High-stress Limit Research Articles

Development of non-linear models to evaluate the NiTi SMA spring actuator

The shape memory alloy (SMA) based actuators are replacing huge and bulky actuators because of its ability to provide high work per unit mass and serves as active prismatic joint to develop precise robotic manipulators. It also helps in developing a light weight manipulators with a simple actuation process. Here, the study presents the relationship between the contraction of Nitinol SMA prings and the input variables such as current and time to effectively interpret the behavioural complexity. In addition, the response of two Shape memory alloy springs in series combination has been discussed. The finite element analysis (FEA) of the SMA wire and spring has also been carried out to predict the fatigue life of SMA wire and spring. The result showed that the contraction rate of SMA spring increases with increase in current and vice-versa. Moreover, the range of current is classified based on its significance. The relationship of current, displacement and time parameters, during the actuation of SMA spring, is a second order polynomial regression model. The applied current and time have positive impact on the contractiong rate of SMA. Several polynomial regression models were developed in order to predict the precise amount of spring actuation. This study also predicts the range of current suitable for its actuation based on its application as actuator. The FEA result shows that the SMA springs can have high endurance stress limit which makes it unique as compared to other commercially available actuators. This study enables to predict the rate of contraction and the deflection trend of SMA based actuators for precise positioning applications.

Structural Designs with Consideration of Both Material and Structural Failures

AbstractThis paper provides a simplified formula for modeling the transition between material and structural failures in static and dynamic loading situations. For static situations, the transition equation allows for the calculation of the ultimate capacity between buckling structural failure and compression material failure modes. For dynamic situations, the transition equation allows for the calculation of a smoothed S-N curve between the constant amplitude fatigue limit, namely, the endurance limit, and the low-cycle, high-stress fatigue limit. The simplified formula is based on a quadratic solution that is curve fit to each failure mode and is verified with existing experimental data.

A test of laboratory based rheological parameters of olivine from an analysis of late Cenozoic convective removal of mantle lithosphere beneath the Sierra Nevada, California, USA

SUMMARY We use the apparent change in mantle structure beneath the Sierra Nevada since ca. 10 Ma, which suggests convective removal of eclogite-rich mantle lithosphere, and scaling laws developed for Rayleigh–Taylor instability to place constraints on the average viscosity coefficient of the mantle lithosphere. By treating the lithosphere as a non-Newtonian fluid obeying power-law creep with an exponent of n= 3.5, we may compare the inferred values of viscosity coefficient with those obtained from laboratory experiments on olivine and eclogite. The values that we obtain overlap those predicted by laboratory-based flow laws for the range of geotherms implied by heat flux measurements within the Sierra Nevada and by metamorphic geothermometry and geobarometry of xenoliths in volcanic rock erupted in the Sierra Nevada at ca. 10 Ma. Thus, this comparison offers support for laboratory-derived flow laws, and specifically for the high stress limit suggested by Evans & Goetze (1979). Conversely, this agreement shows that the high strength of cold mantle minerals does not prohibit its removal by convective instability.

Stress-enhancement of certain spectral lines of Sb in Ge

The piezospectroscopy of Sb in Ge, with a compressive force F ‖ 〈1 1 1〉, has been reinvestigated using state-of-the-art instrumentation. In the high stress limit, where the splitting of the donor states is an order of magnitude larger than the valley-orbit (chemical) splitting of the ground state, the results are remarkable, yielding for E ‖ F, a series of nine very sharp stress-induced components, five of which belong to the np 0 (1) series. It is not clear if the other four also belong to this series. For E ⊥, seven components, mainly of the np ± (1) and nf ± (1) series, are observed.

Computer simulation of martensitic transformations in constrained, two-dimensional crystals under external stress

This article reports a computer simulation study of the microstructures produced by martensitic transformations. In the present work, the transformation strain is dyadic, and the transformation is athermal and irreversible. The transformation occurs in a two-dimensional crystal that is constrained in a matrix that has no net transformation strain and may be subject to external stress. The crystal is divided into elementary cells. The transformation is simulated by computing the elastic strain energy in the linear elastic approximation and transforming the most-favored cell in each step to generate the minimum-energy transformation path. The simulation generates the microstructure at each step of the transformation and plots a temperature-transformation (TT) curve by computing the chemical driving force required to maintain the transformation and assuming that it is proportional to the undercooling. The results show that the matrix constraint causes complex, multivariant microstructures and separatesMsandMf. Multiple variants partly relax the shear part of transformation strain but interfere so that the transformation is difficult to maintain. The dilational part of the transformation strain produces interesting microstructures, such as “butterfly martensite,” in partially transformed crystals. It also increases ΔM since it produces a hydrostatic stress that cannot be compensated by mixing variants. The applied stress can be divided into hydrostatic and deviatoric components. The hydrostatic component changesMswithout altering the microstructure or ΔM. The deviatoric stress changes the relative energies of the variants and produces a microstructure that is rich in the favored variant. It also increases ΔM, since single-variant transformations must be sustained against an accumulating, uncompensated shear. The thermal resistance (ΔM) increases with the magnitude of the deviatoric stress until a high-stress limit is reached and only one variant appears. The microstructure is most complex at intermediate stress, where both variants develop in a complex internal stress field. Cyclic stress dramatically increases the extent of transformation at given maximum load. The martensite that has already formed becomes a source of intense internal stress when the stress is reversed, promoting further transformation.

