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.     

Combined implementing the hole-drilling method and reflection hologram interferometry for residual stresses determination in cylindrical shells and tubes

Main features inherent in simplified approach to residual stresses determination in cylindrical shells and tubes, external diameter of which is not less than 60 mm, by combing the hole-drilling method and reflection hologram interferometry are discussed in detail. Initial experimental information in a form of hole diameter increments in principal stress directions is derived from high-quality reflection holograms recorded near cylindrical objects of intermediate curvature value. Converting measured parameters into required stress values is based on the transition model that corresponds to plane stress conditions of pure membrane type. The technique developed is capable of determining residual stress component values within 5% accuracy in an absence of stress gradients over the probe hole diameter when a type of residual stress field corresponds to the transition model adopted. The accuracy analysis involved is based on matrix formulation of conventionally direct problem and an assumption on a pure membrane character of residual stress field under study for thin-walled shell. Required error estimations in a case of inspecting thick-walled cylindrical tube are obtained by combining the above-mentioned approach and an analogy of reconstructed fringe patterns with actual and artificial interferograms, which follow from drilling blind hole of the same geometrical parameters in thick-walled plates. Experimental verification of the developed approach is founded upon a determination of actual stresses in thin-walled cylindrical shell and obtaining residual stress distributions at the proximity of welded joint in thick-walled cylindrical tube.     

Analysis of interfacial thermal stresses for damaged structures: new theoretical model

The use of the composites for the reinforcement of the beams and structures metallic and non-metallic, is one of the recent methods of the rehabilitation by composites, what permits to replace the classic techniques of the assembly based on soldering, bonding, etc. But this technique gives stresses concentrations to the level of the zone of the assembly. The methods of rehabilitation by composites permit to prolong the life span of these structures under a reduced exploitation cost and with less pollution to the environment. In this article, an original survey on the stresses between the structure and the composite (fiber reinforced polymer [FRP]) was finalized, taking account, as well, of the mechanical and thermal loadings, as well as the effects of deformation shear lag. This originality puts in evidence a new theoretical model which takes into account the thermal effect of the stresses concentration that has not been treated seriously by the previous studies.     

Fracture of diamond coatings by high velocity sand erosion

This paper describes a study of the behaviour of diamond coatings when subjected to solid particle erosion from sand particles. The coatings were deposited by chemical vapour deposition (CVD) onto tungsten substrates and tested using a high velocity air–sand erosion test facility. The erosion tests were conducted using particle impact velocities of between 33 and 268 m/s. Examination of the eroded test specimens showed that the principal damage features were circumferential cracks and pin-holes. Comparison with Hertz impact theory revealed that the measured circumferential crack diameters were more than double the predicted Hertzian contact diameter. Moreover, a trend of increasing circumferential crack diameter with coating thickness, which is not predicted by Hertz, was found. Instead, the crack diameters showed good agreement with those predicted by the theory of stress wave reinforcement, which is more commonly associated with liquid impact damage of brittle materials. During impact, the bulk compression and shear waves are reflected at the rear surface of debonded regions of the coating to return to the front surface and reinforce the Rayleigh surface wave, which generates a tensile stress. Where this stress exceeds the local tensile strength of the coating, a ring of cracks surrounding the area of impact is created. The results from the present study therefore suggest that stress wave reflection is responsible for the formation of the cracks at locally debonded regions of the coating. This hypothesis was supported by images acquired using scanning acoustic microscopy, which showed that circumferential cracks and pin-holes were only found on areas of the coating that had become delaminated by multiple particle impacts during the erosion tests.     

Structural characteristics and residual stresses in oxide films produced on Ti by pulsed unipolar plasma electrolytic oxidation

Oxide films, 7–10 µm thick, were produced on commercially pure titanium by plasma electrolytic oxidation in a sodium orthophosphate electrolyte using a pulsed unipolar current with frequency (f) and duty cycle (δ) varying within f = 0.1–10 kHz and δ = 0.8–0.2, respectively. The coatings comprised a mixture of an amorphous phase with nanocrystalline anatase and rutile phases, where the relative rutile content range was 17–25 wt%. Incorporation of phosphorus from the electrolyte into the coating in the form of PO₂ ^–, PO₃ ^2– and PO₄ ^3–, as demonstrated by EDX and FT-IR analyses, contributed to the formation of the amorphous phase. Residual stresses associated with the crystalline coating phase constituents were evaluated using the X-ray diffraction sin² ψ method. It was found that, depending on the treatment parameters, internal direct and shear stresses in anatase ranged from–205 (±17) to–431 (±27) MPa and from–98 (±6) to–145 (±10) MPa, respectively, whereas the rutile structure is comparatively stress-free.     

The ultimate state of polymeric materials and laminated and fibrous composites under asymmetric high-cycle loading

The prediction of the high-cycle fatigue strength of polymeric and composite materials in asymmetric loading is considered. The problem is solved on the basis of a nonlinear model of ultimate state allowing us to describe all typical forms of the diagrams of ultimate stresses. The material constants of the model are determined from the results of fatigue tests in symmetric reversed cycling, in a single fatigue test with the minimum stress equal to zero, and in a short-term strength test. The fatigue strength characteristics of some polymers, glass-fiber laminates, glass-fiber-reinforced plastics, organic-fiber-reinforced plastics, and wood laminates in asymmetric tension-compression, bending, and torsion have been calculated and approved experimentally. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 87–102, January–February, 2008.     

Influence of metal electrodes on c‐axis orientation of AlN thin films deposited by DC magnetron sputtering

Nanocrystalline aluminum nitride (AlN) thin films were deposited on two types of metallic seed layers on silicon substrates, (111) textured Pt and (110) Mo, by reactive DC magnetron sputtering at low temperature (200 °C). Both textured films of Pt and Mo promote nucleation, thereby improving the crystallinity and epitaxial growth condition for AlN thin films. The deposited films were examined by X‐ray diffraction, scanning electron microscopy and atomic force microscopy techniques. The results indicated that the preferred orientation of crystallites greatly depends upon the kinetic energy of the sputtered species (target power) and seed layers used. Furthermore, AlN thin films with c‐axis perpendicular to the substrate grew on both types of metal electrodes at all power levels larger than 100 W. By comparing the structural properties and compressive stresses at perfect c‐axis orientation conditions, it is evident that AlN films deposited on (110) oriented Mo substrates exhibited superior properties as compared with Pt/Ti seed layers. Furthermore, less values of compressive stresses (?3 GPa) as compared with Pt/Ti substrates (?7.08 GPa) make Mo preferentially better candidate to be employed in the field of suspended Micro/Nano ‐ electromechanical systems (MEMS/NEMS) for piezoelectric devices. Copyright © 2017 John Wiley & Sons, Ltd.     

圆柱基体热障涂层制备工艺中的残余应力分析

由于基体和热障涂层各层材料的热膨胀系数不同,在温度变化时各部分变形大小也不同,从而导致涂层内部产生残余应力。本文利用过盈配合模型求解圆柱形基体上热障涂层的残余应力,计算了涂层的厚度、弹性模量和热膨胀系数对残余应力的影响,并从应力角度探讨热障涂层的剥落失效。     

Rolling of a Rigid Cylinder over a Half-Plane with Initial Stresses (Harmonic and Bartenev–Khazanovich Potentials)

An asymmetric quasistationary problem for a prestressed half-plane with harmonic and Bartenev–Khazanovich potentials is solved based of the linearized theory of elasticity. The Mehler–Fock integral transform is used to solve the differential equations that describe the stress–strain state of the half-plane. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted