Efficient modelling of delamination buckling in composite cylindrical shells under axial compression

Composite cylindrical shells and panels are widely used in aerospace structures. These are often subjected to defects and damage from both in-service and manufacturing events. Delamination is the most important of these defects. This paper deals with the computational modelling of delamination in isotropic and laminated composite cylindrical shells. The use of three-dimensional finite elements for predicting the delamination buckling of these structures is computationally expensive. Here combined double-layer and single-layer of shell elements are employed to study the effect of delamination on the global load-carrying capacity of such systems under axial compressive load. It is shown that through-the-thickness delamination can be modelled and analysed effectively without requiring a great deal of computing time and memory. A parametric study is carried out to study the influence of the delamination size, orientation and through-the-width position of a series of laminated cylinders. The effect of material properties is also investigated. Some of the results are compared with the corresponding analytical results. It is shown that ignoring the contact between the delaminated layers can result in wrong estimations of the critical buckling loads in cylindrical shells under compressive load.     

Numerical analysis of fracture in ceramic coatings subjected to thermal loading

In this paper the general purpose finite element code ANSYS has been employed to analyse fracture in ceramic coatings subjected to thermal loading. An approach is developed in which hypothetical material properties have been considered as material data for coupled (thermal and structure) finite element analysis. These properties were chosen by assumed changes in some functional properties of ZrO₂-G.G. coatings. The aim was to evaluate the stress intensity factors in different coatings. Furthermore, to demonstrate the influence of crack length and coating geometry on the stress intensity in coatings, finite element analyses were carried out for various cases. The normalized stress intensity factors were obtained. The results showed that the shorter the crack length and the thinner the coating, the sounder the coatings. Furthermore, coatings representing a wide range of thermal and mechanical properties have a close normalized stress intensity factor values. It is also concluded that the finite element technique can be used to optimize the design and the processing of ceramic coatings.     

Micromechanical modeling of interface damage of metal matrix composites subjected to off-axis loading

A three dimensional micromechanics based analytical model is presented to investigate the effects of initiation and propagation of interface damage on the elastoplastic behavior of unidirectional SiC/Ti metal matrix composites (MMCs) subjected to off-axis loading. Manufacturing process thermal residual stress (RS) is also included in the model. The selected representative volume element (RVE) consists of an r × c unit cells in which a quarter of the fiber is surrounded by matrix sub-cells. The constant compliance interface (CCI) model is modified to model interfacial de-bonding and the successive approximation method together with Von-Mises yield criterion is used to obtain elastic–plastic behavior. Dominance mode of damage including fiber fracture, interfacial de-bonding and matrix yielding and ultimate tensile strength of the SiC/Ti MMC are predicted for various loading directions. The effects of thermal residual stress and fiber volume fraction (FVF) on the stress–strain response of the SiC/Ti MMC are studied. Results revealed that for more realistic predictions both interface damage and thermal residual stress effects should be considered in the analysis. The contribution of interfacial de-bonding and thermal residual stress in the overall behavior of the material is also investigated. Comparison between results of the presented model shows very good agreement with finite element micromechanical analysis and experiment for various off-axis angles.     

Micromechanical modelling of viscous sintering and a constitutive equation with sintering stress

The sintering stress is defined for viscous sintering, where the deformation of particles takes place, and its magnitude is computed by the viscoplastic finite element method using a micromechanical model. The computed sintering stress is compared with existing models for other sintering mechanisms. Although modelling of the sintering process is different, a similar tendency of the change in sintering stress with densification is observed. The influence of the sintering mechanism on the sintering stress is discussed. A constitutive law is developed by introducing the sintering stress, approximated by a simple equation, into the constitutive equation for viscous porous materials and applied to the sintering of polycrystalline materials. Grain boundary diffusion and grain growth are taken into consideration through the viscosity in the constitutive equation. The sintering curve calculated by the constitutive equation shows good agreement with the experimental data.     

Viscoplastic–plastic modelling of IN792

At high temperatures metallic materials behave in a viscous manner exemplified by strain rate dependence, stress relaxation and creep deformation. At low temperatures however, these effects are extremely small, and the behaviour is strain rate independent and shows no or very small relaxation effects. Finally there exists an intermediate region, in which the material behaviour is close to strain rate independent for high strain rates but at the same time shows time dependent inelastic effects, such as stress relaxation and creep. For IN792 this occurs at temperatures around 650 °C. The article describes the extension of a power-law viscoplastic model describing the behaviour of IN792 at 850 °C, also to describe the behaviour at 650 °C, by bounding the elastic–viscoplastic stress-space by a plastic yield surface. The model parameters have been estimated using data from creep test and tailored step relaxation tests, and the model fits well to both the step relaxation data aimed at resembling relevant component conditions and long term creep data.     

