Projecting low-dimensional chaos from spatiotemporal dynamics in a model for plastic instability

We investigate the possibility of projecting low-dimensional chaos from spatiotemporal dynamics of a model for a kind of plastic instability observed under constant strain rate deformation conditions. We first discuss the relationship between the spatiotemporal patterns of the model reflected in the nature of dislocation bands and the nature of stress serrations. We show that at low applied strain rates, there is a one-to-one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops. We then show that the model equations are spatiotemporally chaotic by demonstrating the number of positive Lyapunov exponents and Lyapunov dimension scale with the system size at low and high strain rates. Using a modified algorithm for calculating correlation dimension density, we show that the stress-strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low-dimensional chaos. This is made quantitative by demonstrating that the model equations can be approximately reduced to space-independent model equations for the average dislocation densities, which is known to be low-dimensionally chaotic. However, the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands.

Predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics

The way in which basal tractions, associated with mantle convection, couples with the lithosphere is a fundamental problem in geodynamics. A successful lithosphere-mantle coupling model for the Earth will satisfy observations of plate motions, intraplate stresses, and the plate boundary zone deformation. We solve the depth integrated three-dimensional force balance equations in a global finite element model that takes into account effects of both topography and shallow lithosphere structure as well as tractions originating from deeper mantle convection. The contribution from topography and lithosphere structure is estimated by calculating gravitational potential energy differences. The basal tractions are derived from a fully dynamic flow model with both radial and lateral viscosity variations. We simultaneously fit stresses and plate motions in order to delineate a best-fit lithosphere-mantle coupling model. We use both the World Stress Map and the Global Strain Rate Model to constrain the models. We find that a strongly coupled model with a stiff lithosphere and 3-4 orders of lateral viscosity variations in the lithosphere are best able to match the observational constraints. Our predicted deviatoric stresses, which are dominated by contribution from mantle tractions, range between 20-70 MPa. The best-fitting coupled models predict strain rates that are consistent with observations. That is, the intraplate areas are nearly rigid whereas plate boundaries and some other continental deformation zones display high strain rates. Comparison of mantle tractions and surface velocities indicate that in most areas tractions are driving, although in a few regions, including western North America, tractions are resistive. Citation: Ghosh, A., W. E. Holt, and L. M. Wen (2013), Predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics.

Influence of system size on spatiotemporal dynamics of a model for plastic instability: Projecting low-dimensional and extensive chaos

This work is a continuation of our efforts to quantify the irregular scalar stress signals from the Ananthakrishna model for the Portevin-Le Chatelier instability observed under constant strain rate deformation conditions. Stress related to the spatial average of the dislocation activity is a dynamical variable that also determines the time evolution of dislocation densities. We carry out detailed investigations on the nature of spatiotemporal patterns of the model realized in the form of different types of dislocation bands seen in the entire instability domain and establish their connection to the nature of stress serrations. We then characterize the spatiotemporal dynamics of the model equations by computing the Lyapunov dimension as a function of the drive parameter. The latter scales with the system size only for low strain rates, where isolated dislocation bands are seen, and at high strain rates, where fully propagating bands are seen. At intermediate applied strain rates corresponding to the partially propagating bands, the Lyapunov dimension exhibits two distinct slopes, one for small system sizes and another for large. This feature is rationalized by demonstrating that the spatiotemporal patterns for small system sizes are altered from the partially propagating band types to isolated burst type. This in turn allows us to reconfirm that low-dimensional chaos is projected from the stress signals as long as there is a one-to-one correspondence between the bursts of dislocation bands and the stress drops. We then show that the stress signals in the regime of partially to fully propagative bands have features of extensive chaos by calculating the correlation dimension density. We also show that the correlation dimension density also depends on the system size. A number of issues related to the system size dependence of the Lyapunov dimension density and the correlation dimension density are discussed.

