Showing papers on "Stress relaxation published in 1994"

Piezospectroscopic Determination of Residual Stresses in Polycrystalline Alumina

Abstract: The residual stresses created in polycrystalline aluminum oxide as a result of its constrained anisotropic thermal contraction are measured with the technique of piezospectroscopy using the fluorescence from trace Cr[sup 3+] impurities. The average residual stresses in the crystallographic a and c directions are determined as a function of grain size for a high-purity alumina, as is the width of the stress distribution (assuming it to be Gaussian). Over the range of grain sizes investigated, from 2 to 16 [mu]m, the residual stresses exhibit a dependence on grain size consistent with the prediction of the Evans-Clarke model of thermal stress relaxation by grain boundary diffusion.

Giant photoexpansion in As2S3 glass

Abstract: When illuminated with a focused beam from He‐Ne lasers, As2S3 films with thickness of ∼50 μm exhibit the thickness expansion reaching to 3 μm, which is approximately 10 times as great as that expected from the conventional photoexpansion phenomenon. The enhancement seems to be caused by photorelaxation of strain generated by photoexpansion.

Strained state of Ge(Si) islands on Si: Finite element calculations and comparison to convergent beam electron‐diffraction measurements

Abstract: In this letter we present calculations by three‐dimensional finite element method and measurements by convergent beam electron diffraction of the displacement field resulting from misfitting Ge0.85Si0.25 islands on Si(001). A good agreement between the results of both methods indicates that the three‐dimensional finite element method is a reliable tool to calculate the strain, and thus the stress field, in such nanostructures. As a result both methods show that the substrate substantially takes part in the elastic relaxation process in such heteroepitaxial systems.

Effect of strain rate on the fracture behaviour of skin

Abstract: The effect of strain rate on the stress-strain behaviour of skin is studied. It is observed that the plastic set in the skin is dependent on strain rate. The scanning electron micrographs of the fractured skin sample shows thicker fibrils and thinner one at low strain rates. The plastic flow is clearly brought out in the stress-strain curves at different strain rates. The stress relaxation behaviour at any given strain is clearly brought out in the 3-dimensional plot.

Precipitation and relaxation in strained Si1−yCy/Si heterostructures

Abstract: We have studied the thermal stability of Si1−yCy/Si (y=0.007 and 0.014) heterostructures formed by solid phase epitaxial regrowth of C implanted layers. The loss of substitutional C was monitored over a temperature range of 810–925 °C using Fourier transform infrared absorbance spectroscopy. Concurrent strain measurements were performed using rocking curve x‐ray diffraction to correlate strain relaxation with the loss of substitutional C from the lattice. Loss of C from the lattice was initiated immediately without an incubation period, indicative of a low barrier to C clustering. The activation energy as calculated from a time to 50% completion analysis (3.3±5 eV) is near the activation energy for the diffusion of C in Si. Over the entire temperature range studied, annealing to complete loss of substitutional C resulted in the precipitation of C into β‐SiC. The precipitates are nearly spherical with diameters of 2–4 nm. These precipitates have the same crystallographic orientation as the Si matrix but th...

Stress relaxation in short sisal-fiber-reinforced natural rubber composites

Abstract: Stress relaxation behavior of chemically treated short sisal fiber-reinforced natural rubber composite was studied. The effect of bonding agent, strain level, fiber loading, fiber orientation, and temperature has been studied in detail. The existence of a single relaxation pattern in the unfilled stock and a two-stage relaxation mechanism for the fiber-filled composite is reported. The relaxation process is influenced by the bonding agent, which indicated that the process involved fiber-rubber interface. The rate of stress relaxation increased with fiber loading, whereas it decreased with aging. © 1994 John Wiley & Sons, Inc.

