Showing papers on "Strain rate published in 2002"

Constitutive analysis in hot working

Abstract: Constitutive equations including an Arrhenius term have been commonly applied to steels with the objective of calculating hot rolling and forging forces. The function relating stress and strain rate is generally the hyperbolic-sine since the power and exponential laws lose linearity at high and low stresses, respectively. In austenitic steels, the equations have been used primarily for the peak stress (strain) associated with dynamic recrystallization (DRX) but also for the critical and steady state stresses (strains) for nucleation and first wave completion of DRX. Since the peak strain is raised by the presence of solutes and fine particles, the stress is raised more than by simple strain hardening increase, thus causing a marked rise in activation energy in alloy steels. In contrast, large carbides, inclusions or segregates, if hard, may lower the peak strain as a result of particle stimulated nucleation. Due to the linear relation between stress and strain at the peak, flow curves can be calculated from the constitutive data with only one additional constant. Maximum pass stresses can also be calculated from a sinh constitutive equation determined in multistage torsion simulations of rolling schedules. Comparison is made between carbon, micro-alloyed, tool and stainless steels and to ferritic steels which usually do not exhibit DRX. Parallels to the effects of impurities and dispersoids on the constitutive equations for Al alloys are briefly discussed.

Pulse shaping techniques for testing brittle materials with a split hopkinson pressure bar

Abstract: We present pulse shaping techniques to obtain compressive stress-strain data for brittle materials with the split Hopkinson pressure bar apparatus. The conventional split Hopkinson pressure bar apparatus is modified by shaping the incident pulse such that the samples are in dynamic stress equilibrium and have nearly constant strain rate over most of the test duration. A thin disk of annealed or hard C11000 copper is placed on the impact surface of the incident bar in order to shape the incident pulse. After impact by the striker bar, the copper disk deforms plastically and spreads the pulse in the incident bar. We present an analytical model and data that show a wide variety of incident strain pulses can be produced by varying the geometry of the copper disks and the length and striking velocity of the striker bar. Model predictions are in good agreement with measurements. In addition, we present data for a machineable glass ceramic material, Macor, that shows pulse shaping is required to obtain dynamic stress equilibrium and a nearly constant strain rate over most of the test duration.

Dynamic recrystallization of quartz: correlation between natural and experimental conditions

Abstract: Quartz veins in the Eastern Tonale mylonite zone (Italian Alps) were deformed in strike-slip shear. Due to the synkinematic emplacement of the Adamello Pluton, a temperature gradient between 280°C and 700°C was effected across this fault zone. The resulting dynamic recrystallization microstructures are characteristic of bulging recrystallization, subgrain rotation recrystallization and grain boundary migration recrystallization. The transitions in recrystallization mechanisms are marked by discrete changes of grain size dependence on temperature. Differential stresses are calculated from the recrystallized grain size data using paleopiezometric relationships. Deformation temperatures are obtained from metamorphic reactions in the deformed host rock. Flow stresses and deformation temperatures are used to determine the strain rate of the Tonale mylonites through integration with several published flow laws yielding an average rate of approximately 10−14s−1 to 10−12s−1. The deformation conditions of the natural fault rocks are compared and correlated with three experimental dislocation creep regimes of quartz of Hirth & Tullis. Linking the microstructures of the naturally and experimentally deformed quartz rocks, a recrystallization mechanism map is presented. This map permits the derivation of temperature and strain rate for mylonitic fault rocks once the recrystallization mechanism is known.

Myocardial function defined by strain rate and strain during alterations in inotropic states and heart rate

Abstract: For porcine myocardium, ultrasonic regional deformation parameters, systolic strain (esys) and peak systolic strain rate (SRsys), were compared with stroke volume (SV) and contractility [contractil...

