Surface Stress Field Research Articles

Conceptual and numerical models of ring-fault formation

Most ring faults of collapse calderas are primarily shear fractures the initiation and development of which depends on the state of stress in the host rock. The state of stress in a volcano is controlled by the loading conditions, such as magma-chamber geometry and pressure, but also by the mechanical properties of its rock units and structures (such as existing contacts, faults, and joints). Ring-fault formation is thus essentially a problem in rock physics. Field observations show that some ring faults are dip–slip, whereas others are partly faults (shear fractures) and partly ring dykes (extension fractures). Although slip on existing ring faults is much more common in basaltic edifices (shield volcanoes) than in true composite volcanoes, in both types of volcanoes most caldera unrest periods do not result in ring-fault slip. Here I present new conceptual and numerical models of caldera formation in volcanoes with shallow spherical (circular) or oblate ellipsoidal (sill-like) magma chambers. In the layered models, the host rock above the chamber is composed of 30 comparatively thin layers with stiffnesses (Young's moduli) alternating between 1 GPa and 100 GPa. The chamber itself is located in a single, thick layer. The crustal segment hosting the chamber is either 20 km or 40 km wide but has a constant thickness of 20 km. The loading conditions considered are: (1) a crustal segment subject to 5 MPa tension; (2) crustal segment subject to excess magmatic pressure of 10 MPa at the bottom (doming of the volcanic field containing the chamber); (3) a combination of tension and doming; and (4) chamber subject to underpressure (negative excess pressure) of 5 MPa. The main results are as follows: (1) Excess pressure and underpressure in a chamber normally favour dyke injection rather than ring-fault formation. (2) For doming or tension, a spherical magma chamber favours dyke injection except when the layer hosting the chamber is very soft (10 GPa) or one with recent dyke injections, in which case the surface stress field favours ring-fault formation. (3) For a sill-like chamber in a 20-km wide crustal segment, a ring-fault can be generated by either tension or tension and doming; for a 40-km wide segment, doming alone is sufficient to generate a ring fault. (4) Since individual layers in a volcano may develop different local stresses, stress-field homogenisation through all the layers between the chamber and the surface is a necessary condition for ring-fault formation. (5) Because the mechanical properties of the layers that constitute basaltic edifices are more uniform than those that constitute true composite volcanoes, it follows that stress-field homogenisation, and thus ring-fault formation or slip, is more commonly reached in basaltic edifices than in composite volcanoes. (6) Both for basaltic edifices and composite volcanoes, the stress fields most likely to initiate ring faults are those generated around sill-like chambers subject to tension, doming, or both.

Impact des conditions d'usinage sur la zone du matériau affectée par le procédé

Machining processes can introduce residual stresses at the surface of machined workpieces and can modify the microstructure and texture in a volume close to the surface. Such changes are important when controlling the behaviour of these workpieces during the workpiece lifetime. It is thus necessary to quantify residual stresses and texture components and to determine the machining-induced microstructure to understand and predict the behaviour of modified surfaces. In this study, particular attention was paid to pure copper considered as a modelling system. The influence of the nose radius, the cutting speed and the lubricant on the surface stress field and the surface texture was quantified by means of XRD techniques. The microstructural modifications at the specimen surface and in depth were evaluated using scanning electron microscopy. The electrochemical behaviour of modified surfaces were studied from local measurements using the electrochemical microcell technique.

Stress Dependence of Sapphire Cathodoluminescence from Optically Active Oxygen Defects as a Function of Crystallographic Orientation

The cathodoluminescence (CL) spectrum of the synthetic sapphire single crystal has been studied with respect to the different crystallographic planes of the crystal in order to describe the tensorial stress dependence of the band related to oxygen defects. Experiments provide the link between CL spectral shift and stress, which is referred to as the piezo-spectroscopic (PS) relationship. Using the biaxial stress field developed at the tip of cracks generated from the corners of a Vickers indentation, we clearly detected stress dependence for the cumulative band arising from the F+-center transition of optically active oxygen vacancies. The matrix of PS coefficients along different crystallographic axes of single-crystal sapphire could be precisely determined. The shallow nature of the electron probe may enable the characterization of surface stress fields with a spatial resolution that may not be easily available by conventional laser probes. The PS calibration results collected on oxygen-defect bands allow the direct determination of unknown surface residual stress fields stored in sapphire substrates for electronics applications.