Determination of the steady-state shear viscosity from measurements of the apparent viscosity for some common types of viscometers

Considering a number of model fluids, the relation between the (measurable) apparent viscosity ηa and the (true) shear viscosity η is studied for some commonly used viscometers, like capillary, slit, plate-plate and concentric cylinders (including the influence of the bottom of the cylinder), as well as for one laboratory type of viscometer. As long as η is a purely monotonic function, a shift factor β < 1 allows one to deduce η from ηa. Though in general variable, it frequently suffices for practical purposes to use a constant shift factor (the constant being characteristic of the type of viscometer used). This does not apply to dilute solutions or any fluids with two plateau values for η. For plastic fluids, it is shown that Casson or Bingham behavior can — if valid at all — only describe the high shear stress limit of ηa.

Crossover between different growth regimes in crack formation.

The formation of cracks in brittle materials is investigated for arbitrary dependence of the crack growth on the stresses at its boundary. It is shown that, despite the possible complexity of the growth law, the shape of the crack for large sizes and long times is determined by the high-stress limit of the growth law, provided only that the probability of cracking increases with stress. This result may help to explain the appearance of long and straight cracks in many fracture processes. Other pattern-formation models are expected to show the same features.

The influence of uniaxial stress on the hopping conductivity in p-InSb. The anisotropy of the hopping conductivity

We report on the investigation of the influence of uniaxial stress up to 4 kbar on hopping conductivity and its abisotropy in p-InSb:Ge with the acceptor concentration 10 15-10 17 cm −3. It was shown that hopping conductivity became anisotropic when the stress was applied. In high-stress limit the value of the anisotropy coefficient is in accordance with the theoretical predictions K  σ ⊥/σ ⊥ = m ⊥/m  ≊ 3.5 . It was shown that the stress dependence of the effective volume of acceptor wave function is nonmonotone. It decreases at low compression and increases at high compression.

Electron-hole liquid in germanium under high stress.

The properties of the electron-hole liquid (EHL) in Ge are examined as a function of uniaxial 〈111〉 stress with use of spectral and temporal measurements of the electron-hole--recombination luminescence. We are the first to observe the EHL phase in the high-stress limit (\ensuremath{\sigma}\ensuremath{\gtrsim}70 kgf/${\mathrm{mm}}^{2}$, where 1 kgf/${\mathrm{mm}}^{2}$==10 MPa) at T=2 K, based on fits to calculated spectral line shapes. The dependence of the measured EHL densities on uniaxial 〈111〉 stress agrees well with that predicted by sophisticated many-body calculations. Measurements of the EHL lifetime are also reported for uniaxial 〈111〉 stresses from 5.6 to 23.9 kgf/${\mathrm{mm}}^{2}$. The density dependence of the EHL lifetime indicates a constant value for the electron-hole enhancement factor, ${g}_{\mathrm{eh}}$(0), for electron-hole--pair densities&gt;3.5\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. This result disagrees with theoretical predictions, but is consistent with experimental results reported by others.

Properties of electron-hole liquid in highly stressed silicon

Two independent studies of the electron-hole liquid in stressed Si have provided different values for the ground-state density and the critical temperature of this important Fermi fluid. One set of experiments (by Gourley and Wolfe) was performed using the strain-well configuration while the other (by Forchel et al.) employed uniform strain. These differences raise questions of whether there was some basic difference between the two experimental systems or whether the discrepancies lay in the different methods used for data analysis. In the present joint paper these differences are discussed, several aspects of the data are reanalyzed, some new results are presented, and to a large degree the previous differences are removed. In order to test for possible differences between the line-shape analyses, we use the detailed fitting procedure of Forchel et al. on the strain-well data of Gourley and Wolfe and thereby find a ground-state density of (3.7 +- 0.2) x 10/sup 17/ cm/sup -3/ in the high-stress limit where the effective masses no longer have a stress dependence.

Constant strain increment for exponential tendons in the high-stress limit.

It is theoretically shown that, in the high-stress limit, the exponentially stiffening tendon will have constant strain increment along its length, regardless of changes in cross-sectional area.

Far-infrared absorption spectrum of excitons in [111]-stressed germanium: High-stress limit

A series of experiments were performed to study the far-infrared absorption spectrum of excitons in stressed Ge with the stress axis along the [111] direction. The spectra were taken with stress ranging from 9 to 38 kg/${\mathrm{mm}}^{2}$ and with polarization of the far-infrared electric field parallel and perpendicular to the stress axis. The $1S\ensuremath{-}2P$ and $1S\ensuremath{-}3P$ transitions were observed. The line positions and the relative absorptions associated with the $1S\ensuremath{-}2P$ transitions are in good agreement with a simple theoretical model. The model only considers the lower conduction-band minima and the upper valence-band maxima at high stress in the formation of excitons. The binding energy of excitons at infinite stress is 2.70\ifmmode\pm\else\textpm\fi{}0.08 meV.

