Effect of substrate constraint on spinodal decomposition in an elastically inhomogeneous thin film

Spinodal decomposition in a binary thin film is studied by a three-dimensional (3D) phase field model. A cubic thin film with an (001) orientation is considered. The focus is on the effect of the types of substrate constraint on the morphological evolution during spinodal decomposition as compared to the corresponding bulk. The elastic strain effect is incorporated by solving the elasticity equations for an elastically inhomogeneous thin film with a free surface and constrained by a substrate. Temporal evolution for the composition field, and thus the morphological evolution, is obtained by solving the Cahn-Hilliard equation using a semi-implicit Fourier-spectral method. It is shown that a biaxial substrate constraint has essentially no effect on the spinodally decomposed two-phase morphology which is primarily controlled by the cubically anisotropic elastic interactions. The asymmetry in the strain components along the [100] and [010] directions from the substrate constraint results in the preferential alignment along one of the two directions. In the particular case of a harder phase whose lattice parameter increases with composition, a tensile substrate constraint along the film plane leads to the alignment of two-phase microstructures parallel to the tensile direction. This article is based on a presentation made in the 2003 Korea-Japan symposium on the “Current Issues on Phase Transformations”, held at Marriott Hotel, Busan, Korea, November 21, 2003, which was organized by the Phase Transformation Committee of the Korean Institute of Metals and Materials.     

Bending of beams with elastically non-linear coatings

Young’s moduli of thermally sprayed materials are known to be substantially lower than those of well-sintered materials, due to elastic openings and partial closings of microcracks. Under compressive stresses some microcrack faces come into contact, which leads to the increase of Young’s moduli and to non-linear elastic behavior. The bending of beams with elastically non-linear coatings on the compression face caused by external moments or residual stresses is analyzed theoretically. Examples of stress distributions are given for a model ceramic coating. Different coating and substrate elastic properties and thicknesses are considered. The difference between the presented non-linear and previously used linear solutions is shown to be important at high compressive stresses, especially in ceramic coatings with high densities of microcracks.     

Intrinsic instability of electromigration induced mass transport in a two-dimensional conductor

The instability of electromigration induced mass transport within a thin-film conductor and its relation to catastrophic growth of voids in the later stage of electromigration failure are studied. To isolate intrinsic instability of mass transport from extrinsic defects, a void-free homogeneous conductor is examined in which surface and interface diffusion are neglected. Explicit conditions are derived for linearized instability and the effects of various diffusion mechanisms on instability are identified. It is found that thermomigration and electromigration provide the major driving forces for linear instability of uniform mass transport. In particular, thermomigration plays the dominant role in the onset of linear instability. The parameters which govern the onset of linear instability are the current density and temperature of the conductor. Linear instability can occur when Joule heating due to current crowding leads to sufficiently high temperature rise. The results appear to provide new insight into the understanding of some experiments where catastrophic void growth was observed in the later stage of electromigration failure when the amount of mass loss and temperature rise were sufficiently high.     

Irreversible atomic rearrangements in elastically deformed metallic glasses

The atomistic behaviour of elastically deformed Ni₅₀Zr₅₀ metallic glasses obtained at different quenching rates was studied by molecular dynamics. Deformation induces the irreversible rearrangement of atomic clusters of various chemical composition. The relative amount of Ni and Zr atoms participating in irreversible rearrangements depends on the quenching rate. The rearrangements are related to the potential energy difference between initial and final cluster configurations, connected in turn with volume effects. The role of local structures was investigated by focusing the attention on icosahedral coordination. The numerical findings indicate that icosahedral clusters become involved in rearrangements only after the average strain has overcome a certain value. Therefore, at small elastic strain only small atomic clusters with spatial organization different from the icosahedral one rearrange. The different involvement in rearrangements of different local structures is tentatively related to apparent local strain.     

Equilibrium particle morphologies in elastically stressed coherent solids

We determine the three-dimensional equilibrium shapes of particles with a purely dilatational misfit in an elastically anisotropic medium with cubic symmetry. We have identified a succession of cuboidal shapes with four-fold rotational symmetry that minimize the total energy of the system. In the process of determining these equilibrium morphologies, we have also developed a computationally efficient approach to determine the equilibrium shape which is many orders of magnitude faster than a standard implementation of Newton's method. For small elastic stress a (100) cross-section of the three-dimensional equilibrium shape agrees well with the two-dimensional calculation. However, for larger values of the elastic stress, the agreement is not as good. Elastic-stress-induced configurational forces are identified as the reason for the non-spherical equilibrium shapes.     

