Role Of Strain Gradients Research Articles

Atomistic View Onto Solid State Dewetting: The Role of a Strain Gradient

We present a detailed study of solid state dewetting choosing epitaxial bismuth films on silicon as a model system. Exploiting both diffraction and imaging methods, we determine atomistic parameters like unit cell coverage, lattice spacings and gradients thereof through the analysis of x-ray diffraction crystal truncation rods. We use a Johnson-Mehl-Avrami-Kolmogorov model to describe the kinetics of the dewetting process on an atomic scale. The role of a vertical strain gradient, that impedes solid state dewetting, is revealed and a detailed model for the atomic jump diffusion during dewetting is presented.

Size Effect on Onset and Subsequent Evolution of Adiabatic Shear Band: Theoretical and Numerical Analysis

The adiabatic shear instability of ductile materials has attracted more and more attentions of researchers and groups, who have been sparing no effort in further understanding of the underlying mechanism since the first experimental depiction of adiabatic shear instability by Zener and Hollomon. As for the adiabatic shear instability, many factors account for its occurrence, including heat conduction, inertia effect, microstructure effect and so on. However, lots of experimental evidence has shown that metal materials display a strong size effect when the characteristic length scale is in the order of microns. The size effect has also been observed in the analysis of shear band in the ductile materials because the order of the bandwidth stays within the microscale range. However, a comprehensive understanding of the whole process of adiabatic shear banding (ASB), including the early onset and the subsequent evolution, is still lacking. In this work, a gradient plasticity model based on the Taylor-based nonlocal theory feasible for the linear perturbation analysis and convenient for numerical calculation is proposed to investigate the strain gradient on the onset of ASB and the coupling effect of heat conduction, inertia effect and strain gradient at the early stage, as well as on the subsequent evolution process at later stages. As for the onset of ASB, the linear perturbation method is used to consider the effect on the initial formation of ASB. After the investigation of the onset of ASB, the characteristic line method is applied to describe the subsequent nonlinear evolution process of ASB. Three stages of ASB evolution are clearly depicted during the evolution process, and the significance of size effect on the ASB nonlinear evolution process of ASB at different stages is analyzed. With the help of linear perturbation analysis and characteristic line method, a comprehensive description of the role of strain gradient in the ASB from the early onset to the end of the evolution is provided.

3D modeling of unconstrained HPT process: role of strain gradient on high deformed microstructure formation

During tribological contact’s life, different deformation paths lead to the formation of high deformed microstructure, in the near-surface layers of the bodies. The mechanical conditions (high pressure, shear) occurring under contact, are reproduced through unconstrained High Pressure Torsion configuration. A 3D finite element model of this HPT test is developed to study the local deformation history leading to high deformed microstructure with nominal pressure and friction coefficient. For the present numerical study the friction coefficient at the interface sample/anvils is kept constant at 0.3; the material used is high purity iron. The strain distribution in the sample bulk, as well as the main components of the strain gradients according to the spatial coordinates are investigated, with rotation angle of the anvil.

Exciton Drift in Semiconductors under Uniform Strain Gradients: Application to Bent ZnO Microwires

Optimizing the electronic structures and carrier dynamics in semiconductors at atomic scale is an essential issue for innovative device applications. Besides the traditional chemical doping and the use of homo/heterostructures, elastic strain has been proposed as a promising possibility. Here, we report on the direct observation of the dynamics of exciton transport in a ZnO microwire under pure elastic bending deformation, by using cathodoluminescence with high temporal, spatial, and energy resolutions. We demonstrate that excitons can be effectively drifted by the strain gradient in inhomogeneous strain fields. Our observations are well reproduced by a drift-diffusion model taking into account the strain gradient and allow us to deduce an exciton mobility of 1400 ± 100 cm(2)/(eV s) in the ZnO wire. These results propose a way to tune the exciton dynamics in semiconductors and imply the possible role of strain gradient in optoelectronic and sensing nano/microdevices.