The Early Stages of Quantum Dot Self-Assembly: A Kinetic Monte Carlo Simulation

The influence of a periodic strain field in a silicon substrate on the nucleation of surface atomic clusters is studied using a Kinetic Monte Carlo (KMC) model for Ge quantum dot formation. The effect of strain on island diffusion is determined by calculating the binding energy of an island with the Modified Embedded Atom potential. KMC simulations have been carried out on the basis of diffusion pathways on reconstructed Si surfaces and effective island diffusion kinetics. It is found that island diffusion coupled with surface stress fields play a dominant role in precisely forming atomic clusters during the early stages of evolution under an extremely weak inhomogeneous stain field. The results explain experimental observations on the ordering of Ge self-assembled quantum dos along underlying buried interfacial dislocation arrays in a relaxed 800 A Si0 85Ge0 15 buffer layer.

Statistical Analysis of Surface and Sub-Surface Residual Stress Fields in Retrieved Alumina Femoral Heads after Long-Term Implantation

The surface of retrieved alumina (Al2O3) femoral heads was investigated by piezo-spectroscopic techniques based on confocal photo-stimulated fluorescence. The micrometric spatial resolution of the laser beam impinging on the investigated joint surface (typically about 1 $m in lateral resolution) enabled us estimating patterns and magnitude of residual stress in extremely narrow zones, at least comparable with the grain size of the material. According to a statistical collection of data on a microscopic level, it was possible to assess the retrieved femoral heads in-toto, thus extending the microscopic analysis to the entire surface of the joint. A stress field was found, which mainly arose from loading history, and displacements acting on the femoral head during its lifetime. Residual stress data enabled us to draw interesting conclusions about the role of the material microstructure and the peculiar kinetic mechanisms involved with the use of the joint. Spectroscopic techniques, which are complementary to in vitro testing procedures and theoretical stress analyses based on finite-element methods, can be very useful in improving the design of the femoral head and in optimizing the microstructural characteristics of the ceramic materials employed.

Fluorescence spectroscopic analysis of surface and subsurface residual stress fields in alumina hip joints

We aim to establish a confocal spectroscopic technique able to study the features of fluorescence spectra arising from native Cr3+ impurity in polycrystalline alumina (Al2O3) as a biomaterial and to use their emission lines as microscopic probes for the characterization of residual stress fields stored in artificial hip prostheses during their implantation in vivo. As an application of the technique, we report for the first time concerning the evolution of microscopic (residual) stress fields stored on the surface and in the subsurface of N=7 retrieved Al2O3 hip joints after exposure in the human body from a few months to 19 yr. The micrometric diameter of the laser beam waist impinging on the joint surface (typically about 1 microm in lateral resolution) enables us to estimate the patterns and magnitude of residual stress with high spatial resolution, at least comparable with the grain size of the material. In addition, a selected confocal configuration for the optical probe enables minimization of the probe size along the in-depth direction. According to a statistical collection of data on the microscopic level for retrieved femoral heads in toto, a residual stress field arising from loading history in vivo during the lifetime of the Al2O3 femoral head can be revealed. Finally, an interpretation is given of microscopic wear mechanisms in Al2O3 artificial hip joints consistent with the observed evolution of surface residual stress fields on elapsed time in vivo.

