Elastic Flexure Research Articles

Effects of a viscoelastic lithosphere on the isostatic bedrock response

The lithosphere responds to loading by elastic flexure which is followed by viscous relaxation, the amount of which depends on the stress duration. This study compares results of an Earth model in which the lithosphere is modelled as a purely elastic layer and as a more general viscoelastic solid overlain by a rigid crust. It shows the emergence of a noticeable difference in the short wavelength (1×10 2–5×10 2 km) component of the bedrock deformation after loading durations of the order of 10 5–10 6 yr assuming a lower lithosphere viscosity of the order of 10 23–10 24 Pa.s. In particular, for the long-term loading hypothesised to be imposed by the East Antarctic ice sheet, we find that a viscoelastic lithosphere yields a more local deformation pattern to which ice sheet dynamics are highly sensitive. It confirms that modelling of the Antarctic long-term evolution would benefit from a fully coupled ice/bedrock approach in which the lithosphere would be represented by a viscoelastic solid.

Elastic flexure of bilayered beams subject to strain differentials

The residual stresses present in a thin film and the curvature formed at its substrate during deposition have been a great concern to electrochemists and process engineers. Here a new hybrid analytical method is presented to reanalyze the flexural problem subjected to a strain differential in the general case. It was shown that the present solutions for ultrathin films agree with Stoney's equation. Moreover, single or dual neutral axes resulted, depending on materials and thickness ratios between the film and the substrate. Quantitative differences with others in the solutions of deformed curvature and residual stress are discussed in a representative case of GaAs top coat/Si substrate wafers.

Technique for combining incoherent interferometric images

We discuss the use of a physically constrained iterative deconvolution algorithm to combine and deconvolve images taken with interferometric imaging arrays. To demonstrate this method we have simulated imaging with the Large Binocular Telescope [Proc. SPIE3352, 23 (1998)]. This is a two-element interferometer in which each element is under adaptive-optics control for atmospheric compensation and in which the fixed baseline is maintained by active control to compensate for elastic flexure of steel under variable gravitational loading. We show how images taken at different position angles, by means of the two 8.4-m apertures, co-phased across the 14.6-m center-to-center separation, can be used to tomographically reconstruct an astronomical object at the full-aperture (23-m) diffraction limit of the Large Binocular Telescope.

Evolution of the North Caucasus foredeep: constraints based on the analysis of subsidence curves

