Showing papers on "Strain rate published in 1995"

Experimental constraints on the dynamics of the partially molten upper mantle: Deformation in the diffusion creep regime

Abstract: Experiments have been conducted to investigate the effect of melt on the creep behavior of water-free olivine aggregates deformed in the dislocation creep regime. The influence of the melt phase is modest at melt fractions less than ∼0.04. However, at melt fractions > 0.04, the creep rate of melt-added samples is enhanced by more than an order of magnitude relative to melt-free aggregates. This unexpectedly large influence of melt on strain rate arises because deformation occurs by grain boundary sliding (GBS) accommodated by a dislocation creep process. Four observations support this hypothesis. (1) The strain rate enhancement observed in the dislocation creep regime can be related to the stress concentration caused by the reduction in the solid-solid grain boundary area. (2) Both melt-free and melt-added samples exhibit strain rates indicating that deformation is limited by slip on (010)[100], the easiest slip system in olivine. (3) The GBS mechanism occurs near the transition between diffusion and dislocation creep. (4) Grains in specimens deformed in the GBS regime are not significantly flattened, even after ∼50% shortening. In melt-free aggregates, a transition from the GBS mechanism to dislocation creep limited by slip on (010)[001], the hardest slip system, is observed with an increase in grain size. A transition to (010)[001] limited creep was not observed for partially molten aggregates because grain growth was inhibited by the presence of melt. The results of this study indicate that the viscosity of the upper mantle may decrease by at least an order of magnitude if the retained melt fraction exceeds 0.04 or if the onset of melting results in a reduction in grain size and a concomitant transition from (010)[001] to (010)[100] limited creep.

Mechanotransduction in bone : role of strain rate

Abstract: Bone tissue can detect and respond to its mechanical environment, but there is no consensus for how bone cells detect mechanical loads. Some think that cells sense tissue deformation (strain) and respond when strain is abnormally high. However, strains in bone tissue are usually very small, and it is questionable whether bone cells are sensitive enough to detect them. Another theory suggests that mechanical loads are coupled to the bone cells by stress-generated fluid flow within the bone tissue, which is dependent on the rate of change of bone strain. We applied bending loads to the tibiae of adult rats to create equivalent peak strains in the bone tissue but with varied rates of strain. Bone formation was significantly increased in the two experimental groups when the highest strain rates were compared with lower strain rates (P < 0.01), and the amount of new bone formation was directly proportional to the rate of strain in the bone tissue. These results suggest that relatively large strains alone are not sufficient to activate bone cells. High strain rates and possibly stress-generated fluid flow are required to stimulate new bone formation.

The effect of grain size on the high-strain, high-strain-rate behavior of copper

Abstract: Copper with four widely differing grain sizes was subjected to high-strain-rate plastic deformation in a special experimental arrangement in which high shear strains of approximately 2 to 7 were generated. The adiabatic plastic deformation produced temperature rises in excess of 300 K, creating conditions favorable for dynamic recrystallization, with an attendant change in the mechanical response. Preshocking of the specimens to an amplitude of 50 GPa generated a high dislocation density; twinning was highly dependent on grain size, being profuse for the 117- and 315-μm grain-size specimens and virtually absent for the 9.5-μm grain-size specimens. This has a profound effect on the subsequent mechanical response of the specimens, with the smaller grain-size material undergoing considerably more hardening than the larger grain-size material. A rationale is proposed which leads to a prediction of the shock threshold stress for twinning as a function of grain size. The strain required for localization of plastic deformation was dependent on the combined grain size/shockinduced microstructure, with the large grain-size specimens localizing more readily. The experimental results obtained are rationalized in terms of dynamic recrystallization, and a constitutive equation is applied to the experimental results; it correctly predicts the earlier onset of localization for the large grain-size specimens. It is suggested that the grain-size dependence of shock response can significantly affect the performance of shaped charges.