Microstructural mechanisms during hot working of commercial grade Ti–6Al–4V with lamellar starting structure

Abstract: The hot deformation behavior of commercial grade Ti–6Al–4V with a lamellar starting microstructure is studied in the temperature range 750–1100 °C and strain rate range 3×10 −4 –10 s −1 with a view to model the microstructural evolution. On the basis of flow stress data obtained as a function of temperature and strain rate in compression, a processing map for hot working has been developed. In the ranges 800–975 °C and 3×10 −4 –10 −2 s −1 , globularization of lamellae occurs for which an apparent activation energy of 455 kJ mol −1 has been estimated using the kinetic rate equation. Stress-dependent thermal activation analyses proposed by Schock and Cocks et al. have shown that the apparent activation energies are in the range 160–245 kJ mol −1 and the normalized activation volumes are in the range 20–80, which suggest that cross-slip is the rate controlling process during globularization. The variation of primary α grain size with Zener–Hollomon parameter ( Z ) in the globularization region exhibited a linear relationship on a log–log scale. At strain rates slower than 10 −1 s −1 and temperatures below 900 °C, cracking at the prior β grain boundaries/triple junctions occurs, which sets the lower limits for globularization. At strain rates higher than 10 −1 s −1 in the α+β range, the material exhibited flow instabilities manifested as adiabatic shear bands. These bands are intense below 800 °C and above 1 s −1 and caused cracking along the bands. In the β phase field, dynamic recrystallization (DRX) occurs at about 1100 °C and in the strain rate range 10 −3 –10 −1 s −1 . The apparent activation energy for DRX of β is about 172 kJ mol −1 which is close to that for self-diffusion in β phase (153 kJ mol −1 ). The application of these results in the design of bulk metalworking processes for achieving microstructural control is discussed.

Frictional-viscous flow of phyllosilicate-bearing fault rock: Microphysical model and implications for crustal strength profiles

Abstract: It is widely believed that around the brittle-ductile transition, crustal faults can be significantly weaker than predicted by conventional two-mechanism brittle-ductile strength envelopes. Factors contributing to this weakness include the polyphase nature of natural rocks, foliation development, and the action of fluid-assisted processes such as pressure solution. Recently, ring shear experiments using halite/kaolinite mixtures as an analogue for phyllosilicaterich rocks for the first time showed frictional-viscous behavior (i.e., both normal stress and strain rate sensitive behavior) involving the combined effects of pressure solution and phyllosilicates. This behavior was accompanied by the development of a mylonitic microstructure. A quantitative assessment of the implications of this for the strength of natural faults has hitherto been hampered by the absence of a microphysical model. In this paper, a microphysical model for shear deformation of foliated, phyllosilicate-bearing fault rock by pressure solution-accommodated sliding along phyllosilicate foliae is developed. The model predicts purely frictional behavior at low and high shear strain rates and frictional-viscous behavior at intermediate shear strain rates. The mechanical data on wet halite + kaolinite gouge compare favorably with the model. When applied to crustal materials, the model predicts major weakening with respect to conventional brittle-ductile strength envelopes, in particular, around the brittle-ductile transition. The predicted strength profiles suggest that in numerical models of crustal deformation the strength of high-strain regions could be approximated by an apparent friction coefficient of 0.25-0.35 down to depths of 15-20 km.

Nucleation and microtexture development under dynamic recrystallization of copper

Abstract: Microstructure and microtexture evolution during dynamic recrystallization (DRX) was investigated in compression of polycrystalline copper in the temperature range from 473 K to 723 K and at strain rates from 10−3s−1 to 10−1s−1. A compression texture of near 〈101〉 direction, evolved by low temperature deformation, is gradually weakened and randomized by the progress of DRX at higher temperature, where 〈101〉 component still exists. New DRX grains are evolved by the operation of bulging of serrated grain boundaries, which is accompanied either by rotation of a bulged portion or twinning at the back of the migrating boundary. The mechanisms of dynamic nucleation and necklace DRX are discussed.

An examination of the constitutive equation for elevated temperature plasticity

Abstract: It was 25 years ago that the symposium on rate processes in plasticity was organized. Since then, advances in transmission electron microscopy, large-scale computation as well as molecular dynamics simulation, etc. have contributed much to our understanding of elevated temperature plasticity. The constitutive relation that links the stress–strain rate–grain size–temperature relation (Mukherjee–Bird–Dorn, MBD correlation) was presented in 1968/1969 to describe the elevated-temperature crystalline plasticity. This equation has held up well during the intervening quarter of a century. It has been applied to metals, alloys, intermetallics, ceramics, and tectonic systems, and it has worked equally well. It made the depiction of deformation mechanism maps in normalized coordinates a reality and provided a rationale for estimating life prediction by giving a quantitative estimate of the steady-state creep rate in creep damage accumulation relationship. In the case of particle-dispersed systems as well as metal matrix composites, the introduction of the concept of a threshold stress was a substantial improvement in creep studies. One of the significant applications of the MBD relation has been in superplasticity. The concept of scaling with either temperature or with strain rate, inherent in this relationship, seems to be obeyed as long as the rate-controlling mechanism is unchanged. The application of this relation to high strain-rate superplasticity and also to low-temperature superplasticity has been illustrated. Experimental data demonstrate that superplasticity of nanocrystalline metals and alloys follows the general trend of the constitutive relation but with important differences in the level of stress and strain hardening rates. It is shown that in the nanocrystalline range, molecular dynamics simulation has the potential to yield data on stress–grain size–temperature dependencies at very low grain size ranges where experimentalists cannot conduct their studies yet.

