Showing papers on "Strain rate published in 1991"
TL;DR: In this paper, the flow behavior of steels during deformation in the roll gap was simulated by means of single hit compression tests performed in the temperature range 800 °C to 1200 °C.
Abstract: The flow behavior of steels during deformation in the roll gap was simulated by means of single hit compression tests performed in the temperature range 800 °C to 1200 °C. Strain rates of 0.2 to 50 s−1 were employed on selected low-carbon steels containing various combinations of niobium, boron, and copper. The stress/strain curves determined at the higher strain rates were corrected for deformation heating so that constitutive equations pertaining to idealized isothermal conditions could be formulated. When dynamic recovery is the only softening mechanism, these involve a rate equation, consisting of a hyperbolic sine law, and an evolution equation with one internal variable, the latter being the dislocation density. When dynamic recrystallization takes place, the incorporation of the fractional softening by dynamic recrystallization in the evolution equation makes it possible to predict the flow stress after the peak. These expressions can be employed in computer models for on-line gage control during hot-rolling.
455 citations
TL;DR: In this paper, the authors investigated the effect of orthopyroxene activity and loading orientation on the creep behavior of San Carlos olivine in controlled chemical environments at a total pressure of 0.1 MPa.
Abstract: To investigate the rheological behavior of the Earth's upper mantle, over 100 high-temperature deformation experiments have been performed on single crystals of San Carlos olivine in controlled chemical environments at a total pressure of 0.1 MPa. Constitutive equations have been determined which describe the dependence of creep rate on applied stress, temperature and oxygen fugacity in terms of power law relations. In addition, the effects of orthopyroxene activity and loading orientation on the creep behavior have been investigated. For samples of each of three compression directions, [101]c, [011]c and [110]c, buffered by orthopyroxene or magnesiowustite, either two or three power law equations are required to describe the dependence of strain rate at fixed stress on temperature and oxygen fugacity over the full range of experimental conditions. It is proposed that in each power law regime a different creep mechanism controls the creep rate. For all of the experimental conditions, the activation energy for creep is independent of the stress level and the stress exponent is constant at 3.5±0.1. Activation energies for the various creep mechanisms varied from 230 to 1000 kJ/mol; and oxygen fugacity exponents lie in the range −0.03 to 0.4. From the constitutive equations determined based on the power law equations for all of the creep mechanisms, e˙-T-fo2 deformation maps were constructed at a stress of 1 MPa for olivine.
281 citations
TL;DR: In this paper, the extinction limits of methane-air flames at different equivalence ratios in the stationary case were derived for different levels of methane oxidation chemistry and the influence of temporally periodical change of the strain rate on the flame front behavior.
238 citations
TL;DR: In this article, an incompressible finite element model was used to study the plane strain deformation of two-phase aggregates deformed by dislocation creep, where the model calculated the overall flow law of the aggregate as well as the stress and strain rate variations within it.
Abstract: An incompressible finite element model has been used to study the plane strain deformation of two-phase aggregates deformed by dislocation creep. Input for the model includes the power law flow laws of the two end-member phases and their volume fractions and configuration. The model calculates the overall flow law of the aggregate as well as the stress and strain rate variations within it. The input flow laws were experimentally determined for monomineralic aggregates of clinopyroxene and plagioclase. Results were calculated for a temperature of 1000°C, strain rates from 10−4 to 10−12S−1, and stresses of 1–1000 MPa. For these conditions, the end-member flow laws intersect on a log stress versus log strain rate plot at 10−8S−1. Some runs were made on finite element grids fit to an actual diabase texture (∼64% pyroxene, ∼ 36% plagioclase.) Other runs were made on idealized geometries to test the effects of varying the volume fraction of two phases, shape of inclusions, and relative strengths of inclusion and matrix. Important results include the following: (1) The model results satisfy the requirement that the aggregate strength must lie between the bounds set by the end-member flow laws and those set by assumptions of uniform stress and uniform strain rate. (2) The calculated diabase flow law matches well with that experimentally determined. (3) The aggregate strength within the uniform stress and uniform strain rate bounds is primarily affected by volume fraction, although certain phase geometries can also affect the strength. (4) Although the flow law for an aggregate of power law phases need not be a simple power law, we find it to be a good approximation. We have developed two simple methods of estimating the strength of an aggregate, given the end-member flow law parameters and volume fractions; both give results that agree with the finite element model calculations. (1) One method takes into account the phase geometry and gives a strength for the aggregate at any strain rate. (2) The other method can be used even if the phase geometry is unknown and gives expressions for the aggregate flow law parameters.