Using a database of more than 130 wells the Alpine evolution of the North Caucasus foredeep can be described in three main periods. (1) The Early Jurassic to Middle–Late Cretaceous (including the Cenomanian) relates to the initial rifting phase and was characterised by succession of comparatively high rates of subsidence and uplift. During this stage, many events in the eastern and western parts were synchronous, whereas some of them appeared to be smoothed in the Stavropol high. The southern border of the area had a more complex behaviour often moving in the opposite direction relative to the rest of the area. The main peculiarities of evolution of the Great Caucasus region can be explained if we adopt the hypothesis of Stamply and Pillevuit (1993)and suppose that the Early Jurassic extension of the trough was accompanied by a strong left-lateral transform movement. As a result the central part of the Great Caucasus trough formed as a pull-apart basin. Analysis of the style of movements of the southern border of the Scythian plate as well as data on tectonics and volcanism in the Great and Lesser Caucasus showed that other regional compressional and extensional Mesozoic events could also have a transform component. Shear stresses within the lithosphere of the Great Caucasus can be due to oblique subduction or even transform movements at the plate boundary to the south of the Caucasus region ( Dercourt et al., 1993). (2) The period from the Late Cretaceous to the Middle Eocene (from the Turonian to the Bartonian) relates to the oceanic suture of the Lesser Caucasus and was characterised in the Great Caucasus area by alternating subsidence and uplift events of considerably lower amplitude (at least up to the Maastrichtian). Beginning in the Late Paleocene, subsidence curves for almost all the area reflect the same events, but in the western part and also in the north of the central part the rate of movements was considerably higher and since the Late Paleocene short term events in this area took place on the background of rather fast subsidence at nearly constant rate. We believe that this subsidence and formation of the East Black Sea depression have the same origin. We consider strong differences in evolution of the eastern, western and central parts during the second stage to be due to closure of the Lesser Caucasus oceanic basin and arrival of the Nakhichevan block. This led to changes of configuration of the plate boundary and resulted in reorganisation of stress and displacements within the Caucasus region. This reorganisation was a reason for the opening of the East Black Sea depression and rapid subsidence of the western and central parts of the area at the end of the second stage. (3) The period from the Middle Eocene to the present relates to the development of a foreland basin coeval with shortening and uplift in the adjacent Great Caucasus range. It was characterised by alternation of relatively short uplift and longer subsidence events. An important feature of this stage is that although the amplitude of movements varied from place to place, these events were synchronous in all parts of the foredeep (at the Stavropol region sediments preserved only for the beginning of this stage). Formation and evolution of the foredeep during the third stage can not be explained exclusively by elastic flexure. To do this we used the model of a small-scale convection within the asthenosphere ( Mikhailov et al. 1996, 1999). By the comparison of numerical results with the data on the evolution of the North Caucasus foredeep we concluded that there were four main stages of compression in the processes of formation of the Great Caucasus mountain belt. The first compression took place before the Maykopian (between 39.5 and 36.0 Ma). The other three were in the Tarkhanian (16.6–15.8 Ma), Konkian–Early Sarmatian (14.3–12.3 Ma) and Pontian (7.0–5.2 Ma). The different width of the Great Caucasus trough by the beginning of the compression, as well as variations in thickness of the lithosphere and a different thermal state can cause interruption of the formation of the foredeep at the Stavropol high.

Foredeep basins: the main features and model of formation

The comparative study of the foredeep basins of the northern Caucasus, Alpine and Apennine foredeeps revealed that there are no significant differences between outer and inner foredeeps situated at the front and the back of the crustal-scale thrust. So the driving mechanism should be essentially the same for internal and external foredeeps and elastic flexure should not be supposed as the only (sometimes as the main) mechanism of foredeep formation. The common feature of the foredeep evolution is a phase of slow subsidence lasting for 50 million years or more (passive margin stage sensu stricto) and then relative uplift followed by rapid subsidence. This twofold event of relative uplift (the duration is several million years) giving way to rapid subsidence may be repeated several times. The relative uplift or nearly equal to zero subsidence of the foredeep basins appeared to be synchronous with phases of external compression within adjacent mountain belts, as well as rapid subsidence took place between phases of external compression. Thus, the first stage of relative uplift could be recognised as the first stage of the foredeeps formation. To describe the development of the foredeeps at both sides of the compressional belts a model of evolution of the Earth's outer shell has been employed. The model predicts that when the Earth's outer shell has been once disturbed by external intraplate- or mantle-induced forces, small-scale convection within the asthenosphere arises. This convection causes deformation in the lithosphere of orogenic belts over a long period of time after the external forces stop. This manifests in uplift of belts and subsidence at their periphery. The suggested model shows a good agreement with data on the foredeeps structure and evolution. In particular, application of the model enabled us to explain the thickness of sediments in the foredeep basins and their shape, the formation of the foredeeps not only at the front but also at the back of asymmetric compressional thrust belts, uplift of foredeeps during compression in the belts and rapid subsidence after this compression stops. Numerical results for the Great Caucasus region showed that the first compressional event at the orogenic stage took place there before the formation of the Maykopian sediments, i.e. 39.5 Ma, in the end of the closure of the Arabian Ocean. The three further compressional events can also be recognised: one of them being between 16.6 and 15.8, the other between 14.3 and 12.3 Ma, and the last one between 7.0 and 5.2 Ma.