From the basic mechanics of orthogonal metal cutting toward the identification of the constitutive equation

Abstract: This paper proposes a methodology to identify the material coefficients of constitutive equation within the practical range of stress, strain, strain rate, and temperature encountered in metal cutting. This methodology is based on analytical modeling of the orthogonal cutting process in conjunction with orthogonal cutting experiments. The basic mechanics governing the primary shear zone have been re-evaluated for continuous chip formation process. The stress, strain, strain rate and temperature fields have been theoretically derived leading to the expressions of the effective stress, strain, strain rate, and temperature on the main shear plane. Orthogonal cutting experiments with different cutting conditions provide an evaluation of theses physical quantities. Applying the least-square approximation techniques to the resulting values yields an estimation of the material coefficients of the constitutive equation. This methodology has been applied for different materials. The good agreement between the resulting models and those obtained using the compressive split Hopkinson bar (CSHB), where available, demonstrates the effectiveness of this methodology.

Determination of laminar flame speeds using digital particle image velocimetry: Binary Fuel blends of ethylene, n-Butane, and toluene

Abstract: The atmospheric laminar flame speeds of mixtures of air with ethylene, n-butane, toluene, ethylene-n-butane, ethylene-toluene, and n-butane-toluene were experimentally and computationally investigated over an extended range of equivalence ratios. Binary fuel blends with 1:1, 1:2, and 2:1 molar ratios were examined. Experimentally, the laminar flame speeds were determined using digital particle image velocimetry (DPIV). Since the use of DPIV enables the mapping of the two-dimensional flow field adhead of the flame, the reference speed based on the minimum axial velocity point as well as the imposed strain rate can be identified simultaneously. The latter can now be unambiguously determined by the radial velocity gradient at the minimum velocity point. By systematically varying the imposed strain rate, the corresponding laminar flame speed was obtained through nonlinear extrapolation to zero strain rate. The associated experimental accuracy of the DPIV measurements was also assessed and discussed. Computationally, the laminar flame speeds were simulated for all single-component fuel/air and binary fuel blend/air mixtures with a detailed kinetic model. Comparison of experimental and computed flame speeds shows generally good agreement. A semiempirical mixing rule was developed. The mixing rule which requires only the knowledge of the flame speeds and flame temperatures of the individual fuel constituents, is shown to provide acurate estimates for the laminar flame speeds of binary fuel blends under the conditions tested.

Strain Response from Polypyrrole Actuators under Load

Abstract: The strain generated by an actuator material when subjected to an external force is a key performance parameter. However, very little is known about the performance of polymer actuator materials when subjected to external loads. Increasing external loads were applied to polypyrrole films and the actuator response was found to decrease linearly. Analysis of the effects of the applied load on actuator strain showed that the rate of strain decrease with increasing load depended upon the difference in the Young’s modulus of the polymer in the doped and undoped states. A simple analytical model shows good agreement with the experimental data.

Two-dimensional ultrasonic strain rate measurement of the human heart in vivo

Abstract: A study is presented in which the feasibility of two-dimensional strain rate estimation of the human heart in vivo has been demonstrated. To do this, ultrasonic B-mode data were captured at a high temporal resolution of 3.8 ms and processed off-line. The motion of the RF signal patterns within the two-dimensional sector image was tracked and used as the basis for strain rate estimation. Both axial and lateral motion and strain rate estimates showed a good agreement with the results obtained by more established, one-dimensional techniques.

