Change In Strain Energy Research Articles

Anisotropic elasticity studies of work hardening in epilayers

A force formalism is proposed to investigate the interactions between a semicoherent heterophase interface and free surfaces in anisotropic finite-thickness bilayers. The present approach enables the estimation of the mechanical forces acting on interfaces, which arise from inhomogeneous elastic fields between the neighboring materials. These short-range fields are produced by the superposition of coherency strains and the elastic strain fields of dislocation patterns, where the individual Burgers vectors are defined by requiring the global force balance on any internal plane perpendicular to the interfaces. Predictions in heterogeneous free-standing bilayers are compared to results for the homogeneous elasticity problem (i.e., both materials having the same stiffness) and the limiting case of infinite bicrystals. Examples of applications to pure misfit interfaces are given with controlled misfit dislocation spacings by continuously varying the alloy composition. The effect of dislocation density on the stability of semicoherent interfaces interacting with free surfaces is discussed in terms of the change in elastic strain energy of Pt/Pd bilayer systems.

Stability analysis of a pressure‐solution surface

We present a linear stability analysis of a dissolution surface subjected to non‐hydrostatic stress. A sinusoidal perturbation is imposed on an initially flat solid/fluid interface, and the consequent changes in elastic strain energy and surface energy are calculated. Our results demonstrate that if the far‐field lateral stresses are either greater, or much smaller than the fluid pressure, the perturbed configuration has a lower strain energy than the initial one. For wavelengths greater than a critical wavelength this energy decrease may be large enough to offset the increased surface energy. Under these conditions, the perturbation grows unstably. If these conditions are not met, the surface becomes flat. The growth rate and wavelength of the maximally unstable mode depend on the mechanism of matter transport. We conclude that the instability discussed in this paper may account for the formation of stylolites and other pressure‐solution phenomena, such as roughening of grain contacts.

Effect of deformation temperature on fatigue and fracture behavior in TiAl polysynthetically twinned crystals

The temperature and orientation dependence of cyclic deformation, fatigue life, and fracture behavior in TiAl polysynthetically twinned (PST) crystals were investigated, focusing on the change of plastic strain energy and deformation mode in the γ domains. Stress-controlled fatigue tests were performed at 1 or 10 Hz using the same stress amplitude in tension and compression (R=−1) over a temperature range from −196 °C to 700 °C. The fatigue strength at ϕ=45 deg (ϕ being the angle between the loading axis and lamellar planes) decreased monotonically with increasing temperature. At ϕ=0 deg, the fatigue strength was high up to 500 °C, but the fatigue life decreased rapidly above 600°C because of dynamic recovery and interlamellar separation. The plastic strain energy—stress amplitude curves in specimens fatigued with ϕ=45 deg increased monotonically with stress amplitude for all temperatures and for higher temperatures with ϕ=0 deg. At 25 °C and −196 °C with ϕ=0 deg, three regions in the plastic strain energy—stress amplitude curves were observed. This anomalous change in the plastic strain energy at lower temperatures was due to a transition in primary deformation mode between twinning and slip by ordinary dislocations in some domain orientations.

The Fatigue and Hysteresis Behaviour of Filled Epoxidized Natural Rubber Compounds

The paper reports on the fatigue behaviour of white rice husk ash (WRHA), silica and carbon black-filled ENR 50 vulcanizates. The properties investigated include the stress-strain behaviour, effect of coupling agent and hysteresis. Carbon black filled vulcanizates showed the highest stress-strain behaviour followed by silica and WRHA. This observation was supported by the plot of accumulated strain energy versus extension ratio. Carbon black showed the highest value followed by silica and WRHA. The incorporation of silane coupling agent has improved the fatigue life of WRH-filled vulcanizates. Hysteresis studies showed that as the filler loading increased there was an increase in hysteresis and carbon black filled vulcanizate exhibited the highest hysteresis i.e. the most sensitive towards changes in strain energy.