The effect of entanglements on the rheological behavior of polybutadiene critical gels

Abstract: We investigated the stress relaxation behavior of critical gels originating from six nearly monodisperse, highly entangled polybutadiene melts of different molecular weight from 18000 to 97 000 g/mole. The polymers were vulcanized by a hydrosilation reaction which takes place nearly exclusively at the pendant 1,2-vinyl sites distributed randomly along the polybutadiene chain. The BSW spectrum represents the relaxation of the initial uncrosslinked precursor. A characteristic parameter is the longest relaxation time of the precursor. Crosslinking increases this longest time even further. Surprisingly, the relaxation spectrum of the precursor is not altered much by the crosslinking except for an additional long time behavior. At the gel point (critical gel), this long time behavior is self-similar. It follows the typical power law as described by the Chambon-Winter gel equation, G(t) = St −n , in the terminal zone. The critical relaxation exponent was found to be close to n = 0.5 over a range of stoichiometric ratios and for all precursor molecular weights analyzed. A new scaling relationship was found between the gel stiffness, S, and the precursor molecular weight of the form: S ∼ M , where exponent z from the zero shear viscosity-molecular weight relationship, η0 ∼ M , is commonly found to be z = 3.3 – 3.6.

Densification, anisotropic deformation, and plastic flow of SiO2 during MeV heavy ion irradiation

Abstract: The response of SiO2 thin films and implantation masks to 4.0 MeV Xe irradiation is studied. Trenches in silica deform dramatically after irradiation with 3×1015 ions/cm2. In situ wafer curvature measurements show that thin planar silica films first densify by 3.6% during irradiation. The resulting stress then relaxes viscously by radiation‐enhanced Newtonian flow. At a flux of 3×1010 Xe ions/cm2s the measured shear viscosity was 6×1013Pa s. We find evidence that an irradiation induced anisotropic deformation mechanism is present in the silica films. In equilibrium, this deformation leads to an average compressive saturation stress as large as 4.5×107 Pa.

Indentation analysis of biphasic articular cartilage : nonlinear phenomena under finite deformation

Abstract: The nonlinear indentation response of hydrated articular cartilage at physiologically relevant rates of mechanical loading is studied using a two-phase continuum model of the tissue based on the theory of mixtures under finite deformation. The matrix equations corresponding to the governing mixture equations for this nonlinear problem are derived using a total Lagrangian penalty finite element method, and solved using a predictor-corrector iteration within a modified Newton-Raphson scheme. The stress relaxation indentation problem is examined using either a porous (free draining) indenter or solid (impermeable) indenter under fast and slow compression rates. The creep indentation problem is studied using a porous indenter. We examine the finite deformation response and compare with the response obtained using the linear infinitesimal response. Differences between the finite deformation response and the linear response are shown to be significant when the compression rate is fast or when the indenter is impermeable. The finite deformation model has a larger ratio of peak-to-equilibrium reaction force, and higher relaxation rate than the linear model during the early relaxation period, but a similar relaxation time. The finite deformation model predicts a slower creep rate than the linear model, as well as a smaller equilibrium creep displacement. The pressure distribution below the indenter, particularly near the loaded surface is also larger with the finite deformation model.

Flow parameters associated with hydrodynamic cell injury.

Abstract: Two flow parameters are proposed for the analysis of flows that have potential to damage animal cells. They are the state of stress (characterized by the second invariant of the stress tensor) and the flow classification parameter R(D) (which is related to the possibility of stress relaxation). We consider the flow that occurs when a 1.7-mm bubble collapses at a liquid interface. Using these two parameters, we show the regions in which the flow is strong in terms of high hydrodynamic stresses and elongation characteristics.

