Flow Activation Volume Research Articles

The Effect of Pressure‐Dependent Viscosity on the Dynamics of the Post‐Overturn Lunar Mantle

AbstractMare‐basalt volcanism is concentrated on the lunar nearside. A plausible explanation for this asymmetric distribution is long‐wavelength (spherical harmonic degree‐1) mantle convection driven by upwellings of the overturned ilmenite‐bearing magma ocean cumulates (IBCs). The pattern of lunar mantle convection depends in part on the rheological properties of ilmenite. This study explores the effect of pressure‐dependent ilmenite viscosity on the instability of an overturned IBC layer initially at the core‐mantle boundary and the pattern of lunar mantle convection through three‐dimensional numerical simulations. We show that the convective patterns are sensitive to the activation volume for viscous flow. An effective activation volume of 10 cm3/mol would reduce the internal convection in the overturned IBC layer and promote the hemispherical upwelling. However, when the activation volume is too small, vigorous convection in the overturned IBC layer would inhibit heat from concentrating on one hemisphere. When the activation volume is too large, the size of the upwelling plumes is restricted, preventing a stable long‐wavelength structure in the upper mantle. Decompression melting during asymmetric upwelling would produce the localization of mare basalts on the lunar surface.

Hot Deformation Behavior Coordination and Processing Maps of 40Cr/Q345B Bimetallic Blank by Centrifugal Casting

The compact cast-rolling compound forming of bimetallic ring is an efficient process for manufacturing large bimetallic rings. The difference in hot deformation behavior of the two metals directly affects the coordinated deformation of bimetals during hot rolling. In this paper, hot compression tests of 40Cr/Q345B bimetallic blank produced by centrifugal casting were carried out at temperatures of 950–1200 °C and strain rates of 0.005–5 s−1. Based on the comparisons of flow stress behavior, activation energy, and activation volume, hot deformation behavior coordination of 40Cr/Q345B bimetallic blank was investigated. Processing maps were established to study the optimum processing windows for 40Cr/Q345B bimetallic blank. Under the same deformation conditions, 40Cr shows lower overall flow stress than Q345B, which facilitate the coordinated deformation of the bimetallic blank during rolling, and the flow stress difference between 40Cr and Q345B decreases with the increase of temperature. It was connected with the increase in the second phase particles pinning effect for higher MnS content in Q345B. The common rate-controlling mechanism for 40Cr and Q345B is the thermal breaking of attractive junctions and movement of jogged screw dislocations. The bimetallic blanks exhibit good deformation coordination in the optimum processing window (1030–1100 °C and 0.5–1 s−1 with a strain of 0.6).

Effect of solutes on the rate sensitivity in Ti-xAl-yMo-zV and Ti-xAl-yMo-zCr β-Ti alloys

The strain rate sensitivity (m) of Ti-xAl-yMo-zV and Ti-xAl-yMo-zCr bcc-Ti alloys has been investigated as a function of composition by a high throughput approach based on diffusion multiples and mechanical property screening by micropillar compression. It is shown that the influence of a solute species depends on the alloy composition. In particular, increasing levels of Mo result in a decrease of m in Ti-xAl-yMo-zV alloys, while they do not have a significant effect in the Ti-xAl-yMo-zCr system. The measured m values are related to the active deformation systems and to the flow stress and activation volume of the investigated alloys.

Serrated flow of CuZr-based bulk metallic glasses probed by nanoindentation: Role of the activation barrier, size and distribution of shear transformation zones

