Showing papers on "Strain rate published in 1999"

Subgrid-scale stress modelling based on the square of the velocity gradient tensor

Abstract: A new subgrid scale model is proposed for Large Eddy Simulations in complex geometries. This model which is based on the square of the velocity gradient tensor accounts for the effects of both the strain and the rotation rate of the smallest resolved turbulent fluctuations. Moreover it recovers the proper y 3 near-wall scaling for the eddy viscosity without requiring dynamic procedure. It is also shown from a periodic turbulent pipe flow computation that the model can handle transition.

Indentation power-law creep of high-purity indium

Abstract: Using a variety of depth-sensing indentation techniques, the creep response of high-purity indium, from room temperature to 75 °C, was measured. The dependence of the hardness on the variables of indentation strain rate (stress exponent for creep (n)) and temperature (apparent activation energy for creep (Q)) and the existence of a steady-state behavior in an indentation test with a Berkovich indenter were investigated. It was shown for the first time that the indentation strain rate (-este-/h) could be held constant during an experiment using a Berkovich indenter, by maintaining the loading rate divided by the load (-este-/P) constant. The apparent activation energy for indentation creep was found to be 78 kJ/mol, in accord with the activation energy for self-diffusion in the material. Finally, by performing -este-/P change experiments, it was shown that a steady-state path independent of hardness could be reached in an indentation test with a geometrically similar indenter.

Flow behavior and globularization kinetics during hot working of Ti–6Al–4V with a colony alpha microstructure

Abstract: The effect of process variables on flow response and microstructure evolution during hot working of Ti–6Al–4V with a colony alpha preform microstructure was established using isothermal hot compression tests. Testing was conducted on material with prior-beta grain sizes of 100 μm or 400 μm at strain rates of 0.001–10 s−1, test temperatures between 815 and 955°C, and height reductions of 40–80%. All of the flow curves exhibited a peak stress followed by moderate flow softening. The absence of a grain/colony size dependence of flow behavior, coupled with relatively low values of the strain rate sensitivity of the flow stress (∼0.05–0.30), led to the conclusion that deformation was controlled by dislocation glide/climb processes. Flow softening was interpreted in terms of deformation heating and substructure/texture evolution. The dependence on strain rate and temperature of the kinetics of dynamic globularization of the colony microstructure was complex and appeared to be of second-order importance compared to the effects of strain per se, thus suggesting the dominance of dislocation-type processes for the control of globularization as well.

Strain Rate Induced Amorphization in Metallic Nanowires

Abstract: Using molecular dynamics simulations with a many-body force field, we studied the deformation of single crystal Ni and NiCu random alloy nanowires subjected to uniform strain rates but kept at 300 K. For all strain rates, the Ni nanowire is elastic up to 7.5% strain with a yield stress of 5.5 GPa, far above that of bulk Ni. At high strain rates, we find that for both systems the crystalline phase transforms continuously to an amorphous phase, exhibiting a dramatic change in atomic short-range order and a near vanishing of the tetragonal shear elastic constant perpendicular to the tensile direction. This amorphization which occurs directly from the homogeneous, elastically deformed system with no chemical or structural inhomogeneities exhibits a new mode of amorphization.

Hydrogen transport near a blunting crack tip

Abstract: The hydrogen transport model of Sofronis and McMeeking was used in order to simulate the effect of the hydrostatic stress and trapping on the hydrogen distribution in a plastically deforming steel. In this model it is assumed that hydrogen atoms diffuse through lattice sites and that trap sites are filled by lattice diffusion. These trap sites are formed due to plastic deformations. Coupled diffusion elastic–plastic finite element analyses were carried out in order to investigate the hydrogen concentration in lattice and trap sites near a blunting crack tip under small-scale yielding conditions. The numerical results of Sofronis and McMeeking were reproduced and it was found that in their model hydrogen is created. The hydrogen balance is satisfied by including a strain rate factor in the hydrogen transport equation. As a consequence no differences were found at steady state, i.e. at low strain rates. The strain rate factor decreases the hydrogen concentration in lattice sites due to the filling of trap sites. When the strain rate is sufficiently high, the lattice sites can be almost depleted of hydrogen while trap sites remain saturated. The modified hydrogen transport model predicts strong dependence of the hydrogen concentration in lattice sites on the strain rate, while the hydrogen concentration in trap sites is not affected significantly. The modified hydrogen transport model provides greater insight into the strain rate dependence of hydrogen embrittlement as observed in tensile tests.

