Showing papers on "Strain rate published in 1987"

Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence

Abstract: The alignment between vorticity and eigenvectors of the strain‐rate tensor in numerical solutions of Navier–Stokes turbulence is studied. Solutions for isotropic flow and homogeneous shear flow from pseudospectral calculations using 1283 grid points have been examined. The Taylor Reynolds number is 83 or greater. In both flows there is an increased probability for the vorticity to point in the intermediate strain direction and at three‐fourths of the sample points this strain is positive (extensive). This propensity for vorticity alignment with a positive intermediate strain is a consequence of angular momentum conservation, as shown by a restricted Euler model of the coupling between strain and vorticity. Probability distributions for intermediate strain, conditioned on total strain, change from a symmetric triangular form at small strain to an asymmetric one for large strain. The most probable value of the asymmetric distribution gives strains in the ratios of 3:1: −4. The evolution of the distribution from a symmetric to an asymmetric form as the strain magnitude increases is essentially the same in both flows, indicating a generic structure of intense turbulence. The alignment between the gradient of a passive scalar and eigenvectors of the strain‐rate tensor for Prandtl numbers of 0.1, 0.2, 0.5, and 1.0 has also been studied. There is an increased probability for the scalar gradient to align in the most compressive strain direction, and the average gradient is larger when it is pointing in that direction. Estimates for the scalar dissipation from the turbulent kinetic energy, its dissipation, and the root‐mean‐square scalar value are in reasonable agreement with calculated scalar dissipation if no explicit Prandtl number dependence is used in the estimate. Statistical analysis of scalar dissipation conditioned on energy dissipation yields a power‐law relation between conditioned mean values. Both simulated flows are found to obey the qualitative predictions of the Gurvich–Yaglom (lognormal) intermittency model. Energy and scalar intermittency exponents are estimated and compared to measured values.

Measurement of the temperature profile during shear band formation in steels deforming at high strain rates.

Abstract: A torsional Kolsky bar (split-Hopkinson bar) was used to deform tubular specimens of AISI 1018 cold rolled steel and AISI 1020 hot rolled steel at a nominal strain rate of 103s−1. Shear bands were observed to form in both steels, and the temperature of the material in the bands was measured by determining the infrared radiation emitted at the metal surface. For this purpose, a linear array of ten indium-antimonide detectors was used to determine temperature history at ten neighboring points lying across the projected path of the shear band. Results showed that shear bands in these steels are relatively wide, that the maximum temperature rise in the band is about 450°C and that the temperature distribution across the band is consistent with results of stability analyses. The two steels have very different work hardening rates and the strain at which localization is first observed is very different for the two steels : in the cold-rolled steel it occurs at about 15% strain, while in the hot-rolled the strain is near 100%. This result also is consistent with predictions of the analyses.

Analytical Characterization of Shear Localization in Thermoviscoplastic Materials

Abstract: : Critical conditions for shear localization in thermoviscoplastic materials are obtained in closed form for idealized models of simple shearing deformations. The idealizations, which include the neglect of heat conduction, inertia, and elasticity, are viewed as quite acceptable for many applications in which shear bands occur. Explicit results obtained for the idealized, but fully nonlinear problem show the roles of strain rate sensitivity, strain hardening, and initial imperfection on the localization behavior. Numerical solutions for two steels are shown to exhibit the principal features reported for torsional Kolsky bar experiments on these steels. Mathematically exact critical conditions obtained for the fully nonlinear problem are compared with critical conditions obtained by means of linear perturbation analysis gives better agreement with the predictions fo the fully nonlinear analysis.

The growth of unstable thermoplastic shear with application to steady-wave shock compression in solids*

Abstract: T he catastrophic growth of unstable thermoplastic shear following the transition from homogeneous deformation to heterogeneous localized deformation through distributed shear banding is studied through approximate analytic and computational methods. The calculations provide expressions for shear band widths, spacing, catastrophic growth times and the rate of stress communication between shear bands. The optimum shear band width and spacing are found to be consistent with a minimum work principle. The model predicts that the product of the energy dissipated and the localization time in the shear localization process is invariant with respect to changes in the driving strain rate. Such behavior has been noted in the steady-wave shock compression of a number of solids. The calculations are applied to heterogeneous shear localization observed in the shock compression of aluminum.