We report on the effect of Al and Co alloying in vitreous Cu50Zr50 on local deformation and serrated flow as a model for relating the size and localization of shear transformation zones (STZ) to Poisson ratio and strain-rate sensitivity of metallic glasses. Alloying with Al results in significant variations in mechanical performance, in particular, in Young's modulus, hardness and strain-rate sensitivity. Increasing strain-rate sensitivity with increasing degree of alloying indicates a reduced tendency for shear localization. In parallel, a gradual transition from inhomogeneous to homogeneous plastic flow is observed. Using a statistical analysis of the shear stress associated with the initiation of the first pop-in in the load-displacement curve during spherical indentation, the activation volume for plastic flow at the onset of yielding is reported. This analysis is employed for experimental evaluation of the compositional dependence of activation barrier, size and distribution of STZs. It is demonstrated that the STZ size does not change significantly upon Al alloying and encompasses a local volume of around 22–24 atoms. However, the barrier energy density for the initiation of a single STZ progressively increases. The broader distribution of STZs impedes their accumulation into larger-size flow units, leading to a lower number and reduced size of serrations in the load-displacement curve. On the contrary, lower barrier energy densities enable a larger quantity of STZs to be activated simultaneously. These STZs can easily percolate into large flow units, promoting plastic flow through their interaction. We employ Poisson's ratio as an indicator for plasticity to shown that this interpretation can be transferred to other types of metallic glasses. That is, larger flow units were found for metallic glasses with higher Poisson ratio and more pronounced plasticity, while the flow units in alloys with very low Poisson ratio and high brittleness are significantly reduced in size and more homogeneously distributed throughout the material.

A micromechanical approach to the stress–strain relations, strain-rate sensitivity and activation volume of nanocrystalline materials

This review highlights a secant viscosity approach that has wide applicability for the determination of mechanical properties of nanocrystalline materials. Along the way we also add some new elements and provide fresh perspectives. This approach was originally proposed for the nonlinear, time-dependent, work-hardening creep of dual-phase composites (Li and Weng, J Mech Phys Solids 45:1069–1083, 1997a), but by conceiving a nanocrystalline material as a composite of the stronger grain interior and the softer grain-boundary (GB, or grain-boundary affected zone GBAZ), it becomes possible to extend it to calculate the grain-size dependence of their flow stress, strain-rate sensitivity, and activation volume. We also use it to explain how the flow stress first increases and then decreases as the grain size decreases from the coarse grain to the nanometer range, leading to the Hall–Petch and the inverse Hall–Petch relations. The critical state at which the slope of the strength variation with respect to the grain size becomes zero also yields the strongest material state. In this way the two most important parameters for material design—the maximum strength and the critical grain at which it occurs—can be obtained. The strain-rate sensitivity parameters are also shown to follow a similar pattern as the flow stress, but the activation volume varies in an exactly reverse way.

Flow Activation Volume in Composites of Polystyrene and Multiwall Carbon Nanotubes with and without Functionalization

A new experimental protocol for the evaluation of the flow activation volume is proposed. It is based on step-shear experiments carried out on polymer melts. The flow activation volume evaluated agrees with the volume of a tube confining the chain, and is the same for the polymer melt and its composites with as received and functionalized carbon nanotubes. The functional groups bonded to the carbon nanotubes surface facilitate the polymer melt flow, eliminating the solid-like behavior in the high temperature flow region. A model for the morphology of polymer melts with carbon nanotubes is discussed. Polymer–nanotube interaction energies are discussed and the relaxation time of these interactions is estimated. The link between the solid-like behavior at the flow region and the strong shear thinning observed for the carbon nanotube composites is explained analyzing the different response to shear flow of each of the three networks considered by a model for the morphology of these composites.

What is the flow activation volume of entangled polymer melts?

We evaluate the flow activation volume in polymer melts of isotactic polypropylene and atactic polystyrene with step-shear experiments at different melt temperatures. The melt is initially sheared with constant shear rate until the attainment of a melt state with nearly constant viscosity. Perturbations to this experiment, involving shear steps in short-time intervals with decreasing rates, are induced next. Measurements of the shear stress value at each shear rate step allow the evaluation of an experimental (apparent) flow activation volume. The true flow activation volume is evaluated by extrapolating the experimental data to infinite shear stress values. The value obtained is larger than the physical volume of the chain and agrees with the volume of a tube confining chains with a molecular weight between M n and M w. Besides supporting the validity of tube model, experiments based on this protocol may be used on model polymer samples, in composites with nanoparticles and in polymer blends to access the validity of mechanisms considered by flow models.