A Study of the Evolution and Characteristics of the Invariants of the Velocity Gradient Tensor in Isotropic Turbulence

Abstract: Since the availability of data from direct numerical simulation (DNS) of turbulence, researchers have utilized the joint PDFs of invariants of the velocity gradient tensor to study the geometry of small-scale motions of turbulence. However, the joint PDFs only give an instantaneous static representation of the properties of fluid particles and dynamical Lagrangian information cannot be extracted. In this paper, the Lagrangian evolution of the invariants of the velocity gradient tensor is studied using conditional mean trajectories (CMT). These CMT are derived using the concept of the conditional mean time rate of change of invariants calculated from a numerical simulation of isotropic turbulence. The study of the CMT in the invariant space (RA, QA) of the velocity-gradient tensor, invariant space (RS, QS) of the rate-of-strain tensor, and invariant space (RW, QW) of the rate-of-rotation tensor show that the mean evolution in the (Σ, QW) phase plane, where Σ is the vortex stretching, is cyclic with a characteristic period similar to that found by Martin et al. (1998) in the cyclic mean evolution of the CMT in the (RA, QA) phase plane. Conditional mean trajectories in the (Σ, QW) phase plane suggest that the initial reduction of QW in regions of high QW is due to viscous diffusion and that vorticity contraction only plays a secondary role subsequent to this initial decay. It is also found that in regions of the flow with small values of QW, the local values of QW do not begin to increase, even in the presence of self-stretching, until a certain self-stretching rate threshold is reached, i.e. when Σ≈0.25 〈QW〉1/2. This study also shows that in regions where the kinematic vorticity number (as defined by Truesdell 1954) is low, the local value of dissipation tends to increase in the mean as observed from a Lagrangian frame of reference. However, in regions where the kinematic vorticity number is high, the local value of enstrophy tends to decrease. From the CMT in the (−QS, RS phase plane, it is also deduced that for large values of dissipation, there is a tendency for fluid particles to evolve towards having a positive local value of the intermediate principal rate of strain.

Molecular-dynamics study of ductile and brittle fracture in model noncrystalline solids

Abstract: Molecular-dynamics simulations of fracture in systems akin to metallic glasses are observed to undergo embrittlement due to a small change in interatomic potential. This change in fracture toughness, however, is not accompanied by a corresponding change in flow stress. Theories of brittle fracture proposed by Freund and Hutchinson indicate that strain rate sensitivity is the controlling physical parameter in these cases. A recent theory of viscoplasticity in this class of solids by Falk and Langer further suggests that the change in strain rate sensitivity corresponds to a change in the susceptibility of local shear transformation zones to applied shear stresses. A simple model of these zones is developed in order to quantify the dependence of this sensitivity on the interparticle potential.

Mechanical Behavior of an Ni-Ti Shape Memory Alloy Under Axial-Torsional Proportional and Nonproportional Loading

Abstract: Several biaxial proportional and nonproportional loading experiments are reported for thin-wall tubes of a pseudoelastic Ni-Ti shape memory alloy (SMA). In addition to the mechanical behavior, temperature was measured during the experiments. It is shown that the phase transformation exhibits asymmetrical behavior in the case of tension-compression cycling. The transformation strain rate is determined for selected histories by numerical differentiation of data. Under nonproportional loading, the rate of phase transformation does not follow a generalized J{sub 2}-J{sub 3} criteria based on results of micromechanical simulations for proportional loading. The role of simultaneous forward and reverse transformations on the nonproportional transformation response is examined using a simple micromechanical model, and the direction of the inelastic strain rate is adequately predicted. Load- and strain-controlled experiments at different strain rates, with and without hold times, are reported and coupled thermomechanical effects are studied.

