Showing papers on "Strain rate published in 1984"
TL;DR: In this article, a new method of modeling material behavior which accounts for the dynamic metallurgical processes occurring during hot deformation is presented, which considers the workpiece as a dissipator of power in the total processing system and evaluates the dissipated power co-contentJ = ∫o σ e ⋅dσ from the constitutive equation relating the strain rate (e) to the flow stress (σ).
Abstract: A new method of modeling material behavior which accounts for the dynamic metallurgical processes occurring during hot deformation is presented. The approach in this method is to consider the workpiece as a dissipator of power in the total processing system and to evaluate the dissipated power co-contentJ = ∫o σ e ⋅dσ from the constitutive equation relating the strain rate (e) to the flow stress (σ). The optimum processing conditions of temperature and strain rate are those corresponding to the maximum or peak inJ. It is shown thatJ is related to the strain-rate sensitivity (m) of the material and reaches a maximum value(J max) whenm = 1. The efficiency of the power dissipation(J/J max) through metallurgical processes is shown to be an index of the dynamic behavior of the material and is useful in obtaining a unique combination of temperature and strain rate for processing and also in delineating the regions of internal fracture. In this method of modeling, noa priori knowledge or evaluation of the atomistic mechanisms is required, and the method is effective even when more than one dissipation process occurs, which is particularly advantageous in the hot processing of commercial alloys having complex microstructures. This method has been applied to modeling of the behavior of Ti-6242 during hot forging. The behavior of α+ β andβ preform microstructures has been exam-ined, and the results show that the optimum condition for hot forging of these preforms is obtained at 927 °C (1200 K) and a strain rate of 1CT•3 s•1. Variations in the efficiency of dissipation with temperature and strain rate are correlated with the dynamic microstructural changes occurring in the material.
1,121 citations
TL;DR: In this paper, the role of the strain and strain rate gradients in raising the apparent torsion peak strain ep above the ep values obtained from homogeneous tension or compression testing is clarified.
917 citations
TL;DR: In this paper, the authors present an assessment of the current understanding of the phenomenon of serrated plastic flow, which manifests itself as serrations, load drops, jerkiness or other discontinuities in the stress-strain curves obtained in constant extension rate tensile tests, and as sudden bursts of strain in constant loading rate tests and in constant load (stress) creep tests (the so called staircase creep).
Abstract: This paper attempts an assessment of the current understanding of the phenomenon of “serrated plastic flow”, which manifests itself as serrations, load drops, jerkiness or other discontinuities in the stress-strain curves obtained in constant extension rate tensile tests, and as sudden bursts of strain in constant loading rate tests and in constant load (stress) creep tests (the so called staircase creep). Though one can identify at least seven physical processes that can cause serrations, the discussion here is restricted mainly to serrated yielding in tension tests originating from dynamic strain ageing (dsa). The characteristics of the five types of serrations that have been identified so far and the experimental conditions under which they occur are discussed. The various models of serrated flow that have been put forward are reviewed critically. Some recent results on 316 stainless steel are presented to illustrate the effects of grain size, temperature and strain rate on serrated flow. Manifestations ofdsa other than serrations such as a negative strain rate sensitivity, positive temperature dependence for flow stress and work hardening, and the ductility minimum are also discussed. Finally the various issues to be resolved are enumerated.
534 citations
TL;DR: The transition from frictional to quasi-plastic behavior in quartz-of-eldspathic crust has been studied in this article, showing that the peak shear resistance increases with depth through the frictional regime to peak at the transition, beneath which it falls off exponentially with increasing temperature.
Abstract: The cutout depth of microseismic activity in continental fault zones appears to correspond to the onset of greenschist metamorphic conditions at about 300°C It can generally be modeled as the transition from frictional to quasi-plastic behavior in quartzofeldspathic crust Shear resistance increases with depth through the frictional regime to peak at the transition, beneath which it falls off exponentially with increasing temperature Larger earthquake ruptures (ML>55) nucleate around this transition depth where the highest concentrations of strain energy may accumulate Varying depth and amplitude of the peak shear resistance along strike induce fluctuations in strain energy concentration at the base of the seismogenic zone Factors affecting the depth of the transition include crustal composition, geometry and mode of faulting, fluid pressure levels in the frictional regime, and water content in the quasi-plastic regime, quasi-plastic strain rate, and geothermal gradient Evaluation of their relative importance is complicated because several are interdependent However, compositional change may cause abrupt irregularities in seismogenic depth and peak shear resistance, while regional variations in heat flow look to be particularly effective in creating long-wavelength heterogeneities in strain energy concentration affecting faulting style
346 citations
TL;DR: In this paper, a power law form of flow law was used to fit the creep data of Heavitree quartzite samples with different amounts of available water, at 15 kbar confining pressure, 800°-1100°C, 10−4 to 10−7/s strain rate, and 1-10 kbar deviatoric stress.