Study of interaction curves for composite laminate subjected to in-plane uniaxial and shear loadings

In this study an attempt has been made to incorporate the effect of transverse shear on the stability of moderately thick/very thick composite laminated plates under in-plane compressive and shear loading using a Simple Higher Order Shear Deformation Theory based on four unknown displacement functions (u₀,v₀,w_b,w_s) instead of five which is commonly used in most of the higher order theories. The finite element method is employed to study the initial buckling load of laminated plates. The change in initial buckling response of thick rectangular antisymmetric laminates with respect to the fibre orientation angle has been studied. The interaction curves (between N_x and N_xy for different parameters of the laminates) are studied in detail.     

Elastic tensor of the forsterite (Mg2SiO4) under pressure

A complete elastic tensor of the low-pressure structure of the magnesium orthosilicate (Mg₂SiO₄, forsterite) is determined by an ab initio technique for the pressure range P=0–240 kB. The geologically important quantities: density, sound velocity, Young's modulus, Poisson's ratio, crystal anisotropy, are derived from the calculated data. A systematic increase of crystal's anisotropy with pressure has been noticed. The results agree well with the available experimental data.     

Study by resonant ultrasound spectroscopy of the elastic constants of the β phase in Cu---Al---Ni shape memory alloys

The evolution with temperature of the elastic constants of the metastable β phase in a Cu-27.96 at.%Al-3.62 at.% Ni shape memory alloy (SMA) has been studied by resonant ultrasound spectroscopy (RUS). The corresponding elastic constants of this cubic phase have been measured near the martensitic transformation temperature in a single crystal. Above the martensitic transformation temperature, an anomalous behavior has been found in the C′elastic constant which shows a softening as the temperature decreases. The internal friction value Q⁻¹ has been obtained in this temperature range from the RUS spectra. The mechanisms associated with the Q⁻¹ increase must be related to {1 1 0} shear.     

Micromechanical analysis of layered systems of MMCs subjected to bending––effects of thermal residual stresses

A three-dimensional finite element micromechanical model is presented to study the effects of manufacturing process thermal residual stresses on the mechanical behavior of layered systems of metal matrix composites subjected to four point bending. The presented model contains layered systems, consisting of layers of monolithic titanium alloy (IMI834) and unidirectional fiber reinforced titanium metal matrix composite (SiC/Ti). A representative volume element (RVE) was defined and appropriate boundary conditions were imposed to apply bending and temperature change simultaneously on the model. In an agreement with experimental data, the model is able to predict asymmetric behavior of the composite in tension and compression on the bottom and top surfaces of the beam. This is due to the existence of a high level of thermal residual stresses arising from cool-down from manufacturing temperature. As a result of this asymmetric behavior, the neutral axis of the beam during bending moves from the mid-surface through the compressive part of the beam.     

Micromechanical modelling of layered systems containing titanium alloy and titanium MMC subjected to bending

Abstract

The mechanical behaviour of layered systems, consisting of layers of monolithic titanium alloy, (IMI834) and titanium metal matrix composite, (Ti-MMC) is examined. A finite element based micromechanical model was developed to investigate the mechanical response of the systems subjected to four point bending. Two types of layered systems were examined: the first designated as C type with Ti-MMC in the centre of the beam, and IMI834 on the outside, and an S type which consists of a Ti-MMC layer on the outside and IMI834 on the inside. A representative volume element (RVE)was defined and boundary conditions imposed to simulate bending of the layered systems. While the S type system exhibited higher stiffness and linear behaviour up to fracture, the C type system exhibited more ductile behaviour prior to fracture. The overall predicted behaviour of the two systems was in good agreement with experimental results.     

Micromechanical behaviour of Si-based particulate assemblies: A comparative study using DEM and atomistic simulations