Elastic Strain Energy Change During Matrix Cracking in Unidirectional, Fiber-reinforced Ceramic Composites

The fracture resistance of ceramics can be signi®cantly enhanched by incorporatng strong ®bers aligned with the loading direction [1±6]. The initial damage in unidirectional, ®ber-reinforced ceramic composites is often in the form of a matrix crack (or matrix cracks), which is perpendicular to the loading direction and bridged by intact ®bers. To achieve the optimum toughening effect for ceramic composites, relatively weak interfaces between ®bers and the matrix, which can debond and slide against a frictional force during matrix cracking, are required [1±6]. In the existing analyses for the matrixcracking problem, two cases have been considered: load-induced cracking [7±14] and residual stressinduced cracking [7, 9, 15]. Using the energy-balance condition during crack propagation, the critical stress for steady-state matrix cracking has been derived [7±15]. The energy terms involved are as follows: (1) Ue, the elastic strain energy in the ®ber and the matrix, (2) Us, the energy due to sliding at the debonded interface, (3) Gi, the energy due to interface debonding, (4) Gm, the energy due to matrix cracking, and (5) W, the work done by the external load, if a loading stress is applied. When the matrix crack length, c, advances a distance dc, the corresponding energy changes are dUe, dUs, dGi, dGm, and dW. The matrix-cracking criterion can be obtained from the energy balance condition, such that dUe ‡ dUs ‡ dGi ‡ dGm ˆ dW

Stiffness determination and deformation analysis for a trial excavation in Oxford Clay

Block samples of the heavily overconsolidated Oxford Clay were retrieved from a 10m deep, instrumented, trial excavation at Elstow, Hertfordshire, and from a nearby brick pit. Triaxial stress path tests were conducted on 100 mm diameter specimens to determine appropriate stiffness parameters for numerical modelling of the excavation. Each test followed a succession of constant p' (mean effective normal stress) and constantq (deviator stress) paths in the extension region. Small axial and radial strains were measured locally using a proximity transducer system, permitting stiffness parameters for the coupled deviatoric and volumetric behaviour to be derived and plotted against changes of strain energy for modelling purposes. The maximum shear stiffness, G0, was also determined using bender elements. During the multistage tests, stiffness behaviour at small strains appeared to be governed by the recent strain history and recent stress history effects were not as prominent as those reported in the literature for other clay soils. Finite element modelling of the excavation was carried out, employing a non-linear cross-anisotropic elastic model in which stress path dependent stiffnesses were specified. Predicted lateral displacements were modestly overestimated by comparison with field measurements, but vertical displacements were generally underpredicted and to a greater degree. Des blocs d'échantillonnage d'argile d'Oxford fortement préconsolidée ont été prélevés dans une fouille de recherche instrumentée, profonde de 10m, à Elstow dans le Hertfordshire, ainsi que dans une argilière voisine. On a effectué des essais de parcours de contraintes triaxiales sur des échantillons de 100 mm de diamètre pour déterminer les paramètres de rigidité convenant à une modélisation numérique de la fouille. Chaque essai a suivi une succession de parcours de contrainte constante p' (contrainte intergranulaire normale moyenne) et de contrainte constante q (contrainte déviatrice) dans la zone d'allongement. On a mesuré localement les petites contraintes axiales et radiales à l'aide d'un réseau de capteurs de proximité en vue de calculer les paramètres de rigidité pour le comportement dévuatorique et volumétrique jumelé et de les mettre en corrélation avec les variations d'énergie de contrainte à des fins de modélisation. In a également déterminé la rigidité maximale au cisaillement G0 à l'aide d'é1éments de flexion. Dans les essais à étages multiples, la rigidité aux petites contraintes a semblé &circtre dictée par les contraintes subies récemment, et les effets des tensions récentes ne semblent pas aussi importants que ceux dont font état d'autres travaux portant sur d'autres sols argileux. On a effectué une mod6lisation de la fouille par é1éments finis en utilisant un mod&gravele élastique trans-anisotrope non linéaire où l'on a précisé des rigidités tributaires des parcours de contrainte. Les déplacements latéraux prédits ont été 1égèrement supérieurs aux déplacements mesurés sur le terrain, tandis que les déplacements verticaux ont W généralement sous-estimés et dans de plus grandes proportions.

The pentamer channel stiffening model for drug action on human rhinovirus HRV-1A.