On electrostatic instability of a space-charged jet of dielectric liquid

On the basis of the dispersion equation for the nonaxisymmetric capillary waves at the surface of a strongly volumetrically charged cylindrical jet of an ideal incompressible dielectric liquid, it has been found that, for liquids with their dielectric permittivity changed in a wide range of values, there may occur electrostatic instability of the jet’s side surface.     

On stabilization of capillary instability of dielectric liquid jet by volume electric charge

The dispersion equation is analyzed for axisymmetric capillary waves at the surface of a volumetrically charged cylindrical jet of ideal incompressible dielectric liquid. It is shown that, for liquids of minor dielectric permittivity, there is the possibility of total stabilization of the jet capillary instability by means of volume electric charge.     

On the role of the viscosity of liquids in the realization of Kelvin-Helmholtz instability

An ideal model of two immiscible liquids is analyzed, the lower of which is viscous and the upper one, moving with a constant velocity parallel to the interface, is ideal. It is shown that, in the linear approximation, the role of the viscosity of the two liquids results in the decrement of the damping of waves on the interface.     

On the formation of laser induced self-organizing nanostructures

Laser induced self-organizing rippled nanostructures on steel are formed by femtosecond laser pulses. They are applied as hydrophobic surfaces. A low fluence results in ‘regular ripples’ with a spatial repetition of 300-500 nm, orientated perpendicular to the laser polarization direction. In twinned areas ‘pre-ripples’ with much smaller wavelength (about 150 nm) are observed, with a different orientation. We found indications that the energy absorption depends on the crystal orientation and that pre-ripples are only formed at very low fluence. Pre-ripples initiate on secondary carbides or on grain boundaries. At higher energy, regular ripples initiate in areas with pre-ripples; at even increasing fluence disordered structures are obtained.     

Effect of elastic interaction on nucleation: I. Calculation of the strain energy of nucleus formation in an elastically anisotropic crystal of arbitrary microstructure

We analyze the anisotropic elastic interaction of a nucleating particle with an arbitrary pre-existing coherent microstructure. Under the assumption that the length scale of the microstructure is considerably larger than the size of the nucleus, their elastic interaction energy can be expressed as a linear function of the nucleus’s volume, and combined directly with the chemical nucleation driving force in the classical nucleation theory. Using cubic → cubic and cubic → tetragonal transformations as examples, we evaluate the elastic energy associated with the formation of a nucleus in a pre-existing microstructure. It is found that, similar to other stress-generating crystalline defects, coherent precipitates could have a significant effect on the spatial location of nuclei, resulting in correlated nucleation where the existing particles dictate where the new particles appear. This effect seems to be generic for nucleation in coherent solids and it could be responsible for the formation of self-organized morphological patterns during coherent transformations.     

Cubic to tetragonal martensitic transformation in a thin film elastically constrained by a substrate

A 3-dimensional phase-field model is developed to describe the cubic to tetragonal martensitic phase transformation in a thin film attached to a substrate. Elasticity solutions are derived for both elastically anisotropic and isotropic thin films with arbitrary domain structures, subject to the mixed boundary conditions for stress-free and constrained states. The model is applied to an Fe-31%Ni alloy system. The nucleation process as well as the final domain structure strongly depends on the substrate constraint. At a smaller undercooling, the increased strain energy effect results in a lower volume fraction of martensite, a finer domain structure and a longer nucleation period. This article is based on a presentation made in the 2002 Korea-US symposium on the “Phase Transformations of Nano-Materials,” organized as a special program of the 2002 Annual Meeting of the Korean Institute of Metals and Materials, held at Yonsei University, Seoul, K orea on October 25–26, 2002.     