In this paper, we investigate the micromechanical behaviour of Si-based particulate systems subjected to tri-axial compression loading. The investigations are based on three-dimensional discrete element modelling (DEM) and simulations. At first, we compare the variation of mean compressive stress for a silicon assembly subjected to tri-axial compression, predicted at two different scales: at the particulate scale, using the DEM simulation (mono-dispersed particulates) and at the atomistic scale using the molecular dynamics (MD) simulation results for silicon mono-crystal reported by Mylvaganam and Zhang (2003) [K. Mylvaganam, L. Zhang, Key Eng. Mater. 233–236 (2003) 615–620]. Both the simulation methods considered the silicon assembly subjected to an identical (tri-axial) loading condition. We observed a good qualitative agreement between the DEM and MD simulation results for the mean compressive stress when the assembly was subjected to small volumetric strain. However, at large volumetric strain, the mean stress of the silicon assembly predicted from MD simulation did not scale-up with the DEM results. This discrepancy could be due to that MD simulation is only valid for particle contacts, which are independent of one another and does not consider the inherent ‘discrete’ nature of particulates and the induced anisotropy prevailing at particulate scale. The micromechanical behaviour of particulate assemblies strongly depends on the inherent discrete nature of the particles, their single-particle properties and the induced anisotropy during mechanical loading. At the second stage, using DEM, we present the evolution of macroscopic compressive stress and several micromechanical features for four cases of the commonly used Si based poly-dispersed particulate assemblies (Si, SiC,Si₃N₄ and SiO₂) under tri-axial compression loading. We also present the evolution of several other phenomena occurring at particulate scale, such as the energy dissipation characteristics due to sliding contacts and the features of fabric structures developed during mechanical loading. The study shows that the single-particle properties of the Si based assemblies considered here significantly affect the micromechanical behaviour of the assemblies and DEM is a powerful tool to get insights on the internal behaviour of discrete particulates under mechanical loading.     

Torsional moments on buildings subjected to wind loads

A numerical method is presented for the determination of wind-induced torsional moments on isolated or a group of rigid buildings of arbitrary cross-section. The method combines the boundary element method to account for the potential flow and the discrete vortex method to take care of the viscous flow characteristics of the wind and works iteratively in time. Thus the wind pressure distribution around the cross-section of a building is determined and the resulting torsional moment is easily computed. Numerical examples involving one or two buildings are treated by the proposed method and the results are compared against experimental ones. The method appears to be a valuable tool for the rapid determination of wind-induced torsion on buildings with satisfactory accuracy, especially because there is almost nothing on the subject in wind codes, while experiments are time consuming and expensive.     

Thermal and mechanical properties of simultaneous and sequential full-interpenetrating polymer networks

An investigation of the thermal and mechanical characteristics of new full-interpenetrating polymer networks (full-IPNs), prepared by simultaneous and sequential synthesis paths, has been performed in the temperature regions above and below the glass transition. It has been observed that simultaneous full-IPNs exhibit higher values of density than sequential full-IPNs, as a consequence of an enhanced intermolecular packing. This peculiarity leads to an increase of the glass transition temperature and to a larger “γ-suppression” effect for the γ₂-relaxation characterizing the polycyanurate phase of simultaneous full-IPNs, which has been ascribed to reduction of the free-volume available for the molecular group rearrangements.     

Self-consistent modelling of non-linear effective properties of polycrystalline ferroelectric ceramics

A constitutive model for the non-linear effective behaviour of ferroelectric ceramics is presented. The model is developed on the basis of the effective medium approximation (EMA), which describes the interaction of the crystallites in a statistical way. Additionally, a particular simplified domain configuration within the crystallites and the possibility of domain wall motion are taken into account. In connection with a thermodynamic criterion for the domain wall displacement the volume fractions of the domains can be calculated dependent on the crystallite orientation and the applied load in a self-consistent manner. This mechanism leads to an extrinsic contribution to the effective behaviour. If the domain wall displacement is associated with energy dissipation the macroscopic behaviour is non-linear and hysteretic.     

Anelastic relaxation processes due to hopping of interstitial oxygen in scandium

The anelastic spectrum of the solid solution Sc–O has been investigated on a polycrystalline sample from 360 to 570 K for oxygen concentrations varying between 0.024 and 0.91 at.% O, as estimated by electrical resistivity and intentional doping. Two relaxation processes appear at 430 and 520 K for the vibration frequency of 3.5 kHz; both peaks are stable with thermal cycling and their intensities increase with the oxygen content.

The process at lower temperature has been tentatively interpreted as due to the stress-induced hopping of oxygen atoms between the non equivalent tetrahedral and octahedral interstitial sites. A possible mechanism for the higher temperature process could be the dissolution/formation of interacting O–O pairs.     

Thermal stability and crystallization kinetics of sputtered amorphous Si3N4 films

The crystallization of thin silicon nitride (Si₃N₄) films deposited on polycrystalline SiC substrates was investigated by X-ray diffractometry as a function of annealing time. The amorphous Si₃N₄ films were produced by means of reactive r.f. magnetron sputtering. Annealing at temperatures between 1300 and 1700 °C led to the formation of crystalline films composed of -Si₃N₄ and β-Si₃N₄. The fraction of β-Si₃N₄ in the films reaches approximately 40% at temperatures above 1550 °C. Both polymorphic modifications were formed simultaneously during the crystallization process. A transformation of -Si₃N₄ to β-Si₃N₄ could not be observed in the time and temperature range investigated. The crystallization process of amorphous Si₃N₄ can be described according to the Johnson–Mehl–Avrami–Kolmogorov (JMAK) formalism, assuming a three-dimensional, interface controlled grain growth from pre-existing nuclei. The rate constants show an Arrhenius behaviour with an activation enthalpy of approximately 5.5 eV.     

