DR: In this article, a hydrodynamic analysis is presented that allows straightforward calculation of the relaxation time for isostatic recovery within a mantle in which the viscosity varies continuously with depth, and it is demonstrated that the strain rates within such flows are in fact greater than the critical strain rate envisaged by Weertman in his theoretical rheological model of the mantle.
Abstract: This paper is concerned with the interpretation of isostatic recovery data in terms of the flow properties of the earth's mantle A hydrodynamic analysis is first presented that allows straightforward calculation of the relaxation time for isostatic recovery within a mantle in which the viscosity varies continuously with depth However, it transpires that no curve of this type (ie, choice of a reference viscosity and a rate of change of viscosity with depth) can of itself adequately explain the available observational data from the Fennoscandian and Laurentide ice sheets and the pluvial Lake Bonneville Proceeding onward it is then demonstrated that the strain rates within such flows are in fact greater than the critical strain rate envisaged by Weertman (1970) in his theoretical rheological model of the mantle Below this critical value, diffusion creep is the dominant flow process, and the flow can be modeled by a Newtonian viscosity But above this value, dislocation glide takes over, and the viscosity exhibits a decrease with increasing strain rate This feature is then incorporated into the theoretical model, and the isostatic recovery data are interpreted in such a way as to provide experimental values of the strain rate dependent viscosity that can be compared with the values in Weertman's rheological model It is demonstrated that the data become most self-consistent and exhibit the most satisfactory agreement with Weertman's model when the increase of mantle viscosity with depth is given roughly by exp (5 × 10^(−4)z), where z is the depth in kilometers Thus in addition, the analysis would appear to provide some verification of Weertman's model of the mantle flow properties It is further demonstrated that the much larger increase of viscosity with depth predicted by McConnell (1968) and others from previous analyses of isostatic recovery data is an artifice induced by the nature of such flows in which the strain rate decreases with depth; this led to an apparent increase of viscosity that is much larger than the actual variation
TL;DR: In this paper, a superplastic Zn-40 wt.% Al alloy was used to measure the texture of both phases in both phases as a function of the strain rate.
TL;DR: In this paper, the authors investigated the effect of strain aging on sapphire filaments with the tensile axis parallel to the c axis and found that the flow stress exhibited a power-law dependence on strain rate.
Abstract: Yielding and flow in uniaxial, constant-strain-rate tensile tests of single-crystal sapphire filaments oriented with the tensile axis parallel to the c axis were studied between 1760° and 1875°C. The existence of a strain-aging effect leading to non-reproducible upper yield points was established. The flow stress exhibited a power-law dependence on strain rate, with stress exponents ranging from 8.50 at 1775° to 12.4 at 1875°C. The apparent activation enthalpies calculated from constant-temperature experiments reflect a dependence of flow stress on temperature which includes both substructure and deformation-mechanism temperature dependencies. The preliminary activation enthalpies calculated from differential temperature and differential strain-rate (constant-structure) experiments are comparable to the value for defect diffusion in sapphire, 80 kcal/mol. From direct evidence, the {101} planes are identified as the dominant slip planes with the 1/3 〈101〉 Burgers vectors inferred from the testing geometry.
TL;DR: A constitutive equation for parallel-fibered elastic tissue is developed in the form of a non-linear hereditary integral based on relaxation tests to predict results of constant strain rate tests, hysteresis loops and sinusoidal tests.
TL;DR: In this article, the authors investigated the relationship between yield stress and strain rate in a 5kbar 500°C CO2 apparatus for deformation of single-crystal samples of synthetic quartz and found that the relationship was consistent with the Weertman power law and the Alexander and Haasen dislocation multiplication model.
Abstract: The 5-kbar 500°C CO2 apparatus developed by Griggs and Heard in the late 1950's has been renovated and adapted for deformation of single-crystal samples of synthetic quartz. The O+ cores were taken from the seed area of crystal Xo (8515H/106Si) and deformed at 500°C at strain rates of 7 × 10−3 to 5 × 10−8 s−1 in a systematic investigation of the relationship of (upper) yield stress and strain rate. A secondary series of experiments at 6 × 10−6 s−1 examined the temperature dependence of (upper) yield stress from 250° to 500°C. The yield stress-strain rate relationship was found to follow a power flow law, e˙ = A σn. Values of A = 5.82 (±1.87) × 10−7 and n = 3.64 ± 0.18 were determined at 500°C. Yield stress and temperature showed an exponential relationship of the form σy = [α exp (Q/RT)]1/n. Average activation energy over the range studied was Q = 31.6 ± 3.5 kcal/mol. The data seemed to indicate that either Q decreased or n increased with decreasing temperature. No sharp discontinuity in the σy versus T relationship was noted in contrast with previous observations of the ‘critical weakening temperature.’ The observed temperature and strain rate relationships were consistent with the Weertman power law and the Alexander and Haasen dislocation multiplication model. Stress-strain curves obtained in this study exhibited yield point and strain-hardening characteristics consistent with observations on hydrolytically weakened quartz published by others. Deformation features showed a dependence on strain rate, temperature, and variations in OH content within the sample consistent with previous observations.