Flow activation volume of polystyrene/multiwall carbon nanotubes composites

We applied the rate theory of plastic deformation to evaluate the flow activation volume in polystyrene melts and in its composites with different concentrations of multiwall carbon nanotubes. The experiments consisted in the analysis of a perturbation induced to the melt by varying the shear rate of a monotonic test at a melt state with nearly constant viscosity. The variation consisted on the application of shear steps with lower shear rate during short-time intervals. The material’s response to the perturbation allows a flow activation volume to be evaluated. For the pure polymer, the flow activation volume compares to the volume of a tube confining the chains, confirming the validity of tube model. Addition of nanotubes to the melt affects the melt response in the high temperature flow region, resulting in the development of a plateau in G′(ω). This plateau is linked to interactions of chains with nanotubes. However, the flow activation volume was not affected by the addition of nanotubes, suggesting that tube model holds also for composites of polymer melts with carbon nanotubes.

A unified mechanistic model for size-dependent deformation in nanocrystalline and nanotwinned metals

We present a unified mechanistic model to rationalize size-dependent flow stress, activation volume and strain-rate sensitivity for metals with either nanocrystalline grains or nanoscale twins. The non-uniform partial dislocation model for flow stress [Asaro and Suresh, Acta Mater, Vol. 53, pp. 3369–3382, 2005; Gu et al., Scripta Mater, Vol. 62, pp. 361–364, 2010] is generalized here to consider both grain-size dependence and twin-thickness dependence of nanotwinned metals. A non-homogeneous nucleation model is proposed to predict the dependence of activation volume on both grain-size and twin-thickness. With the activation volume predicted from the non-homogeneous nucleation model and the flow stress obtained via the non-uniform partial dislocation model, strain-rate sensitivity as a function of characteristic structural length scale is also evaluated. This provides a unified approach from envisioning partial dislocation emission for the three size-dependent parameters characterizing the plastic deformation mechanism, flow stress, activation volume and strain-rate sensitivity, so that each one of these parameters is predicted when the geometry of the grains or nanotwins is known. The model predictions are shown to be consistent with a variety of available experimental data.

Influence of chemistry and microstructure on the activation volume of TiAl alloys

Repeated stress-relaxation experiments are conducted from RT to 1073 K on three different γ + α2 TiAl alloys (Ti–46Al with 8Ta, 8Nb or 7Nb). One is a conventional duplex alloy, the two other are novel “convoluted” cast titanium aluminides developed for turbine applications. The data include measurements of the flow stress and activation volume of these alloys at 293, 673, 873, 923, 1023 and 1073 K. Despite differences in composition, processing and microstructure, the values and evolution with temperature or with stress of these parameters are relatively similar for the three alloys. This observation, coupled with the agreement of present results with data in the literature for similar alloys, leads to conclude that the strain-rate dependence of plastic flow in alloys of this class is governed by features of the γ-phase that are relatively insensitive to the α2 phase morphology. The convoluted alloys furthermore feature a yield stress anomaly.

Mechanics of very fine-grained nanocrystalline materials with contributions from grain interior, GB zone, and grain-boundary sliding

In this paper, we formulated an atomically-equivalent continuum model to study the viscoplastic behavior of nanocrystalline materials with special reference to the low end of grain size that is typically examined by molecular dynamic (MD) simulations. Based on the morphology disclosed in MD simulations, a two-phase composite model is construed, in which three distinct inelastic deformation mechanisms disclosed from MD simulations are incorporated to build a general micromechanics-based homogenization scheme. These three mechanisms include the dislocation-related plastic flow inside the grain interior, the uncorrelated atomic motions inside the grain-boundary region (the GB zone), and the grain-boundary sliding at the interface between the grain and GB zone. The viscoplastic behavior of the grain interior is modeled by a grain-size dependent unified constitutive equation whereas the GB zone is modeled by a size-independent unified law. The GB sliding at the interface is represented by the Newtonian flow. The development of the rate-dependent, work-hardening homogenization scheme is based on a unified approach starting from elasticity to viscoelasticity through the correspondence principle, and then from viscoelasticity to viscoplasticity through replacement of the Maxwell viscosity of the constituent phases by their respective secant viscosity. The developed theory is then applied to examine the grain size- and strain rate-dependent behavior of nanocrystalline Cu over a wide range of grain size. Within the grain-size range from 5.21 to 3.28 nm, and the strain rate range from 2.5 × 10 8 to 1.0 × 10 9/s, the calculated results show significant grain-size softening as well as strain-rate hardening that are in quantitative accord with MD simulations [Schiotz, J., Vegge, T., Di Tolla, F.D., Jacobsen, K.W., 1999. Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Phys. Rev. B 60, 11971–11983]. We have also applied the theory to investigate the flow stress, strain-rate sensitivity, and activation volume over the wider grain size range from 40 nm to as low as 2 nm under these high strain rate loading, and found that the flow stress initially displays a positive slope and then a negative one in the Hall–Petch plot, that the strain-rate sensitivity first increases and then decreases, and that the activation volume first decreases and then increases. This suggests that the maximum strain rate sensitivity and the lowest activation volume do not occur at the smallest grain size but, like the maximum yield strength (or hardness), they occur at a finite grain size. These calculated results also confirm the theoretical prediction of Rodriguez and Armstrong [Rodriguez, P., Armstrong, R.W., 2006. Strength and strain rate sensitivity for hcp and fcc nanopolycrystal metals. Bull. Mater. Sci. 29, 717–720] on the basis of grain boundary weakening and the report of Trelewicz and Schuh [Trelewicz, J.R., Schuh, C.A., 2007. The Hall–Petch breakdown in nanocrystalline metals: a crossover to glass-like deformation. Acta Mater. 55, 5948–5958] on the basis of hardness tests. In general the higher yield strength, higher strain rate sensitivity, and lower activation volume on the positive side of the Hall–Petch plot are associated with the improved yield strength of the grain interior, but the opposite trends displayed on the negative side of the plot are associated with the characteristics of the GB zone which is close to the amorphous state.