Lineament Analysis and Geophysical Modelling of the Alba Patera Region on Mars

Global data sets of images, topography and gravity are available for Mars from several orbiter missions. At the eve of new global data from Mars Global Surveyor (MGS), the capabilities of 3D geophysical modelling based on areal topography and gravity data combined with geologic-tectonic image interpretation is demonstrated here. A unique structure is chosen for the model calculations: the Alba Patera volcanic complex at the northern border of the Tharsis rise. Five groups of graben are discriminated: Ceraunius Fossae, Catenae, Tantalus Fossae (radial group) radial to the Tharsis rise, mainly associated to the formation of Tharsis, and Alba and Tantalus Fossae (circular group), younger than the other graben and circular around Alba Patera. Combining 3D elastic flexure of the lithosphere due to a 3D topographic surface load with 3D gravity models results in a rather thick lithosphere (150–200 km) and thick crust (60–100 km). In another model estimate it has been assumed that the circular grabens are induced by the stresses from the surface load of Alba Patera. In a first order calculation the surface stresses under a point load have been determined resulting in a good correlation of the stress maximum with the location of the circular grabens for a 50-km thick lithosphere. This is in accordance with earlier results from this method, but in contradiction with the thick lithosphere derived from flexure-gravity models. One possibility for this contradiction may be that the different models represent two evolutionary points of Alba Patera. (1) The correlation of stresses with the circular grabens may represent an older stage of evolution with a thinner lithosphere. (2) The flexure-gravity models represent a younger to present stage with a thick lithosphere. The results of the lithosphere thicknesses are compared with an admittance calculation and different thermal evolution models which determine comparable thicknesses (≈150 km). More detailed models including 3D stress models should wait for new data sets from MGS. The results from the lineament analysis and geophysical modelling are summarized in an evolution model for Alba Patera.

Structural analysis: a historical approach

This volume provides a concise, historical review of the methods of structural analysis and design - from Galileo in the seventeenth century, to the present day. Through it, students in structural engineering and professional engineers will gain a deeper understanding of the theory behind the modern software packages they use daily in structural design. This book also offers the reader a lucid examination of the process of structural analysis and how it relates to modern design. The first three chapters cover questions about the strength of materials, and how to calculate local effects. An account is then given of the development of the equations of elastic flexure and buckling, followed by a separate chapter on masonry arches. Three chapters on the overall behaviour of elastic structures lead to a discussion of plastic behaviour, and a final chapter indicates that there are still problems needing solution.

Effects of Vibration on Mechanical Properties and Biomass Allocation Pattern ofCapsella bursa-pastoris(Cruciferae)

The herbaceous dicot speciesCapsella bursa-pastoris(Cruciferae) was used to determine the influence of chronic mechanical perturbation on the biomass allocation pattern (i.e. dry weight distribution among roots, stems and reproductive structures) and the mechanical properties of roots and stems (i.e. tensile breaking stress and Young's modulus). It was hypothesized that mechanically stimulated plants would allocate more of their total biomass to root systems and less to shoots compared to control plants and that the breaking stress (a measure of strength) and Young's modulus (a measure of material stiffness) would increase for roots and decrease for stems because these responses would adaptively reduce the bending moment at the base of shoots and increase the anchorage strength of root systems. It was also hypothesized that mechanical perturbation would maladaptively reduce the relative fitness of individuals by reducing biomass allocation to their reproductive organs and the ability to broadcast seeds by means of elastic stem flexure. These hypotheses were tested by vibrating cultivated plants for 60 s every day during the course of growth to maturity and comparing their dry weight distributions and the mechanical properties of their body parts (measured in tension) to those of undisturbed control plants. Based on a total of 51 experimentally manipulated and 44 control plants for which mechanical properties were successfully tested, chronic organ flexure resulted in more massive root systems and less massive vegetative shoots, increased the magnitudes of root breaking stress and Young's modulus and had the reverse effect on stems, reduced the dry weight of reproductive structures at maturity, delayed the formation of the first mature flower and fruit, and accelerated the on-set of plant senescence compared to control plants. These responses to chronic organ flexure are interpreted to be vegetatively adaptive, since they reduce the probability of stem and root failure as a consequence of wind-pressure or foraging, and to be reproductively maladaptive, since they reduce reproductive effort and the ability to mechanically discharge seeds.