Abstract: Creep and constant strain rate experiments have been performed on Heavitree quartzite samples with different amounts of available water, at 15 kbar confining pressure, 800°–1100°C, 10−4 to 10−7/s strain rate, and 1–10 kbar deviatoric stress. Some samples were dried by vacuum heating, others were left as is, and others had 0.1–0.5 wt % water added to them before being mechanically sealed in a Pt tube and deformed. When the creep data are fit to a power law form of flow law, they show, with increasing water available, a decrease in the activation energy from 44 to 41 to 35 kcal/mol, and a decrease in the stress exponent from 3.3 to 2.3 to 1.8. Samples deformed at 900°C and 10−6/s showed corresponding changes in preferred orientations from a diffuse maximum parallel to to a small circle girdle about σ1 and a change in deformation lamellae orientations from basal to basal plus prismatic. The samples also showed corresponding textural changes, from little recovery and no recrystallization, to greater recovery with moderate amounts of fine grain boundary recrystallization and small isolated melt pockets (<1 vol %), to even greater recovery with less continuous but coarser recrystallization and somewhat more extensive grain boundary melt (<3 vol %). The low stress exponent of the water added samples may be due to a component of grain boundary sliding, allowed by the grain boundary recrystallization and melt in these samples, but there is no microstructural evidence for such a mechanism. The change in slip systems of the original grains in the water added samples might be due in part to some relaxation of grain boundary constraints. The ease of recovery in the as is and water-added samples suggests that deformation of these samples was glide controlled and the chief mechanical effect of the added water may be to enhance dislocation glide.
228 citations
220 citations
TL;DR: In this article, experimental observations of shear bands, their role in deformation and their significance in the nucleation of recrystallized grains and the development of annealing textures are discussed.
203 citations
TL;DR: In this article, the critical resolved shear stress (CRSS) for (111) to (010) slip was found to depend on the test temperature and orientation of the samples, as other investigators have previously observed, but also on the sense of applied stress.
183 citations
TL;DR: In this article, a geometrical model is used to show how the recovery of this damage by boundary migration, enhances the normal grain growth process, based on the postulate of Holm el al.
175 citations
TL;DR: In this article, a series of constant strain rate experiments was performed on a vacuum-dried, high-purity, fine-grained clinopyroxenite using NaCl and NaF as confining media in a Griggs-type piston-cylinder apparatus.
Abstract: A systematic suite of constant strain rate experiments was performed on a vacuum-dried, high-purity, fine-grained clinopyroxenite using NaCl and NaF as confining media in a Griggs-type piston-cylinder apparatus. The experiments were carried out over a range of temperatures from 400° to 1100°C, strain rates from 10−3 to 10−7 s−1, and confining pressures from 170 to 1990 MPa. At T = 600°C and e˙ = 1.1 × 10−5 s−1, three modes of deformation occur with increasing confining pressure: (1) Macroscopic faulting associated with low strength and stress drops, (2) stable microfracturing and plastic deformation associated with pressure-dependent strength, and (3) plastic deformation (mechanical twinning and 〈001〉 slip) with high strengths which are insensitive to pressure variations. In experiments at P = 1500 MPa, within this high-pressure plastic mode, two regimes of flow are clearly defined. At low to intermediate temperatures and high strain rates, flow strengths are insensitive to changes in strain rate and temperature. Optical and transmission electron microscope observations indicate that plastic strain is accomplished by mechanical twinning on (100) and (001) and by {100}〈001〉 slip. In contrast, at high temperatures and low strain rates the flow stress is strongly dependent on temperature and strain rate. Specimens deformed in this regime show evidence of recovery, multiple slip, and recrystallization; and plastic strain is much more homogeneous. The flow data within each regime can be satisfactorily fit to thermally activated power laws. In the low-temperature regime n (the stress exponent) = 83 ± 16 and E* (the activation energy for flow) = 220 ± 40 kJ/mol. We believe that these parameters reflect flow dominated by the kinetics of dislocation glide associated with mechanical twinning and (100)〈001〉 slip. In the high-temperature regime, n = 5.3 ± 1.1 and E* = 380 ± 30 kJ/mol. These parameters describe creep by multiple slip accompanied by increased rates of diffusion and recovery.
