Diffusion interaction of growth steps in vacuum deposition

The interaction of two straight parallel growth steps under saturation conditions was studied using a modified Langmuir adsorption model. It is shown that as the growth steps approach each other, the rate of their motion decreases, which explains the effect of hindered coalescence of condensate islands during vacuum deposition with layer-by-layer filling of atomic layers. The cause of this phenomenon is found to be the overlap of surface diffusion layers which are a source of material for the growth steps. Features of surface diffusion and nucleation under conditions close to the saturation conditions are determined. It is shown that the nucleation of islands of a new atomic layer at supersaturation and the nucleation of islands of vacancies in the underlying layer at unsaturation are asymmetric. The results can be used to develop a technology to produce thin films by vacuum deposition.     

Micro-plasticity of surface steps under adhesive contact: Part I—Surface yielding controlled by single-dislocation nucleation

Mechanics of nano- and meso-scale contacts of rough surfaces is of fundamental importance in understanding deformation and failure mechanisms of a solid surface, and in engineering fabrication and reliability of small surface structures. We present a micro-mechanical dislocation model of contact-induced deformation of a surface step or ledge, as a unit process model to construct a meso-scale model of plastic deformations near and at a rough surface. This paper (Part I) considers onset of contact-induced surface yielding controlled by single-dislocation nucleation from a surface step. The Stroh formalism of anisotropic elasticity and conservation integrals are used to evaluate the driving force on the dislocation. The driving force together with a dislocation nucleation criterion is used to construct a contact-strength map of a surface step in terms of contact pressure, step height, surface adhesion and lattice resistance. Atomistic simulations of atomic surface-step indentation on a gold (1 0 0) surface have been also carried out with the embedded atom method. As predicted by the continuum dislocation model, the atomistic simulations also indicate that surface adhesion plays a significant role in dislocation nucleation processes. Instabilities due to adhesion and dislocation nucleation are evident. The atomistic simulation is used to calibrate the continuum dislocation nucleation criterion, while the continuum dislocation modeling captures the dislocation energetics in the inhomogeneous stress field of the surface-step under contact loading. Results show that dislocations in certain slip planes can be easily nucleated but will stay in equilibrium positions very close to the surface step, while dislocations in some other slip planes easily move away from the surface into the bulk. This phenomenon is called contact-induced near-surface dislocation segregation. As a consequence, we predict the existence of a thin tensile-stress sub-layer adjacent to the surface within the boundary layer of near-surface plastic deformation. In the companion paper (Part II), we analyze the surface hardening behavior caused by multiple dislocations.     

Atomistic simulations and continuum modeling of dislocation nucleation and strength in gold nanowires

The strength of true metallic nanowires and nanopillars (diameters below 100 nm) is known to be higher than the strength of bulk metals and is most likely controlled by dislocation nucleation from free surfaces. Dislocation nucleation is a thermally activated process that is sensitive to both temperature and strain rate. However, most simulations rely on high strain rate molecular dynamics to investigate strength and nucleation, which is limited by short molecular dynamics time scales. In this work, the energetics of dislocation nucleation in gold nanowires are computed using atomistic simulations, and transition state theory is used to estimate the strength at experimental strain rates revealing detailed information outside the realm accessible to molecular dynamics simulations. This allows investigation into the competition between thermally activated dislocation nucleation and other failure mechanisms such as elastic and structural instabilities. Additionally, the mechanisms of dislocation nucleation are compared against analytical continuum models which allow a better understanding of the nucleation process including the effects of the wire surfaces. This study helps clarify and consolidate our understanding of the nature of dislocation nucleation in small structures.     

Localized deformation and fracture of polycrystals at mesolevel

Recent experiments have shown that shear band formation and rotation of structural elements at the mesolevel are fundamental to the development of plastic deformation and fracture of solids. Attention should be focused on a mesovolume of deformed material because the local stress and strain differ from those averaged at the macroscale. The discrete nature of the microshears and restricted deformation of the mesofragments should be accounted for. Rotation of the different mesofragments being parts of a grain, grains, grain conglomerates, etc., plays an important role in plasticity. Moreover, knowledge of the local parameters is needed for developing plasticity theories and fracture criteria. Models have been proposed within the framework of the physical mesomechanics. They take into account structural elements of different scales for simulating shear band nucleation and propagation in addition to mesofragment rotations. Calculations have been made for different mesovolumes under dynamic loading. In this work, a new criterion of plasticity is considered at the mesolevel. It accounts for the nucleation of plastic shears at the surfaces and interaction of structural elements. The numerical technique combines both the continuum mechanics approach and discrete cellular automata method.     