Rate effects and cyclic loading of sensitive clays

Abstract: The paper presents the results of a series of monotonic and cyclic triaxial tests carried out to study the influence of the rate of strain and load cycles on the undrained shear strength of three undisturbed sensitive clays from eastern Canada. For structured clays (naturally overconsolidated), pore pressures generated at a given deviator are essentially independent of the strain rate, while the peak strength envelope is lowered as the strain rate is decreased. For destructured clay (normally consolidated), a lower strain rate results in an increase in pore pressure generation during shearing, due to the tendency of the clay skeleton to creep, while the peak strength envelope remains the same. Nevertheless, from a quantitative standpoint, the increase in shear strength caused by an increase in strain rate is similar for both structured and normally consolidated clay, and it is linear for at least five log cycles of strain rate.

The Orientation of Spheroidal Microorganisms Swimming in a Flow Field

Abstract: This paper shows how to calculate local equilibrium orientations of inhomogeneous spheroidal particles placed in a flow field. The results can be applied either to dilute suspensions of inert particles or to swimming microorganisms; illustrative examples are chosen with the latter appli­cation in mind. The centre of mass of a particle is displaced from the geometric centre C along the axis of symmetry, and the orientation of this axis (represented by the unit vector p ) is determined from the balance between the gravitational couple, non-zero when p is not vertical, and the viscous couple exerted by the surrounding fluid. Fluid and particle inertia are neglected. ‘Local equilibrium’ means that p is stationary in a suitable frame of reference, which may be the laboratory frame or one rotating rigidly relative to it, at the values of fluid velocity, vorticity and rate of strain evaluated at C in the absence of the particle. It is also shown how to determine the stability of local equilibria. Stable equilibrium values of p are calculated explicitly for a number of experimentally realizable flow fields, including vertical Poiseuille flow in a pipe, conical sink flow, two-dimensional straining and shearing flows in a vertical plane, and the wake of a falling sphere. The analysis is particularly simple for spherical particles, when the local rate of strain does not contribute to the viscous couple. The results have implications for laboratory manipulation of the trajectories of swimming algae, and for the develop­ment of collective behaviour and the existence of critical phenomena in suspensions of them.

Yielding and deformation behavior of the single crystal superalloy PWA 1480

Abstract: Interrupted tensile tests were conducted to fixed plastic strain levels in 100 ordered single crystals of the nickel based superalloy PWA 1480. Testing was done in the range of 20 to 1093 C, at strain rate of 0.5 and 50 percent/min. The yield strength was constant from 20 to 760 C, above which the strength dropped rapidly and became a strong function of strain rate. The high temperature data were represented very well by an Arrhenius type equation, which resulted in three distinct temperature regimes. The deformation substructures were grouped in the same three regimes, indicating that there was a fundamental relationship between the deformation mechanisms and activation energies. Models of the yielding process were considered, and it was found that no currently available model was fully applicable to this alloy. It was also demonstrated that the initial deformation mechanism (during yielding) was frequently different from that which would be inferred by examining specimens which were tested to failure.

Histograms of helicity and strain in numerical turbulence.

Abstract: Histograms of the normalized values of the helicity and the smallest principal component of the rate of strain are found for one realization of a ${128}^{3}$ isotropic simulation of forced turbulence. In regions of high dissipation the strain has a structure indicating sheets. Peak-to-valley ratios in the helicity histograms are less than in other numerical flows and this ratio decreases further when the helical large scales are filtered or active regions characterized by the strain are sampled.

Steel Mechanical Properties at Different Strain Rates

Abstract: Dynamic test results reported by different investigators on structural steel, deformed reinforcing bars, and deformed wires subjected to monotonic tension are used for deriving empirical expressions for the ratios of static to dynamic values of the yield and ultimate stresses, yield and ultimate strains, and the strain at the end of the yield plateau. The principal variables in the expressions are the rate of straining and the steel static yield strength. These expressions are then used for developing dynamic constitutive models for monotonically loaded steel.

Effect of composition and grain size on slow plastic flow properties of NiAl between 1200 and 1400 K

Abstract: A series of about 15-micron diameter polycrystalline B2 crystal structure NiAl alloys ranging in composition from 43.9 to 52.7 Al (at. pct) have been compression tested at constant velocities in air between 1200 and 1400 K. All materials were fabricated via powder metallurgy techniques with hot extrusion as the densification process. Seven intermediate compositions were produced by blending various amounts of two master heats of prealloyed powder; in addition, a tenth alloy of identical composition, 48.25 Al, as one of the blended materials, was produced from a third master heat. Comparison of the flow stress-strain rate behavior for the two 48.25 Al alloys revealed that their properties were identical. The creep strength of materials for Al/Ni not above 1.03 was essentially equal, and deformation could be described by a single stress exponent and activation energy. Creep at low temperatures and faster strain rates is independent of grain sizes and appears to be controlled by a subgrain mechanism. However, at higher temperatures and slower strain rates, diffusional creep seems to contribute to the overall deformation rate.