Projecting low and extensive dimensional chaos from spatio-temporal dynamics

We review the spatio-temporal dynamical features of the Ananthakrishna model for the Portevin-Le Chatelier effect, a kind of plastic instability observed under constant strain rate deformation conditions. We then establish a qualitative correspondence between the spatio-temporal structures that evolve continuously in the instability domain and the nature of the irregularity of the scalar stress signal. Rest of the study is on quantifying the dynamical information contained in the stress signals about the spatio-temporal dynamics of the model. We show that at low applied strain rates, there is a one-to-one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops. We then show that the model equations are spatio-temporally chaotic by demonstrating the number of positive Lyapunov exponents and Lyapunov dimension scale with the system size at low and high strain rates. Using a modified algorithm for calculating correlation dimension density, we show that the stress-strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low dimensional chaos. This is made quantitative by demonstrating that the model equations can be approximately reduced to space independent model equations for the average dislocation densities, which is known to be low-dimensionally chaotic. However, the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands. The stress signals in the partially propagating to fully propagating bands turn to have features of extensive chaos.

Microstructure Development, Nanomechanical, and Dynamic Compression Properties of Spark Plasma Sintered TiB2-Ti-Based Homogeneous and Bi-layered Composites

The growing threats due to increased use of small-caliber armor piercing projectiles demand the development of new light-weight body armor materials. In this context, TiB2 appears to be a promising ceramic material. However, poor sinterability and low fracture toughness remain two major issues for TiB2. In order to address these issues together, Ti as a sinter-aid is used to develop TiB2-(x wt pct Ti), (x = 10, 20) homogeneous composites and a bi-layered composite (BLC) with each layer having Ti content of 10 and 20 wt pct. The present study uniquely demonstrates the efficacy of two-stage spark plasma sintering route to develop dense TiB2-Ti composites with an excellent combination of nanoscale hardness (similar to 36 GPa) and indentation fracture toughness (similar to 12 MPa m(1/2)). In case of BLC, these properties are not compromised w.r.t. homogeneous composites, suggesting the retention of baseline material properties even in the bi-layer design due to optimal relief of residual stresses. The better indentation toughness of TiB2-(10 wt pct Ti) and TiB2-(20 wt pct Ti) composites can be attributed to the observed crack deflection/arrest, indicating better damage tolerance. Transmission electron microscope investigation reveals the presence of dense dislocation networks and deformation twins in alpha-Ti at the grain boundaries and triple pockets, surrounded by TiB2 grains. The dynamic strength of around 4 GPa has been measured using Split Hopkinson Pressure Bar tests in a reproducible manner at strain rates of the order of 600 s(-1). The damage progression under high strain rate has been investigated by acquiring real time images for the entire test duration using ultra-high speed imaging. An attempt has been made to establish microstructure-property correlation and a simple analysis based on Mohr-Coulomb theory is used to rationalize the measured strength properties.

Texture evolution during hot deformation of Moly-TZM

Moly-TZM was deformed at constant strain rate of 1.0 s(-1) to investigate the high strain rate deformation behaviour by microstructural and stress response change within a temperature range of 1400-1700 degrees C. To correlate the deformation behaviour with orientational change, recrystallization and recovery of the material, the microstructural investigation was undertaken using scanning electron microscopy (SEM) of electron back scattered diffraction (EBSD). Depending on the grain size and orientation spread recrystallized grains were identified and texture was calculated. Change in grain boundary characteristics with increasing temperature was determined by the misorientation angle distribution for the deformed and recrystallized grains. Subgrain coalescence and increase in subgrain size with increasing temperature was observed, indicating recrystallization not only occurred from the nucleation of the dislocation free grains in grain boundaries but also from the subgrain rotation and merging of the subgrains by annihilation of the low angle grain boundaries. Detailed studies on the evolution of texture of recrystallized grains showed continuous increase in <001> fiber texture in recrystallised grains, in contrast to a mixed fiber <001> +<111> for the deformed grains.

