Showing papers on "Strain rate published in 1994"

Deformation behaviour of ultra-fine-grained copper

Abstract: Mechanical behaviour and structural changes, such as the evolution of grain and dislocation structures and the formation of slip lines and grain-boundary-sliding traces, of a submicron-grained (SMG) copper during room-temperature compression have been studied. It is suggested that the absorption of dislocations into grain boundaries (GBs) is due to the migration and sliding of some highly non-equilibrium GBs during the deformation process and is influenced by high level internal stresses. From this point of view, the unusual behaviour of SMG copper, in particular, the high yielding and flow stresses, the absence of strain hardening, high plasticity and low strain rate sensitivity, are explained. Analogies of the mechanical behaviour of SMG copper with mechanical properties of metallic materials at large plastic strains in stage IV are discussed.

Critical Appraisal of Limiting Strain Rates for Compression Testing of Ceramics in a Split Hopkinson Pressure Bar

Abstract: The split Hopkinson pressure bar (SHPB) is being widely used to determine the dynamic compressive strength of ceramics and ceramic composites. However, extreme caution needs to be exercised while testing these high-strength ceramics at high strain rates. The highest strain rate at which ceramics can be tested using an SHPB without violating the underlying assumptions is found to be in the range of 2500-3000/s. It is also shown that at very high loading rates, dispersion in the transmitted pulse can lead to discrepancies in measuring the dynamic failure strength of ceramics.

Further considerations on the determination of laminar flame speeds with the counterflow twin-flame technique

Abstract: The accuracy of the laminar flame speed determination by using the counterflow twin-flame techniquehas been computationally and experimentally examined in light of the recent understanding that linear extrapolation of the reference upstream velocity to zero strain rate would yield a value higher than that of the laminar flame speed, and that such an overestimate can be reduced by using either lower strain rates and/or larger nozzle separation distances. A systematic evaluation of the above concepts has been conducted and verified for the ultralean hydrogen/air flames, which have relatively large Karlovitz numbers, even for small strain rates, because of their very small laminar flame speeds. Consequently, the significantly higher values of the previous experimentally measured flame speeds, as compared with the independently calculated laminar flame speeds, can now be attributed to the use of nozzle separation distances that were not sufficiently large and/or strain rates that were not sufficiently small. Thus, by using lower strain rates and larger nozzle separation distances, the experimentally and computationally redetermined values of these ultralean hydrogen/air flames agree well with the calculated laminar flame speeds. The laminar flame speeds of methane/air and propane/air mixtures have also been experimentally redetermined over extensive ranges of the equivalence ratio and are found to be slightly lower than the previously reported experimental values.

Dynamic recrystallization in high-strain, high-strain-rate plastic deformation of copper

Abstract: When copper is deformed to high plastic strain (y ~ 34) at high strain rates (~ ~ I04 s -1) a microstructure with grain sizes of ~0.1 am can be produced. It is proposed that this microstructure develops by dynamic recrystallization, which is enabled by the adiabatic temperature rise. By shock-load- ing the material, and thereby increasing its flow stress, the propensity for dynamic recrystallization can be enhanced. The grain size-flow stress relationship observed after cessation of plastic deformation is consistent with the general formulation proposed by Derby (Acta metall, mater. 39, 955 (1991)). The temperatures reached by the specimens during dynamic deformation are calculated from a constitutive equation and are found to be, for the shock-loaded material, in the 500-800 K range; these temperatures are consistent with static annealing experiments on shock-loaded specimens, that show the onset of static recrystallization at 523 K. A possible recrystallization mechanism is described and its effect on the mechanical response of copper is discussed.

A new elongational rheometer for polymer melts and other highly viscoelastic liquids