229 citations
01 Jan 1991
TL;DR: In this article, the extinction conditions for an opposed-flow nozzle-type burner system are calculated by a numerical integration, and the results explain differences found by different investigators on influences of dilution on extinction strain rates and show that most counterflow burners are closer to the plug flow limit than to the potential flow limit.
Abstract: Velocity fields, and extinction conditions for methane-air diffusion flames are measured for an opposed-flow nozzle-type burner system and calculated by a numerical-integration, routine for pressures from 0.25 to 2.5 atm and for dilutions having fixed stoichiometric mixture fractions with oxidizer-stream oxygen mass fractions from 0.233 to 0.190. Imposition of boundary conditions ranging from potential flow to plug flow reveals that changes on the order of a factor of two in the oxidizer-side strain rate at extinction can be produced by changes in opposed-flow burner design. It is shown that the maximum velocity gradient, however which occurs on the fuel side of the main reaction zone, achieves a value at extinction that is relatively insensitive to the boundary conditions of the flow. The results explain differences found by different investigators on influences of dilution on extinction strain rates and show that most counterflow burners are closer to the plug-flow limit than to the potential-flow limit. Strain rates at extinction without dilution are shown to increase with increasing pressure over the above-stated range, countrary to previously observed behaviors with dilution or at very high pressures. This behavior is explained as a consequence of decreasing peak radical concentration with increasing pressure.
226 citations
210 citations
TL;DR: The variation of strength and stiffness was explained equally well by the linear, power function and quadratic relationship to apparent density, and the cubic relationship between stiffness and apparent density showed a less good fit.
181 citations
TL;DR: In this paper, double-hit compression tests were performed on low-carbon steels containing various combinations of niobium, boron, and copper over a wide range of temperatures and strain rates pertinent to hot rolling.
Abstract: Double-hit compression tests were performed on low-carbon steels containing various combinations of niobium, boron, and copper over a wide range of temperatures and strain rates pertinent to hot rolling. The kinetics of static recrystallization are characterized in terms of the mean flow stresses, which lead to more accurate results than alternative methods. The fractional softening defined by the mean flow stress method was first corrected for adiabatic heating using a simple procedure. Appropriate expressions are given for the recrystallization kinetics as a function of predeformation, temperature, and strain rate. Particular attention is paid to the effect of preloading strain rate on recrystallization kinetics. It is shown that there is a one order of magnitude increase in softening rate when the strain rate is increased by two orders of magnitude. Thus, Simple extrapolations of laboratory data determined at conventional strain rates to high-speed mill conditions are likely to be inaccurate.
161 citations
01 Jan 1991
TL;DR: In this article, the one-dimensional Navier-Stokes equations were compared with the Hiemenz potential flow formulation, and it was shown that the Navier Stokes equations reduce to expressions for (i) the pressure gradient profile normal to the flame and (ii) the strain rate profile in the variable density system.
Abstract: The one-dimensional formulation of the opposed flow strained flame problem, starting from the cylindrical Navier-Stokes equations, is described and compared with the older, Hiemenz potential flow formulation. The eigenvalue in the newer formulation is shown to be a stress on the fluid, and it is shown that the Navier-Stokes equations reduce to expressions for (i) the pressure gradient profile normal to the flame, and (ii) the strain rate profile in the variable density system. The basic features of hydrogen and hydrocarbon flame chemistry are reviewed, and the importance of the temperature T i at which the system becomes effectively chain branching is demonstrated in the context of flame extinction. It is suggested that in a sense T i fulfils the function of an ignition temperature. The responses of flames to applied stresses are discussed for diffusion flames, and for premixed flames in both the symmetric back-to-back and the asymmetric unburnt-to-burnt configurations. It is shown that, in opposed flow systems of fixed geometry and finite dimensions, the behaviour of the symmetric back-to-back flames which are not too close to the inlet nozzles are for practical purposes characterized entirely by the applied stress. However, because of viscous effects, particularly near the nozzles, this applied stress cannot be measured directly with precision. Repercussions on extinction limit measurements, and on indirect determinations of one-dimensional burning velocities, are indicated. The use of measurements on expanding spherical flames for the determination of burning velocity is briefly discussed, as also are the effects of flow configuration on the stress and strain rate profiles at extinction.
144 citations
135 citations
TL;DR: In this article, the effect of strain rate on strength has been evaluated for two widely different rock types, a brittle limestone (Tyndallstone) and a ductile salt rock (Lanigan potash rock).