Chemical-free graphene by unzipping carbon nanotubes using cryo-milling

Current paper reports synthesis of chemical free graphene by unzipping of the carbon nanotubes (CNTs) using high strain rate deformation at 150K. A specially designed cryomill operating at 150 K was used for the experiments. The mechanism of unzipping was further explored using molecular dynamics (MD) simulations. Both experimental and simulation results reveal two modes of unzipping through radial and shear loading. (C) 2015 Elsevier Ltd. All rights reserved.

Damage quantification under sliding and seizure condition using first-of-a-kind fretting machine

In a practical situation, it is difficult to model exact contact conditions clue to challenges involved in the estimation of contact forces, and relative displacements between the contacting bodies. Sliding and seizure conditions were simulated on first-of-a-kind displacement controlled system. Self-mated stainless steels have been investigated in detail. Categorization of contact conditions prevailing at the contact interface has been carried out based on the variation of coefficient of friction with number of cycles, and three-dimensional fretting loops. Surface and subsurface micro-cracks have been observed, and their characteristic shows strong dependence on loading conditions. Existence of shear bands in the subsurface region has been observed for high strain and low strain rate loading conditions. Studies also include the influence of initial surface roughness on the damage under two extreme contact conditions. (C) 2013 Elsevier B.V. All rights reserved.

Review: Overcoming the paradox of strength and ductility in ultrafine-grained materials at low temperatures

Ultrafine-grained (UFG) materials with grain sizes in the submicrometer or nanometer range may be prepared through the application of severe plastic deformation (SPD) to bulk coarse-grained solids. These materials generally exhibit high strength but only very limited ductility in low-temperature testing, thereby giving rise to the so-called paradox of strength and ductility. This paradox is examined and a new quantitative diagram is presented which permits the easy insertion of experimental data. It is shown that relatively simple procedures are available for achieving both high strength and high ductility in UFG materials including processing the material to a very high strain and/or applying a very short-term anneal immediately after the SPD processing. Significant evidence is now available demonstrating the occurrence of grain boundary sliding in these materials at low temperatures, where this is attributed to the presence of non-equilibrium grain boundaries and the occurrence of enhanced diffusion along these boundaries.

Material response and failure mechanism of unidirectional metal matrix composites under impulsive shear loading

The material response and failure mechanism of unidirectional metal matrix composite under impulsive shear loading are investigated in this paper. Both experimental and analytical studies were performed. The shear strength of unidirectional C-f/A356.0 composite and A356.0 aluminum alloy at high strain rate were measured with a modified split Hopkinson torsional bar technique. The results indicated that the carbon fibers did not improve the shear strength of aluminum matrix if the fiber orientation aligned with the shear loading axis. The microscopic inspection of the fractured surface showed a multi-scale zigzag feature which implied a complicated shear failure mechanism in the composite. In addition to testing, the micromechanical stress field in the composite was analyzed by the generalized Eshelby equivalent method (GEEM). The influence of cracking in matrix on the micromechanical stress field was investigated as well. The results showed that the stress distribution in the composite is quite nonhomogeneous and very high shear stress concentrations are found in some regions in the matrix. The high shear stress concentration in the matrix induces tensile cracking at 45 degrees to the shear direction. This in turn aggravates the stress concentration at the fiber/matrix interface and finally leads to a catastrophic failure in the composite. From the correlation between the analysis and experimental results, the shear failure mechanism of unidirectional C-f/A356.0 composite can be elucidated qualitatively.

Effect of Particle Size on the Formation of Adiabatic Shear Band In Particle Reinforced Metal Matrix Composites

In this paper, the effect of particle size on the formation of adiabatic shear band in 2024 All matrix composites reinforced with 15% volume fraction of 3.5, 10 and 20 mum SiC particles was investigated by making use of split Hopkinson pressure bar (SHPB). The results have demonstrated that the onset of adiabatic shear banding in the composites strongly depends on the particle size and adiabatic shear banding is more readily observed in the composite reinforced with small particles than that in the composite with large particles. This size dependency phenomenon can be characterized by the strain gradient effect. Instability analysis reveals that high strain gradient is a strong driving force for the formation of adiabatic shear banding in particle reinforced metal matrix composites (MMCp).