Gravimetric constraints on the rheology of the Indian and Tarim Plates in the Karakoram continent–continent collision zone

Bouguer gravity anomalies in the region of the Western Himalayas, Karakoram and Tien Shan show large negative values, but classical isostatic models are insufficient to account for the detailed pattern of the observed anomalies. In the past years gravimetric surveys in the Karakoram (Marussi, Caputo and others in 1954) have been extended and densified. The full body of available gravimetric data, including the pendulum observations by De Filippi in 1913–14 and Hedin in 1929–33 have been re-analyzed. Terrain corrections have been computed systematically for all available data using an algorithm and Digital Terrain Model. The isostatic anomalies along a profile from the Indo-Gangetic foredeep, across the Karakoram Range and terminating in the Tarim Basin show the oscillating values already noticed by Marussi. This oscillatory pattern can be explained by a model in which the convergent boundaries of the Indian and Tarim plates deform by elastic flexure, besides isostasy. The gravity data are used to constrain the numerical values of the model parameters, particularly the flexural rigidity of the plates. For the Indian Plate it is found that the best fitting value of the flexural rigidity is D=5×10 24 N m, a value very similar to those reported in the Central Himalayas. The flexural rigidity of the Tarim Plate turns out to be considerably larger, D=7×10 25 N m, which makes the Tarim more rigid than the neighboring Central Tibet. Both plates are loaded by an estimated shear force of 7 10 12 N m −1 located in a region corresponding to the Nanga Parbat Haramosh syntaxis. It is concluded that the Indo–Asian continental collision in Western Himalaya and Karakoram results in the development of flexural basins on both sides, unlike in Central Himalaya where the collision produces a flexural basin, the Ganga Basin, to the South and, to the North, the indentation of an isostatically supported Tibetan Block with possible rheological layering and eastward lateral extrusion.

Rheology of the Indian and Tarim plates in the Karakoram continent-to-continent collision zone

Bouguer gravity anomalies in the region of Western Himalayas, Karakoram and Tien Shan show large negative values, but classical isostatic models are insufficient to account for the detailed pattern of the observed anomalies. In the past years the gravimetric surveys in the Karakoram done by Marussi, Caputo and others in 1954 have been extended and intensified. The full body of available gravimetric data, including the pendulum observations by De Filippi and Hedin at the beginning of this century, have been re-analyzed. Terrain corrections have been computed systematically for all available data using a unique algorithm and Digital Terrain Model. The isostatic anomalies along a profile from the Indo-Gangetic foredeep, across the Karakoram range and terminating in the Tarim basin show the oscillating values already noted by Marussi. It is here proposed that this oscillatory pattern can be explained by a model in which the convergent boundaries of the Indian and Tarim plates deform by elastic flexure, besides isostasy. The gravity data constrain the numerical values of the model parameters, particularly the flexural rigidity of the plates. For the Indian plate the best fitting value of the flexural rigidity is D = 5 1024 N m, a value very similar to those reported in Central Himalaya. The flexural rigidity of the Tarim plate turns out to be considerably larger D = 7 1025 N m, which makes the Tarim more rigid than the neighboring Central Tibet. Both plates are loaded by an estimated shear stress of 7 1012 N m-1 located in a region corresponding to the Nanga Parbat Haramosh syntaxis. It is concluded that the Indo-Asian continental collision in the Western Himalaya and Karakoram resulted in the development of flexural basins on both sides, unlike the Central Himalaya where the collision produced a flexural basin, the Ganga basin, to the south and, to the north, the indentation of an isostatically supported Tibetan block with possible rheological layering and eastward lateral extrusion.

An ultraprecision stage for alignment of wafers in advanced microlithography

We present an ultraprecision stage specially designed to align wafers for the microlithography of integrated circuit patterns of sub-0.3 μm design rules. The whole stage mechanism is composed of two individually operating xyθ-stages: a global stage to provide initial coarse alignment of wafers in stepping mode; and a micro stage to produce fine controlability in nanometer range. The global stage is configured with three linear motors kinematically linked to produce xyθ-motions without resorting to precision guideways. The micro stage corrects positional errors in the global stage by activating three piezoelectric microactuators housed in an elastic flexure. These two stages are simultaneously controlled as a dual servo system, because the main emphasis is given to achieving an overall positioning reproducibility of 20 nanometers in xyθ-motions in aligning wafers of 200-mm size.