Direct synchrotron x-ray measurements of local strain fields in elastically and plastically bent metallic glasses

In situ high-energy synchrotron X-ray diffraction was conducted on elastically and plastically bent bulk metallic glass (BMG) thin plates, from which distinct local elastic strain fields were mapped spatially. These directly measured residual strain fields can be nicely interpreted by our stress analysis, and also validate a previously proposed indirect residual-stress-measurement method by relating nanoindentation hardness to residual stresses. Local shear strain variations on the cross sections of these thin plates were found in the plastically bent BMG, which however cannot be determined from the indirect indentation method. This study has important implications in designing and manipulating internal strain fields in BMGs for the purpose of ductility enhancement.     

角钢切分轧制工艺的实现

为提高角钢轧制效率,在四辊万能轧机上开发了一种新的仿X形孔型设计方法,实现了角钢的切分轧制,可一次轧制出2根等边或不等边角钢成品。介绍了该X形轧辊组件的设计和具体的轧制工艺。     

Deformation induced thermoremanent magnetisation in an FeMnNiCr antiferromagnetic alloy

In an austenitic Fe_61.5Mn₂₃Ni₇Cr_8.5 antiferromagnetic (afm) alloy deformation results in a splitting between magnetisation-vs.-temperature curves measured during field cooling (FC) below the Néel temperature and those measured at the same field after zero-field cooling (ZFC). Furthermore, a thermoremanent magnetisation (TRM) appears that corresponds to the splitting between zero-field and field cooled thermomagnetic measurements for a given cooling field and scales with the degree of deformation. This TRM is attributed to the deformation induced defects which act as a source of uncompensated magnetic moments and interact with the bulk afm moments. This interpretation is also supported by the fact that the net magnetic moments vanish above the Néel temperature. The TRM does not saturate in fields of up to 7 T, applied during cooling, and cannot be switched by fields up to 7 T. Within the investigated field range of −7 T to 7 T the magnetisation-vs.-field curves show a stable shift along the magnetisation axis. Thus, the uncompensated moments appear to be strongly exchange coupled to the afm matrix surrounding them. Within the series of experiments the maximum TRM reached after FC in 7 T corresponds to about 4 × 10⁻⁴μ_B/atom (Bohr magneton) of the maximum deformed afm sample. The Néel temperature decreases due to deformation.     

三切分棒材轧制活套高度差与预切分轧件偏移

分析了三线切分稳定生产的关键是保证切分后轧件尺寸的均匀性。在生产中由于预切分轧件偏移或切分入口导卫安装不当极易造成生产事故。结合切分后轧件三线活套高度差,给出了预切分轧件的偏移量与三线活套高度差的关系,并在生产应用中取得了良好结果。     

On instability and spontaneous capillary disintegration of charged jets. Part I: Linear analytical investigations

This article is devoted to a review of analytical computations of the stability of capillary wave motion on the surface of charged jets of incompressible liquids using a linear approximation based on a small parameter that is the ratio of the wave amplitude to the jet radius of a jet under various complicating factors.     

Homogenization-based topology optimization integrated with elastically isotropic lattices for additive manufacturing of ultralight and ultrastiff structures

The integration of topology optimization with lattice structures has shown great potential for the additive manufacturing (AM) of lightweight structures with superior mechanical properties and multifunctional characteristics. To further improve the design manufacturability, structural efficiency, structural isotropy and computational efficiency, the homogenization-based topology optimization (HMTO) method was proposed to integrate with plate–lattices exhibiting superior mechanical properties and excellent elastic isotropy. The validity of the proposed method was demonstrated by comparing the optimized models with conventional models composed of truss–lattices and solid materials. Results show that the proposed method highly improves stiffness and energy absorption capability.     

On the thermally induced interfacial delamination of a segmented coating

The thermally induced interfacial delamination problem of a segmented coating is investigated using finite element method (FEM). The coating-substrate system, modeled as a coated semi-infinite medium with periodic segmentation cracks within coating, is assumed to be exposed to convective cooling from surface. The failure criterion based on the interfacial fracture toughness is adopted, in which the energy release rate for an interface crack is considered to be the driving force for interfacial delamination extension. The results confirm that a segmented coating has higher delamination resistance than an intact one under the same thermal transients, as the segmentation crack spacing is smaller than a critical value. Based on dimensional analysis, sensitivity analyses of the crack driving force are also obtained as a function of various dimensionless parameters such as time, convection severity and material constants. These results may provide some helpful references for the integrity of coating-substrate systems under thermal loading.