Abstract: In polymer melt elongational rheometry only by the rotary clamp technique large elongations can be obtained homogeneously. However, as described in this paper, there still remain disadvantages that led to the development of a new rheometer with the following main features: The dimensions of the required sample are small (60 × 7 × 2 nun3), the sample is supported by a cushion of inert gas and, after having reached the test temperature of up to well above 300°C, it can be extended by a new type of clamps that make use of metal conveyor belts. The resulting tensile force is measured with a resolution of better than 100 mgf (0.001 N). The strain rate range is 0.001-1 s−1, and the maximum Hencky strain is 7, corresponding to a maximum stretch ratio of 1100. Within the sample, the temperature variation in time and space is less than 0.1°C. For the evaluation and documentation of the test performance, a video camera records the top and side views of the sample that carries a marking powder to permit the evaluation of the true strain rate. The operation of the instrument is easy, and so is the sample preparation, but care must be taken concerning the necessary isotropy and ‘internal homogeneity’. Examples of test results are given for several polymer melts at various temperatures: (1) Polystyrene up to a total Hencky strain larger than 7 at 170°C, (2) several types of polyethylene (LDPE, LLDPE, HDPE) at 150°C, (3) poly(amide) at 250°C, and (4) poly(ethersulfone) at 350°C. The wide applicability of the new rheometer is demonstrated by adding results obtained from samples of bread dough. The surface tension has no influence on the results if an error of 3% can be tolerated. From the results it follows that by means of the newly developed rheometer many problems in polymer melt elongation have been solved.

Comparison of constant pressure and constant volume nonequilibrium simulations of sheared model decane

Abstract: We present the results of nonequilibrium molecular dynamics simulations of a model decane fluid performed at constant pressure and compare them with results previously obtained from simulations performed at constant volume. The strain rate dependence of the viscosity at constant pressure is found to differ from that obtained previously at constant volume. The shear thickening at high strain rates observed in constant volume simulations vanishes when the simulations are performed at constant pressure. We also investigate the question of how our low strain rate data for decane can be accurately extrapolated to zero strain rate. We find a well defined first Newtonian region in which the viscosity is independent of strain rate to within errors. The value of the viscosity that we obtain in this region agrees well with the zero strain rate viscosity calculated from the Green–Kubo formula at equilibrium.

A model for particle cavitation in rubber-toughened plastics

Abstract: An energy-balance criterion for cavitation of rubber particles, which was proposed in an earlier paper [A. Lazzeri and C. B. Bucknall, J. Mater. Sci.28 (1993) 6799], is developed by including a term for the energy stored in the matrix and released during expansion of the voids. The model relates the critical volume strain at cavitation to the radius of the rubber particle, and to the shear modulus, surface energy and failure strain of the rubber. The effects of temperature, strain rate and type of stress field upon cavitation behaviour and the resulting toughness of the two-phase polymer are discussed in terms of the model.

Young Measure‐Valued Solutions for Non-Newtonian Incompressible Fluids1

Abstract: For the model of a nonlinear bipolar fluid, in which the highest order viscosity vanishes, and the viscous part of the stress tensor satisfies a growth condition of the form the rate of strain tensor, we demonstrate the existence of Young-measure valued solutions for these solutions are proven to be weak solutions for and for and unique regular weak solutions for

Strain-rate effect on brittle failure in compression

Abstract: A simple model of an array of interacting, dynamically growing wing cracks is used to simulate the rate-dependent dynamic damage evolution and subsequent brittle failure of solids under compression. The validity of the model is discussed. Parameters which identify the overall failure by the coalescence of compression-induced, interacting, tensile microcracks are calculated in closed form, and relations between microstructure and the corresponding rate dependency of the overall response are examined in some detail. It is shown that the experimentally observed change in the compressive failure stress with increasing strain rate, may be considered to be a consequence of the generation and dynamic growth of interacting, compression-induced, tensile microcracks. Examples of brittle failure in uniaxial stress and uniaxial strain conditions, respectively, produced in the Hopkinson compression bar and normal plate-impact experiments, are discussed in terms of this model.

Effect of strain rate on the fracture behaviour of skin

Abstract: The effect of strain rate on the stress-strain behaviour of skin is studied. It is observed that the plastic set in the skin is dependent on strain rate. The scanning electron micrographs of the fractured skin sample shows thicker fibrils and thinner one at low strain rates. The plastic flow is clearly brought out in the stress-strain curves at different strain rates. The stress relaxation behaviour at any given strain is clearly brought out in the 3-dimensional plot.

A process model for friction welding of AlMgSi alloys and AlSiC metal matrix composites—I. Haz temperature and strain rate distribution

Abstract: The present investigation is concerned with the development of an overall process model for the microstructure and strength evolution during continuous drive friction welding of AlMgSi alloys and AlSiC metal matrix composites. In Part I the different components of the model are outlined and analytical solutions presented which provide quantitative information about the HAZ temperature distribution for a wide range of operational conditions. Moreover, a general procedure for modelling the HAZ strain rate distribution has been developed by introducing a series of kinematically admissible velocity equations which describe the material flow fields in the radial, the rotational, and the axial direction, respectively. Calculations performed for both types of materials show that the effective strain rate may exceed 1000 s −1 in positions close to the contact section due to the high rotational velocities involved. Application of the model for evaluation of the response of AlMgSi alloys and AlSiC metal matrix composites to the imposed heating and plastic deformation is described in an accompanying paper (Part II).