Strength and Plasticity of Ultra-Fine Grained Zirconium at Low Temperatures

Plasticity of ultra-fine grained (UFG) zirconium (grain size ~ 0.4 µm), produced by intensive plastic deformation (IPD) - a combination of extrusion, annealing, and drawing, have been studied within the temperature range 300 – 4.2 K in uniaxial compression. It was found that decrease of grain sizes in the result of IPD leads to considerable increase of strength characteristics for the UFG zirconium in comparison with coarse-grained (CG) zirconium (in 6 times at 300 K and 4 times at 77 K); and plasticity of the UFG zirconium keeps rather large (strain > 0.15). Two stages of the strain-hardening and decrease of the activation volume for plastic flow with deformation have been registered. A conclusion was made about the identity of basic deformation mechanisms in the UFG and CG zirconium: simultaneous action and mutual influence of intragrain dislocation gliding and twinning.

Mechanical properties of nanocrystalline nickel films deposited by pulse plating

Abstract This paper reports the mechanical properties of Ni films fabricated by pulse electrodeposition. Transmission electron microscope revealed that the prepared films had an average grain size of 25 nm with a narrow size distribution and the absence of dislocations. Small grain size leads to an increasing hardness as high as 7.8 GPa while Young's moduli keep a constant bulk value of 215 GPa, resulting in an increasing ratio of hardness ( H ) to elastic modulus ( E ). Interestingly, the wear resistance was also improved significantly. Under a constant normal load of 500 μN, the penetration depths of indenter slightly increased from 25 nm to 30 nm and the coefficient of friction varied from 0.12 to 0.20, depending on sliding scans. Depth sensing instrumented indentation experiments performed at different loading rates on specimens revealed an increasing rate-sensitivity of hardness, which concerns with a significantly small activation volume for plastic flow.

Flow stresses and activation volumes for highly deformed nanoposts

Recent interest in high-strength nanocrystalline structures has prompted a call for understanding scale effects in deformation mechanisms. One aspect, producing nanostructures by severe plastic deformation, promoted the present examination of nanoposts undergoing large strain compression. On e-beam lithography produced nanoposts of both aluminum and permalloy with radii ranging from 50 to 150 nm, single and repeat compression tests produced measurements of flow stress and apparent activation volume. Flow stresses, continuously measured with a nanoindenter allowed theoretical assessment of the deformation mechanism. It was concluded that the high stresses (1–3 GPa) and small activation volumes (1–10 b 3) where b is the modulus of the Burgers vector, were consistent with dislocation nucleation. A traditional model is shown to give good first order accountability for these two face-centered cubic metals.