Lineshape and electron-phonon coupling for the indirect exciton in GaP

The authors formulate a theory of indirect excitons in GaP under uniaxial stress including the valence-band degeneracy and the camel's back structure of the conduction band. In the high-stress limit they separate relative and centre-of-mass motion and obtain analytic expressions for the exciton dispersion, which are then used to calculate the exciton lineshapes. Comparison with experimental line shapes from wavelength-modulated spectra yields energy band parameters in particular for the lowest conduction bands. In addition, they analyse the strength of different phonon replicas to determine the relative magnitude of the electron-phonon coupling to the zone-boundary phonons assisting the indirect-gap absorption.

Properties of the electron-hole liquid in Si: Zero stress to the high-stress limit

We have measured the properties of the electron-hole liquid (EHL) in Si as a function of stress from $\ensuremath{\sigma}=0 \mathrm{to} 163$ kg/${\mathrm{mm}}^{2}$ which is well into the high-stress limit where the valence bands are decoupled. These measurements provide a useful test of many-body theories for EHL in crystals with a simple band structure. To produce these high stresses and to achieve some unique experimental advantages not realized in uniform-stress geometries, we have employed a well-characterized Hertzian stress geometry to strain ultrapure crystals of Si. This geometry creates an electronic potential minimum which confines both electrons and holes inside the crystal volume. At low temperature the $e\ensuremath{-}h$ pairs spatially condense into a small volume (${10}^{\ensuremath{-}6}$ ml) of EHL at the bottom of the well. Because the liquid volume is small the EHL exists in a region of effectively uniform stress. This idea is confirmed by separate uniform-stress experiments which are included as a part of our study. We study the EHL properties by analyzing its photoluminescence with spectral, spatial, and time resolution under conditions in which stress, temperature, and photoexcitation level are varied over wide limits. In our spectral analysis, which incorporates stress-dependent band structure, we determine the Fermi energies and $e\ensuremath{-}h$ pair density as it decreases from 3.5 \ifmmode\times\else\texttimes\fi{} ${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ at zero stress to 3.5 \ifmmode\times\else\texttimes\fi{} ${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ in the high-stress limit. Corresponding measurements of the intrinsic EHL time decay show that the lifetime increases from 0.14 to 3.0 \ensuremath{\mu}s over the same stress range. Combining the density and lifetime measurements, we are able to investigate the density dependence of the enhancement factor ${g}_{\mathrm{eh}}(0)$ and the Auger process which dominates $e\ensuremath{-}h$ recombination. We have measured a phase diagram for excitonic gas-EHL at high stress and find a critical point of ${T}_{c}\ensuremath{\approx}20 \mathrm{K}$, ${n}_{c}\ensuremath{\approx}2.5\ifmmode\times\else\texttimes\fi{}{10}^{17} {\mathrm{cm}}^{\ensuremath{-}3}$. In the high-stress limit the measured EHL binding energy is in the range $\ensuremath{\varphi}=1\ensuremath{-}1.4$ meV. Additional spatial data reveal the presence of a repulsive force between droplets, possibly a "phonon wind," which inhibits large droplet formation. In general, the stress dependence of the ground-state properties shows trends which are in agreement with existing theories. However, some interesting discrepancies between our data and these theories are found.

The effects of high uniaxial stress on the far infra-red impurity spectra of high purity n- and p-type silicon

The stress dependence of the shallow impurity states of high purity n- and p-type silicon is studied by means of far infra-red spectroscopy up to a high stress limit, where the spectra observed are almost independent of the magnitude of the stress applied. In addition to the predicted behaviour, a small decrease in frequency of the 1 s( B 2)- np ± series of donor lines is observed with a uniaxial <100> stress. A significant movement of the np 0 series relative to the np ± series is also detected. In the case of p-type silicon, the bands are decoupled with the result that the acceptor states at high stress are associated with a single band having oblate ellipsoidal energy surfaces. The spectrum with stress applied along a <111> direction is explained qualitatively by a first order variational calculation of the states concerned.

Electron-hole droplets in germanium in the high stress limit

We have observed electron-hole droplets in germanium stressed uniformly in the <111> direction to the high stress limit. The measured values of the density, binding energy and phase diagram are in good agreement with theoretical calculations.

Electron Scattering by Neutralized Acceptors in Germanium. II. Zinc

Electron scattering by neutralized zinc acceptors in germanium has been studied between 1.5 and 4.2°K through the cyclotron resonance technique under the application of uniaxial compressional stress. Without stress, it is found, the carrier lifetime in zinc-doped germanium becomes so short that the cyclotron resonance linewidth appreciably suffers from the lifetime broadening. Application of uniaxial stress, however, drastically increases the electron lifetime, and analyses of the electron resonance signals with and without stress show that zinc, the dopant itself, is responsible for such a short lifetime. The scattering relaxation time of electrons by neutral zinc impurities is thus derived only under a high stress limit applied in order to avoid mixing of the lifetime broadening. The derived value agrees in a rather surprising manner with the theoretical one based on the positron-helium atom scattering model after Kestner et al.