An Analytical Approach to Elastic-Plastic Stress Analysis of Rolling Contact

Abstract: Based on a stress invariant hypothesis and a stress/strain relaxation procedure, an analytical approach is forwarded for approximate determination of residual stresses and strain accumulation in elastic-plastic stress analysis of rolling contact. For line rolling contact problems, the proposed method produces residual stress distributions in favorable agreement with the existing finite element findings. It constitutes a significant improvement over the Merwin-Johnson and the McDowell-Moyar methods established earlier. The proposed approach is employed to study combined rolling and sliding for selected materials, with special attention devoted to 1070 steel behavior. Normal load determines the subsurface residual stresses and the size of the subsurface plastic zone. On the other hand, the influence of tangential force penetrates to a depth of 0.3a, where a is the half width of the contact area, and has diminishing influence on the residual stresses beyond this thin layer. A two-surface plasticity model, commensurate with nonlinear kinematic hardening, is utilized in solution of incremental surface displacements with repeated rolling. It is demonstrated that a driven wheel undergoes greater plastic deformation than the driving wheel, suggesting that the driven wheel experiences enhanced fatigue damage. Furthermore, the calculated residual stresses are compared with the existing experimental data from the literature with exceptional agreements.

Role of dislocation blocking in limiting strain relaxation in heteroepitaxial films

Abstract: The residual strain following relaxation in a variety of Si1−xGex heteroepitaxial films grown on (001) Si wafers has been compared with the values of residual strain predicted by the theory based on the incremental movements of isolated threading dislocation segments. It is found that for very thin films (40–500 nm) the measured residual strains after relaxation are significantly higher than the values predicted by this theory. For thicker films, the residual strains are very close to the predicted values. The effect of the interactions of parallel dislocations on the residual strain are investigated using the model developed by Willis, Jain, and Bullough [Philos. Mag. A 62, 115 (1990)] for a two‐dimensional array of dislocations. It is found that the experimental data cannot be explained by this model since it predicts even lower values of residual strain than the model based on isolated threading segments. The residual strains are also compared with predictions based on Freund’s treatment of the blockin...

Strain-Rate Sensitivity, Relaxation Behavior, and Complex Moduli of a Class of Isotropic Viscoelastic Composites

Abstract: A micromechanical principle is developed to determine the strain rate sensitivity, relaxation behavior, and complex moluli of a linear viscoelastic composite comprised of randomly oriented spheoidal inclusions. First, by taking both the matrix and incluions as Maxwell or Voigt solids, it is found possible to construct a Maxwell or a Voigt composite when the Poisson ratios of both phases remain constant and the ratios of their shear modulus to shear viscosity (or their bulk counterparts) are equal; such a specialized composite can never be attained if either phase is purely elastic. In order to shed some light for the obtained theoretical structure, explicit results are derived next with the Maxwell matrix reinforced with spherical particles and randomly oriented disks. General calculations are performed for the glass/ED-6 system, the matrix being represented by a four parameter model

Room-Temperature Creep of High-Strength Steels

Abstract: The room-temperature creep behaviour of three high strength steels has been investigated. Several parameters such as creep stress, loading rate, stress history and heat treatment has been altered and their influence on the low temperature creep has been reported. The primary creep in all three alloys agreed well with the logarithmic creep law and the creep mechanism has been identified as pure dislocation creep. Higher stresses and high loading rates led to increased creep strains and strain rates. Reloading after a period of creep resulted in significantly decreased creep strains and no recovery of the time dependent deformation could be detected. The yield strength of the materials per se had no influence on the room temperature creep whereas the same material with decreased 0.2% offset strength showed significantly reduced time dependent deformation. The possible interaction between primary creep and stress corrosion cracking has been discussed.

Thermomechanical relaxation of residual stress in shot peened nickel base superalloy

Abstract: The thermal and thermomechanical behaviour of the relaxation of the residual stresses of a shot peened Astroloy superalloy under tensile cyclic loads has been evaluated by X-ray diffraction and investigated. The stress relaxation under purely thermal conditions (550 and 650°C) and thermomechanical conditions (pulsating tensile loading at 650°C) as afunction of the exposure time is presented. The purely thermal relaxation is interpreted by annihilation and reorganisation of the crystalline defects induced by shot peening, whereas the mechanical relaxation is linked to cyclic plasticity of materials. In consequence, the thermomechanical relaxation is essentially due to the complex mechanism of the concurrent thermal and mechanical effects. A model is used to predict the residual stresses induced by the specified shot peening conditions and their relaxation under the specified thermal/thermomechanical conditions.MST/1963