TL;DR: In this article, the effect of the anisotropy of the material has been shown to have a significant effect on axial stress, strain and strain rate of a cylinder.
Abstract: The finite-strain theory has been used to study the creep behaviour of a thick-walled cylinder under large strains. The analysis is divided into two parts. In part 1 the creep deformation of a thick-walled cylinder of an anisotropic material subjected to internal pressure has been discussed. The effect of the anisotropy has been depicted graphically. It is found that the anisotropy of the material has a significant effect on the axial stress, strain and strain rate. Part 2 of the paper deals with the creep analysis of cylinders of either isotropic or anisotropic materials subjected to combined internal and external pressures. The effect of the anisotropy is found to be similar to that found in part 1. It is seen, however, that the introduction of external pressure results in decreasing the strain rate and thus increasing the life of the cylinder.
01 Jan 1974
TL;DR: In this paper, experiments were performed on continously graded asphaltic material to check the validity of a procedure which involves the calculation of the vertical and horizontal stress distribution through the pavement using linear or nonlinear elastic theory and the evaluation of the corresponding permanent strain distribution from the results of appropriate laboratory tests; summation of the permanent strain with depth gives the permanent deformation of the surface.
Abstract: Experiments were performed on continously graded asphaltic material to check the validity of a procedure which involves the calculation of the vertical and horizontal stress distribution through the pavement using linear or non-linear elastic theory and the evaluation of the corresponding permanent strain distribution from the results of appropriate laboratory tests; summation of the permanent strain with depth gives the permanent deformation of the surface. Dense bitumen macadam made with nominally 100-per bitumen and crushed rock aggregate (porphyry) of 25-mm maximum particle size were used. Repeated load, triaxial tests were used. Tests were conducted under controlled stress conditions, and resilient as well as permanent strains were measured. A series of creep tests were also performed. The six major variables investigated were vertical stress, temperature, confining stress, frequency of the vertical stress pulse, rest periods and binder content. The studies showed that an increase in temperature caused a substantial increase in strain. An increase in vertical stress caused an increase in strain and an increase in confining stress caused a decrease in strain. The level of static confining stress which gave the same strain as the dynamic confining stress was approximately equal to the mean level of that stress. The realistic changes in the relative lengths of vertical and confining stress pulses did not affect the strain. The rate of strain appeared to be time dependent at frequencies above 1 Hz. Rest periods between vertical stress pulses had negligible effect on strain. An optimum binder content of 4 percent existed for maximum resistance to strain between 10 and 30 c. At 40 C, better resistance was achieved with a 3 percent binder content. There was some evidence of a simple relationship between dynamic test results and those from simple creep tests. Interpretation of the results in terms of mix stiffness as a function of bitumen stiffness was encouraging. The results obtained from laboratory tests when applied to the pavement design problem produced reasonable values of rut depth.
TL;DR: The effect of discontinuous increases in strain rate on the yield behavior of specimens undergoing type A serrated yielding has been investigated in this article, where a transition in the subsequent yield behavior from further type A yielding to continuous yielding was observed.
TL;DR: In this paper, the effect of strain rate on the stress corrosion cracking (SCC) of an austenitic stainless steel in MgCl2 solutions was investigated by using a constant strain rate method over the r...
Abstract: The effect of strain rate on the stress corrosion cracking (SCC) of an austenitic stainless steel in MgCl2 solutions has been investigated by using a constant strain rate method over the r...
TL;DR: In this paper, an incremental solution is presented for plane strain conditions, the cylindrical inclusion being assumed rigid, while the matrix obeys the Mises yield criterion and its associated flow rule and has a very small or zero linear work-hardening characteristic.
TL;DR: In this paper, an Eyring-type activated flow analysis is employed to calculate both activation energy and shear activation volume over the range of experimental conditions studied, and the results are interpreted in terms of a two-phase amorphous microstructure consisting of both ordered and disordered regions.
Abstract: Tensile and compressive yield stress as well as tensile and compressive flow stress are determined as functions of strain rate, temperature, and thermal history for atactic polystyrene, isotactic polystyrene, polycarbonate, and poly-(methyl methacrylate). An Eyring-type activated flow analysis is employed to calculate both activation energy and shear activation volume over the range of experimental conditions studied, and the results are interpreted in terms of a two-phase amorphous microstructure consisting of both ordered and disordered regions. Similar values for yielding activation energies and activation energies obtained from dynamic mechanical analysis suggest that at temperatures well below Tg, yielding is controlled by cooperative local segmental motion. With increasing temperature, increasing degrees of local segmental motion are involved. Only when the test temperature approaches Tg does a transition to cooperative long-chain motion occur. Equivalent values for shear activation volume ...
TL;DR: In this article, a dual fracture-yield criterion was proposed to govern the failure of plain concrete as an isotropic homogeneous continuum, and two modes of failure are possible, i.e., the material element may fail either in shear or in tension depending upon the corresponding strain state.