The influence of different rheological parameters on the surface deformation and stress field of the Aegean–Anatolian region

The Aegean–Anatolian region is characterised by an inhomogeneous deformation pattern with high strain rates and a high seismicity both at the boundaries and in the plate interior. This pattern is controlled by the geometry and rheology of the structural units involved and their tectonic setting. A numerical analysis with a finite-element model of the region is used to quantify the influence of different rheological parameters. Viscoelastic material behaviour is implemented for the mantle lithosphere, whereas the crust is modelled with an elastic–plastic rheology. The variation of the inelastic material properties (viscosity and plastic strength) quantifies the influence of these material parameters on the deformation, stress, and strain patterns. Comparison of the modelled results with geodetic and geophysical observations reveals that the viscosity of the mantle lithosphere is the key to explaining the inhomogeneous deformation pattern. The best-fit model yields a viscosity of 1020 Pa s beneath Anatolia, whereas adjacent regions have viscosities between 1021 and 1023 Pa s. The model also explains the intra-plate seismicity and the stress field as well as its partitioning into regions with strike-slip and normal faulting. The final model is in good agreement with seismological, geodetic, and geological observations. Local deviations can be tracked down to small-scale structures, which are not included in the model.

Microstructural Effects in Multilayers with Large Moduli Contrast Loaded by Flat Punch

An efficient solution methodology is employed for the frictionless contact of half-planes built up with large number of layers to study the effect of microstructural refinement on the surface and subsurface stress fields. Half-planes with increasing numbers of alternating stiff and soft layer pairs spanning a fixed depth below the top surface are considered to determine the convergence behavior of the contact pressure and subsurface stresses relative to the corresponding quantities in fully or partially homogenized configurations with macroscopically equivalent properties. The results indicate that not all stress components converge to the corresponding values in the fully homogenized configuration with increasing microstructural refinement. This is only achieved by a partial homogenization wherein the layered half-plane is homogenized below a certain depth with the top surface layers retained. The number of retained surface layers required for an accurate stress field reproduction depends on the punch length and microstructural scale and depth of the alternating layers. The characteristic contact pressure profiles observed in the layered configurations suggest a basis for the development of a sensing technique for the microstructural architecture and property identification of the subsurface region.

Finite-element and XRD methods for the determination of the residual surface stress field and the elastic–plastic behaviour of duplex steels

Duplex stainless steels have a complex microstructure with comparable volume fractions of austenite and ferrite. Due to differences in the mechanical properties, a heterogeneous distribution of stresses is generated in both phases. In this paper, a finite-element method and a thermo-mechanical model are described for determining the residual surface stress distribution on duplex steels. The stress distribution is calculated after various surface treatments and under straining conditions. The numerical calculations are then compared with the experimental results in order to verify the accuracy of the method. An original method based on successive XRD measurements is then proposed to study the elastic–plastic properties of both phases. The results are compared with those obtained from surface observations.

Thermomechanical Analysis of Semi-infinite Solid in Sliding Contact With a Fractal Surface

A thermomechanical analysis is presented for a semi-infinite elastic solid sliding against a rigid, rough surface characterized by fractal geometry. A piecewise-linear distribution of the contact pressure was obtained by superposition of overlapping triangular pressure elements. The normal surface displacements due to the effects of contact pressure, shear traction, and thermoelastic distortion caused by frictional heating are incorporated in the influence coefficients of the matrix-inversion method. Results for a smooth, cylindrical surface sliding over a semi-infinite elastic solid demonstrate the accuracy of the analysis and provide reference for comparison with results obtained with the rough (fractal) surface. The effects of surface topography and interaction between neighboring asperity microcontacts on the surface and subsurface temperature rise and stress field of the elastic semi-infinite solid are discussed in the context of numerical results. The significance of frictional heating on the contact pressure, temperature rise, and stresses is interpreted in terms of the Peclet number and topography (fractal) parameters. The results provide insight into the likelihood for cracking and plastic flow at the surface due to the combined effects of mechanical and thermal surface tractions.

Advances in local mechanoelectrochemistry for detecting pitting corrosion in duplex steels

The goal of this study was to demonstrate that a relationship exists between surface stress and pitting corrosion. The surface stress field generated by polishing was first calculated using a thermomechanical model and a finite element code. Pitting corrosion tests performed at the microscale along the austenite/ferrite interface using the electrochemical microcell technique were then analyzed considering the microstructure, and the residual surface stress field calculated numerically under the microcapillary. Mechanical criteria are proposed leading to an enhancement of pitting corrosion of duplex steels.