Fracture simulations using large-scale molecular dynamics

Abstract: We report on recent molecular-dynamics (MD) fracture simulations of mode-I tensile loading at high strain rates. Because cracks emit sound waves, previous simulations became unreliable beyond one sound traversal time. Using massively parallel MD, we show how to eliminate unwanted boundary effects and study unimpeded crack propagation mechanisms. In order to represent tensile stress conditions near the crack tip, we employ uniaxial, homogeneously expanding periodic boundary conditions, examining the effects of strain rate, temperature, and interaction potential. Because our samples are sufficiently large, we see dislocations being emitted from the crack tip at nearly the shear-wave sound speed ${\mathit{c}}_{\mathit{s}}$. As they move many lattice spacings away from the crack, they slow down, finally moving at about 2/3${\mathit{c}}_{\mathit{s}}$. Each time dislocations are emitted, the crack tip ``fishtails,'' and at sufficiently high strain, the crack can fork; dislocations can climb and become nucleation sites for additional microcracks. We find that we can suppress ductile behavior by including viscous damping in the equations of motion, thereby demonstrating a transition to brittle crack propagation as static, zero-strain-rate conditions are approached. Finally, we show that, by altering only the attractive tail of the pair potential, we can change a ductile material into a brittle one. Under dynamic crack propagation, the distinction between ductile and brittle behavior is blurred: in brittle materials, dislocations are asymptotically bound to the crack tip, while in ductile materials, they can escape.

On the Hall-Petch relationship and substructural evolution in type 316L stainless steel

Abstract: Tensile specimens of Type 316L stainless steel having grain sizes in the range 3.1–86.7 μm were deformed to 34% strain at temperatures 24, 400 and 700°C and strain rate 1 × 10−4s−1 to investigate the Hall-Petch (H-P) relationship, the nature of stress-strain curves and the substructure development. Upto ∼5% strain the H-P relationship exhibits bi-linearity whereas the single Hall-Petch relation is exhibited at larger strains. The presence of bi-linearity is explained by the back stress associated with the difference in the dislocation densities in the vicinity of grain boundary and in the grain interior. The log stress (σ)-log strain (e) plots depict three regimes and follow the relationship σ = Ken in each regime, but with varying magnitudes of the strength coefficient (K) and strain-hardening exponent (n).

Influence of temperature and strain rate on slip and twinning behavior of zr

Abstract: The stress-strain behavior of pure Zr was studied systematically at various temperatures and strain rates. At 76 K, Zr deforms predominantly by twinning, whereas above room temperature (RT), slip is the controlling deformation mode. A transition in the rate-controlling deformation mode from slip to twinning has been observed to occur at intermediate temperatures during the course of plastic deformation. Above 373 K, slip dominates the entire course of deformation. The transition from slip to twinning in the stress-strain behavior is linked to differing strain-hardening rates and temperature sensitivities of the two deformation modes.

Hydrogen-enhanced localization of plasticity in an austenitic stainless steel

Abstract: Microscopic observations and the results of static strain aging, stress relaxation, and strain rate change tests on 310s stainless steel foils, with and without hydrogen, have been presented to complement the stress-strain curves in a previous article. The hydrogen-free specimens showed minute yield points during static strain aging, while the hydrogen-containing specimens demonstrated “preyield microstrain. ” Thermal activation analysis of the strain rate change and stress relaxation plots led to the conclusion that the activation area for dislocation motion is decreased by hydrogen. Microstructural examination with the scanning electron microscope (SEM) revealed extensive strain localization, while transmission electron microscopy (TEM) studies showed microtwinning and austenite faulting in hydrogenated specimens tested at room temperature. The relation of hydrogen-induced changes in plastic deformation to hydrogen embrittlement is discussed.

The relationship between indentation and uniaxial creep in amorphous selenium

Abstract: Ultralow load indentation techniques can be used to obtain time-dependent mechanical properties, termed indentation creep, of materials. However, the comparison of indentation creep data to that obtained during conventional creep testing is difficult, mainly due to the determination of the strain rate experienced by the material during indentation. Using the power-law creep equation and the equation for Newtonian viscosity as a function of stress and strain rate, a relationship between indentation strain rate,{center_dot}{epsilon}{sub {ital l}}={ital @};Dh/{ital h}, and the effective strain rate occurring during the indentation creep process is obtained. Indentation creep measurements on amorphous selenium in the Newtonian viscous flow regime above the glass transition temperature were obtained. The data was then used to determine that the coefficient relating indentation strain rate to the effective strain rate is equal to 0.09, or{center_dot}{epsilon}=0.0{center_dot}{epsilon}{sub {ital l}}.

