Transmission electron microscopy observations of misfit dislocations in GaAsP epitaxial films

Transmission electron microscopy observations have been made of misfit dislocation structures in GaAsP epitaxial films in foils both parallel to (1) the interface between the epitaxial film and the substrate and (2) the {1 1 1} glide planes. These observations support a near surface source mechanism of dislocation multiplication for relief of the epilayer misfit. It is also suggested that the recently observed surface reconstruction in the III-V compounds might allow for an easier nucleation of dislocations at the surface than hitherto thought. Furthermore, an efficient Lomer dislocation has been observed forming from two 60° glide dislocations thus supporting the hypothesis that all dislocations found in these foils, including the sessile Lomer type, originate from a glide process.     

Dislocation nucleation and propagation during thin film deposition under compression

In this paper, we study the nucleation of dislocations and their subsequent propagation, during thin film deposition, using the three-dimensional (3D) molecular dynamics (MD) method. Aiming to reveal the generic mechanisms, the case of tungsten on a substrate of the same material is investigated. The substrate is under uniaxial compression along the [1 1 1] direction, with the thermodynamically favored surface being horizontal. The simulation results indicate that the nucleation starts with a surface step where an atom is squeezed to the layer above, generating a half-dislocation loop at the surface. It may then either propagate into the film or become the bottom of a sessile dislocation loop. In the first case, the dislocation loop, having a Burgers vector on a (1 0 1) glide plane, propagates along the direction on the surface, and extends to about two atomic layers along the [1 1 1] direction. In the second case, the missing layer propagates along the [1 0 0] direction on the surface, extending to about four atomic layers along the [1 1 1] direction. In this case, the sessile dislocation has a Burgers vector on the plane (0 1 1).     

Quasicontinuum study the influence of misfit dislocation interactions on nanoindentation

Multiscale simulations using the quasicontinuum (QC) method with the embedded-atom method (EAM) potential are performed to examine the mechanical response of Cu–Ag bilayer film during nanoindentation tests. An attempt is made, from the viewpoint of collective interaction among misfit dislocations on the interface, to account for the strengthening and weakening mechanisms of interface on Cu–Ag bilayer film. The details of misfit dislocation nucleation, motion and collective interaction on Cu/Ag and Ag/Cu interfaces are discussed systematically, respectively. The investigation shows that the property and performance of Cu–Ag bilayer film mainly depend on the mechanical property of upper film. Both the strengthening and weakening effects are closely related to the collective interaction among misfit dislocations on the interface. Due to the pinning effect of interface on misfit dislocation, both the local interface migration and the voids can be observed at the core region of misfit dislocations. For nanoindentation on Cu/Ag bilayer film, the plastic deformation is localized chiefly in the lower Ag substrate and the void will disappear with the redistribution of misfit dislocations, which indicate that there are distinct protective and strengthening effects of the upper Cu film on the lower Ag substrate. While, for nanoindentation on Ag/Cu bilayer film, both the upper Ag film and the lower Cu substrate experience plastic deformation and the voids will not disappear, which imply that there are an obvious weakening effect of the upper Ag film on the lower Cu substrate. In addition, the multiscale simulation results are consistent with the experimental results.     

Density of grain boundaries and plasticity size effects: A discrete dislocation dynamics study

Discrete dislocation dynamics simulations are carried out to systematically investigate the microstructural and geometrical size dependence of films under tension that have a varying number of grains through their thickness. By varying film thickness, grain size and aspect ratio, more insight is gained into the competition between grain boundary hardening and film thickness effects. This provides a seamless link between previous dislocation plasticity studies and qualitative agreement with experimental data. In the simulations, plasticity arises from the collective motion of discrete dislocations of edge character. Their dynamics is incorporated through constitutive rules for nucleation, glide, pinning and annihilation. Grain boundaries are treated as impenetrable to dislocation motion. The numerical results show that the grain size dependence of yield in thin films as well as in bulk polycrystals is controlled by the density of grain boundaries.     