Atomic scale stresses and strains in Ge∕Si(001) nanopixels: An atomistic simulation study

Recent progress in the growth of nanostructures on nonplanar (patterned) substrates has brought to the forefront issues related to atomic-level surface and subsurface stress and strain field variations, as these govern the process of formation of such nanostructures and strongly affect their physical properties. In this work, we use atomistic simulations to study the atomically resolved displacements, stresses, strains, and the strain energy in laterally finite nanoscale Si(001) mesas, uncovered and covered with the lattice-mismatched Ge overlayers. The spatial variations of the stress are examined both across the surface profile of the mesas and in the direction down to the substrate. We find that the hydrostatic stress and strain at the Ge∕Si interface undergo rapid changes from tensile in the interior of the Si mesa to compressive in the Ge overlayer, with the transition taking place over distances of the order of Si lattice constant. Substantial relaxation of the hydrostatic stress and strain, in both the lateral and vertical directions, is observed in the Ge overlayer, in the Si(001) mesa interior, and in the substrate. Atomic displacement fields, computed in the Ge overlayer and in the Si(001) mesa interior, demonstrate considerable inhomogeneity due to both finite geometry effects and the lattice-mismatched Ge overlayer–induced stresses. The maximum magnitude of displacements is as large as 0.7Å, even in the case of uncovered Si(001) mesa. Moreover, we find nonzero displacements in the Si substrate as far deep as 100ML (monolayer) from the Ge∕Si interface, showing that a substantial degree of the misfit-induced stress accommodation occurs through relaxation in the Si(001) mesa interior and the substrate. The topology of the equal displacement contours, in regions adjacent to the mesa edges and corners, is close to semielliptical. To reveal the impact of stress accommodation in the mesa interior and in the substrate, we compute the strain energies of the Ge overlayer atoms as a function of both the Si(001) mesa height and the Ge overlayer thickness. We find that the normalized (per Ge atom) elastic energy of a fixed thickness overlayer decreases with increasing mesa depth. At a fixed mesa height, the Ge overlayer energy per Ge atom increases as a function of Ge overlayer thickness. In both cases, the dependencies are shown to be adequately fitted with exponential forms. The shear stresses in both bare and 16ML thick Ge overlayer covered mesa systems show dramatic variations in both lateral and vertical directions. These variations are responsible for nonlinear stress-strain behavior in the regions around the finite geometry features (i.e., edges and corners).

Determination of the surface stress field for stainless steels having different microstuctures

The method of residual stress determination based on X-ray diffraction has been used for the study of different types of stainless steels: single phase or multiphase microstructures, different inclusion contents. A thermomechanical model associated with a finite element code is proposed for the determination of the stress field in relationship with the actual microstructure and texture of the materials. The numerical calculations are validated by comparing the obtained results to those experimentally determined and by scanning electron microscope observations on the initiation zones of microcracks.

A review of the general theory of thermoelastic stress analysis

Thermoelastic stress analysis (TSA) is now a well-known experimental technique providing information on the surface stress field in structures. Many studies have assessed the potential of the technique for a number of applications and some useful and detailed reviews of these investigations are available, focusing mainly on the experimental aspects related to the measurement of the thermoelastic signal. In this work, instead, a complete and detailed insight into the origins of the various forms of the equations describing the thermoelastic effect is given with reference to the concepts of the thermodynamic theory of a continuum. A discussion on the theory leading to the thermoelastic effect law is intended to give a useful overview of the applications and real limitations of TSA.

Finite-element method for the determination of the surface stress field from the real microstructure of anisotropic materials

A method is described for determining the surface stress distribution from the real microstructure of materials. The major advantages of the analyses, including the determination of anisotropic mechanical and crystallographic properties, are identified. The calculation involves the development of image analysis processing and the implementation in the finite-element code Cast3M of a new procedure for meshing the real microstructure and material models capable of describing the complex behaviour of real materials. The method is applied to the case of austenoferritic stainless steels.