The role of cavity growth mechanisms in determining creep-rupture under multiaxial stresses

Abstract: — The effect of stress state on the time and strain to failure has been considered in terms of currently accepted models of cavity growth. It is shown that the increasing contributions of compressive stress cause changes in cavity growth mechanisms which lead to increases in ductility. A tensile component of stress is necessary to provide the driving force for cavity growth by diffusion of vacancies and hence only strains in the presence of a tensile stress can lead to creep-dominated failure in creep-fatigue. Equivalent stress functions for isochronous stress rupture have been derived in terms of the cavity growth models and their corresponding relationships for calculating damage in terms of strain fractions developed. It is shown that it is difficult to discriminate between the various models on the basis of available experimental data. However, the analysis allows data to be assessed within the framework of physically based mechanisms and suggests methods which lead to conservative lower bound estimates of endurance. It is concluded that the shape of the isochronous creep rupture locus depends on the controlling process of cavity growth and that a detailed analysis of uniaxial creep ductility is necessary to obtain a complete description of the multiaxial behaviour. In many instances such an analysis will prove more valuable than simply performing creep tests over a limited range of stress states. Increasing contribution of principal stress to the failure process leads to a greater value for the equivalent stress in the presence of a compressive component compared with the von Mises equivalent value. However, the equivalent stress is reduced in the tensile quadrant of bi-axial stress. Hence the degree of conservatism arising from using the von Mises equivalent stress will vary with stress and may become slightly non-conservative. The relationship between equivalent stress functions for application in a time fraction assessment of creep and the calculation of creep damage by a strain fraction method has been demonstrated. Finally, guidance is given on how a limited data base of uniaxial rupture properties can be used to obtain a conservative estimate of behaviour under multiaxial loading.

An x-ray method for direct determination of the strain state and strain relaxation in micron-scale passivated metallization lines during thermal cycling

Abstract: We describe a method for directly determining the strain state of passivated metal lines. Synchrotron radiation in the grazing incidence geometry is used to directly measure the in-plane interplanar spacing along the length and width of the lines, while the strain normal to the surface of the line is measured using conventional diffraction methods. The entire strain state is thereby defined. Previous work has measured out-of-plane reflections, fit them to a straight line as a trigonometric function of the angle of orientation, and extrapolated to determine the principal strains. The equivalence of the two x-ray methods on the same sample is demonstrated at room temperature before and after thermal cycling. For short time strain relaxation experiments during thermal cycling, measurement of the three principal strains leads to the direct calculation of the stress relaxation. We apply the strain determination technique to Al--0.5%Cu lines passivated with Si[sub 3]N[sub 4] as the lines are thermally cycled from room temperature to 450 [degree]C and back. The strain state, stress state, and strain relaxation of the lines are calculated at several temperatures during thermal cycling.

Strain relief in linearly graded composition buffer layers: A design scheme to grow dislocation‐free (<105 cm−2) and unstrained epilayers

Abstract: The strain relaxation in linearly graded composition InGaAs layers grown on (001) GaAs substrates by molecular beam epitaxy is studied by transmission electron microscopy (TEM) and double crystal x‐ray diffraction (DCXRD). The dislocation distribution in these layers does not coincide with the predicted equilibrium dislocation distribution [J. Tersoff, Appl. Phys. Lett. 62, 693 (1993)]. The dislocation density in the dislocation‐rich layer thickness is slightly smaller than the equilibrium density. The thickness of the dislocation‐rich region is different in the [110] and [110] directions. A good correspondence exists between the TEM and DCXRD strain measurements. The dislocation distribution observed by TEM has made it possible to design a scheme to grow dislocation‐free and unstrained top layers on linearly graded composition buffer layers.