Basic strain gradient plasticity theories with application to constrained film deformation

A family of basic rate-independent strain gradient plasticity theories is considered that generalize conventional J2 deformation and flow theories of plasticity to include a dependence on strain gradients in a simple way. The theory builds on three recent developments: the work of Gudmundson (J. Mech. Phys. Solids 52 (2004), 1379‐1406) and Gurtin and Anand (J. Mech. Phys. Solids 57 (2009), 405‐421), proposing constitutive relations for flow theories consistent with requirements of positive plastic dissipation; the work of Fleck and Willis (J. Mech. Phys. Solids 57 (2009), 161‐177 and 1045‐1057), who clarified the structure of the new flow theories and presented the underlying variational formulation; and observations of Evans and Hutchinson (Acta Mater. 57 (2009), 1675‐1688) related to preferences for specific functional compositions of strains and strain gradients. The starting point in this paper is the deformation theory formulation of Fleck and Hutchinson (J. Mech. Phys. Solids 49 (2001), 2245‐2271) which provides the clearest insights into the role of strain gradients and serves as a template for the flow (incremental) theory. The flow theory is constructed such that it coincides with the deformation theory under proportional straining, analogous to the corresponding coincidence in the conventional J2 theories. The generality of proportional straining is demonstrated for pure power-law materials, and the utility of power-law solutions is illustrated for the constrained deformation of thin films: the compression or extension of a finite layer joining rigid platens. Full elastic-plastic solutions are obtained for the same problem based on a finite element method devised for the new class of flow theories. Potential difficulties and open issues associated with the new class of flow theories are identified and discussed.

Role of Strain Gradient and Dynamic Transformation on the Formation of Nanocrystalline Structure Produced by Severe Plastic Deformation

Formation of nanocrystalline structure by severe plastic deformation has studied extensively. Although ultra fine grained structure (grain size larger than 100 nm) had been obtained in many processes such as heavy cold rolling, equal channel angular pressing (ECAP) or accumulative roll bonding (ARB), the formation of nano grained structure (< 100 nm) is limited to processes such as ball milling, shot peening or drilling. In the present study, high pressure torsion (HPT) deformation and drilling were carried out to understand the conditions necessary to obtain nano grained structure in steels. The results of HPT experiments in pure Fe showed that HPT has superior ability of strengthening and grain refinement probably due to a strain gradient but the saturation of grain refinement occurs before reaching nano grained structure. Drilling experiments in high carbon martensitic steel revelaed that nano grained ferrite forms at the drilled hole surface only when the transformation from ferrite to austenite takes place during drilling. Considering various other processes by which nano grained ferrite was produced, it is proposed that heavy strains with large strain gradients together with dynamic transformation are necessary to reach nano grained ferrite structure.

Formation of Surface Nanocrystalline Structure in Steels by Shot Peening and Role of Strain Gradient on Grain Refinement by Deformation

The amount of strain provided by shot peening (SP) was estimated by comparing the shot-peened surface structure to the cold-rolled structure. The grain size of recrystallized structure beneath the shot-peened nanocrystalline (NC) surface after annealing was similar to that of the specimen after cold-rolling (equivalent strain eeq=ca. 6) and annealing. The eeq larger than 6 seems to be given to the surface region by SP. This strain amount is consistent with the necessary condition (eeq>7) to produce NC structure proposed in the previous study. The large strain gradient is also generated at the shot-peened surface. The strain gradient has been suggested as one of important factors on strengthening and on grain refinement. The deformation by SP is complex; the role of strain gradient was investigated by using high-pressure torsion (HPT) process. The maximum hardness (Hv 5 GPa) in the Fe–0.03mass%C disk after HPT-straining was twice higher than the hardness (2.4 GPa) obtained by cold-rolling. At the center of HPT-processed disk, where shear strain is nominally zero, the hardness increased up to a saturation value of 3.3 GPa. These results in the HPT experiment show that strain gradient contributes to strengthening and to grain refinement. However, the grain refinement was saturated with around 200 nm in layered grain thickness although the HPT-processed disk was applied large strain and strain gradient. This suggests that not only strain gradient and strain but also other deformation conditions are necessary to form NC structure.

Role of strain gradient on grain refinement by severe plastic deformation

The role of strain gradient on strengthening and grain refinement into nanometer scale during severe plastic deformation was studied in iron by using ball milling (BM) and high-pressure torsion (HPT) processes. Layered nanocrystalline structure with a thickness of around 100 nm or less was successfully produced by these processes. The hardness obtained by BM or HPT was more than twice as high as the maximum hardness obtained by homogeneous deformation processes such as equal-channel angular pressing, accumulative roll-bonding or cold-rolling. At the center of the HPT-processed disk, where the shear strain is theoretically zero, the hardness increased with number of turns. The results of BM and HPT experiments show clearly that the strain gradient contributes significantly to strengthening and grain refinement.