152 citations
TL;DR: In this paper, it was shown that in large deformation generalized plasticity, a local maximum-dissipation postulate is equivalent to the condition that the plastic strain rate cannot oppose the total strain rate, when strain space is regarded as a Riemannian manifold.
Abstract: It is shown that in large-deformation generalized plasticity a local maximum-dissipation postulate is equivalent to the condition that the plastic strain rate (in the sense of Rice) cannot oppose the total strain rate, when strain space is regarded as a Riemannian manifold with the instantaneous Lagrangian tangent elastic stiffness as the metric tensor. From this condition, normality conditions in strain space (in this sense) and in the space of the second Piola-Kirchhoff stress (in the usual sense) are derived. With the additive decomposition of strain, the loading surface has essentially the same properties as in infinitesimal-strain plasticity. For the multiplicative decomposition, approximate normality rules are derived.
TL;DR: In this paper, the authors show that fine-grained ceramics are capable of high rates of deformation at quite low stresses (1 to 20 MPa) at high deformation rates, and that microstructural changes can occur during deformation which influence the flow behavior.
Abstract: Several results pertaining to large deformations at fast strain rates in a fine-grained ceramic material are described. Results for strain-rate, grain size, and temperature dependence of the flow stress are presented. They show that (a) ultrafine-grained ceramics are capable of high rates of deformation (about 10−4 to 10−4 s−1) at quite low stresses (1 to 20 MPa); (b) the mechanism of deformation is the enhanced rate of matter transport through the liquid phase segregated in the grain boundaries; (c) either uniaxial compression or tension tests may be used to determine the flow properties, except that a correction must be implemented for friction in the case of compression tests; and (d) microstructural changes can occur during deformation which influence the flow behavior. The ceramic is almost infinitely ductile in compression, whereas in tension elongations as large as W5% in one material, and more than 400% in another, were obtained. A model material, β-spodumene glass-ceramic, was used for this study but the results are likely to hold for other materials with equivalent microstructures, e.g., liquid-phase-sintered or hot-pressed materials such as the nitrogen ceramics
TL;DR: In this paper, a series of laboratory-prepared ice samples were used for compression tests and it was found that, between 0.8% and 8% octahedral shear strain, a small circle girdle fabric developed around the compression axis, and that the strength of the fabric increased along with a decrease in the half-angle.
TL;DR: In this paper, the authors performed uniaxial compression tests on laboratory-made polycrystalline ice samples with randomly oriented grains and found that a minimum strain rate occurs after a time determined by a straight line locus, and at a total octahedral strain of about 0.6%.
TL;DR: In this article, the authors considered the shear wave propagation in a half-space of a nonlinear material, where the surface of the halfspace is subjected to a time dependent but spatially uniform tangential velocity.
Abstract: O ne-dimensional shear wave propagation in a half-space of a nonlinear material is considered. The surface of the half-space is subjected to a time dependent but spatially uniform tangential velocity. The half-space material exhibits strain hardening, thermal softening and strain rate sensitivity of the flow stress. For this system, a well-defined band of intense shear deformation can develop adjacent to the loaded surface, even though the material has no imperfections or other natural length scale. Representative particle velocity and strain profiles, which have been obtained numerically, are described for several different models.
TL;DR: In this article, a silicon carbide whisker-reinforced aluminum alloy (20% SiC fibers in 2024 aluminum) is shown to exhibit tensile ductilities in the order of 300% when deformed under thermal cycling conditions (100 ⇇ 450° C ) and at low stresses ( σ ⋍ 20 MPa ).