Elastic and viscoelastic properties of trabecular bone by a compression testing approach.

Abstract: In this review the advantages and disadvantages of different variants of compression testing of trabecular bone are discussed. Factors affecting the precision and the accuracy of mechanical properties of trabecular bone derived from such tests are analysed. Below are listed some of the important conclusions which can be drawn. Conclusions based on the author's previous studies (I-IX) are shown in italic. 1) Trabecular bone is a viscoelastic solid. 2) Stiffness, strength, ultimate strain, and failure energy are derived from a standard compression test to failure. Viscoelastic properties such as energy dissipation and the relative energy loss (loss tangent) can be obtained from non-destructive cyclic tests. 3) A non-destructive test conducted between a lower load level (zero strain) and an upper strain limit of about 0.8% specimen strain has been developed. The reproducibility of such a test technique has been assessed at different conditions. The reproducibility was best after a number of conditioning cycles in order to achieve a viscoelastic steady state. Orthotropic properties can be determined by non-destructive testing in different directions of cubic specimens. The reproducibility of such testing has been established. 4) The stiffness derived from non-destructive tests will be lower than that obtained from a destructive test because of the non-linearity of the load-deformation curve, but the stiffnesses will be strongly correlated. 5) Stiffnesses derived from destructive and non-destructive tests have an elastic and a viscoelastic contribution. Since the viscoelastic contribution is time dependent, the results will be dependent on strain rate and loading frequency in cyclic tests. 6) Standard testing of small trabecular bone specimens is associated with systematic errors. The most significant of these errors are believed to be related to trabecular disintegrity at the surface of the specimen and to friction at the specimen-platen interface. Structural disintegrity causes an axial strain inhomogeneity resulting in a overestimation of axial strain and a corresponding underestimation of specimen stiffness. Friction at the interface causes an uneven stress and strain distribution in the layer nearest to the test platen resulting in a overestimation of stiffness. The net result of these systematic errors is a 20-40 per cent underestimation of stiffness. 7) The specimen geometry has a highly significant influence on mechanical properties such as stiffness, ultimate strain and energy absorption. A cube with a side length of 6.5 mm and a cylindrical specimen with a length of 6.5 mm and a diameter of 7.5 mm are suggested as standard geometries providing comparable results.

Geometric and radiation effects on steady and unsteady strained laminar flames

Abstract: A detailed numerical investigation was conducted on the effects of the domain size and radiation on thedynamics of opposed jet, strained, laminar premixed, and diffusion flames. The simulation was performed by solving the conservation equations along the stagnation streamline of the counterflow and by using detailed description of the chemistry, molecular transport, and nonluminous thermal radiation at the optically thin limit. Results indicate that the hydrodynamic extinction strain rate increases with the nozzle separation distance because of the reduction of the values of the strain rate distribution within the main reaction zone. The predictions of extinction strain rates in the present study agree well with available experimental data on premixed flames, after using nozzle separation distances equal to the experimental ones. Furthermore, the inclusion of the Soret effect was found to increase the predicted strain rates for near stoichiometric flames. The effect of radiation was assessed for both steady and unsteady flames. The unsteadiness was introduced through sinusoidal variation of the nozzle exit velocities around some mean values. The results indicate that the effect of the radiation on the flame response and extinction becomes important only for near-limit premixed flames and weakly strained diffusion flames, which are characterized by large thicknesses. An asymmetry was also identified in the response of unsteady diffusion flames for which the trough value of the strain rate is near-zero, while the peak value causes substantial straining. The results were explained based on the competition between the mechanisms of reactant leakage and radiative loss as the strain rate is reduced.