Miscibility, viscosity and density of poly (ɛ-caprolactone) in acetone + CO 2 binary fluid mixtures

High-pressure viscosity and density of poly (ɛ-caprolactone) (PCL) (Mw = 14,300; Mw/Mn = 2.34) solutions in acetone and in acetone + CO 2 mixtures have been determined over a temperature range from 323 to 398 K and a pressure range from 7 to 35 MPa. The effect of adding CO 2 on viscosity was investigated for the 5 wt% solutions at CO 2 concentrations of 1, 2, 4 and 40 wt%. The effect of phase separation on viscosity was studied for the 5 wt% polymer solution in the binary fluid mixture with high (40 wt%) carbon dioxide content. The solution viscosities ranged from 0.2 to 0.6 mPa·s with flow activation energies in the range 7–9 kJ mol −1 and flow activation volumes in the range from 12 to 29 cm 3 mol −1. Close-packed volumes estimated from correlation of the data to Doolittle equation were in the range 0.5–0.6 cm 3/g. In ternary solutions containing carbon dioxide, solution densities were higher, reflecting the higher density of compressed CO 2 compared to that of acetone, but viscosities were lowered. A viscosity reduction of about 50% was observed with 40 wt% CO 2 addition. The density and viscosity data for the PCL solutions have been compared with data for solutions of poly (methyl methacrylate) (PMMA) with similar molecular weight in acetone + CO 2. The results show that the acetone + CO 2 binary mixtures are “better” solvents for PCL than PMMA.

High-pressure viscosity and density of poly(methyl methacrylate) + acetone and poly(methyl methacrylate) + acetone + CO 2 systems

High-pressure viscosity and density of solutions of poly(methyl methacrylate) (PMMA) in acetone and in acetone + CO 2 mixtures have been determined in the temperature range from 50 to 125 °C in steps of 25 °C over the pressure range from 7 to 35 MPa in steps of 7 MPa using a falling cylinder type viscometer. Measurements were conducted with PMMA samples of two different molecular weights ( M w = 15,000, M w/ M n = 1.8 and M w = 540,000, M w/ M n = 2.8) at concentrations of 2, 5, 10 and 20 wt.% with M w=540,000, and at concentrations of 10 and 20 wt.% with M w = 15,000 sample. The effect of adding CO 2 on viscosity was investigated for the 5 wt.% solutions with the high molecular weight polymer sample. The viscosities were observed to be relatively low, with values in the range from 0.2 to 1.6 mPa s for these solutions. The flow activation energies were around 5–10 kJ/mol. Flow activation volumes were in the range from 5 to 40 cm 3/mol. Close-packed volumes determined from density correlations were in the range of 0.76–0.98 cm 3/g. The overlap concentrations, c *, were estimated to be in the range 0.045–0.075 g/cm 3. In the presence of CO 2, densities of the solution show an increase, reflecting the higher density of compressed CO 2 compared to that of acetone, but viscosities were significantly lowered, with a reduction of about 30% at 4 wt.% CO 2 additions. The density dependence of viscosity is used to visually illustrate the need for higher pressures in the presence of CO 2 to sustain a given viscosity level.

Nano-sized twins induce high rate sensitivity of flow stress in pure copper

We have investigated the rate sensitivity of flow stress and the extent of strengthening in polycrystalline copper containing different volume fractions of nano-sized twins, but having the same average grain size. The specimens were produced by pulsed electrodeposition, wherein the concentration of twins was varied systematically by varying the processing parameters. Depth-sensing instrumented indentation experiments performed at loading rates spanning three orders of magnitude on specimens with the higher density of twins (twin lamellae width ∼20 nm) revealed an up to sevenfold increase in rate-sensitivity of hardness compared to an essentially twin-free pure Cu of the same grain size. A reduction in twin density for the same grain size (with twin lamellae width ∼90 nm) also resulted in a noticeable reduction in rate-sensitivity and hardness. The presence of a high density of nano-scale twins is also seen to impart significant hardness, which is comparable to that achieved in nano-grained Cu. Post-indentation analyses of indented Cu with nano-scale twins in the transmission electron microscope reveal deformation-induced displacement of coherent twin boundaries (CTBs), formation of steps and jogs along CTBs, and blockage of dislocations at CTBs. These processes appear to significantly influence the evolution of thermal activation volume for plastic flow which is some three orders of magnitude smaller than that known for microcrystalline Cu. Transmission electron microscopy also reveals CTBs with a high density of dislocation debris and points to the possibility that displaced CTBs may serve as barriers to dislocation motion and that they may also provide sources for dislocation nucleation, especially near stress concentrations, very much like grain boundaries. Possible consequences of these trends for deformation are explored.