Development of effective drugs against the rhinovirus (HRV) responsible for the common cold remains a challenge because there are over 100 serotypes. This process could be significantly aided by an understanding of the atomistic mechanism by which such drugs work. We suggest that the most effective drugs against HRV-1A act by stiffening the pentamer channel of the viral coat through which the RNA is released, preventing the steps leading to uncoating. Using molecular dynamics methods we tested this Pentamer Channel Stiffening Model (PCSM) by examining the changes in strain energy associated with opening the pentamer channel through which the RNA is released. We find that the PCSM strain correlates well with the effectiveness of the WIN (Sterling-Winthrop) drugs for HRV-1A. To illustrate the use of the PCSM to predict new drugs and to prioritize experimental tests, we tested three modifications of the WIN drugs that are predicted to be nearly as effective (for HRV-1A) as the best current drug.

On the application of energy release rates

The limits of applicability of the substitution of strain energy for potential energy in energy release rate calculations for Griffith cracks are identified, a discussion notably absent from textbooks. It is also shown that the strain energy change is not adequate to predict the growth of a Griffith crack, and may actually be zero while the potential energy change is not.

Experimental and Finite Element Study of Cryogenic Fracture and Temperature Rise in an Austenitic Stainless Steel Forged Plate.

We consider the cryogenic fracture behavior of an elastic-plastic material and the energy dissipation associated with crack extension. The results of a fracture toughness test are presented for a forged JJ1 type austenitic stainless steel plate at liquid helium temperature. Temperatures of a compact tension specimen were also measured during straining at 4 K. A two-dimensional finite element analysis was used to interpret the experimental measurements. The elastic-plastic fracture behavior was analyzed using the Dugdale model and the incremental strain theory. In the calculations the material was assumed to be elastic-prefectly plastic and to obey the von Mises criterion with its associated flow rule. The dissipated energy can be calculated from the change in total elastic strain energy of the specimen during crack extension. From the calculated dissipated energy, the associated temperature field near the crack tip was predicted and compared with the measured values. Generally good agreement was found between the computed and the measured values.

Nitridation Of Sapphire Substrate Using Remote Plasma Enhanced-Ultrahigh Vacuum Chemical Vapor Deposition At Low Temperature

AbstractA remote plasma enhanced-ultrahigh vacuum chemical vapor deposition (RPE-UHVCVD) system equipped with a radio frequency-inductively coupled plasma (RF-ICP) which produces the reactive nitrogen species was employed to study the nitridation process at low temperature. The sapphire surface nitridated under various conditions was investigated with x-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM). The nitridation process seems to be mostly affected by the RF power even at low temperature since the intensity of the N1s, peak was not dependent on the substrate temperature but on the RF power. The AFM images showed that the protrusion density on the sapphire surface decreased rapidly when the nitridation temperature was decreased. This result suggests that the formation of the protrusions is closely related to the process temperature, indicating that the formation of such protrusions is caused by the change of an elastic strain energy due to the thermal stress. It was possible to nitridate the sapphire surface without protrusion at a very low temperature. The crystallinity of GaN grown at 450 °C was found to be much improved when the sapphire substrate was nitridated at low temperature prior to the GaN layer growth.

Fracture toughness of the fibre-matrix interface in glass-epoxy composites

The failure process arising at a broken fibre end in polymer matrix composite materials has been studied experimentally and analytically using the finite element method. A series of experiments were carried out using S-glass and E-glass single filaments, with different sizings and/or coupling agents, embedded in epoxy matrices with different moduli. A finite element analysis was used to simulate the experiments and calculate the change in strain energy accompanying the observed fracture mode. The strain energy release rate upon arrest of the crack, Garrest, was then calculated. The measured interface debonding energies varied from Garrest=57–342 J m−2, depending primarily on the nature of the fibre sizing and the ratio of moduli of the fibre and matrix. Transverse and shear matrix cracks were characterized by Garrest values of 58–103 J m−2. Subtle changes in the constituent properties or fibre surface treatment resulted in a change in the fracture mode. This measurement and analysis technique may suggest reasons for the variability of previous measurements of interfacial adhesion, and provide a standard method for characterizing fracture modes at broken fibre ends.