Subcritical Crack Growth in CVI Silicon Carbide Reinforced with Nicalon Fibers: Experiment and Model

Abstract: Subcritical crack growth measurements of ceramic-matrix composites have been conducted on materials consisting of CVI SiC matrix reinforced with Nicalon fibers (SiC/SiCf) having C and BN fiber–matrix interfaces. Velocities of effective elastic cracks were determined as a function of applied stress intensity in pure Ar and in Ar plus 2000 ppm O2 at 1100°C. A stage-II regime, where the crack velocity depends only weakly on the applied stress intensity, was observed in the V–K diagrams over a range of applied stress intensities that correspond to the R-curve of the materials. This stage-II behavior was followed by a stage-III, or power-law, regime at higher stress intensity values. Oxygen was observed to increase the crack velocity in the stage-II regime and to shift the stage-II-to-stage-III transition to lower stress intensity values. A 2D micromechanics approach was developed to model the time dependence of observed crack-bridging events and is able to rationalize the measured effective crack velocities, the time dependence of the crack velocity, and the stage-II-to-stage-III transition in terms of the stress relaxation of crack-bridging fibers.

Strain-hardening and recovery during the creep of pure polycrystalline magnesium

Abstract: We report on creep and stress relaxation test results for pure polycrystalline magnesium. The experiments consisted of constant load creep tests conducted until steady-state was obtained followed by stress relaxation tests to study the strain-hardening and recovery behaviour of the materials. The tests were carried out over a range of applied stresses, 20–50 MPa, and test temperatures, 150–250°C, in order to determined stress and temperature dependencies of the high temperature plastic deformation behaviour. The strain-hardening coefficient, H , is derived from the experimentally generated steady-state creep rate, e s , and the dynamic recovery rate, R , data by using the well-known Bailey-Orowan relationship. It is found that the strain-hardening coefficient, H , during steady-state creep remains essentially constant with a magnitude of 0.27 E ( E is the elastic modulus) at 200°C and is independent of the applied stress. The creep strain rate is primarily determined by the recovery rate which is the rate determining mechanism during recovery creep. This set of experimental results is then examined in terms of creep equations and the dislocation network models for recovery creep deformation. It is shown that the present experimental data measured for pure polycrystalline magnesium lend support to the theoretical models based on dislocation link length distribution (dislocation network models) for recovery creep.

Molecular-dynamics simulations of stress relaxation in metals and polymers.

Abstract: Molecular-dynamics simulations of stress relaxation have been performed for models of metals and polymers. A method that employs coupling between the simulation cell and an applied stress as well as an external thermal bath has been used. Two-dimensional models of the materials are defined with interactions described by the Lennard-Jones (Mie 6-12) and harmonic potentials. A special method is employed to generate chains in dense polymeric systems. In agreement with experiments, simulated stress-relaxation curves are similar for metals and polymers. At the same time, there exists an essential difference in the stress-strain behavior of the two kinds of simulated materials. During the relaxation, trajectories of the particles in different materials display a common feature: There exist domains in which movement of the particles is highly correlated. Thus, the simulation results support the cooperative theory of stress relaxation.

Design criteria for structurally stable, highly strained multiple quantum well devices

Abstract: Strain compensation allows the synthesis of infinitely thick heterostructures with many highly strained quantum wells. Design criteria are given for optimized strain and thickness parameters in several device geometries. Strain compensation, using alternating layers of opposite strain, is quantitatively treated using an energy balance analysis. The upper bound to stability for strained multiple quantum wells with and without strain compensation is defined for geometries typically used in optoelectronic devices. Highly metastable structures (composed of many layers of high strain and/or thickness) require low epitaxy temperatures to avoid strain relaxation during growth of individual strained layers, prior to their stabilization in a strain compensated structure.