On the structure and mechanical behaviour of the extending lithosphere in the Baikal Rift from gravity modelling

The crustal structure and lithospheric flexure of the Baikal Rift Zone, Siberia, are examined by means of gravity modelling. We model the Bouguer Anomaly (BA) along five 1200 km long gravity profiles. We first evidence that continuous elastic plate flexure due to surface loading cannot explain the observed BA. Then we introduce plate discontinuities coupled with a realistic brittle-elasto-ductile plate rheology, which allow us to model of external tectonic forces acting on the plates and determination of the Moho geometry. We show that the clearest expression of extensional processes occurs in the central part of the rift, which exhibits the highest crustal thinning. It evolves southwards to a rapidly increasing compression, resulting in an overthickening of the southern plate's crust and in the long-wavelength flexure of the Siberian plate. North of the central rift, crustal thinning (which is always less than 7 km) gives way to a more diffuse zone of deformation inside the Sayan-Baikal folded belt. Based on plate flexure models, we propose that the rift shoulders surrounding the central and north Baikal basins are not supported by upward bending plate, but have a deep crustal root caused by a downward flexure. The other parts of the rift depict two adjacent plates with antithetic flexures. We also infer that the axial mantle material upwarping is not related to a large-scale asthenospheric upwelling, since the lithosphere rheological interfaces are not significantly disturbed.Our results favour the role of horizontal forces and motions, resulting from the India-Asia collision, combined with the effect of inherited tectonic structures (and especially the Paleozoic suture bounding the Siberian craton) for explaining the crustal structure and plate flexure modeled.

Exploration of the plate bending model for predicting the hardness response of coated systems

In a previous paper, we described a new approach to understanding the hardness enhancements provided to ductile substrates by the application of thin hard coatings. The model, based on plate theory, examined the constraining effect of the coating (after cracking) on the “up-welling” movement of plastically displaced material (“pile-up”) in the substrate. The key concepts are that, this upthrust is resisted and constrained by elastic flexure of the coating around the periphery of the contact damage site (e.g. a hardness indentation) and this impedance to deformation appears as an increase in the system hardness. The model led to a plot which can also be used to predict the mechanical properties of coatings necessary to withstand any given scale of contact damage. In this paper the detailed appearance of the plot is further examined with respect to the effects of cracks of differing morphologies. Stronger experimental evidence is also presented to confirm this “master curve” or “design curve” which can be used in coating selection over a wide range of coated systems and contact scales. Our new data also shows how deviations from the master curve can be used to identify regimes in which differing mechanisms are playing some significant role. Thus our current refinements serve to map out the dominant mechanisms in the deformation response of hard coatings and shed light on exactly how the detailed indentation response of coatings can add significant resistance to contact damage of components, even after cracking of the coating has occurred.

Investigation Of Phase Formation During Cold Rolling Of Elemental Zr-Al-Ni-Cu Foils With Bulk Glass Forming Composition

ABSTRACTElemental Zr-Al-Ni-Cu foils of bulk glass forming composition were cold rolled at ambient temperature. The phase transformations during the cold deformation process were monitored with electron and X-ray diffraction and thermal analysis. After 120 deformation cycles a fully amorphous sample was obtained, as indicated by a distinct endothermic glass transition and a large exothermic crystallization reaction. The characteristics of the amorphous phase are compared with a liquid quenched metallic glass and mechanically alloyed elemental powder mixtures of similar composition. The amorphization reaction during cold rolling is similar to mechanical alloying and proceeds by the formation of a fine layered structure of the constituents, a rapid reduction of the layer thickness and of the average grain size to a nanometer scale and dissolution reactions in the hcp Zr lattice. While in the beginning of the cold rolling process the elemental foils were ductile, after several rolling passes the multilayered sample became brittle and, finally, displayed large elastic flexure in the amorphous state. Several thermal treatments of the multilayered and amorphous samples were performed in order to study thermally activated solid-state amorphization reaction as well as phase formation during crystallization.