Twinning in thin films—II. Equilibrium microstructures

We consider the energetics of twinning in misfitting films. While the analysis is general, we consider the case of a misfitting coherent thin film with a cubic crystal structure which transforms to a tetragonal crystal structure on an initially lattice matched cubic substrate; a commonly occurring phase transformation in ferroelectric films. The strain energy change upon twinning, estimated in Paper 1, along with the interfacial energy contributions are incorporated into a thermodynamic analysis of twinning and the equilibrium twinned microstructure is determined as a function of the film thickness, lattice misfit, elastic properties of the film—substrate system, the film surface energy, the film—substrate interface energy and the domain (twin) boundary energy. We develop stability diagrams that examine the role of these parameters in determining the equilibrium microstructure. Our results show that for like variants, a periodic array of domains is always energetically favorable compared to a monovariant film and therefore there is no critical thickness below which the monovariant film is stable. However, the equilibrium wavelength of the twinning microstructure depends on the normalized film thickness as well as the orientation of the domain boundaries with respect to the cubic substrate. Examination of the elastic energy as a function of domain boundary orientation shows that boundaries oriented parallel to the (110) plane of the substrate are preferred. However, (100) oriented boundaries are likely favorable from an interfacial energy viewpoint. The equilibrium wavelength of the microstructure scales as the exponential of the inverse film thickness for small thicknesses, and is either independent of film thickness or proportional to the square root of film thickness at large film thicknesses for the (100) and (110) oriented boundaries, respectively. For the unlike variants case, there is a critical thickness below which the monovariant film is energetically favored. This critical thickness depends on the relative misfit strains, the normalized domain (twin) boundary energy, and the normalized film—substrate interface energy and the normalized surface energies. Finally, we modify this thermodynamic analysis to account for externally applied stress fields and examine their effect on the equilibrium domain structure. Using these results, we derive an expression for the applied stress required to inhibit twinning in these films.

Equilibrium Configuration of Epitaxially Strained Thin Film Surfaces

ABSTRACTThe formation of convex and concave regions on the surface of a strained thin epitaxial film on a thick substrate is analyzed by minimization of energy associated with the configuration. The strain energy change resulting from the formation of undulations is modelled with the strain in the film represented by a continuous distribution of dislocations along the perturbed surface and the interface. A discrete dislocation model is also used when periodic undulations are formed. Results of energy minimization for germanium or germanium-silicon alloy films on silicon substrate illustrate that convex regions tend to grow. On the other hand, convex regions formed to conserve mass in shape changes associated with concave regions become stable with minimum energy under quasi-equilibrium when the mobility of adatoms is low. We have determined the size and radius of curvature of the undulations at minimum energy and conclude that it is favorable to form atomic steps on the surfaces from which dislocation generation and strain relaxation takes place.

Atomic rearrangement at ZnTe/CdSe interfaces.

X-ray-absorption fine-structure spectroscopy and x-ray diffraction have been used to study the local atomic structure of four different short-period ZnTe/CdSe (001) superlattices grown by molecular-beam epitaxy. The data indicate Zn-Se and Cd-Te coordination numbers greater than those expected for sharp interfaces in the superlattice. Although strain would appear to suppress interdiffusion, it is shown that the results are consistent with an interchange of the Zn and Cd atomic planes across the Zn-Se interface and Se and Te atomic planes across the Cd-Te interface. Theoretically, this switch of atomic planes has been shown to be energetically favorable by comparing the changes in chemical bond-formation energies and strain energies between a perfect superlattice and one with the above-mentioned switching of atomic planes. Accommodation of this strain is shown through bond bending and bond stretching at the newly formed interfaces.

Elastic energy release due to domain formation in the strained epitaxy of ferroelectric and ferroelastic films

Twin related domain formation is examined as a strain relaxation mechanism for a heteroepitaxial tetragonal film on a cubic substrate. Elastic relaxations are calculated for a single twin band in which the c axis of the tetragonal domains is either related by a 90° rotation about an axis in the plane of the film or by a 90° rotation about the surface normal. In all cases, the strain energy change is evaluated for both the film and the substrate. A domain pattern map is developed that predicts single domain and multiple domain fields depending on the relative misfit strains and domain wall energy. The concept of a critical thickness, hc, for domain formation is developed. For cases in which the c axis is rotated 90° about an axis in the plane of the film, the critical thickness depends only on the relative coherency strain between the substrate and film and the ratio of the domain wall energy to the stored elastic energy. For the case of a pattern consisting of energetically equivalent domains with the c axis in plane, the equilibrium distance of multiple domains is derived. For such multiple domains, a minimum wall separation distance exists that depends nonlinearly on the film thickness.