Constitutive modeling of nitrogen-alloyed austenitic stainless steel at low and high strain rates and temperatures

In this paper, microstructures-based constitutive relations are introduced to simulate the thermo-mechanical response of two nitrogen-alloyed austenitic stainless steels; Nitronic-50 and Uranus-B66, under static and dynamic loadings. The simulation of the flow stress is developed based on a combined approach of two different principal mechanisms; the cutting of dislocation forests and the overcoming of Peierls–Nabarro barriers. The experimental observations for Nitronic-50 and Uranus-B66 conducted by Guo and Nemat-Nasser (2006) and Fréchard et al. (2008), respectively, over a wide range of temperatures and strain rates are also utilized in understanding the underlying deformation mechanisms. Results for the two stainless steels reveal that both the initial yielding and strain hardening are strongly dependent on the coupling effect of temperatures and strain rates. The methodology of obtaining the material parameters and their physical interpretation are presented thoroughly. The present model predicts results that compare very well with the experimental data for both stainless steels at initial temperature range of 77–1000 K and strain rates between 0.001 and 8000 s⁻¹. The effect of the physical quantities at the microstructures on the overall flow stress is also investigated. The evolution of dislocation density along with the initial dislocation density contribution plays a crucial role in determining the thermal stresses. It was observed that the thermal yield stress component is more affected by the presence of initial dislocations and decreases with the increase of the originated (initial) dislocation density.     

Thermal strain in lead thin films II: strain relaxation mechanisms

A deformation mechanism map was constructed to study the mechanisms of strain relaxation in lead thin films which were deposited on oxidized silicon wafers at room temperature and which were then thermally cycled between room temperature and liquid helium temperature. The stress level, which was calculated from the strain measured by an X-ray diffraction technique, was plotted on the map. By comparing the calculated and experimental stress levels the following observations were obtained. In the cooling process the strain was relaxed rapidly in a field of dislocation glide mechanism for films of greater than 0.2 μm thickness. In the heating process most of the strain was again believed to be relaxed by the glide mechanism. For a film 0.5 μm thick the stress (after the primary relaxation was completed) was found to be (1–1.5) × 10⁹ dyn cm^-2 for the cooling process and (0.17–0.24) × 10⁹ dyn cm^-2 for the heating process at temperatures around 200–280 K. Slow secondary relaxations were observed after the primary relaxations were completed. The measured compressive strain relaxation rate at room temperature was very close to the rate calculated on the assumption of grain boundary diffusion creep. This suggested that the secondary relaxation mechanism of compressive strain was grain boundary diffusion creep at temperatures near room temperature. These suggestions were supported by scanning electron microscopy observations in which dislocation slip lines were observed inside grains and hillocks were observed on grain boundaries.     

Insights on slip transmission at grain boundaries from atomistic simulations

To fully understand the plastic deformation of metallic polycrystalline materials, the physical mechanisms by which a dislocation interacts with a grain boundary must be identified. Recent atomistic simulations have focused on the discrete atomic scale motions that lead to either dislocation obstruction, dislocation absorption into the grain boundary with subsequent emission at a different site along the grain boundary, or direct dislocation transmission through the grain boundary into the opposing lattice. These atomistic simulations, coupled with foundational experiments performed to study dislocation pile-ups and slip transfer through a grain boundary, have facilitated the development and refinement of a set of criteria for predicting if dislocation transmission will occur and which slip systems will be activated in the adjacent grain by the stress concentration resulting from the dislocation pile-up. This article provides a concise review of both experimental and atomistic simulation efforts focused on the details of slip transmission at grain boundaries in metallic materials and provides a discussion of outstanding challenges for atomistic simulations to advance this field.     

Importance of dislocation cores in fatigue fracture

It is pointed out that proposed mechanisms of fatigue fracture should be consistent with Coffin’s Law for constant strain-amplitude cyclic deformation. Most proposed mechanisms are not. The fracture of dislocation cores along their glide planes is consistent with the fact that the law describes the behavior during the first ¼ cycle as well as that after a very large number of cycles. Experimental evidences of the relative weakness of edge dislocation cores is described. Analysis of this weakness by Bullough, and in this article, discussed. It is concluded that this effect plays an important role in fatigue fracture.     

On the geometric origin of Orowan-type kinematic relations and the Schmid yield criterion

Summary It is shown that the Orowan-type kinematic relations as well as the Schmid yield criterion can be derived basing oneself on a formula defining the mean curvature of glide surfaces for a principal congruence of edge dislocation lines accompanied with a particular distribution of secondary point defects. Moreover, it appears that this mean curvature has the physical meaning of a mesoscopic material parameter defining a relation between the evolution of the dislocation state and plastic deformation. It is pointed out that the existence of Orowan-type relations puts kinematic constraints, dependent on the isometry group of glide surfaces, on the dislocation density tensor.     

A dislocation theory of isotropic polycrystalline plasticity

A theory of polycrystalline plasticity is developed in which the polycrystalline solid is modeled as an isotropic continuum. The rate of plastic deformation tensor is shown to be a function of the mobile dislocation density and the dislocation velocity vector summed over all active glide planes. The dislocation velocity vector is expressed in terms of the stress tensor and the normal vector to the dislocation glide plane. The condition of plastic incompressibility yields the fact that the dislocation glide planes are the octahedral shear planes of the stress tensor. As a special case the rate of plastic deformation tensor reduces to a relation analogous to the Prandtl-Reuss flow rule. The theory has been implemented in a 2-dimensional finite element code and two example problems are presented.     