Plastic relaxation of metamorphic single layer and multilayer InGaAs/GaAs structures

Abstract: The plastic relaxation of multilayer structures of strained InGaAs grown above critical thickness on GaAs is reported and compared with the relaxation of single layers and with theory. We show that a composite structure, taken as a whole, follows the same relaxation law as observed in single layers. However, departures of the strains of some component layers from theory show that misfit dislocations are easily pinned at an interface. Implications for the design of relaxed buffer layer growth are discussed.

Stresses generated during oxidation sequences and high temperature fracture

Abstract: This paper deals with the stresses generated during high temperature oxidation and their relationship to scale fracture. In the first part, the objective is to differentiate growth stresses from thermal stresses and give evidence for relaxation phenomena. The results obtained for materials which develop NiO, Cr2O3 or Al2O3 scales indicate that, in most cases, growth stresses in the oxide films are negligible compared to thermal stresses, probably on account of stress relaxation at high temperature. Moreover, the stress sign in the oxide scale is inconsistent with conventional views based on the Pilling-Bedworth ratio, but closely related to the growth mechanism of the oxide: a preponderantly cationic diffusion leads to tensile stresses, whereas a preponderantly anionic diffusion leads to compressive stresses. Thermal stresses are closely related to the differences between the expansion coefficients of the scale and the substrate, but can be modified by parameters which can promote stress relaxation such a...

Elastic stress relaxation in SiGe epilayers on patterned Si substrates

Abstract: A two‐dimensional analysis of the in‐plane misfit stress and its elastic relaxation in rectangular patterned heteroepitaxial SiGe/Si multilayer structures on Si substrate is presented. Based on the model of relaxing film stress the distribution of the misfit stress versus distance from the free surface of a multilayered mesa edge is calculated. By superposition of the isolated stress fields of the mesa edges, the biaxial misfit stress distribution in a finite heteroepitaxial thin‐film structure on thick substrate is obtained. The formalism developed permits the determination of the variation of misfit stress values as a function of material and size characteristics of the patterned multilayer‐substrate system. An elementary application of the theoretical analysis of the biaxial state of stress existing in the structured layer system is discussed briefly.

Microstructural development of eutectic Bi-Sn and eutectic In-Sn during high temperature deformation

Abstract: Eutectic Bi-Sn and In-Sn solder joints were subjected to high temperature deformation in shear in order to determine whether microstructural instabilities are generated during testing. Dynamic recrystallization had previously been observed in Sn-Pb solder joints during creep and fatigue in shear. The current study shows that Bi-Sn can recrystallize during deformation in creep or at constant strain rate, whereas no microstructural changes are observed in In-Sn. Recrystallization of Bi-Sn is concentrated in a narrow band along the length of the sample, parallel to the direction of shear strain, similar to behavior in Sn-Pb. The recrystallization appears to proceed by migration of interphase boundaries rather than by a nucleation and growth mechanism. A minimum total strain is required to induce obvious recrystallization in Bi-Sn, independent of applied stress or strain rate. This value of strain is much higher than the strain at initiation of tertiary creep or at the maximum shear stress. Onset of tertiary creep and strain softening occur as a result of nonuniform deformation in the samples that is independent of the microstructural instabilities. The creep behavior of In-Sn is relatively straightforward, with a single creep mechanism operating at all temperatures tested. The creep behavior of Bi-Sn is temperature-dependent. Two mechanisms operate at lower temperatures, but there is still some question as to whether one or both of these, or a third mechanism, operates at higher temperatures.

Initiation of surface cracks in multilayer ceramic thermal barrier coatings under thermal loads

Abstract: The initiation of surface cracks in thick ceramic thermal barrier coatings systems was studied by using controlled experiments and the corresponding analysis. The experimental boundary conditions consisted of a concentrated heat flux at the surface of the coating and water cooling at the bottom of the substrate. The results showed that tensile stresses were formed at the surface during cooling following stress relaxation during steady state heating. A parametric study showing that a low Young's modulus and a low coefficient of thermal expansion for the coating would reduce these tensile stresses and increase its durability.