Analysis of dislocation nucleation from a crystal surface based on the Peierls-Nabarro dislocation model

Dislocation nucleation from a stressed crystal surface is analyzed based on the Peierls-Nabarro dislocation model. The variational boundary integral approach is used to obtain the profiles of the embryonic dislocations in various three-dimensional nucleation configurations. The stress-dependent activation energies required to activate dislocations from their stable to unstable saddle point configurations are determined. Compared to previous analyses of this type of problem based on continuum elastic dislocation theory, the present analysis eliminates the uncertain core cutoff parameter by allowing for the existence of an extended dislocation core as the embryonic dislocation evolves. Moreover, atomic information can be incorporated to reveal the dependence of the nucleation process on the profile of the atomic interlayer potential as compared to continuum elastic dislocation theory in which only elastic constants and Burgers vector are relevant. Finally, the presented methodology can also be readily used to study dislocation nucleation from the surface heterogeneities such as cracks, steps, and quantum structures of electronic devices.     

Equilibrium shapes of strained islands with non-zero contact angles

The equilibrium morphology of a strained island on an elastic substrate is determined. The island is assumed to partially wet the substrate (Volmer-Weber growth) and thus makes a non-zero contact angle with the surface. Both isotropic and anisotropic misfit strain are allowed. Two- and three-dimensional equilibrium island shapes are determined by using expressions for the elastic strain energy in the small-slope approximation. In this limit, the problem can be reduced to a singular integral-differential equation for the island thickness. We find that when there is a non-zero contact angle, all island shapes, for a given ratio of the elastic stress to surface energy, attain a form that is independent of the specific contact angle under an appropriate scaling. We show that for islands with non-zero contact angles, as the island volume increases, the shape approaches the geometry of a completely wetting island. But when the volume decreases, these islands approach a point while islands with a zero contact angle, approach a finite length line segment of zero volume. Multiple-hump equilibrium shapes are found. Single-humped islands are shown to have a lower chemical potential than multiple-humped islands, implying that they are the most stable. This conclusion is shown to be consistent with a stability analysis of the two-dimensional case. The effects of a tetragonal misfit strain on the three-dimensional island shape is investigated.     

Micro-plasticity of surface steps under adhesive contact: Part II—Multiple-dislocation mediated contact hardening

The study of micro-plastic behavior of rough surface contacts is the critical link towards a fundamental understanding of contact, friction, adhesion, and surface failures at small length scales. In the companion paper (Yu, H.H., Shrotriya, P., Gao, Y.F., Kim, K.-S., 2007. Micro-plasticity of surface steps under adhesive contact. Part I. Surface yielding controlled by single-dislocation nucleation. J. Mech. Phys. Solids 55, 489–516), we have studied the onset of surface yielding due to single-dislocation nucleation from a stepped surface under adhesive contact. Here we analyze the contact hardening behavior due to multiple dislocations in a two-dimensional dislocation model. Continuum micro-mechanical analyses are used to derive the configurational force on the dislocation, while a modified Rice–Thomson criterion is used to model dislocation nucleation. Dislocations nucleated from the surface step are stabilized and pile up as a result of the balance between the resolved driving force and the non-zero lattice resistance in the solid. The dislocation pileup will exert a strong back stress to prevent further dislocation nucleation and thus lead to the contact hardening behavior, the degree of which depends on the slip-plane orientation. Particularly, we find that dislocation interactions between two slip planes can make the contact loading order-of-magnitude easy to nucleate multiple dislocations, which is thus named “latent softening”. A mechanistic explanation shows that the latent softening is closely related to the stress-concentration mode mixity at the surface step. Dislocation nucleation will modify the geometric characteristics of the surface step, so that the contact-induced stress state near the step, as described by the mode mixity, changes, which influences the subsequent dislocation nucleation. Our calculations show that the dislocation pileup on one slip plane can even cause the spontaneous dislocation nucleation on the other slip plane without further increase of the contact load. Furthermore, it is found that rough surface contacts at small length scale can lead to the dislocation segregation and the formation of a surface tensile sub-layer. The discrete-dislocation model presented here and in the companion paper provides novel insights in bridging the atomistic simulations and continuum plastic flow analysis of surface asperity contact.     

Nanoparticles assembly-induced special wettability for bio-inspired materials

Through billions of years of evolution, nature has optimized the programmed assembly of the nano- and micro-scale structures of biological materials. Nanoparticle assembly provides an avenue for mimicking these multiscale functional structures. Bio-inspired surfaces with special wettability have attracted much attention for both fundamental research and practical applications. In this review, we focus on recent progress in nanoparticle assembly-induced special wettability, including superhydrophilic surfaces, superhydrophobic surfaces, superamphiphobic surfaces, stimuli-responsive surfaces, and self-healing surfaces. A brief summary and an outlook of the future of this research field are also provided.     