Abstract: Considering plain concrete as an isotropic homogeneous continuum, a criterion has been proposed to govern the failure of this material. According to this dual fracture-yield criterion, two modes of failure are possible, i.e., the material element may fail either in shear or in tension depending upon the corresponding strain (stress) state. It is shown in this paper that the proposed failure criterion is capable of predicting with accuracy the experimental results obtained from two different types of test. Moreover, it is proposed that the plane of the cleavage crack can be normal to the direction of the maximum tensile strain. This proposal can successfully predict the modes of failure of several experimental observations. A method has also been proposed of obtaining constant stress and strain states during unconfined compression tests.
TL;DR: In this paper, the deformation of α-zirconium has been studied between 375 and 625°C and at strain rates from 5 × 10−6 to 10−1 s−1 by compression testing.
Abstract: The deformation of α-zirconium has been studied between 375 and 625°C and at strain rates from 5 × 10−6 to 10−1 s−1 by compression testing. The yield stress at the lower temperatures was relatively insensitive to strain rate and temperature, whereas at the higher temperatures, it was highly sensitive to strain-rate and temperature.Various mechanisms are considered as being responsible for the athermal range of behaviour and it is concluded that the Orowan stress required to bow out segments of the Frank network is most likely to be controlling in this region. Similar considerations applied to the rate-sensitive range of behaviour suggest that the unpinning of nodes in the dislocation network is ratecontrolling above the transition temperature. In the transition region between the athermal and thermally activated ranges of flow, a maximum in flow stress was observed that is attributed to a dynamic strain-ageing effect caused by the presence of interstitial oxygen.
TL;DR: In this article, a simple device was described for use with the Instron variable speed unit to produce a constant true strain rate in compression or tension, including a facility for making small strain rate changes during a test cycle.
Abstract: A simple device is described for use with the Instron variable speed unit to produce a constant true strain rate in compression or tension. The device includes a facility for making small strain rate changes during a test cycle. The new strain rate is selected from two arbitrary levels ranging from 0.5 to 2.0 times the initial strain rate. The changes are accomplished in 70 ms and are achieved without discontinuities in strain rate. The effect of machine stiffness on the specimen strain rate obtained with this apparatus is also discussed.
TL;DR: In this paper, the velocity v and the density Nm of moving dislocations in the equilibrium state are observed to depend on the strain rate ϵdot as v ∝ ϵ dot 0.42 and Nm ∝ εdot 0.58, respectively, at 600°C.
01 Jan 1974-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this paper, the effects of temperature and strain rate on deformation behavior and dislocation structure were investigated for OFHC copper and type 304 stainless steel and Ferrovac “E” iron.
Abstract: The effects of temperature and strain rate on deformation behavior and dislocation structure were investigated for OFHC copper and type 304 stainless steel. It is shown that the cyclic stress response is inversely related to the cell size for copper cycled at different temperatures ranging from -75 to 650°C. Type 304 stainless steel underwent a change from a planar to a wavy slip character as the temperature was changed from room temperature to 760°C. At elevated temperatures, cells were observed and the size of the cells tended to increase with increase in temperature. The effects of temperature on the cyclic stress-strain parameters were investigated for copper, type 304 stainless steel and Ferrovac “E” iron. On studying the effects of temperature and strain rate on the fracture mechanisms it was found that a time dependent fracture mode was dominant at high temperature levels and low strain rates. However, at high strain rates the life was insensitive to temperature. The role of grain boundary migration on the fracture process was investigated. Grain boundary migration was found to be dependent on strain rate for copper. However, for type 304 stainless steel, the grain boundary migration was inhibited at high temperature (760°C) due to the presence of precipitates at the grain boundaries. In strain cycling of OFHC copper and type 304 stainless steel, it was found that the addition of creep-type damage to fatigue damage resulted in a total damage which was not equal to unity for failure when these different modes were imposed sequentially. The sense of the damage accumulation appeared to have no effect on this summation.
TL;DR: In this paper, a nonlinear, four-parameter, elastic-viscoplastic model was constructed which describes the mechanical behavior of polyester-styrene copolymer.
Abstract: Two constitutive relations have been determined from test results that characterize, respectively, the uniaxial and photomechanical behavior of a polyester-styrene copolymer for strain rates from 10−5 to 3×103 in./in./s and strains up to 40 percent. The high-strain-rate data were obtained by means of a split-Hopkinson-bar apparatus. Intermediate-strain-rate tests, performed with the aid of a drop tower, were reported in an earlier paper. Quasi-static experiments were conducted on a standard testing machine. A nonlinear, four-parameter, elastic-viscoplastic model was constructed which describes the mechanical behavior. The parameters were determined by a least-mean-squares curve-fitting procedure. The viscoplastic parameters were found to obey a power law in strain rate. The photomechanical model was found to be linear with strain well into the plastic-deformation region, while the slope of the strain-birefringence curve for each strain rate also varied by strain rate to a power.