Comparative hot workability of 7012 and 7075 alloys after different pretreatments

Abstract: Hot torsion tests, in the range 250–450 °C and 0.05–5.0 s−1, were performed on AlZnMgCu alloys (7012 and 7075), which had been direct chill cast, homogenized and precipitation treated to give fine, well-dispersed precipitates. Additional tests were conducted on material that had been extruded, solution treated or precipitation treated at deformation temperature. The peak flow stress was related to the strain rate by the hyperbolic sine equation; the activation energy for precipitated alloys was close to that of the bulk self-diffusion of pure aluminium. For solution-treated metal, the peak stress was very high at low temperatures due to dynamic precipitation; as a consequence, the activation energy was about 50% higher than that of precipitated alloys. The ductility was almost independent of temperature in the investigated range, but decreased with rising strain rate. The ductility of the extruded alloys was almost double that of the as-cast material, with the exception of the solution-treated material where, at low temperature, the ductility of the extruded alloy was lower. The original grains were elongated with precipitates on the boundaries. The dynamically recovered subgrains exhibited sub-boundaries with a high density of fine precipitates and an interior network of dislocations also tied to precipitates.

Rate laws for water‐assisted compaction and stress‐induced water‐rock interaction in sandstones

Abstract: Mineral-water interactions under conditions of nonhydrostatic stress play a role in subjects as diverse as ductile creep in fault zones, phase relations in metamorphic rocks, mass redistribution and replacement reactions during diagenesis, and loss of porosity in deep sedimentary basins. As a step toward understanding the fundamental geochemical processes involved, using naturally rounded St. Peter sand, we have investigated the kinetics of pore volume loss and quartz-water reactions under nonhydrostatic, hydrothermal conditions in flow-through reactors. Rate laws for creep and mineral-water reaction are derived from the time rate of change of pore volume, sand-water dissolution kinetics, and (flow rate independent) steady state silica concentrations, and reveal functional dependencies of rates on grain size, volume strain, temperature, effective pressure (confining minus pore pressure), and specific surface areas. Together the mechanical and chemical rate laws form a self-consistent model for coupled deformation and water-rock interaction of porous sands under nonhydrostatic conditions. Microstructural evidence shows a progressive widening of nominally circular and nominally flat grain-grain contacts with increasing strain or, equivalently, porosity loss, and small quartz overgrowths occurring at grain contact peripheries. The mechanical and chemical data suggest that the dominant creep mechanism is due to removal of mass from grain contacts (termed pressure solution or solution transfer), with a lesser component of time-dependent crack growth and healing. The magnitude of a stress-dependent concentration increase is too large to be accounted for by elastic or dislocation strain energy-induced supersaturations, favoring instead the normal stress dependence of molar Gibbs free energy associated with grain-grain interfaces.

The mechanical response of a 6061-T6 A1/A12O3 metal matrix composite at high rates of deformation

Abstract: The mechanical properties of a 6061-T6 aluminum alloy reinforced with a 20 vol.% fraction of alumina particles and of an unreinforced 6061-T6 alloy are studied over a range of strain rates (10-4to 6 x 105s-1) using quasistatic compression, compression and torsion Kolsky Bars, and high strain rate pressure-shear plate impact. At a given strain rate the composite displays increased strength but essentially the same strain hardening as the matrix. However, the composite displays a stronger rate-sensitivity than does the unreinforced alloy at high rates of deformation (>103s-1). The rate-sensitivity of the unreinforced alloy is shown to be largely the result of the imposed strain rate rather than of the rate history. For quasistatic deformations, a model proposed by Bao et al. (1991) describes the behavior of the composite fairly accurately given the behavior of the unreinforced alloy. This paper presents an extension of the model that is able to predict the dynamic behavior of the composite given the dynamic response of the monolithic alloy.