Effect of Temperature and Strain Rate on Mechanical Properties of 63Sn/37Pb Solder Alloy

Abstract: In this study, tensile tests of 63Sn/37Pb solder were carried out at various strain rates from 10 s to 10 s over a wide temperature range from – 40 C to 125 C to study the effect of strain rate and testing temperature on the mechanical properties in a systematic manner. Based on these experimental data, a set of empirical formulae was derived by a statistical method to describe the effect of temperature and strain rate in a quantitative manner and explain the variation in the mechanical properties published in other reports. It is concluded that the empirical formulae can be used to characterize the mechanical properties of 63Sn/37Pb over a wide range of temperatures and strain rates.

The viscoplastic compaction of composite powders

Abstract: A model for the densification of spherical powders is developed for the early stages of cold and hot compaction under general loading. General viscoplastic properties are adopted which reduce to strain hardening plasticity at ambient temperature and to power law creep at elevated temperature. A large strain analysis is carried out to determine the macroscopic compaction behaviour, based on the affine motion of particles with viscoplastic dissipation occurring at the contacts between particles. Random packing is assumed and the model includes the increase in the number of contacts per particle with densification. A general prescription is given for computing the macroscopic stress as a function of strain rate and accumulated strain. Detailed results are presented for yield surfaces and creep dissipation surfaces after isostatic and closed die compaction. A scalar constraint factor is derived for a random mixture of two populations of particles with different sizes and strengths. The predictions include the limiting case of deformable spheres reinforced with rigid spheres of different size.

Influence of pressing speed on microstructural development in equal-channel angular pressing

Abstract: The influence of pressing speed in equal-channel angular (ECA) pressing was investigated using samples of pure Al and an Al-1 pct Mg alloy and a range of pressing speeds from ∼10−2 to ∼10 mm s−1. The results show that the speed of pressing has no significant influence on the equilibrium grain size, at least over the range used in these experiments. Thus, the equilibrium grain sizes were ∼1.2 µm for pure Al and ∼0.5 µm for the Al-1 pct Mg alloy for all pressing conditions. However, it is shown that the nature of the microstructure is dependent on the pressing speed, because recovery occurs more easily at the slower speeds, so that the microstructure is then more equilibrated. There is also indirect evidence for the advent of frictional effects when the cross-sectional dimensions of the samples are at or below ∼5 mm.

A simple parameterization of strain localization in the ductile regime due to grain size reduction: A case study for olivine

Abstract: We propose a simple parameterization of the transition between dislocation creep and grain-size-sensitive creep under conditions characteristic of the lithospheric mantle and derived from the results of laboratory experiments on olivine-rich rocks. Through numerical modeling and linear stability analysis, we determine the conditions under which this transition takes place and potentially leads to strain localization. We pay particular attention to the effect of cooling rate and strain rate which are likely to be dominant parameters in actively deforming tectonic areas. We conclude that at constant temperature, strain localization can only take place if the rheology of the material is nonlinearly related to grain size; that strain localization is facilitated by syndeformation cooling; that there is only a narrow region in the strain rate versus cooling rate parameter space where localization is likely to take place; and that grain growth inhibits strain localization at fast cooling rates but may lead to “grain growth localization” at low cooling rates. We draw attention to the potential consequences of our analysis of strain localization for the style of plate motions at the Earth's surface.

On the extrusion stage of linear friction welding of Ti 6Al 4V

Abstract: The extrusion phase of linear friction welding of Ti 6Al 4V, which has been shown to have an important effect on weld integrity, is investigated. The position of the area at the rubbing interface where the maximum frictional heat input develops is shown to depend on the amplitude of oscillation. This is corroborated with macroscopic examination of the flash and axial shortening data from experiments. An analytical model is developed to predict the strain rates that the material at the plasticised zone of the interface is exposed to, using phenomenological experimental data.

Strain-rate effects on Hardness of glassy polymers in the nanoscale range. Comparison between quasi-static and continuous stiffness measurements

Abstract: Strain rate effects on Hardness and Young's modulus of two glassy polymers, poly(diethylene glycol bis allyl carbonate) (CR39) and bisphenol-A polycarbonate (PC), were studied in the nanoscale range. Before analyzing material behaviors, we focused on a particular phenomenon prevailing at the first stage of the contact between the surface of these polymers and the Berkovitch diamond tip used in the experiments, leading to an apparent increase of the tip defect (i.e., the missing tip of the diamond from having a shape equivalent to a perfect cone). The common methods based on calibration functions of the tip appear to be inaccurate to calculate correctly the contact area at the nanoscale range for these polymers. A new method based on Loubet et al.'s model to calculate the contact area by taking account of the apparent tip defect is proposed. The hardness values obtained this way were compared to the compressive yield stress using Tabor's relationship. A hardness-yield stress ratio close to 2.0, as...

