Orientation dependent size effects in thermal buckling and post-buckling of nanoplates with cubic anisotropy

In this work, a continuum model is presented for size and orientation dependent thermal buckling and post-buckling of anisotropic nanoplates considering surface and bulk residual stresses. The model with von-Karman nonlinear strains and material cubic anisotropy of single crystals contains two parameters that reflect the orientation effects. Using Ritz method, closed form solutions are given for buckling temperature and post-buckling deflections. Regarding self-instability states of nanoplates and their recovering at higher temperatures, an experiment is discussed based on low pressurized membranes to verify the predictions. For simply supported nanoplates, the size effects are lowest when they are aligned in [100] direction. When the edges get clamped, the orientation dependence is ignorable and the behavior becomes symmetric about [510] axis. The surface residual stress makes drastic increase in buckling temperature of thinner nanoplates for which a minimum thickness is pointed to stay far from material softening at higher temperatures. Deflection of [100]-oriented buckled nanoplates is higher than [110] ones but this reverses at higher temperatures. The results for long nanoplates show that the buckling mode numbers are changed by orientation which is verified by FEM.     

Comparison of growth stress measurements with modelling in thin iron oxide films

High temperature oxidation of metals leads to residual stresses both in the metal and in the growing oxide. In this work, the evolution of this residual stresses is theoretically predicted in the growing oxide layers. The origin of these stresses is based on a microstructural model. Using experimental results providing from the oxidation kinetics, and an analysis proposed to describe the growth strain occurring in the thin layers, a set of equations is established allowing determining the stresses evolution with oxidation time. Then, the model is compared with experimental results obtained on both α-Fe and phosphated α-Fe, oxidised at different temperatures. Numerical data are extracted from experiments either with an asymptotic formulation or with an inverse method. These two methods give good agreement with experiments and allow extracting the model parameters.     

Convergence of Computational Methods and Stability of Self-Balanced Stresses under Shrinkage of Spherical Inclusions of a Damageable Material

Some iterative methods for calculating self-balanced stresses under shrinkage of a ball inclusion enclosed in a spherical matrix of a physically nonlinear damageable material. The stability of this system was studied using methods of catastrophe theory. It has been established that the beginning of divergence of the proposed iterative processes coincides with the moment of transition of the system to an unstable position of equilibrium.     

Stress Distribution in an Elastic Body with a Periodically Curved Row of Fibers

Within the framework of a piecewise homogeneous body model, with the use of exact three-dimensional equations of elasticity theory for anisotropic bodies, a method is developed for investigating the stress distribution in an infinite elastic matrix containing a periodically curved row of cophasal fibers. It is assumed that fiber materials are the same and fiber midlines lie in the same plane. The self-balanced stresses arising in the interphase in uniaxial loading the composite along the fibers are investigated. The influences of problem parameters on these stresses are analyzed. The corresponding numerical results are presented.     

Determination of contact stresses in problems on bending of a package of transversely isotropic bars

A mechanomathematical model for bending of packages of transversely isotropic bars of rectangular cross section is proposed. Adhesion, slippage, and separation zones between the bars are considered. The resolving equations for deflections and tangential displacements are supplemented with a system of linear differential equations for determining the normal and tangential contact stresses, and boundary conditions are formulated. A scheme for analytical solution of two contact problems—a package under the action of a distributed load and a round stamp—is considered. For these packages, a transition is performed from the initial system of differential equations for determining the contact stresses, where the unknown functions are interrelated by recurrent relationships, to one linear differential equation of fourth order and then to a system of linear algebraic equations. This transition allows us to integrate the initial system and get expressions for the contact stresses.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 761–778, November–December, 2004.     

Field Theory Approach to the Dynamics of a Continuous Medium: A Perturbation Theory

We propose a perturbation theory that allows solving the equations of motion for the displacement vector in the body of the Earth in the framework of the linear theory of elasticity. We show that tectonic processes are primarily determined by tidal actions. We analyze the tidal effects in the Earth–Moon–Sun system.     