Dynamic strain aging and plastic instabilities

Abstract: A constitutive model proposed by McCormick [(1988) Theory of flow localization due to dynamic strain ageing. Acta. Metall. 36, 3061–3067] based on dislocation-solute interaction and describing dynamic strain aging behavior, is analyzed for the simple loading case of uniaxial tension. The model is rate dependent and includes a time-varying state variable, representing the local concentration of the impurity atoms at dislocations. Stability of the system and its post-instability behavior are considered. The methods used include analytical and numerical stability and bifurcation analysis with a numerical continuation technique. Yield point behavior and serrated yielding are found to result for well defined intervals of temperature and strain rate. Serrated yielding emerges as a branch of periodic solutions of the relaxation oscillation type, similar to frictional stick-slip. The distinction between the temporal and spatial (loss of homogeneity of strain) instability is emphasized. It is found that a critical machine stiffness exists above which a purely temporal instability cannot occur. The results are compared to the available experimental data.

Effect of mechanical cycling on the pseudoelasticity characteristics of TiNi and TiNiCu alloys

Abstract: This paper presents the findings of an experimental study of how mechanical cycling of TiNi and TiNiCu shape memory alloys in the pseudoelastic (PE) state affects their residual elongation after unloading, their critical stress for martensite formation and their hysteresis or amount of energy dissipated during one cycle. Specimens were cycled in two basic modes: hard loading cycles at a constant ϱmax and soft ones at a constant σms. In the hard cycling the authors further investigated how the PE characteristics respond to various strain rates and how the strain rate changes. Each of the examined alloys was cycled in the PE deformation mode at a temperature where each specimen can be deformed at the same constant critical stress for martensite formation in the first cycle of the test. As the number of cycles increases, the residual strain ϱo grows, while both the stress σms for martensite transformation and the hysteresis W decrease. The rate at which ϱo grows depends on σs, σms during cycling and the type of cycling mode. By considering the two factors σs and σms, the rather complicated effect of cyclic deformation on the PE characteristics was explained. Cycling at higher strain rates has been found to increase the residual elongation left after the specimen is unloaded and to cause a more raped decline of the critical stress for martensite formation as cycling continues. After changes in the elongation rate the stability of the cyclic stress-elongation diagram depends on the amount of residual elongation present and on the stability of that diagram during the first cycling at the original elongation rate.

Strain rate effects on shear modulus and damping of normally consolidated clay

Abstract: A laboratory investigation into the effects of shear strain rate on shear modulus and hysteretic damping of normally consolidated clays was carried out. The effects of shear strain rate were examined at cyclic shear strain amplitudes between 10−6 and 10−3 in undrained cyclic torsion shear tests. When the frequency of loading was changed between 0.005 and 0.1 Hz, the equivalent shear modulus was insensitive to the rate of shear straining. On the other hand, the hysteretic damping increased according to the decrease in the shear strain rate. Furthermore, for shear strains less than about 2 × 10−5, the maximum stiffness was hardly influenced by the shear strain rate, type of loading, number of cycles, and the cyclic prestraining; it can therefore be characterized as pseudoelastic shear modulus. On the basis of the test results, it is concluded that when applying the results of laboratory cyclic loading tests to the analysis of in situ cyclic loading problems, the effects of shear strain rate on hysteretic damping should be properly evaluated to match the frequency of loading expected in the field.

On the influence of precipitation on the Portevin-Le Chatelier effect

Abstract: A model describing the interplay of precipitation and dynamic strain ageing is proposed. Both homogeneous and heterogeneous precipitation is considered. It is shown that as a result of precipitation in concentrated solid solutions the critical strains for the occurrence of the Portevin—Le Chatelier effect should exhibit an “inverse” behaviour with temperature and strain rate as compared to the behaviour observed in dilute solid solutions.

Large deformation and fracture behaviour of gels.