Effect of surface energy on the plastic behavior of crystalline thin films under plane strain constrained shear

In this work, a new continuum dislocation based model for crystal plasticity with surface energy effect is proposed. Based on the model, a thin film under plane constrained shear is considered. From the perspective of energy, the yield strength as a function of film thickness has been calculated which is achieved by comparing the energy due to elastic deformation, plastic deformation without surface energy and that with surface energy effect. According to the numerical results, the model including the impenetrable surface assumption can capture the surface dominated deformation mechanism for thin films of nanometer scale. In addition, the transition in dominant deformation mechanisms is also predicted for film thicknesses ranging from tens of nanometers to several microns.     

On the rate sensitivity in discrete dislocation plasticity

Discrete dislocation dynamics simulations are carried out to systematically investigate the rate dependent deformation behaviour of polycrystalline bulk copper by varying the loading rate in the range of 100–25,000 s⁻¹ under tension. The underlying material model not only incorporates the realistic definition of nucleation time but also put emphasis on the role of obstacle density and their strength on dislocation motion. In the simulations, plasticity arises from the collective motion of discrete dislocations of edge character. Their dynamics is incorporated through constitutive rules for nucleation, glide, pinning and annihilation. The numerical results show that the rate sensitivity of yield stress in bulk polycrystals is controlled by the density of Frank-Read sources, obstacles and their strength.     

SEM in-situ investigation on failure of nanometallic film/substrate structures under three-point bending loading

Three-point bending tests on nanocrystalline Cu or Cu/Ni-film/Cu-substrate samples were conducted in-situ with scanning electron microscopy (SEM) observations. The SEM in-situ observations show undulation deformation of the surface of thin film, as the thin film fractures easily at the concave–convex points of deformation and multi-cracks appear on the surface of the thin film in a periodic fashion. The critical wavelength of undulation is calculated based on experimental observations, which are comparable with the theoretical predictions. For the Cu/Ni multi-layered films/substrate structures, the micro-cracking pattern depends on the interfacial strength between the film and the substrate, rather than the interfacial strength between the layers of films.     

An evaluation of the rate-controlling flow process in Newtonian creep of polycrystalline ice

Using experimental data and theoretical calculation for Newtonian creep in polycrystalline ice, it is demonstrated that unlike most other materials, in which the rate-controlling flow process is edge dislocation climb under saturated condition, the rate-controlling flow process of polycrystalline ice is dislocation glide along the basal plane under a constant dislocation density. The dislocation density during Newtonian creep of ice is determined by the initial state instead of the magnitude of the Peierls stress. The transition stress (threshold) from power-law creep to Newtonian creep is controlled by the dislocation density instead of the Peierls stress. The activation energy of the Newtonian creep is similar to that of the self-diffusion due to the requirements of the diffusion of protons during dislocation glide.     

Dislocation controlled wear in single crystal silicon carbide

For better design and durability of nanoscale devices, it is important to understand deformation in small volumes and in particular how deformation mechanisms can be related to frictional response of an interface in the regime where plasticity is fully developed. Here, we show that when the size of the cutting tool is decreased to the nanometer dimensions, silicon carbide wears in a ductile manner by means of dislocation plasticity. We present different categories of dislocation activity observed for single asperity sliding on SiC as a function of depth of cut and for different sliding directions. For low dislocation density, plastic contribution to frictional energy dissipation is shown to be due to glide of individual dislocations. For high dislocation densities, we present an analytical model to relate shear strength of the sliding interface to subsurface dislocation density. Furthermore, it is shown that a transition from plowing to cutting occurs as function of depth of cut and this transition can be well described by a macroscopic geometry-based model for wear transition.     

Microstructure evolution and its influence on deformation mechanisms during high temperature creep of a nickel base superalloy

The interaction of dislocation with strengthening particles, including primary and secondary γ′, during different stages of creep of Rene-80 was investigated by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). During creep of the alloy at 871 °C under stress of 290 MPa, the dislocation network was formed during the early stages of creep, and the dislocation glide and climb process were the predominant mechanism of deformation. The density of dislocation network became more populated during the later stages of the creep, and at the latest stage of the creep, primary particles shearing were observed alongside with the dislocation glide and climb. Shearing of γ′ particles in creep at 871 °C under stress of 475 MPa was commenced at the earlier creep times and governed the creep deformation mechanism. In two levels of examined stresses, as far as the creep deformation was controlled by glide and climb, creep curves were found to be at the second stage of creep and commence of the tertiary creep, with increasing creep rate, were found to be in coincidence with the particles shearing. Microstructure evolution, with regard to γ′ strengthening particles, led to particles growth and promoted activation of other deformation mechanisms such as dislocation bypassing by orowan loop formation. Dislocation-secondary γ′ particles interaction was detected to be the glide and climb at the early stages of creep, while at the later stages, the dislocation bypassed the secondary precipitation by means of orowan loops formation, as the secondary particle were grown and the mean inter-particle distance increased.     