Workability of commercial-purity titanium and 4340 steel during equal channel angular extrusion at cold-working temperatures

Abstract: The deformation and failure of commercial-purity (CP) titanium (grade 2) and AISI 4340 steel (tempered to Rc35) during equal channel angular extrusion were determined at temperatures between 25 °C and 325 °C and effective strain rates between 0.002 and 2.0 s−1. The CP titanium alloy underwent segmented failure under all conditions except at low strain rates and high temperatures. By contrast, the 4340 steel deformed uniformly except at the highest temperature and strain rate, at which it also exhibited segmented failure. Using flow curves and fracture data from uniaxial compression and tension tests, workability analysis was conducted to establish that the failures were a result of flow localization prior to the onset of fracture. This conclusion was confirmed by metallographic examination of the failed extrusion specimens.

Does the tracer gradient vector align with the strain eigenvectors in 2D turbulence

Abstract: This paper investigates the dynamics of tracer gradient for a two-dimensional flow. More precisely, the alignment of the tracer gradient vector with the eigenvectors of the strain-rate tensor is studied theoretically and numerically. We show that the basic mechanism of the gradient dynamics is the competition between the effects due to strain and an effective rotation due to both the vorticity and to the rotation of the principal axes of the strain-rate tensor. A nondimensional criterion is derived to partition the flow into different regimes: In the strain dominated regions, the tracer gradient vector aligns with a direction different from the strain axes and the gradient magnitude grows exponentially in time. In the strain-effective rotation compensated regions, the tracer gradient vector aligns with the bisector of the strain axes and its growth is only algebraic in time. In the effective rotation dominated regions, the tracer gradient vector is rotating but is often close to the bisector of the strain axes. A numerical simulation of 2D (two-dimensional) turbulence clearly confirms the theoretical preferential directions in strain and effective rotation dominated regions. Effective rotation can be dominated by the rotation rate of the strain axes, and moreover, proves to be larger than strain rate on the periphery of vortices. Taking into account this term allows us to improve significantly the Okubo–Weiss criterion. Our criterion gives the correct behavior of the growth of the tracer gradient norm for the case of axisymmetric vortices for which the Okubo–Weiss criterion fails.

Stabilization and high strain-rate superplasticity of metallic supercooled liquid

Abstract: Conventional bulk metallic materials have ordinarily been produced by the melting and solidification processes. The metallic liquid is unstable at temperatures below melting temperature and solidifies immediately into crystalline phases. Consequently, all bulk engineering alloys had been composed of a crystalline structure. Recently, the common concept has been exploded by the findings of the stabilization phenomenon of supercooled liquid for a number of alloys in Mg-, lanthanide-, Zr-, Ti-, Fe-, Co- and Pd–Cu-based systems. The alloys with the stabilized supercooled liquid state have three features in their alloy components, i.e. multi-component systems, significant atomic size ratios above 12%, and negative heats of mixing. The stabilization mechanism has also been investigated from experimental data of structure analyses and fundamental physical properties. The stabilization has enabled the production of bulk amorphous alloys in the thickness range of 1–100 mm by using various casting processes. The bulk amorphous Zr-based alloys exhibit high mechanical strength, high fracture toughness and good corrosion resistance. The stabilization also leads to the appearance of a wide supercooled liquid region before crystallization and enables the achievement of high-strain superplasticity through Newtonian flow in the supercooled liquid region. The Newtonian flow in the strain rate range just below the transition from Newtonian to non-Newtonian flow was also found to cause the suppression of crystallization of the supercooled liquid. In addition to the finding of the stabilization phenomenon, the clarification of the stabilization criteria of the supercooled liquid will lead to the future definite development of bulk amorphous alloys as basic science and engineering materials.