Current Topics in Corrosion: Factors Influencing Stress Corrosion Crack Growth Kinetics

Abstract: One of the problems in relation to predicting the rates of defect growth in structures displaying stress corrosion cracking (SCC) is that knowledge relating to realistic stress corrosion crack velocities is very limited. In monotonic slow strain rate tests (SSRTs) taken to total failure at usual strain rates and in tests on precracked specimens at stress intensity factors in excess of KISCC, stress corrosion crack velocities may be appreciably higher than are likely to occur in service, except in the very late stages of crack growth before a service failure. These differences probably develop partly because of differences in the effective crack tip strain rate, and consideration is given to various expressions for calculating the latter from the applied strain rate. For multiple cracked specimens, as in SSRTs, the importance of considering the number of cracks is demonstrated, in which case it is possible to calculate (involving electrochemical data) the crack velocity-strain rate relationships i...

Models of viscoplasticity some comments on equilibrium (back) stress and drag stress

Abstract: Phenomenological and microstructural motivations for the terms appearing in the title are found in a literature survey. Although the interpretations differ with various investigators a strong tendency is observed to consider plastic flow as rate dependent. It is stated that plastic strain takes time to develop and the existnce of an equilibrium stress is postulated at which plastic strain is fully developed. It is similar to the back stress used in materials science. The drag stress introduced from microdynamical studies performs the same function as the isotropic variable in plasticity. Most of the theories that describe the transient and steady-state behavior of metallic alloys make the inelastic strain rate a function of the over (effective) stress. It is shown that this concept has considerable advantages in the modeling of changes of viscous (time- or rate-dependent) and plastic (time- or rate-independent) contributions to hardening that are observed in cyclic loading and dynamic plasticity.

Dislocation glide motion in 6H SiC single crystals subjected to high-temperature deformation

Abstract: SiC single crystals of 6H polytype were plastically deformed by uniaxial compression at a constant strain rate at temperatures between 1100 and 1800°C, and their critical resolved shear stress τc and strain-rate sensitivity were measured as a function of temperature. The flow rate [ydot] was found to be expressible in the form [ydot] (τc − τi) n exp (−U/kT), where the activation energy U, the stress exponent n and the stress τi were evaluated to be 3·4 ± 0·7 eV, 3·1 ± 0·4 and 3 MPa, respectively. The present study indicates that plastic strain of the SiC crystals under the present deformation conditions was due to dislocation glide motion on the basal slip system. The motion also appears to have been the rate-controlling process of plastic flow. It is concluded through quantitative reasoning that, in the temperature range studied, the basal dislocation motion is dominated by the Peierls mechanism rather than by the solution-hardening mechanism.

Experimental study of strain-rate dependence and pressure dependence of failure properties of granite

Abstract: Effects of the strain rate and pressure on various brittle properties of granite under compressional loading are studied experimentally. Granite specimens were tested to failure under various constant strain rates at confining pressures of 0.1 to 200 MPa. The strain rates in these tests varied from 10-4 to 10-8s-1. The results show that the strength of granite decreases linearly as the logarithm of the strain rate decreases, and that the strain-rate dependence on the strength is enhanced at high confining pressures. The dilatant strain and elastic wave velocity variations with stress were found to be independent of the strain rate if the stress is normalized by the strength. The dilatant-strain-versus-stress curve is significantly affected by confining pressure but the confining pressure effect on the dilatant strain versus normalized stress is small. The acoustic emission rate is accelerated at a stress level closer to the failure strength as the strain rate decreases. Some of the timedependent properties are explained by a theory based on the concept of subcritical stress-corrosion cracking. But it is also clear that the stress-corrosion cracking theory does not provide reasonable explanations of the variation of acoustic emission rate with stress and the variation of strain with stress at the stage immediately before fracture.