Coupled quantum–continuum analysis of crack tip processes in aluminum

A concurrent multiscale method is presented that couples a quantum mechanically governed atomistic domain to a continuum domain. The approach is general in that it is applicable to a wide range of quantum and continuum material modeling methodologies. It also provides quantifiable and controllable coupling errors via a force-based-coupling strategy. The applications presented here utilize an atomistic region that is governed by Kohn–Sham density functional theory and a continuum region governed by linear elasticity with discrete dislocation capabilities. As a validation we compute the core structure of a screw dislocation in aluminum and compare to previously published results. Then we investigate two crack orientations in aluminum and predict the critical load at which crack propagation and crack tip dislocation nucleation occurs. We compute critical loads with both LDA and GGA exchange correlation functionals and compare our results to popular empirical potentials in the context of classical continuum models. Overall this work aims to lay a foundation for future quantum mechanics-based investigations of crack tip processes involving Al alloys and impurity elements.     

A combined first principles and analytical determination of the modulus of cohesion,surface energy,and the additional constants in the second strain gradient elasticity

Mindlin’s (1965) second strain gradient theory due to its competency in capturing the effects of edges, corners, and surfaces is of particular interest. Formulation in this framework, in addition to the usual Lamé constants, requires the knowledge of sixteen additional materials constants. To date, there are no successful experimental techniques for measuring these material parameters which reflect the discrete nature of matter. The present work gives an accurate remedy for the atomistic calculations of these parameters by utilizing the first principles density functional theory (DFT) for the calculations of the atomic force constants combined with an analytical formulation. It will be shown that writing the consistency conditions obtained from the equivalency between the atomistic crystal lattice dynamics of the bulk material and its counterpart in the second strain gradient elasticity is insufficient for the calculations of all the additional constants. As it will be discussed, there are two missing conditions which are then provided by consideration of the free standing film problem that bring the surface effect into account. As a consequence of surface effect consideration, the modulus of cohesion which is one of the important additional constants is calculated. Moreover, an analytical expression for the surface energy in terms of the modulus of cohesion, Lamé constants, materials characteristic lengths, and the film thickness is presented. If the film thickness is much bigger than the magnitude of the characteristic lengths of the material, then the surface energy would no longer depend on the film thickness.     

Bubble nucleation characteristics in pool boiling of a wetting liquid on smooth and rough surfaces

Quantitative measurements are obtained from high-speed visualizations of pool boiling at atmospheric pressure from smooth and roughened surfaces, using a perfluorinated hydrocarbon (FC-77) as the working fluid. The boiling surfaces are fabricated from aluminum and prepared by mechanical polishing in the case of the smooth surface, and by electrical discharge machining (EDM) in the case of the roughened surface. The roughness values (R_a) are 0.03 and 5.89 μm for the polished and roughened surfaces, respectively. The bubble diameter at departure, bubble departure frequency, active nucleation site density, and bubble terminal velocity are measured from the monochrome movies, which have been recorded at 8000 frames per second with a digital CCD camera and magnifying lens. Results are compared to predictions from existing models of bubble nucleation behavior in the literature. Wall superheat, heat flux, and heat transfer coefficient are also reported.     

Micromechanical model for viscoelastic materials undergoing damage

We have derived a stress–strain relationship for viscoelastic materials undergoing damage using a granular micromechanics approach. This approach assumes the material to possess a granular meso-structure such that the material is treated as a discrete or a particulate system. By considering the particle kinematics in terms of Taylor series expansion, a continuum model of the discrete system is obtained. The material rate-dependence and damage are modeled by assuming appropriate inter-granular force–displacement relationships that satisfy thermodynamic constraints. The advantage of this micromechanical approach is that the resultant continuum model retains the discrete nature by incorporating the effect of nearest neighbor grain interactions through the inter-granular force–displacement relationship and orientation vector. As a result, the derived model has the ability to predict a number of material phenomena, such as loading-induced anisotropy, dilation or pressure sensitivity, and secondary creep, which often manifest due to material granularity.     

An augmented multicrack elastoplastic damage model for tensile cracking

In this paper we present the general formulation and numerical aspects of an augmented multicrack elastoplastic damage model aiming to reflect the crack induced anisotropy in concrete like quasi-brittle materials. Consistent evolution laws for the involved internal variables are derived based on the augmented Lagrangian method. The (time) discrete formulation and the corresponding variational structure are investigated, with the Euler–Lagrangian equations defining the closest-point projection approximation of the proposed model. The numerical aspects, such as the stress updating algorithm and the algorithmic consistent tangent moduli, are also discussed in details. It is found that in the developed numerical algorithm the active loading surfaces are determined in such a posterior manner that potential numerical problems due to the iteratively updating procedure in classical algorithms can be avoided. The proposed model is applied to the modeling of tensile cracking in concrete. The behavior of a single crack is characterized by an elliptical cracking surface and a hyperbolic softening function, with the orientations of potential cracks determined by Mohr’s postulate. The model is verified by calculating the single point stress vs. strain relations of concrete under several typical proportional and non-proportional loading cases. Finally, two benchmark tests of concrete structures, i.e. four-point bending beam under cyclic loading (Hordijk, 1992) and double edge notched specimens under mixed tension/shear forces (Nooru-Mohamed, 1992), are numerically simulated. Both predicted load vs. displacement curves and crack patterns agree well with the experimental data.     