Abstract: When gels are used in practice, their large-deformation and fracture characteristics are mostly far more relevant than small-deformation characteristics. In this paper fracture behaviour is discussed of various types of gels, viz. polymer and particle gels, the latter with fairly low and very high volume fraction of particles. First, a general introduction is given on theoretical aspects of fracture mechanics of gels, which involves an essential extension of classical fracture theories. The relationship between large-deformation and fracture behaviour of a gel and its structure proves to be far more complicated than for small-deformation properties. The main reasons for this difference are: (i) the much more important effect of relatively large inhomogeneities on fracture properties and (ii) some very different causes for the strain rate dependence. Not only are the average distance between cross-links and the average stiffness of the strands connecting them of importance, but also the distribution of these parameters. Moreover, inhomogeneities, be it defects (of µm to mm scale) or weak regions (e.g. in composite gels) may have an overriding effect on the fracture properties. To understand the strain rate dependence, one should consider the energies involved as a function of the deformation rate and distinguish between the amount elastically stored during deformation, the amount dissipated due to viscous flow or due to friction processes and the net fracture energy. Moreover crack initiation and fast ‘spontaneous’ crack growth (crack propagation) have to be distinguished. The factors mentioned cause large deformation and fracture properties to be much more strongly dependent on the physical structure of a gel than are the small deformation properties.

High-strain, high-strain-rate behavior of tantalum

Abstract: Tantalum plate produced by a forging-rolling sequence was subjected to high plastic shear strains(γ = 1 → 5.5) at high strain rates (∼4 × 104 s-1) in two experimental configurations: (a) a special hat-shaped geometry and (b) thin disks deformed in a split Hopkinson bar. In parallel experiments, the constitutive behavior of the same material was established through quasi-static and dynamic compression tests at ambient and elevated temperatures. The microstructure generated at high strain rates and retained by rapid cooling from a narrow (200-μm) deformation band progresses from dislocated, to elongated cells, to banded structures, and finally, to subgrains as the shear strain increases from 0 to 5.5. The temperature rise predictions from the constitutive description of the material indicate that the temperature reaches values of 800 K, and it is proposed that thermal energy is sufficient to produce a significant reorganization of the deformation substructure, leading to a recovered structure.

The kinematics of northern South Island, New Zealand, determined from geologic strain rates

Abstract: Relative motions within the distributed plate boundary zone of northern South Island, New Zealand, are determined through an inversion of geologic strain rate estimates. The Quaternary fault slip rate estimates define the shear strain rates, and rock uplift rates provide information on the horizontal divergence rates. An erosion rate to rock uplift rate ratio along with a crustal compensation factor is estimated in order to convert rock uplift rates to horizontal divergence rates. Because of the uncertainty in erosion rates, horizontal divergence rates σ are given a large standard error of ±σ. The three horizontal strain rate components obtained from these data completely define the horizontal velocity gradient tensor. Strain rate distributions are matched with spline polynomial functions, which can be constrained to behave rigidly within specified regions, such as the Pacific or Australian plates. Inversion of the strain rate distribution, assuming uniform erosion rates across the northern South Island, yields a velocity field that has small differences in both magnitude (10% larger) and direction with the NUVEL-1A plate motion model between Pacific and Australian plates. A revised strain rate data set, obtained from a variable erosion model in which erosion rates are a linear function of the log of the average annual rainfall magnitudes, yields a velocity field with expected directions that are indistinguishable from the NUVEL-1A plate motion model between Pacific and Australian plates, but velocity magnitudes are still 10- 15% higher than the plate motion model. Therefore the average values of slip rate on strike-slip faults in Marlborough, required by the NUVEL-1A plate motion model, are typically close to the low end of the published range of slip values for those structures. The major strike-slip structures within the Marlborough region are accommodating 80 - 100% of the total plate motion between Australia and Pacific plates on northern South Island ; as much as 20% of the relative motion could be accommodated by shear generated by folding or thrust faulting with a single orientation between the major structures. The magnitude of plate motion contributed by the major faults indicates that the distributed geodetic shear strains measured across northern South Island, and discussed by Bibby [1981] and Walcott [1984], are not a form of irrecoverable strain but rather a feature of the strain field that will eventually be released primarily as concentrated slip on the strike-slip structures within the region. Strain modeling indicates that the earthquake moment release over the last 150 years within the northwest Nelson province, which is west of the Marlborough region, is at least half an order of magnitude higher than the long-term rate of moment release. Overall, the northwest Nelson region is playing only a minor role in taking up the long-term plate motion.