TL;DR: In this paper, the effective viscosity tensor of an array of spheres centered on the points of a periodic lattice in an incompressible Newtonian fluid is determined, and an integral equation for the traction is derived.
Abstract: : The effective viscosity of a suspension is defined to be the four-tensor which relates the average deviatoric stress to the average rate of strain. The effective viscosity of an array of spheres centered on the points of a periodic lattice in an incompressible Newtonian fluid is determined. The formulation involves the traction exerted on a single sphere by the fluid, and an integral equation for the traction is derived. For lattices with cubic symmetry the effective viscosity tensor involves just two parameters. These are computed numerically for simple, body-centered and face-centered cubic lattices of spheres with solute concentrations up to 90% of the close-packing concentration. Asymptotic results for high concentrations are obtained for arbitrary lattice geometries, and found to be in good agreement with the numerical results for cubic lattices. The low concentration asymptotic expansions of Zuzovsky also agree well with the numerical results. (Author)
TL;DR: In this article, the effect of strain hardening on the flow behavior of superplastic copper alloy Coronze 638 has been analyzed and it was shown that grain growth at low strain rates causes sufficient hardening to compensate for the low strain rate sensitivity, thus preventing the development of sharp necks.
TL;DR: In this article, the dynamics of vortices subject to stretching by a uniform plane straining flow is studied asymptotically and by means of a new class of exact solutions.
Abstract: The dynamics of vortices subject to stretching by a uniform plane straining flow is studied asymptotically and by means of a new class of exact solutions. The asymptotic analysis treats the stretched Burger's vortex sheet for strain rates much greater than the gradient of the sheet strength. It is found that portions of the sheet where the strength density is sufficiently large compared to (viscosity x strain rate)½ will collapse to form concentrated vortices. The exact solutions describe uniform vortices of elliptical cross-section in inviscid fluid subject to stretching parallel to their axes. These solutions complement the description of vortex collapse found by asymptotic methods. The relevance of these results stems from the prevalence of vortex structures subject to strain in turbulent flows.
TL;DR: The AA 5083 alloy was deformed in torsion in the ranges 300-500°C and 1-1 S−1 to a strain of 5 as discussed by the authors The flow stress as a function of strain rose to a maximum value then gradually decreased towards a steady state and had a dependence on temperature and strain rate.
Abstract: The AA 5083 alloy was deformed in torsion in the ranges 300–500°C and 01–1 S−1 to a strain of 5 The flow stress as a function of strain rose to a maximum value then gradually decreased towards a steady state and had a dependence on temperature and strain rate of the traditional form with an activation energy higher than that for pure Al Optical microstructures of specimens quenched after working ranged from elongated grains at 300°C to recrystallized grains at 500°C Transmission electron microscope subgrain structures from all conditions of working were more recovered at higher temperatures and lower strain rates The subgrain diameters are smaller than those in commercial Al mainly as a result of the increased density of particles and this is in agreement with observations in extrusions Since the degree of recovery is not substantially less than in commercial Al, one is led to confirm the theory that the dynamic recrystallization is caused by particles of <06 μm
TL;DR: In this paper, the authors derived a specific internal state variable constitutive law relating uniaxial stress to crack density and crack propagation rate, which is based on the instantaneous crack extension force.
Abstract: Quasi-static propagation and dilation of macroscopic mode I cracks is considered as a source of inelastic strain in crustal rocks undergoing extensional deformations. The approach here is to first characterize the propagation of a single dilating crack and then to consider how a large two-dimensional array of similar, parallel cracks accomodates an applied deformation. The driving force for propagation of each crack, Gi, is found as a function of the applied strain and the instantaneous crack lengths ci. The rate of crack propagation is taken to be a function of the instantaneous crack extension force ċi = ċ (Gi). A specific propagation rate extension force relation is developed that both fits the available experimental data and has vanishing propagation rate at a finite value of G. From these results a specific internal state variable constitutive law is derived relating uniaxial stress to the instantaneous uniaxial strain and crack density. For strains less than those necessary to cause crack propagation, the rock is predicted to behave like a linear elastic solid. Following the onset of propagation, the average stress may continue to increase if the strain rate accommodated by crack growth is slow in comparison to the applied strain rate. For constant strain rate boundary conditions the solutions exhibit strain softening, leading to peak stress and then a stress decrease. The peak stress increases nearly logarithmically with increasing applied strain rate. The response to unloading depends strongly on whether or not cracks heal. Unloading that follows sealing of the cracks with mineral precipitates causes the rock to undergo a permanent nonrecoverable strain.