The influence of room temperature deformation on porosity and permeability in calcite aggregates

Abstract: Changes in permeability and porosity during shortening deformation of Carrara marble and hot-pressed calcite aggregates were measured under high pressure at room temperature using argon as pore fluid. At effective pressures of 30 and 50 MPa, the permeability of Carrara marble increased by up to 2 orders of magnitude with less than 2% strain during which the connected porosity increased by only 0.005. The permeability increased more slowly with further strain up to 18%, during which the connected porosity increased by a further 0.05 to 0.06. At effective pressures of 100 MPa to 200 MPa, these effects were much less marked. In hot-pressed calcite aggregates, deformed at an effective pressure of 50 MPa, the permeability increased by about 2 orders of magnitude after about 12% strain and an increase in connected porosity of about 0.03. Microstructural studies indicate that, in the coarse-grained Carrara marble specimens, both transgranular and grain boundary cracks are present after room temperature deformation. For a given strain, the average length and the linear density of transgranular cracks decrease with increasing effective pressure. In fine-grained, hot-pressed calcite aggregates, dilatancy is mainly due to opening of grain boundary cracks. The very marked increase in permeability with small strain at low effective pressure can be correlated with the proliferation of connected microcracks of relatively large apertures, deduced on the basis of theoretical models.

An improved measure of strain state probability in turbulent flows

Abstract: Probability density functions (PDFs) of the strain‐rate tensor eigenvalues are examined. It is found that the accepted normalization used to bound the intermediate eigenvalue between ±1 leads to a PDF that must vanish at the end points for a non‐singular distribution of strain states. This purely kinematic constraint has led previous investigators to conclude incorrectly that locally axisymmetric deformations do not exist in turbulent flows. An alternative normalization is presented that does not bias the probability distribution near the axisymmetric limits. This alternative normalization is shown to lead to the expected flat PDF in a Gaussian velocity field and to a PDF that indicates the presence of axisymmetric strain states in a turbulent field. Extension of the new measure to compressible flow is discussed. Several earlier results concerning the likelihood of various strain states and the correlation of these with elevated kinetic energy dissipation rate are reinterpreted in terms of the new normali...

The effect of aging on microstructure, room temperature deformation, and fracture of Sn-Bi/Cu solder joints

Abstract: The effects of isothermal aging on the microstructure and mechanical behavior of Sn-Bi/Cu solder joints are reported. Lap shear solder joints of eutectic Sn-Bi solder were aged for 3 to 30 days at 80°C and then loaded to failure in shear. Changes in the joint microstructure including interphase coarsening, intermetallic growth, and evolution of the intermetallic/solder interface are documented. The aging experiments reveal the segregation of the Bi-rich phase of the solder to the intermetallic/solder interface. The ultimate shear strength and ductility of the joints are reported at strain rates of 4.0 × 10−1 to 4.0 × 10−5 S−1 for 3 and 30 days aging. The strength of the joints decreases with strain rate for both aging conditions; the ductility is low and independent of strain rate for the joints aged three days and increases considerably with reduced strain rate for joints, aged 30 days. Fractographs and cross sections of the failed joints detail the effect of aging on the fracture mechanism.

The effect of strain rate sensitivity on dynamic friction of metals

Abstract: A simple model relating the plastic constitutive equation to the static and the dynamic coefficient of friction has been developed. It can describe the time dependent effects in static solid friction, as well as predict some special features of the dynamic friction coefficient which may be of relevance for stick-slip phenomena in solid friction. In particular, the model highlights the effect of the intrinsic material characteristic, viz. the strain rate sensitivity of the flow stress, on the friction properties.

Microstructural control in hot working of IN-718 superalloy using processing map

Abstract: The hot-working characteristics of IN-718 are studied in the temperature range 900 °C to 1200 °C and strain rate range 0.001 to 100 s−1 using hot compression tests. Processing maps for hot working are developed on the basis of the strain-rate sensitivity variations with temperature and strain rate and interpreted using a dynamic materials model. The map exhibits two domains of dynamic recrystallization (DRX): one occurring at 950 °C and 0.001 s−1 with an efficiency of power dissipation of 37 pct and the other at 1200 °C and 0.1 s−1 with an efficiency of 40 pct. Dynamic recrystallization in the former domain is nucleated by the δ(Ni3Nb) precipitates and results in fine-grained microstructure. In the high-temperature DRX domain, carbides dissolve in the matrix and make interstitial carbon atoms available for increasing the rate of dislocation generation for DRX nucleation. It is recommended that IN-718 may be hot-forged initially at 1200 °C and 0.1 s−1 and finish-forged at 950 °C and 0.001 s−1 so that fine-grained structure may be achieved. The available forging practice validates these results from processing maps. At temperatures lower than 1000 °C and strain rates higher than 1 s−1 the material exhibits adiabatic shear bands. Also, at temperatures higher than 1150°C and strain rates more than 1s−1, IN-718 exhibits intercrystalline cracking. Both these regimes may be avoided in hotworking IN-718.