On the determination of residual stress and strain fields by sharp indentation testing.: Part II: experimental investigation

An experimental investigation has been carried out in order to study how residual stress and strain fields can be determined by sharp indentation testing. Aiming at a thorough understanding of the influence from general residual surface stress and strain fields on global indentation parameters, i.e. hardness and contact area, Vickers indentation tests have been performed on specimens first exposed to standard four-point bend (4PB) or single edge notch bend (SEN(B)) loading. The experimental results have been evaluated based on the findings in a parallel theoretical/numerical investigation and are compared with finite element simulations as well as with corresponding results taken from the literature. Good agreement between experiments and numerical results has been found, particularly in a situation with no or little plastic deformation due to preloading.

Self-Organization of Ordered Silver Nanocrystal Arrays on Cubic Mesoporous Silica Surfaces

Regular and oriented silver nanocrystalline arrays loaded on the surface of cubic mesoporous silica MCM-48 material was obtained by an approach of impregnation followed by thermal treatment. The self-assembly of Ag clusters at a suitable temperature influenced by the periodic surface stress field of the ordered mesopore structures is believed to lead to the ordered Ag nanoarrays.

Molecular-dynamics investigation of the surface stress distribution in a Ge/Si quantum dot superlattice

The surface stress distribution in an ordered quantum dot superlattice is investigated using classical molecular dynamics simulations. We find that the surface stress field induced by various numbers~ from 1t o 9! of Ge islands embedded in a Si~001! substrate is in good agreement with analytical expressions based on pointlike embedded force dipoles, explaining the tendency of layered arrays to form vertically aligned columns. The short-ranged nature of this stress field implies that only the uppermost layers affect the surface growth and that their influence decreases rapidly with layer depth. @S0163-1829~99!52028-6#

Elastic surface—substrate interactions

A theory for three–dimensional finite deformations of elastic solids with conforming elastic films attached to their bounding surfaces is described. The Gurtin–Murdoch theory incorporating elastic resistance of the film to strain is generalized to account for the effects of intrinsic flexural resistance. This modification yields a model that can be used to describe equilibrium deformations in the presence of compressive–surface stress fields. An associated variational theory is given and material symmetry considerations are discussed. The theory is illustrated by examples.

Intercomparison of the seasonal cycle of tropical surface stress in 17 AMIP atmospheric general circulation models

The mean state of the tropical atmosphere is important as the nature of the coupling between the ocean and the atmosphere depends nonlinearly on the basic state of the coupled system. The simulation of the annual cycle of the tropical surface wind stress by 17 atmospheric general circulation models (AGCMs) is examined and intercompared. The models considered were part of the Atmospheric Model Intercomparison Project (AMIP) and were integrated with observed sea surface temperature (SST) for the decade 1979–1988. Several measures have been devised to intercompare the performance of the 17 models on global tropical as well as regional scales. Within the limits of observational uncertainties, the models under examination simulate realistic tropical area-averaged zonal and meridional annual mean stresses. This is a noteworthy improvement over older generation low resolution models which were noted for their simulation of surface stresses considerably weaker than the observations. The models also simulate realistic magnitudes of the spatial distribution of the annual mean surface stress field and are seen to reproduce realistically its observed spatial pattern. Similar features are observed in the simulations of the annual variance field. The models perform well over almost all the tropical regions apart from a few. Of these, the simulations over Somali are interesting. Over this region, the models are seen to underestimate the annual mean zonal and meridional stresses. There is also wide variance between the different models in simulating these quantities. Large model-to-model variations were also seen in the simulations of the annual mean meridional stress field over equatorial Indian Ocean, south central Pacific, north east Pacific and equatorial eastern Pacific oceans. It is shown that the systematic errors in simulating the surface winds are related to the systematic errors in simulating the Inter-Tropical Convergence Zone (ITCZ) in its location and intensity. Weaker than observed annual mean southwesterlies simulated by most models over Somali is due to weaker than observed southwesterlies during the Northern Hemisphere summer. This is related to the weaker than observed land precipitation simulated by most models during the Northern Hemisphere summer. The diversity in simulation of the surface wind over Somali and equatorial Indian ocean is related to the diversity of AGCMs in simulating the precipitation zones in these regions.