On the growth strain origin and stress evolution prediction during oxidation of metals

High temperature oxidation of metals leads to residual stresses in the metal and in the oxide. In this work, we try to predict the evolution of the residual stresses in the growing oxides layers, during isothermal oxidation. The origin of these stresses is based on the microstructural model of Clarke, however, another justification is proposed, assuming a proportional dependence of the growth strain with the oxide layer thickness. Using the mechanics of thin layers, as well as the analysis proposed to describe the growth strain, a system of equations are deduced that predict the stresses evolution with oxidation time. Numerical analysis is performed, leading to a set of theoretical curves.     

Residual stress/strain analysis in thin films by X-ray diffraction

Residual stresses are found in the majority of multilayer thin film structures used in modem technology. The measurement and modeling of such stress fields and the elucidation of their effects on structural reliability and device operation have been a “growth area” in the literature, with contributions from authors in various scientific and engineering disciplines.

In this article the measurement of the residual stresses in thin film structures with X-ray diffraction techniques is reviewed and the interpretation of such data and their relationship to mechanical reliability concerns are discussed.     

Dynamic electrochemical impedance spectroscopy measurements of passive layer cracking under static tensile stresses

Electrochemical impedance spectroscopy allows the examination of corrosion susceptibility and resistance for different construction materials, in particular the determination of the properties of their passive films. This technique makes possible the analysis of electrochemical processes in time domain, including rapid phenomena such as changes in the properties of passive films, but it has never been used for passive layer cracking examination. In many cases, fracture of the passive film under tensile stresses leads to stress corrosion cracking. Therefore, investigations of passive layer cracking on austenitic stainless steels under tensile stresses facilitate the understanding of the mechanism of stress corrosion cracking in these common engineering materials. The effect of static tensile stresses on the passive film cracking behaviour of type 304L stainless steel immersed in 0.5 M NaCl solution at room temperature has been investigated. This paper presents the impedance spectra obtained for 304L stainless steel samples at different potential values.Contribution to the 3rd Baltic Conference on Electrochemistry, Gdansk-Sobieszewo, Poland, 23–26 April 2003Dedicated to the memory of Harry B. Mark, Jr. (28 February 1934–3 March 2003)     

Phase field approach with anisotropic interface energy and interface stresses: Large strain formulation

A thermodynamically consistent, large-strain, multi-phase field approach (with consequent interface stresses) is generalized for the case with anisotropic interface (gradient) energy (e.g. an energy density that depends both on the magnitude and direction of the gradients in the phase fields). Such a generalization, if done in the “usual” manner, yields a theory that can be shown to be manifestly unphysical. These theories consider the gradient energy as anisotropic in the deformed configuration, and, due to this supposition, several fundamental contradictions arise. First, the Cauchy stress tensor is non-symmetric and, consequently, violates the moment of momentum principle, in essence the Herring (thermodynamic) torque is imparting an unphysical angular momentum to the system. In addition, this non-symmetric stress implies a violation of the principle of material objectivity. These problems in the formulation can be resolved by insisting that the gradient energy is an isotropic function of the gradient of the order parameters in the deformed configuration, but depends on the direction of the gradient of the order parameters (is anisotropic) in the undeformed configuration. We find that for a propagating nonequilibrium interface, the structural part of the interfacial Cauchy stress is symmetric and reduces to a biaxial tension with the magnitude equal to the temperature- and orientation-dependent interface energy. Ginzburg–Landau equations for the evolution of the order parameters and temperature evolution equation, as well as the boundary conditions for the order parameters are derived. Small strain simplifications are presented. Remarkably, this anisotropy yields a first order correction in the Ginzburg–Landau equation for small strains, which has been neglected in prior works. The next strain-related term is third order. For concreteness, specific orientation dependencies of the gradient energy coefficients are examined, using published molecular dynamics studies of cubic crystals. In order to consider a fully specified system, a typical sixth order polynomial phase field model is considered. Analytical solutions for the propagating interface and critical nucleus are found, accounting for the influence of the anisotropic gradient energy and elucidating the distribution of components of interface stresses. The orientation-dependence of the nonequilibrium interface energy is first suitably defined and explicitly determined analytically, and the associated width is also found. The developed formalism is applicable to melting/solidification and crystal-amorphous transformation and can be generalized for martensitic and diffusive phase transformations, twinning, fracture, and grain growth, for which interface energy depends on interface orientation of crystals from either side.