TL;DR: In this paper, compressive strength tests were conducted on remolded, saturated Fairbanks frozen silt under various constant machine speeds, temperatures and dry densities, and it was found that the initial yield strength σy consistently increases with decreasing dry unit weight.
TL;DR: In this article, the evolution of the structure and local effective stresses with strain has been identified by electron microscopy by pinning the dislocations under load in an Al-Zn alloy.
TL;DR: In this article, three sets of uniaxial compression experiments on polycrystalline ice are described, and it is concluded that tertiary ice flow may limit crystal growth to an equilibrium size.
TL;DR: In this paper, a new impact-tension-compression testing technique based on a one-dimensional elastic-stress-wave theory has been developed, which is applied to investigate dynamic response in pure iron.
Abstract: A new impact-tension-compression testing technique based on a one-dimensional elastic-stress-wave theory has been developed. The technique was applied to investigate dynamic response in pure iron. The experimental results of the loading wave agreed well with the theoretical prediction. The stress, strain, and strain rate of a specimen during impact were evaluated with the aid of a stress-wave analysis. A new experimental technique has been developed to investigate the dynamic-hysteresis loop and the dynamic Baushinger effect in materials. It is presently being developed for applications to dynamic-fatigue studies.
TL;DR: In this paper, a time and temperature dependent plasticity model is formulated in a Lagrangian system to describe finite deformation, where history dependence and large strain behavior are incorporated through the introduction of one tensor internal variable.
TL;DR: The ductile-brittle transition of polypropylene and rubber-modified polypropylenes is strongly affected by both temperature and strain rate, and the competition between crazing and shear yielding dictates the subsequent failure mode as mentioned in this paper.
Abstract: Tensile experiments on polypropylene and various rubber-modified polypropylenes, conducted over a wide range of temperatures and strain rates, have shown that the ductile–brittle transition in these highly crystalline polymers is strongly affected by both temperature and strain rate. Such polymers can either craze or shear yield, depending on the temperature and rate of test. High temperatures and low strain rates favor shear yielding, while low temperatures and high strain rates promote crazing. The ductile–brittle transition of these polymers may be understood as due to an alteration in deformation mode, as proposed by Matsushige et al. The competition between crazing and shear yielding dictates the subsequent failure mode. The dependence of the ductile–brittle transition on the test and material parameters (such as temperature, strain rate, pressure, orientation, notching, and plasticizer) may be ascribed to the respective influences of these parameters on crazing relative to shear yielding.
TL;DR: In this paper, it was shown that the size and orientation of an imperfection is critical in determining whether or not localized necking is initiated along the imperfection, and the influence of strain hardening, strain rate hardening and plastic anisotropy on the occurrence of local necking of imperfect sheet is also examined.
Abstract: Localized necking in sheet metal has been examined for strain paths between uniaxial tension and plane strain (ie, the negative minor strain region of a forming limit diagram) The behavior of sheet with preexisting imperfections has been analyzed and is contrasted to that free of imperfections In particular, it is shown that the size and orientation of an imperfection is critical in determining whether or not localized necking is initiated along the imperfection The influence of strain hardening, strain rate hardening, and plastic anisotropy on localized necking of an imperfect sheet is also examined One of the most significant conclusions obtained from present analysis and from a reexamination of Hill’s theory is the prediction of a critical thickness strain criterion for the onset of localized necking at negative minor strains, regardless of whether or not an imperfection is present The critical thickness strain criterion is observed in Ti alloys, Al alloys, steels, and brass
TL;DR: In this paper, cyclically strained polycrystalline copper was cyclically strained at constant total strain amplitudes and a constant strain rate up to fracture, and cyclic hardening softening curves and the cyclic stress-strain curve were measured.
TL;DR: In this paper, a quantitative study of cavitation damage and fracture of a superplastic copper alloy, Coronze 638, has been made, where cavities are found to nucleate at large particles present in the form of stringers.