Experimental and numerical investigation of the tension and compression strength of un-notched and notched quasi-isotropic laminates

Un-notched and notched (in the form of through-thickness open holes), quasi-isotropic AS4/3501-6 laminate coupons were tested in tension and compression. Basic lamina properties were also determined experimentally. Numerical analyses using linear elastic and progressive damage approaches were conducted. The linear elastic model either significantly underestimated (first-ply failure approach) or overestimated (last-ply failure approach) the strength of un-notched laminates. The progressive damage approach was able to predict accurately the un-notched strength, providing that the non-linear shear behaviour was accounted for and appropriate failure criteria used. It was also demonstrated that the progressive damage approach could be implemented, with satisfactory accuracy and efficiency, for open-hole strength prediction using basic material degradation laws, a shell element model and widely available commercial FEM software (ABAQUS). This is of practical use for industrial applications. In addition, for the purpose of comparison, a characteristic distance approach was also applied to the open-hole strength problem. It was found that using a linear analysis with a properly defined secant shear modulus this approach gave an accurate prediction, however at least one measured value of notched strength is still required for calibration using this approach.     

Fracture of electrostrictive solids subjected to combined mechanical and electric loads

Based on the complex variable method, this paper studies the effects of electric fields on the fracture of an electrostrictive solid under combined mechanical and electrical loads at infinity. The electric field inside a deformed crack is first determined by using the semi-permeable crack model. Then, the complex potentials and the intensity factors of stresses are presented, respectively, in concise and closed forms. Numerical results are also obtained to discuss the effects of applied electric and/or mechanical loads on the induced electric fields inside the crack and the stress intensity factors when the interior of the deformed crack and the surrounding space at infinity are filled with different gases.     

Application of the dynamical flexural resonance technique to industrial materials characterisation

The determination of the Young’s modulus and damping coefficient Q⁻¹ by means of non-destructive vibrating techniques has been applied to bulk and coated industrial materials. Extensions of a previous analytic model of composite beam allow to determine accurately the macroscopic modulus of each component of multilayered structural materials as coated superalloys or nitride-hardened steels. Furthermore, the study of glasses and polymers has been investigated. An attempt of normalisation of the modulus versus temperature curves allows to establish master curves depending on the specific structure, from metallic glasses to polymeric glasses. Finally a comparison of dynamical modulus and Q⁻¹ values measured between resonant (>1 kHz) and subresonant techniques (10⁻³ to 10 Hz) in relation to the loading frequencies applied in real conditions has been under folder. For metallic materials such as forged or rolled titanium alloys, the brittle-to-fragile transition occurs abruptly or smoothly with a shift of 300 K following the range of excitation frequencies.     

Micromechanical analysis of magneto-electro-thermo-elastic composite materials with applications to multilayered structures

The method of asymptotic homogenization was used to analyze a periodic magnetoelectric smart composite structure consisting of piezoelectric and piezomagnetic phases. The asymptotic homogenization model is derived, the governing equations are determined and subsequently general expressions called unit-cell problems that can be used to determine the effective elastic, piezoelectric, piezomagnetic, thermal expansion, dielectric, magnetic permeability, magnetoelectric, pyroelectric and pyromagnetic coefficients are presented. The latter three sets of coefficients are particularly interesting in the sense that they represent product or cross-properties; they are generated in the macroscopic composite via the interaction of the different phases, but may be absent from the constituents themselves. The derived expressions pertaining to the unit-cell problems and the resultant effective coefficients are very general and are valid for any 3-D geometry of the unit cell. The model is illustrated by means of longitudinally-layered smart composites consisting of piezoelectric (Barium Titanate) and piezomagnetic (Cobalt Ferrite) constituents. Closed-form expressions for the effective properties are derived and the results are plotted vs. the volume fraction of the piezoelectric phase. Pertaining to the product properties of this particular magnetoelectric laminate, it is observed that the effective pyroelectric and pyromagnetic coefficients attain a maximum value at a BaTiO₃ volume fraction of 0.5 and maximum values for the magnetoelectric coefficients at a BaTiO₃ volume fraction of 0.4. Likewise, the maximum value of a magnetoelectric figure of merit (characterizing efficiency of energy conversion in longitudinal direction) is also attained at a volume fraction of 0.4.