Discrete dislocation dynamics simulations of surface induced size effects in plasticity

Experiments have shown that the presence of free surfaces may induce harder as well as softer deformation behaviors in a crystalline solid. In order to shed some light on these apparently contradictory findings, two-dimensional discrete dislocation dynamics simulations are performed to investigate the surface induced size effects. The simulations indicate that, depending on the surface density of dislocation sources, a free surface may act either as a dislocation sink or as a net dislocation source, and can accordingly exert opposite effects on dislocation density over a boundary layer thickness of up to 500 nm into the bulk. This finding provides a possible explanation for the apparent contradictions in experimental observations.     

Coating flows of non-Newtonian fluids: weakly and strongly elastic limits

This paper presents an asymptotic analysis of the thickness of the liquid film that coats a smooth solid substrate when it is withdrawn from a bath of non-Newtonian fluid, and compares the results with experimental measurements. The film thickness is, to a good approximation, uniform above the point where the film is withdrawn from the fluid bath, and depends on the rotation rate, the fluid properties and the substrate geometry. Theoretical predictions of the film thickness for a number of different substrate geometries (an inclined plate, roller and fiber) are presented, and are compared with experimental measurements in a single roller geometry. Results are obtained for two different limits of the Criminale–Ericksen–Filbey constitutive equation in which the fluid rheology is either weakly elastic and dominated by shear thinning, or strongly elastic and dominated by elastic stresses. A lubrication analysis yields a thin-film equation which characterizes the film thickness as a function of spatial position. The rheological properties of the test fluids are measured independently using steady and oscillatory shearing deformations. The viscometric parameters are then used, in conjunction with the governing thin-film equation, which is solved using matched asymptotics, to give a quantitative prediction of the thickness of the fluid coating. The onset of an instability which causes the film thickness to vary with axial position along the roller is also observed experimentally.     

A 2xxx aluminum alloy crept at medium temperature: role of thermal activation on dislocation mechanisms

Fuselage skin of the future supersonic civil transport aircraft requires a material resistant to long-term creep at temperatures ranging from 100 to 130 °C. A candidate is the 2650 aluminum alloy which presents such properties at relatively high temperatures (130 °C=0.43T_melting). From an accelerated creep test conducted at 150 °C under a 280 MPa load and subsequent observations of the dislocation microstructures by transmission electron microscopy, the role of thermal activation on dislocation mechanisms is analyzed. It appears that thermal activation favors cross-slip activity and allows dislocations to glide in non-close-packed planes, namely the {0 0 1} planes. This is the first time that evidence of primary {0 0 1} glide is reported. Associated to a strain-assisted decrease of the precipitate density, thermal activation softens the material and seems to contribute to the acceleration of the strain rate (tertiary stage) by facilitating bypassing of precipitates and the production of mobile dislocations. The different creep stages are explained in terms of individual dislocation mechanisms and not by referring to the evolution of dislocation substructures.     

Implicit algorithm for finite deformation hypoelastic–viscoplasticity in fcc metals

An implicit objective stress update algorithm is proposed for a hypoelastic–viscoplastic model. A thermal/dynamic yield function, which is derived based on the thermal activation analysis and dislocation interaction mechanisms, is used, along with the Consistency approach and the framework of additive viscoplasticity, in deriving the proposed model for fcc metals. The corotational formulation approach is utilized in developing the proposed model in the finite deformation field. For the case of the Newton–Raphson iteration method, a new expression for the consistent (algorithmic) tangent stiffness matrix of rate‐dependent metals is derived by direct linearization of the stress update algorithm. Finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program ABAQUS. Numerical implementation for a simple tensile problem is used for validating the material parameters of the OFHC Copper under low and high strain rates and temperatures. The numerical results of the adiabatic true stress–true strain curves compare very well with the experimental data. The effectiveness of the present approach is tested by studying strain localization in a simple plane strain problem. Results indicate excellent performance of the present framework in describing the strain localization problem and in obtaining mesh‐independent results. Copyright © 2006 John Wiley & Sons, Ltd.