Abstract: The effect of the strain rate on strength has been evaluated for two widely different rock types, a brittle limestone (Tyndallstone) and a ductile salt rock (Lanigan potash rock). Results of static and dynamic fatigue tests on Tyndallstone, a dolomitic limestone, show an increase in strength with increasing strain or stressing rate although the rate effect is very small. Although the static and dynamic fatigue tests are expected to yield the same stress corrosion parameter, no such agreement has been observed. Dynamic fatigue tests of the more ductile salt rock showed a substantial rate effect. The usual strength criteria, that consider the influence of confining pressure alone, are no longer adequate to describe the strength of Lanigan potash. A general strength criterion, that incorporates the effect of both the confining pressure and the strain rate, is proposed.
TL;DR: In this article, the authors investigate the behavior during compaction under diagenetic conditions and evaluate the importance of stress-induced solution transfer (9pressure solution9) as a compaction mechanism.
Abstract: Experiments have been carried out on dry and fluid-saturated quartz sands to investigate the behaviour during compaction under diagenetic conditions and to evaluate the importance of stress-induced solution transfer (9pressure solution9) as a compaction mechanism. The experiments were performed at temperatures ( T ) in the range 150–350°C, applied effective stresses (σ e ) up to 20.7 MPa and pore fluid pressures (P 1 ) of 12.5 and 15.5 MPa, using material with a grain size ( d ) in the range 20–100 μm and an initial porosity of 45–52%. Dry quartz sands underwent significant compaction during the loading stage, but showed very little compaction creep once full load was achieved (i.e. essentially time-independent compaction). In contrast, fluid-saturated material at constant applied effective stress showed substantial time-dependent compaction (i.e. creep). With increasing temperature, there is a decreasing number of grains in the wet-compacted sand which show intragranular cracks and an increasing number of grains which show dissolution features at contacts with adjacent grains. In addition, there is a decreasing dependence of the volumetric strain rate, β on σ e , with both increasing volumetric strain (e v ) and increasing σ e and a decreasing dependence of β on e v with increasing temperature. These observations suggest that, for wet quartz sand, a gradual change might occur from compaction creep controlled by time-dependent microcracking, at T = 250–300 °C, to compaction creep controlled by stress-induced intergranular solution transfer at T = 300–350 °C.
TL;DR: In this article, a strain-controlled low cycle fatigue tests have been conducted in air between 298-873 K to ascertain the influence of temperature on LCF behavior of nitrogen-alloyed type 316L stainless steel.
TL;DR: In this paper, the effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) were examined, and it was shown that even a strain rate as small as 0.25 suppresses the Rayleigh shear instability mechanism, in the sense that the r.m. wave steepness cannot amplify by more than a certain factor, and must eventually decay.
Abstract: The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ < 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ e 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows.
TL;DR: In this paper, the initial and subsequent yield surfaces of annealed AISI type 304 stainless steel have been experimentally determined in the axial-torsional stress space.
TL;DR: In this paper, the authors developed models for elastic-plastic, rate-independent materials with power-law strain hardening and considered the material as incompressible and compressible.
Abstract: We developed models for elastic-plastic, rate-independent materials with power-law strain hardening. The models considered the material as incompressible and compressible
TL;DR: In this article, a detailed study of metal structures absorb energy by gross distortion under impact conditions depends on the generic type of structure, and the analysis reveals clearly the roles of inertia and strain rate in impact conditions.
TL;DR: In this paper, experimental results on the deformation and failure of clamped beams, made from aluminium alloy or mild steel and struck by a mass, are reported, complete engineering and true stress-strain curves at strain rates up to 140 s -1 are presented for the materials.
TL;DR: In this article, a phenomenological constitutive equation for homogeneous suspensions of macrosized fibres is proposed, where the local averaged orientation of the fibres are represented by a director field, which evolves in time in a manner similar to the rotation of a prolate spheroid.
Abstract: A new phenomenological constitutive equation for homogeneous suspensions of macrosized fibres is proposed. In the model, the local averaged orientation of the fibres is represented by a director field, which evolves in time in a manner similar to the rotation of a prolate spheroid. The stress is linear in the strain rate, but the viscosity is a fourth-order tensor that is directly related to the director field. In the limit of low-volume fractions of fibres, the model reduces properly to the leading terms of the constitutive equation for dilute suspensions of spheroids. The model has three parameters: the aspect ratio R of the fibres, the volume fraction Φ, and A, which plays the role of the maximum-volume fraction of the fibres. Experimental shear data are used to estimate the parameter A, and the resulting model is used in a boundary-element program to study the flow past a sphere placed at the centre line of a cylinder for the whole range of volume fractions from 0.01 to near maximum volume fraction. The agreement with experimental data from Milliken et al. [1] is good.