Shear and elongational flow properties of polypropylene meltsa)

Abstract: The rheological properties of polypropylene melts were investigated in oscillatory shear flow, capillary rheometry, and uniaxial elongation at constant tensile stress as well as constant strain rate. At small stresses the steady‐state elongational viscosity of linear conventional polypropylene has the threefold value of the shear viscosity. With increasing stress both the shear and elongational viscosity decrease. The transient elongational viscosity at constant strain rate is equal to the threefold value of the linear viscoelastic stressing viscosity as calculated from the relaxation time spectrum. In contrast, long chain branched polypropylene shows a maximum in the steady‐state elongational viscosity and pronounced strain hardening in experiments at constant strain rate above an elongation of e=1. These phenomena are obtained by less than three branches per molecule. The description of the strain hardening by means of the Lodge model underestimates the measured data at deformation rates less than e=0.2 s−1. An improvement is obtained by adding a rubber‐like stress component to the tensile stress.

Softening and microstructural change following the dynamic recrystallization of austenite

Abstract: To characterize the dynamic recrystallization behavior of austenite, continuous-torsion tests were carried out on a Mo steel over the temperature range 950 ‡C to {dy1000} ‡C, and at strain rates of 0.02, 0.2, and 2 s-1. Interrupted-torsion tests also were performed to study the characteristics of postdynamic recrystallization. Quenches were performed after increasing holding times to follow the development of the postdynamic microstructure. Finally, torsion simulations were carried out to assess the importance of metadynamic recrystallization in hot-strip mills. The postdynamic microstructure shows that the growth of dynamically recrystallized grains is the first change that takes place. Then metadynamically recrystallized grains appear and contribute to the softening of the material. The rate of metadynamic recrystallization and the meta-dynamically recrystallized grain size depend on strain rate and temperature and are relatively independent of strain, in contrast to the observations for static recrystallization. True dynamic recrystallization-controlled rolling (DRCR) is shown to require such short interpass times that it does not occur in isolation in hot-strip mills. As these schedules involve 20 to 80 pct softening by metadynamic recrystallization, a new concept known as metadynamic recrystallization-controlled rolling (MDRCR) is introduced to describe this type of situation.

High-temperature deformation of 6061 Al

Abstract: The creep behavior of powder metallurgy (PM) 6061 Al, which has been used as a metal matrix alloy in the development of discontinuous silicon carbide reinforced aluminum (SiCAl) composites, has been studied over six orders of magnitude of strain rate. The experimental data show that the steady-state stage of the creep curve is of short duration; that the stress dependence of creep rate is high and variable; and that the temperature dependence of creep rate is much higher than that for self-diffusion in aluminum. The above creep characteristics are different from those documented for aluminum based solid-solution alloys but are similar to those reported for discontinuous SiCAl composites and dispersion-strengthened (DS) alloys. Analysis of the experimental data shows that while the high stress dependence of creep rate in 6061 Al, like that in DS alloys, can be explained in terms of a threshold stress for creep, the strong temperature dependence of creep rate in the alloy is incompatible with the predictions of available threshold stress models and theoretical treatments proposed for DS alloys.

Hydrogen effects on deformation -- relation between dislocation behavior and the macroscopic stress-strain behavior

Abstract: Direct observations of the effects of H on dislocation mobility, carried out using an environmental cell TEM technique, have shown that the presence of H in solid solution increases the dislocation velocities at constant stress for edge, screw, and mixed dislocations and for isolated dislocations and dislocations in tangles.'' This increased dislocation velocity due to H has been observed in fcc, bcc, and hcp systems and in relatively pure'' materials, in solid solution alloy, in precipitation strengthened alloys, and in gamma prime strengthened alloys. Hydrogen softening'' or increased dislocation mobility due to hydrogen has been shown to result from elastic shielding'' which minimizes the elastic interaction between dislocations and obstacles. In contrast to the microscopic observations, many stress-strain measurements show an increase in the measured stress for plastic deformation when H is used as an alloy element. There remain significant differences in observations of the effects of H on the flow stress of metals. The present paper discusses one aspect of this problem, the effects of H on shear localization, which may account for the discrepancies.