A micromechanics-based strain gradient damage model for fracture prediction of brittle materials – Part I: Homogenization methodology and constitutive relations

In this paper, we first describe a homogenization methodology with the aim of establishing strain gradient constitutive relations for heterogeneous materials. The methodology presented in this work includes two main steps. The first one is the construction of the average strain-energy density for a well-chosen RVE by using a homogenization technique. The second one is the transformation of the obtained average strain-energy density to that for the continuum. An important characteristic of this method is its self-consistency with respect to the choice of the RVE: the strain gradient constitutive law built by using the present method is independent of the size and the form of the RVE. In the frame of this homogenization procedure, we have constructed a strain gradient constitutive relation for a two-dimensional elastic material with many microcracks by adopting the self-consistent scheme. It was shown that the effective behavior of cracked solids depends not only on the crack density but also on the average crack size with which the strain gradient is associated. The proposed constitutive relation provides a starting point for the development of an evolution law of damage including strain gradient effect, which will be presented in the second part of this work.     

Morphological evolution of heteroepitaxial islands during Stranski–Krastonov growth

Three-dimensional finite element method is used to simulate the formation, self-assembly and shape transition of heteroepitaxial islands during Stranski–Krastonov growth. In the formulation, strain energy, surface energy, surface anisotropy and elastic anisotropy of a cubic lattice structure are taken into account. In the simulations, the SiGe/Si material system is used as a model system. An empirical surface energy as a function of surface orientation is proposed. The minimum energy surfaces are identified based on existing experimental observations. The simulation results show that the coupling of elastic energy relaxation, surface energy anisotropy and elastic anisotropy strongly influences the surface roughening morphology, self-assembly and shape transition of epitaxial islands, resulting in diverse evolution pathways.     

On a general concept for the analysis of crack growth and material damage

For finite strain dynamics a variational model of crack evolution is formulated within the generalized oriented continuum methodology. In this approach position- and direction-dependent deformation and strain measures are used to describe the (macro)motion of the body with defects, which may evolve relative to the moving body. The inelastic behaviour of continua with evolving defects is represented by phenomenological equations including the transversal crack evolution. A strain-induced crack propagation criterion is defined by the difference between the strain energy release rate and the rate of the surface energy of the crack. A possible nucleation of microcracks in terms of the average drag coefficient of the crack configuration is proposed. Based on the crack growth criterion presented in this paper, the kinking of cracks is investigated using variational concepts. A constitutive damage model of Kachanov's type accounting for the crack density is derived in terms of the free energy functional and a dissipation potential.     

Temperature evolution associated with phase transition from quasi static to dynamic loading

Thermo-mechanical coupling is an intrinsic property of first order martensitic transformation. In this paper, we study the temperature evolution during phase transition at a wider strain rates from quasi static to impact loading to reveal the thermodynamic nature of the strain rate effect of phase transition materials. Based on the laws of thermodynamics and the principle of maximum dissipated energy, a thermal-mechanically coupled model was proposed. The model shows that, in the quasi static case, the temperature profile grades around the moving phase boundary, while for the dynamic case, thermal response of the specimen can be reached homogeneously due to random nucleation. The predicted results of the model are in good agreement with the experimental results, suggesting that the interaction between the self-heating effect and the temperature dependence of phase transition behavior plays a leading role in the process of the transformation deformation mechanism associated with the loading rate.

     

Mechanics of corrugated surfaces

Experimental studies of the surface stress of solids typically work with surfaces that are not perfectly planar. The experiment then probes an effectively averaged surface stress. The evolution of the surface morphology, for instance during film growth or reconstruction, is also affected by the surface stress acting on a corrugated surface. Here, we analyze the mechanics of rough surfaces in a continuum framework. In a generalization of the approach of Weissmüller and Duan [2008. Phys. Rev. Lett. 101, 146102] to solids with anisotropic elasticity, anisotropic surface stress and anisotropic roughness, we focus on the effectively averaged surface stress that determines the mean compensating stress in the bulk. Important concepts are the projection of out-of-plane stresses at inclined segments of a surface into the macroscopic surface plane, and the transverse coupling between the out-of-plane and in-plane components of the surface-induced stress in the bulk. We show that the coupling of the surface stress at a corrugated surface into a planar substrate depends on the geometry of the corrugation exclusively through the surface orientation distribution function. Special geometries are inspected with an eye on illustrating the impact of anisotropic elasticity as well as geometric anisotropy, which both feed into the anisotropy of the effective surface stress.