Earthquake recurrence and glacial loading in western Washington

The tectonic setting of the Puget lowland was simpler during late Tertiary time (10 6 –10 7 yr) when the transfer of stress from subduction was not modulated by periodic glacial loading. Each advance of the Cordilleran Ice Sheet during the Quaternary Period created an additional 10–13 MPa of vertical load that may have stabilized the thrust sheet beneath the Puget lowland, causing background tectonic stresses to accumulate beyond the strength of active faults in their unglaciated condition. Conversely, deglaciation may have been accompanied by a brief episode of intense seismicity caused by decreasing overburden stress, elevated pore pressures, and elastic flexure in the shallow crust, and by viscous drag at the base of the crust during relaxation of isostatic anomaly. If accumulated tectonic stress was effectively “erased” during deglaciation, then some, or nearly all, of the present interglacial may have been seismically quiet relative to the modern regime. Such a scenario would complicate the use of paleoseismic approaches to establish the recurrence frequency of damaging earthquakes in this heavily populated region.

Effects of heteroflocculation of powders on mechanical properties of zirconia alumina composites

Zirconia-toughened alumina (ZTA) composites colloidally processed from dense aqueous suspensions (>50 vol% solids) had ZrO2 content varying from 5 to 30 vol%. Tetragonal zirconia (TZ) was used in the unstabilized, transformable form (0Y-TZ), in the partially transformable form, partially stabilized with 2 mol% yttria (2Y-TZ), and in the non-transformable form stabilized with 3 mol% yttria (3Y-TZ). After sintering in air to ∼ 99% theoretical density, the elastic properties, flexure strength and fracture toughness were examined at room temperature. Dynamic moduli of elasticity of fully deagglomerated compositions did not show the effects of microcrack formation during sintering, even for materials with unstabilized zirconia. In all compositions made from submicron powders and with low content of dispersed phase (less than 10 to 20 vol %), the strength increased with increasing ZrO2 content to a maximum of ∼ 1 GPa, irrespective of the degree of stabilization of t-ZrO2. With increasing content of the dispersed phase (> 20 vol%), heteroflocculation of powder mixtures during wet-processing led to the formation of ZrO2 grain clusters of increasing size. Residual tensile stresses built within cluster/matrix interfaces upon cooling not only facilitated the t-m ZrO2 phase transformation in final composites with transformable t-ZrO2, but also led to lateral microcracking of ZrO2/Al2O3 interfaces. This enhanced fracture toughness, but at larger ZrO2 contents the flexure strength always decreased due to intensive microcracking, both radial and lateral. The important microstructural aspects of strengthening and toughening mechanisms in ZTA composites are related in discussion to the effects of heteroflocculation of powder mixtures during wet-processing.

Gravity anomalies and crustal loading at and adjacent to the Alpine Fault, New Zealand

Abstract An analysis of Bouguer and isostatic gravity anomalies from the convergent plate boundary, central South Island, New Zealand, is developed using constraints from seismic refraction data, plate tectonics, and an elastic flexure model. Between 50 and 80 km of late Tertiary plate convergence is assumed so that relatively dense, subducted mantle is included in the gravity model. An elastic plate with a free edge and an effective elastic thickness (Te) that varies laterally between 10 and 30 km is used to simulate the deflection of the Pacific plate beneath the central South Island. Loading on the plate is in the form of topography of the Southern Alps and the excess mass of subducted Pacific mantle. For a weak plate with Te = 10 km, only 50 km of subducted plate, and hence convergence, is required to explain the Bouguer gravity anomalies. For a stronger plate model, where Te varies between 15 and 35 km, c. 80 km of convergence is required. The latter model is preferred as it is more consistent with a...