Threshold creep behaviour of discontinuous aluminium and aluminium alloy matrix composites: An overview

Abstract: Several sets of creep data for aluminium and aluminium alloy matrix composites reinforced by silicon carbide particulates, silicon carbide whiskers or alumina short fibres are analysed. It is shown that for this class of discontinuous composites the threshold creep behaviour is inherent. Applying the concept of threshold stress, the true stress exponent of minimum creep strain rate of approximately 5 follows from the analysis even when the matrix solid solution alloy exhibits Alloy Class creep behaviour, for which the value of 3 for the true stress exponent is typical. The creep strain rate in the discontinuous aluminium and aluminium alloy matrix composites is shown to be matrix lattice diffusion controlled. The usually observed high values of the apparent stress exponent of creep strain rate and the high values of the apparent activation energy of creep are then rationalized in terms of the threshold creep behaviour. However, the origin of the threshold stress decreasing with increasing temperature but not proportional to the shear modulus in creep of discontinuous aluminium and aluminium alloy matrix composites is still awaiting identification. The creep-strengthening effect of silicon carbide particulates, silicon carbide whiskers and alumina short fibres is shown to be significant, although the particulates, whiskers and short fibres do not represent effective obstacles to dislocation motion.

Earthquake strain rates and instantaneous relative motions within central and eastern Asia

Abstract: SUMMARY We use the spatial distribution of moment tensors of earthquakes in this century to estimate the velocity field in Asia within a Eurasian reference frame. In a least-squares inversion, strain rates on the surface of the Earth are matched with continuous spline functions in order to recover the velocity gradient tensor associated with the seismic moment release in Asia. Earthquakes account for 40–60 per cent of the expected motion of India relative to Eurasia, with the missing component of strain rate equivalent to about 20 mm yr−1 of N-S shortening between Siberia and India. In this solution, South China rotates counterclockwise and moves eastwards relative to Siberia. Using rigid plate constraints, we next investigate the characteristics of the complete horizontal strain field in Asia that accommodates plate motions. Our strain-rate solutions are analogous to the response of a Newtonian thin viscous sheet in which the rate of work done by the straining medium in accommodating the velocity boundary conditions is a minimum. In these solutions the Euler pole for India relative to Eurasia is constrained (NUVEL-1A; DeMets et al. 1994), but in the process of fitting the VLBI velocity at Shanghai, China (Ward 1994; Heki et al. 1995), the Euler pole for South China is determined in the inversion. A solution that both fits the velocity at Shanghai, China and yields a strain-rate field consistent with the earthquake mechanisms is one where the South China block has a motion relative to Siberia described by the pole at (51°N, 131°E, 0.3 deg Myr−1). Comparison of the complete strain field that accommodates plate motion with the seismic strains indicates that earthquake moment release rates in this century within Mongolia are about a factor of 4 larger than the long-term rate. Within Gansu-Ningxia, the earthquake moment rates have been about a factor of 2 higher than the long-term rate. The strike-slip faulting within Mongolia, Gansu-Ningxia, western Sichuan and Yunnan is possibly a direct result of velocity boundary conditions imposed on the South China block by forces unrelated to continental collision of India and Eurasia, such as forces associated with subduction along the margins of South-eastern Asia. Verification of this requires a better understanding of the role of pre-existing zones of weakness within the Asian continental lithosphere.

Development of the MPC Omega Method for Life Assessment in the Creep Range

Abstract: A methodology for characterizing and assessing the behavior of materials after service in the creep range has been developed and used on a broad range of materials and components. It incorporates the results of relatively short-term tests and improved databases on materials properties. The essence of the method is the definition of a material performance characteristic which the authors refers to by the symbol {Omega}{sub p}. This coefficient effectively describes the rate at which a material`s ability to resist stress is degraded by strain. While {Omega}{sub p} is a function of stress, temperature, and mode of loading, it is amenable to parametric representation and is, therefore, useful in predicting life and strain accumulation. Time to failure and total accumulated strain are shown to be consequences of a characterizing strain rate, as defined herein, and an appropriate {Omega}{sub p} for the operating conditions and geometry of interest. Accumulated strain, future strain, current creep rate, remaining life, total damage, and damage rate are among the quantities which are easily calculated. The development of the method employs and extends the concepts of Larson-Miller, Monkman-Grant, Robinson, Theta Projection, Kachanov, and Norton.