Plastic deformation behaviour in Ni 3Ti single crystals with D0 24 structure

The plastic deformation behaviour of Ni 3Ti single crystals with the D0 24 structure was investigated in compression tests. Two slip planes of the type {1 1 ̄ 00} and (0001) were selected depending on crystal orientation. Temperature dependences of the critical resolved shear stress (CRSS), strain rate sensitivity of flow stress, activation volume and dislocation structure were examined. Anomalous strengthening slightly appeared for the {1 1 ̄ 00}<11 2 ̄ 0> prism slip system in a narrow temperature range between 300 and 500 °C. Accompanying the yield stress anomaly (YSA) were small jogs formed on 1/3<11 2 ̄ 0> screw dislocations, acting as pinning points for motion of the dislocations and resulting in a zigzag shape of dislocation lines inclined to the Burgers vector by ±15~20°. In contrast, a remarkable YSA was found for the (0001) basal slip system over a wide temperature range between −196 and 800 °C. At low temperatures at and below 300 °C, 1/3<2 1 ̄ 1 ̄ 0> superlattice dislocations were dissociated into two 1/3<10 1 ̄ 0> super-Shockley partials bounded by an SISF after unloading. Above 300 °C, the dissociation mode of 1/3<2 1 ̄ 1 ̄ 0> superlattice dislocations changed to APB-type splitting accompanied by a large increase in CRSS. The strong YSA was caused by the Kear-Wilsdorf locking of 1/3<2 1 ̄ 1 ̄ 0> screw dislocations from the (0001) slip plane onto the {01 1 ̄ 0} planes.

High-pressure density and viscosity of polystyrene solutions in methylcyclohexane

High-pressure density and viscosity data of polystyrene solutions in methylcyclohexane have been generated at 340, 360, 380 and 400 K using a falling-cylinder type viscometer up to 35 MPa. Measurements were conducted with two different molecular weight polystyrene samples ( M w=50 000 and 700 000) in the concentration ranges of 3–14 wt.% (for M w=50 000) and 1–5 wt.% (for M w=700 000). Isothermal density and viscosity of these solutions increased linearly with pressure in all the concentration ranges investigated. The flow activation volume and flow activation energy of the polymer solutions were in the range of 29–55 cm 3 mol −1 and 7–10 kJ mol −1, respectively. It was found that the activation volume increased with temperature, and the activation energy decreased with pressure. Viscosity was correlated with density employing a Doolittle type equation η= A exp[ B/(1− V 0 ρ)]. The estimated closed packed volumes ( V 0) from these correlations were in the range of 0.66–0.72 cm 3 g −1 for these solutions.

Miscibility, density and viscosity of polystyrene in n-hexane at high pressures

The demixing pressures, densities and viscosities of solutions of nearly monodisperse polystyrene samples ( M w/ M n < 1.1) in n-hexane have been determined. Measurements were conducted with samples of different molecular weights ( M w = 4000–50 000) at concentrations up to 8 mass% over a pressure range from 5 to 70 MPa and a temperature range from 323 to 423 K. The demixing pressures were observed to increase with molecular weight (from about 10 MPa for M w = 4000 to 50 MPa for M w = 50 000) and show high sensitivity to temperature (Δ P/Δ T being about −1 MPa°C −1) in the range investigated. Density and viscosity data were collected in the one-phase homogeneous regions, and viscosity was correlated with an equation of the form η = Aexp{ B/(1 − V 0 ρ ), which is based on the free-volume considerations. For a given system, the viscosities increase with solution density (or pressure). At a fixed solution density, viscosity increases with polymer concentration or molecular weight. Depending upon the system, viscosities have ranged from 0.15 to 0.45 mPa s. Flow activation volumes and flow activation energies were about 40 cm 3 mol −1 and 6 kJ mol −1, respectively. The demixing and viscosity data have been also compared with the results obtained in n-butane and n-pentane for one sample ( M w = 9000). In going from n-butane to n-hexane, the demixing pressures decrease while the viscosities become higher.