Lithospheric bending at subduction zones based on depth soundings and satellite gravity

A global study of trench flexure was performed by simultaneously modeling 117 bathymetrie profiles (original depth soundings) and satellite‐derived gravity profiles. A thin, elastic plate flexure model was fit to each bathymetry/gravity profile by minimization of the L1 norm. The six model parameters were regional depth, regional gravity, trench axis location, flexural wavelength, flexural amplitude, and lithospheric density. A regional tilt parameter was not required after correcting for age‐related trend using a new high‐resolution age map. Estimates of the density parameter confirm that most outer rises are uncompensated. We find that flexural wavelength is not an accurate estimate of plate thickness because of the high curvatures observed at a majority of trenches. As in previous studies, we find that the gravity data favor a longer‐wavelength flexure than the bathymetry data. A joint topography‐gravity modeling scheme and fit criteria are used to limit acceptable parameter values to models for which topography and gravity yield consistent results. Even after the elastic thicknesses are converted to mechanical thicknesses using the yield strength envelope model, residual scatter obscures the systematic increase of mechanical thickness with age; perhaps this reflects the combination of uncertainties inherent in estimating flexural wavelength, such as extreme inelastic bending and accumulated thermoelastic stress. The bending moment needed to support the trench and outer rise topography increases by a factor of 10 as lithospheric age increases from 20 to 150 Ma; this reflects the increase in saturation bending moment that the lithosphere can maintain. Using a stiff, dry‐olivine rheology, we find that the lithosphere of the GDH1 thermal model (Stein and Stein, 1992) is too hot and thin to maintain the observed bending moments. Moreover, the regional depth seaward of the oldest trenches (∼150 Ma) exceeds the GDH1 model depths by about 400 m.

Modelling the hardness response of coated systems: the plate bending approach

In order to design the hard coating best suited to engineer the surface of a given substrate for a particular application, it is important that we have a clear picture of the mechanisms by which thin hard coated systems work. In this paper we describe a quantitative model designed to explore the increase in systems' hardness attributable to stresses created on the coating by the upthrust of substrate. material flowing plastically in response to indentation. Thus the model considers how the upwelling of displaced substrate material creates an upward pressure on the coating inducing elastic flexure which, in turn, resists the substrate deformation. The influence of this flexure has been investigated using a combination of existing analytical solutions (e.g. plate theory) to determine the overall effect on the indentation response of coated systems. The resulting model is critically compared with previous work. Experimental verification is provided by diverse experimental data from indentation tests on thin (1–24 μm) coatings of TiN and Cr on various metal substrates, sugar on chocolate substrates and other results drawn from the literature. The model helps to identify Eh 3/ d 3 H 0 as a dimensionless parameter which provides a means of condensing all available data onto a single “master” curve. Further developments are discussed.

Nanoindentation studies of the chemomechanical effect in sapphire

For the first time, nanoindentation techniques have been used to study chemomechanical effects due to water, alcohols and myristic acid on the detailed surface mechanical response (e.g. elastic flexure, stiffness, dislocation nucleation and plasticity) of (10–12) single-crystal sapphire. Because the magnitude of surface tension forces at these small scales can be comparable with the applied load, the experiments have been performed on samples annealed, quenched into various environments and tested after the liquid had been allowed to evaporate. At low loads and indentor displacements (i.e. ⩽ 60 nm), two separate effects have been identified: the occurrence of a soft surface layer together with significant differences in the elastic-plastic deformation transition. The experiments were repeated after a 4 week exposure to ambient laboratory atmosphere and in each case, the behaviour had moved towards that displayed by the original water-quenched sample. The results are explained in terms of physisorption and chemisorption on dislocation nucleation behaviour and subsequent plasticity. At higher loads, the results showed that the previously conflicting evidence from microhardness testing concerning these effects is not surprising, because no differences in the load-displacement responses were seen. However, scanning electron microscopy of the indentations showed significant differences in the deformation behaviour. Low-load creep experiments were also performed but, in contrast to reported microhardness responses, showed no real evidence for time-dependent deformation behaviour. The results presented clearly show the advantages and potential of nanoindentation techniques for investigating these effects.