Deformation and Failure of Zr57Ti5Cu20Ni8Al10 Bulk Metallic Glass Under Quasi-static and Dynamic Compression

Abstract: We have examined the mechanical behavior of Zr57Ti5Cu20Ni8Al10 bulk metallic glass under uniaxial compression at strain rates from 10−4to 3 × 103 s−1. The failure stress decreases with increasing strain rate, and shear-band formation remains the dominant deformation mechanism. A consideration of basic properties of adiabatic shear bands makes it appear unlikely that shear bands formed under quasi-static loading are adiabatic; in the dynamic case, the time scales of deformation and thermal conduction are similar, indicating that a more sophisticated calculation is required. In the dynamic tests, however, high-speed cinematography reveals evidence that the mechanism of failure involves an adiabatic component.

Dynamic Compression Testing of Soft Materials

Abstract: Low-strength and low-impedance materials pose significant challenges in the design of experiments to determine dynamic stress-strain responses. When these materials are tested with a conventional split Hopkinson pressure bar, the specimen will not deform homogeneously and the tests are not valid. To obtain valid data, the shape of the incident pulse and the specimen thickness must be designed such that the specimens are in dynamic equilibrium and deform homogeneously at constant strain rates. In addition, a sensitive transmission bar is required to detect the weak transmitted pulses. Experimental results show that homogeneous deformations at nearly constant strain rates can be achieved in materials with very low impedances, such as a silicone rubber and a polyurethane foam, with the experimental modifications presented in this study. ©2002 ASME

Microstructure evolution under compressive plastic deformation of magnesium at different temperatures and strain rates

Abstract: Substructure development in polycrystalline magnesium compressed at different temperatures and strain rates was investigated by means of light microscopy, X-ray diffractometry (texture and line-broadening analysis), and in some cases also by TEM or SEM. The fracture of the specimens is accompanied by shear banding. Dynamic recrystallisation starting above RT must be taken into account. The experimental results reflect the interaction between twinning and dislocation slip during the deformation, which leads to significant texture changes.

Timescales for the evolution of seismic anisotropy in mantle flow

Abstract: [1] We study systematically the relationship between olivine lattice preferred orientation and the mantle flow field that produces it, using the plastic flow/recrystallization model of Kaminski and Ribe [2001]. In this model, a polycrystal responds to an imposed deformation rate tensor by simultaneous intracrystalline slip and dynamic recrystallization, by nucleation and grain boundary migration. Numerical solutions for the mean orientation of the a axes of an initially isotropic aggregate deformed uniformly with a characteristic strain rate show that the lattice preferred orientation evolves in three stages: (1) for small times , recrystallization is not yet active and the average a axis follows the long axis of the finite strain ellipsoid; (2) for intermediate times , the fabric is controlled by grain boundary migration and the average a axis rotates toward the orientation corresponding to the maximum resolved shear stress on the softest slip system; (3) for , the fabric is controlled by plastic deformation and average a axis rotates toward the orientation of the long axis of the finite strain ellipsoid corresponding to an infinite deformation (the “infinite strain axis”.) In more realistic nonuniform flows, lattice preferred orientation evolution depends on a dimensionless “grain orientation lag” parameter Π(x), defined locally as the ratio of the intrinsic lattice preferred orientation adjustment timescale to the timescale for changes of the infinite strain axis along path lines in the flow. Explicit numerical calculation of the lattice preferred orientation evolution in simple fluid dynamical models for ridges and for plume-ridge interaction shows that the average a axis aligns with the flow direction only in those parts of the flow field where Π ≪ 1. Calculation of Π provides a simple way to evaluate the likely distribution of lattice preferred orientation in a candidate flow field at low numerical cost.

Mechanical behavior of Ti–6Al–4V at high and moderate temperatures—Part I: Experimental results

Abstract: This study investigates the plastic deformation of titanium alloy Ti–6%Al–4%V under low and moderate strain rates and various temperature conditions. Mechanical testing is performed in the temperature range 650–1340 K (710–1950 °F) and under constant strain rate loading ranging from 10 −3 to 10 s −1 . The test results are correlated with the evolution of the microstructure and compared to published data. The flow stress of this alloy is strongly dependent on both temperature and deformation rate, with the temperature effect becoming negligible in the upper part of the temperature range investigated. At temperatures above 800 K (980 °F) the flow stress decreases sharply with temperature. The effect of deformation rate on this transition is investigated and the possible mechanisms responsible for the behavior are discussed. Based on these experimental results, a physically-based constitutive law is developed in the sequel of this paper.