Impact response and failure mechanisms of ultrahigh modulus polyethylene fiber composites and polyethylene fiber-carbon fiber hybrid composites

The impact response and failure mechanisms of ultrahigh modulus polyethylene (UHMPE) fiber composites and UHMPE fiber-carbon fiber hybrid composites have been investigated. Charpy impact, drop weight impact and high strain rate impact experiments have been performed in order to study the impact resistance, notch sensitivity, strain rate sensitivity and hybrid effects. Results obtained from dynamic and quasi-static measurements have been compared. Because of the ductility of UHMPE fibers, the impact energy absorption of UHMPE fiber composites is very high, thereby leading to excellent damage tolerance. By hybridizing with UHMPE fibers, the impact properties of carbon fiber composites can be greatly improved. The impact and shock failure mechanisms of these composites are discussed.

Effect of Pb Volatilization on Dielectric Properties of 0.77PbMg1/3(Nb0.9Ta0.1)2/3O3-0.23PbTiO3

Lead magnesium niobate-lead titanate (PMN-PT) is an intriguing candidate for applications in many electronic devices such as multi-layer capacitors, electro-mechanical transducers etc. because of its high dielectric constant, low dielectric loss and high strain near the Curie temperature. As an extension of our previous work on Ta-doped PMNT-PT aimed at optimizing the performance and reducing the cost, this paper focuses on the effect of Pb volatilization on the dielectric properties of 0.77Pb(Mg1/3(Nb0.9Ta0.1)2/3)O3-0.23PbTiO3. The dielectric constant and loss of the samples are measured at different frequencies and different temperatures. The phase purity of this compound is determined by X-ray diffraction pattern. It is found that the volatilization during sintering does influence the phase formation and dielectric properties. The best condition is sintering with 0.5 g extra PbO around a 4 g PMNT-PT sample.

Shear Localization In Dynamic Deformation: Microstructural Evolution

Investigations made by the authors and collaborators into the microstructural aspects of adiabatic shear localization are critically reviewed. The materials analyzed are low-carbon steels, 304 stainless steel, monocrystalline Fe-Ni-Cr, Ti and its alloys, Al-Li alloys, Zircaloy, copper, and Al/SiCp composites. The principal findings are the following: (a) there is a strain-rate-dependent critical strain for the development of shear bands; (b) deformed bands and white-etching bands correspond to different stages of deformation; (c) different slip activities occur in different stages of band development; (d) grain refinement and amorphization occur in shear bands; (e) loss of stress-carrying capability is more closely associated with microdefects rather than with localization of strain; (f) both crystalline rotation and slip play important roles; and (g) band development and band structures are material dependent. Additionally, avenues for new research directions are suggested.

Plastic deformation in Ce-based bulk metallic glasses during depth-sensing indentation

The deformation behavior and the effect of the loading rate on the plastic deformation features in (numbers indicate at.%) Ce60Al15Cu10Ni15, Ce65Al10Cu10Ni10Nb5, Ce68Al10Cu20Nb2, and Ce70Al10Cu20 bulk metallic glasses (BMGs) were investigated through nanoindentation. The load-displacement (P-h) curves of Ce65Al10Cu10Ni10Nb5, Ce68Al10Cu2, and Ce70Al10Cu20 BMGs exhibited a continuous plastic deformation at all studied loading rate. Whereas, the P-h curves of Ce60Al15Cu10Ni15 BMG showed a quite unique feature, i.e. homogeneous plastic deformation at low loading rates, and a distinct serrated flow at high strain rates. Moreover, a creep deformation during the load holding segment was observed for the four Ce-based BMGs at room temperature. The mechanism for the appearance of the "anomalous" plastic deformation behavior in the Ce-based BMGs was discussed. (c) 2006 Elsevier B.V. All rights reserved.