Temperature and strain‐rate dependence of the flow stress of ultrapure tantalum single crystals

Abstract: Measurements of the temperature dependence of the cyclic flow stress of ultrapure tantalum single crystals (RRR ⪆ 14000) are extended to lower temperatures. After cyclic deformation well into saturation at 400 K, the temperature dependence of the flow stress is measured between 80 and 460 K at five different plastic resolved shear-strain rates, e, in the range 2 × 10−5 to 6 × 10−3 s−1. Below a critical temperature Tk the flow stress is dominantly controlled by the mobility of screw dislocations. A recent theory of Seeger describes the “thermal” component, σ*, of the flow stress (resolved shear stress) in the temperature and stress regime where the strain rate is determined by the formation and migration of kink pairs. The analytical expressions are valid in well-defined ranges of stress and temperature. The evaluation of the experimental data yields a value for the formation enthalpy of two isolated kinks 2Hk = 0.98 eV. From the low-stress (σ* < 10 MPa) data at higher temperatures the diffusion coefficient of kinks is evaluated as Dk = 2.0 × 10−6 m2 s−1. The product of the density of mobile screw dislocations and the distance between insurmountable obstacles is found to be 2 × 10−5 m−1. The stress dependence of the kink-pair formation enthalpy Hkp follows the theoretically predicted curve in the elastic-interaction stress regime. At the transition to the line-tension approximation (near σ* ≈ 80 MPa) the activation volume increases rather abruptly. Moreover, the quantitative analysis involves kinks other than those of minimum height. The most likely candidates are kinks on {211} planes.

Formulation of Static Recrystallization of Austenite in Hot Rolling Process of Steel Plate

Abstract: A critical condition for static recrystallization of austenite (γ) in plate rolling process has been formulated in terms of the change in average dislocation density. The latter was calculated from the decrease in stress due to recovery and recrystallization observed by the double deformation tests. The main results are summarized as follows:(1) The relation among stress, strain and average dislocation density has been formulated. By the present formulation, deformation stress for practical conditions of the controlled rolling of plate can be calculated as a function of temperature, strain, strain rate and γ grain size.(2) The behavior of static recovery and recrystallization taking place during holding period after deformation has also been formulated as a function of dislocation density. This formulation makes it possible to estimate the critical condition for static recrystallization during an interval time between the successive rolling passes of plate.(3) Deformation conditions such as temperature, strain, strain rate, γ grain size and interval time between passes affect the critical condition for recrystallization. The shorter interval time elevates the temperature limit of non recrystallization.

INELASTIC PROPERTIES OF ICE Ih AT LOW TEMPERATURES AND HIGH PRESSURES

Abstract: The aim was to explore the rheological behavior of H/sub 2/O ices under conditions appropriate to the interiors of the icy satellites of the outer planets in order to give insight into their deformation. To this end, we have performed over 100 constant-strain-rate compression tests at pressures to 500 MPa and temperatures as low as 77 K. The effect of increasing confining pressure on stress-strain behavior and deformation mechanisms depends on the test temperature. At a strain rate of 3.5 x 10/sup -5/ s/sup -1/, ice I/sub h/ fails catastrophically at temperatures below 165 K at all pressures tested (0.1 to 350 MPa). Failure strength increases sharply with increasing pressure. At P > 30 MPa, ice I/sub h/ fails by a shear instability producing faults in the maximum shear stress orientation and failure strength typically is independent of pressure. We have also studied the frictional sliding characteristics of ice I/sub h/ by shortening cylindrical specimens sawn and ground at 45/sup 0/ to the cylindrical axis. We observed sudden (stick slip) frictional sliding with the maximum shear strength necessary to overcome static friction tau obeying the simple law tau (MPa) = 8.5 + 0.2 sigma/sub n/ (MPa) where sigma/sub n/ ismore » the normal stress on the sliding surface. This law was determined over the range 17 less than or equal to sigma/sub n/ less than or equal to 240 MPa and is insensitive to temperature and sliding rate over the range of conditions we explored. Stress-strain curves under ductile conditions typically display a linear quasi-elastic stage followed by macroscopic yield, strain softening and finally a flat steady state flow. Optical study of thin sections of samples taken to various strains shows that macroscopic yield corresponds to the first optical evidence of internal plastic deformation, that nucleation and rapid growth of new grains accompanies strain softening and that steady-state flow corresponds to the attainment of a steady-state recrystallization structure.« less

Effect of Hydrogen on the Intergranular Stress Corrosion Cracking of Alloy 600 in High Temperature Aqueous Environments

Abstract: Slow strain rate tests (SSRTs) on differently shaped tensile specimens machined from two heats of Alloy 600 tubing were conducted at 350 C in deaerated aqueous solutions containing small a...