Estimation of depth‐dependent fault slip from measured surface deformation with application to the 1906 San Francisco Earthquake

We estimate the depth distribution of slip in the 1906 San Francisco earthquake by applying new inversion methods to triangulation data collected near Point Arena, California. Modeling crustal deformation from antiplane slip in a half‐space, we define three regularizing functionals to produce minimum‐norm inverse problems. These functionals measure components of the coseismic change in elastic strain energy, stress magnitude, and stress variability and are all quadratic in slip. Orthogonality conditions define finite‐dimensional representations of slip estimates. Coefficients of basis functions in these representations are estimated by damped least squares with damping parameter and faulting depth chosen by cross validation. The best resulting estimates exhibit right lateral slip to depths of 15 to 20 km with about 6 m of surface slip. This is consistent with directly observed offsets of cultural landmarks at the surface and indicates deeper faulting than has been previously inferred for the 1906 earthquake.

On transformation shear of precipitated zirconia particles

A model is proposed to investigate the transformation shear of the precipitated zirconia particles which undergo a stress-induced lattice transformation from tetragonal to monoclinic symmetry. Kinematically admissible twinning planes and the corresponding twinning elements are determined according to the continuum theory of dispacive phase transformation. It is postulated that only one twinning mode prevails in each transformed particle and that the minimization of elastic strain energy change dictates the morphology of the transformed variants. The transformation shear is determined by the twinning mode and the volume fraction of the corresponding variant. Numerical calculations show that each of the six kinematically admissible twinning modes may be kinematically favorable and therefore operate in a constrained particle. The actual transformation shear in a transformed particle is shown to be dependent on the transformation stress, on the particle shape as well as on the lattice orientation relative to the principal axes of the ellipsoidal particle.

Energy Release Due to Domain Formation in the Strained Epitaxy of Multivariant Films

AbstractTwin related domain formation is examined as a strain relaxation mechanism for a heteroepitaxial tetragonal film on a cubic substrate. Elastic relaxations are calculated for a single twin band in which the c-axis of the tetragonal domains is either related by a 90* rotation about an axis in the plane of the film or by a 90* rotation about the surface normal. In all cases, the strain energy change is evaluated for both the film and the substrate. A domain pattern map is developed that predicts single domain and multiple domain fields depending on the relative misfit strains and domain wall energy. The concept of a critical thickness, hc, for domain formation is developed. For cases in which the c-axis is rotated 90* about an axis in the plane of the film, the critical thickness depends only on the relative coherency strain between the substrate and film and the ratio of the domain wall energy to the stored elastic energy. For the case of a pattern consisting of energetically equivalent domains with the c-axis in plane, the equilibrium distance of multiple domains is derived. For such multiple domains, a minimum wall separation distance exists which depends non-linearly on the film thickness.

Effect of fibre angle on fracture properties of unidirectional flyash filled FRP composites

The fracture properties of unidirectional flyash filled and unfilled glass fibre and carbon fibre reinforced epoxy resin composites are studied in relation to the variation of width ratio ( a W ) and fibre angle. The results indicate that the fracture toughness, fracture surface energy and change in elastic strain energy are dependent on the width ratio but the effect of fibre angle between 30 and 60° is not very dependent on fracture properties due to the arrest of the crack path in fibre composites by flyash particles.

Spinal flexion and locomotor energetics in kangaroo, monkey, and tiger

It has been suggested that galloping is the most economical gait for mammals to use in high-speed locomotion, because galloping makes it possible for kinetic energy associated with leg movements to be stored briefly as strain energy in elastic structures in the back. When this strain energy is returned in elastic recoil, it reduces the total amount of work done by the muscles. This hypothesis was tested in the context of the passive mechanical properties of mammalian intervertebral joints in sagittal bending. The specific strain energies absorbed (EIN/mass) were expressed as power functions of the changes in intervertebral angle (Δθiv) from the unloaded excised states: EIN/mass = C(Δθiv)D, where C and D are constants for each species. Observed changes in spinal deformation were used to estimate changes in intervertebral angles and corresponding changes in specific strain and recoil energies for a hopping kangaroo (Macropus rufus) and a galloping monkey and tiger (Cercopithecus aethiops and Panthera tigris). The specific recoil energies were compared with the energies associated with limb swing during galloping and hopping. The percent contributions of spinal recoil energy to limb kinetic energy were about 2, 5.5, and 0.2 for kangaroo, monkey, and tiger, respectively. The results are discussed in terms of galloping and hopping energetics.