15 May 1991-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this article, a simple classification of plastic instabilities and the instability conditions are given in terms of phenomenological parameters, such as the strain-hardening rate h, the strain rate sensitivity S of flow stress and the derivative ϕ of stress with respect to temperature.
Abstract: A simple classification of plastic instabilities and the instability conditions are given in terms of phenomenological parameters, such as the strain-hardening rate h, the strain rate sensitivity S of flow stress and the derivative ϕ of stress with respect to temperature. The type S instabilities associated with negative values of the strain rate sensitivity resulting from dynamic strain aging are discussed in some detail. The emphasis is on recent results pertaining to critical strains for the occurrence of the Portevin-Le Chatelier effect. A successful theoretical description of the critical strains in terms of a model based on the evolutionary kinetics of mobile and forest dislocation densities is presented. A delay of the onset of discontinuous yielding to strains where the relaxed strain rate sensitivity, as introduced by McCormick, is sufficiently negative is also discussed. Finally, the consequences of the interaction of material elements by dislocation cross-slip for stability conditions are dealt with. A numerical exercise illustrating propagative deformation behaviour is demonstrated.
TL;DR: In this article, a detailed microstructural investigation of the superplastically deformed specimens reveals the occurrence of extensive concurrent grain growth and internal cavitation, which is an important factor influencing the total elongation to failure obtained in superplastic materials.
Abstract: A fine-grained yttria stabilized tetragonal zirconia exhibits an optimum superplastic elongation to failure of ∼ 700% at 1823 K and a strain rate of 8.3 × 10−5s−1. A detailed microstructural investigation of the superplastically deformed specimens reveals the occurrence of extensive concurrent grain growth and internal cavitation. An expression is developed to characterize the extent of deformation enhanced concurrent grain growth, as influenced by experimental factors such as true strain, strain rate and temperature. The variation in the level of concurrent cavitation with strain rate conforms closely to the variation in elongation to failure with strain rate. It is demonstrated that the tendency towards cavity interlinkage in a direction perpendicular to the tensile axis is an important factor influencing the total elongation to failure obtained in superplastic materials.
TL;DR: In this article, the authors describe a dynamic indentation (DI) technique suitable for the determination of the high strain rate flow behavior of ductile metals and alloys and illustrate its use by characterizing the high-strain rate flow behaviour of iron and OFHC copper.
Abstract: The objective of the paper is to describe a dynamic indentation (DI) technique suitable for the determination of the high strain rate flow behaviour of ductile metals and alloys and illustrate its use by characterizing the high strain rate flow behaviour of iron and OFHC copper. The DI technique is first described in detail and the dynamic hardness-strain data of iron and copper obtained using the technique is presented. It is also demonstrated that it is a suitable technique for characterizing the high strain rate flow behaviour as long as certain validity conditions are met. It is shown that these validity conditions are fully met in the case of copper and at low strain levels in iron. The reliability of the DI technique is finally demonstrated by comparing the present data with the literature data on similar materials and finally a critique of the DI technique is provided.
TL;DR: In this article, a generalized piezoelectric strain rate gage was proposed to measure an average strain rate at a point of a structure, by combining the effective surface electrode, appropriate skew angle and the correct polarization profile.
Abstract: Piezoelectric strain rate gages have been designed using linear piezoelectric theory and relatively simple circuitry that can be used to measure an average strain rate at a point of a structure. By combining the effective surface electrode, appropriate skew angle and the correct polarization profile, a uniaxial strain rate gage that measures only the strain rate along a specified direction and a pure shear strain rate gage that measures the in‐plane shear strain rate are developed. Experimental as well as theoretical results are presented. Various types of generalized piezoelectric strain rate gages are also introduced and discussed.
TL;DR: In this article, the kinetics of viscous sintering are determined for models consisting of cylinders intersecting so as to form cells with cubic, tetrahedral, and octahedral shapes.
Abstract: The kinetics of viscous sintering are determined for models consisting of cylinders intersecting so as to form cells with cubic, tetrahedral, and octahedral shapes. These models are shown to be quite resistant to Rayleigh instabilities, and to densify at similar rates. The constitutive parameters (free strain rate, uniaxial viscosity, and Poisson's ratio) are presented for all of the models.
TL;DR: In this paper, constant true strain tests were carried out over a wide strain-rate range from 0.0001 to 100/s at an optimum superplasticity temperature of 833 K in air.