Role of strain gradient on the formation of nanocrystalline structure produced by severe plastic deformation

In the present study, the formation of nanocrystalline structure by high speed drilling was investigated. Several micrometers thick nanocrystalline layer was observed at the top surface of drilled hole. Nanocrystalline layers showed high hardness and good thermal stability. The estimation of necessary dislocation density to produce nanocrystalline structure and the comparison between the estimated and measured strain gradient near the drilled hole surface was conducted. It is proposed that deformation with a large strain gradient is an important condition to produce nanocrystalline structure.

On the role of strain gradients and long-range internal stresses in the composite model of crystal plasticity

The aim of this study was to extend the simple two-component composite model of plasticity of single-phase materials containing a heterogeneous dislocation distribution by including the effect of finite strain gradients in the transition from the regions of high local dislocation density and flow stress to neighbouring regions of low dislocation density and flow stress. For this purpose, a simple one-dimensional model of a dislocation wall structure was considered. In this model, a periodically varying local density of statistically stored dislocations, associated with alternating positive and negative gradients of the local flow stress, was assumed. Special attention was focused on the role of the geometrically necessary dislocation distribution and the deformation-induced long-range internal stresses. It was shown that the geometrically necessary dislocations ensure compatibility of deformation by giving rise to long-range internal stresses which, superimposed on the external stress, cause a redistribution of the stress on a local scale, thus permitting the simultaneous deformation of soft and hard regions. Moreover, it could be shown that the local density of the geometrically necessary dislocations can be described alternatively in terms of either the local strain gradient or the local flow stress gradient and that it is related unambiguously to the local distribution of the statistically stored dislocations. The macroscopic flow stress, formulated as the spatial average of the local flow stress, has been found not to depend explicitly on the density of geometrically necessary dislocations, unless the geometrically necessary dislocations of one glide system are intersected by glide dislocations of another glide system. This result implies that, in Taylor-type descriptions of the macroscopic flow stress, the simple superposition of the (mean) density of geometrically necessary dislocations on the (mean) density of statistically stored dislocations is not well founded.

The role of strain gradients in the grain size effect for polycrystals

The role of grain size on the overall behaviour of polycrystals is investigated by using a strain gradient constitutive law for each slip system for a reference single crystal. Variational principles of Hashin-Shtrikman type are formulated for the case where the strain energy density is a convex function of both strain and strain gradient. The variational principles are specialized to polycrystals with a general multi-slip strain gradient constitutive law. An extension of the Hashin-Shtrikman bounding methodology to general strain gradient composites is discussed in detail and then applied to derive bounds for arbitrary linear strain gradient composites or polycrystals. This is achieved by an extensive study of kernel operators related to the Green's function for a general “strain-gradient” linear isotropic incompressible comparison medium. As a simple illustrative example, upper and lower bounds are computed for linear face-centred cubic polycrystals: a size effect is noted whereby smaller grains are stiffer than large grains. The relation between the assumed form of the constitutive law for each slip system and the overall response is explored.

On the role of strain gradients in adiabatic shear banding

The effect of higher order strain gradients on adiabatic shear banding is investigated by considering the simple shearing of a heat conducting thermoviscoplastic material with a gradient-dependent flow stress. The competition between the gradient-dependent plastic flow and heat conduction and their influence on the shear band width and structure are examined. Two internal length scales, i.e., the deformation internal length and the thermal internal length, are incorporated into the linear stability analysis, which shows that the band width size scales either with the square root of the strain gradient coefficient (in the absence of heat conduction) or the thermal conductivity (in the absence of strain gradients), respectively. The numerical computation for the nonlinear problem reveals that the “diffusive” effect of the strain gradient is much stronger than that of the heat conduction and dictates the constitutive response of the material in the postlocalization regime, and shows that the deformation length scale is much larger than the termal length scale. The band width predicted by the gradient theory agrees reasonably well with the experimental observations found in the literature.