Abstract: The study deals with constant true strain tests carried out over a wide strain-rate range from 0.0001 to 100/s at an optimum superplasticity temperature of 833 K in air. The tensile axis is selected to be parallel to an extrusion direction for all tests, and the flow stress for each strain rate is determined at a fixed small true strain. The microstructural morphology of composites is discussed as well as the flow stress behavior and elongation. A high-strain-rate superplasticity is found in an as-extruded 20-vol-pct Si3N4/6061 aluminum composite; the maximum elongation of 620 pct is recorded at a strain rate of 2/s. 13 refs.
15 Nov 1991-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this paper, the ability of a whisker-reinforced composite to undergo high-strain-rate superplasticity depends upon the morphology, crystal structure and chemistry of the whiskers, as well as on the chemical composition at the whiskermatrix interfaces.
Abstract: Superplasticity has been observed in several whisker-reinforced aluminum composites at extremely high strain rates of approximately 0.1–1 s−1. These composites include β-SiC-2124Al, β-Si3N4-2124Al, α-Si3N4-7064Al and β-Si3N4-6061Al. The materials generally exhibited a strain rate sensitivity value of about 0.3 and a maximum elongation of about 300%. The exact deformation mechanism leading to superplasticity is apparently a unique one. Experimental results indicated that the ability of a whisker-reinforced composite to undergo high-strain-rate superplasticity depends upon the morphology, crystal structure and chemistry of the whiskers, as well as on the chemical composition at the whisker-matrix interfaces. It is proposed that the presence of a low melting point region, or in some cases a liquid phase, at the whisker-matrix interfaces is responsible for the observed phenomenon of superplasticity at very high rates. These regions are present at the deformation temperature as a result of solute segregation. It is noted that the phenomenon is not observed in all whisker-reinforced composites despite tha fact that they contain fine grain sizes. Thus a fine matrix grain size is a necessary but insufficient condition for the observation of high-strain-rate superplasticity in whisker-reinforced composites.
TL;DR: In this paper, the effects of increasing strain rate on the tensile strength of concrete were investigated using a split-Hopkinson pressure bar (SHPB) and finite element method (FEM) analysis.
TL;DR: In this article, superplastic deformation of alumina ceramics was studied at 1400° to 1450°C and at a strain rate of 4 × 10−5 to 5 × 10 −4 s−1.
Abstract: Superplastic deformation of alumina ceramics was studied at 1400° to 1450°C and at a strain rate of 4 × 10−5 to 5 × 10−4 s−1. MgO and ZrO2 were introduced to suppress dynamic grain growth. The latter was especially effective; grain growth was minimal in 10-vol%-ZrO2-containing material. Both materials were superplastically stretched under biaxial tension to 100% engineering strain with good surface finishing, demonstrating the feasibility of superplastic forming for alumina ceramics.
TL;DR: In this article, the authors modeled the strain and strain rate transients which accompany small perturbations from steady state deformation in the regime of dynamic strain ageing and developed a transient behaviour map which shows the transient behaviour as a function of the strain rate sensitivity of flow stress and the machine stiffness.
Abstract: Stress and strain rate transients which accompany small perturbations from steady state deformation in the regime of dynamic strain ageing are modelled. The constitutive relation employed includes the local solute concentration at arrested mobile dislocations as a time dependent state variable. Using linear perturbation theory it is shown that four types of transient behaviour are possible: monotonic decay, oscillatory decay, oscillatory growth and monotonic growth of the perturbation. A transient behaviour map is developed which shows the transient behaviour as a function of the strain rate sensitivity of flow stress and the machine stiffness. The results of the analysis are compared with recent experimental measurements of transient yield behaviour associated with dynamic strain ageing.
TL;DR: In this paper, the dynamic stress-strain behavior of an electrorheological (ER) fluid was studied using a Rheometric Mechanical Spectrometer with a specially fabricated high voltage, parallel plate cell.
Abstract: The dynamic stress‐strain behavior of an electrorheological (ER) fluid was studied using a Rheometric Mechanical Spectrometer with a specially fabricated high voltage, parallel plate cell. With this apparatus, dynamic properties were determined as a function of the applied field, strain, volume fraction, and oscillation frequency. The experimental technique is rapid and represents a convenient way of obtaining dynamical information of ER fluids. The ER fluid used in the study consists of the hydrated lithium salt of poly(methylacrylate) dispersed in a chlorinated paraffin oil. When an electric field is applied, the suspension behaves elastically at low strains and undergoes plastic deformation at high strain, which is characterized by field‐dependent yield stress. This ER fluid behaves like an elastic Bingham fluid.