Showing papers on "Stress relaxation published in 2002"

Transient phenomena in thixotropic systems

Abstract: A nonlinear rheological model which accounts for the time-dependent elastic, viscous and yielding phenomena is developed in order to describe the flow behavior of thixotropic materials which exhibit yield stress. A key feature of the formulation is a smooth transition from an ‘elastically’ dominated response to a ‘viscous’ response without a discontinuity in the stress–strain curve. The model is phenomenological and is based on the kinetic processes responsible for structural changes within the thixotropic material. As such, it can predict thixotropic effects, such as stress overshoot during start-up of a steady shear flow and stress relaxation after cessation of flow. Thus this model extends a previously proposed viscoplastic model [J. Rheol. 34 (1991) 647] to include thixotropy. An analysis and comparison to experimental data involving oscillatory shear flow are provided to evaluate the accuracy of the model and to estimate the model parameters in a prototype concentrated suspension. The experiments were conducted using a series of concentrated suspensions of silicon particles and silicon carbide whiskers in polyethylene. The data obtained with this experimental system indicated much better agreement between the theory and experiments that obtained in earlier work.

Active fluidization of polymer networks through molecular motors.

Abstract: Entangled polymer solutions and melts exhibit elastic, solid-like resistance to quick deformations and a viscous, fluid-like response to slow deformations. This viscoelastic behaviour reflects the dynamics of individual polymer chains driven by brownian motion1: since individual chains can only move in a snake-like fashion through the mesh of surrounding polymer molecules, their diffusive transport, described by reptation2,3,4, is so slow that the relaxation of suddenly imposed stress is delayed. Entangled polymer solutions and melts therefore elastically resist deforming motions that occur faster than the stress relaxation time. Here we show that the protein myosin II permits active control over the viscoelastic behaviour of actin filament solutions. We find that when each actin filament in a polymerized actin solution interacts with at least one myosin minifilament, the stress relaxation time of the polymer solution is significantly shortened. We attribute this effect to myosin's action as a ‘molecular motor’, which allows it to interact with randomly oriented actin filaments and push them through the solution, thus enhancing longitudinal filament motion. By superseding reptation with sliding motion, the molecular motors thus overcome a fundamental principle of complex fluids: that only depolymerization makes an entangled, isotropic polymer solution fluid for quick deformations.

Impression creep and other localized tests

Abstract: Impression creep and impression fatigue, both using cylindrical indenters, are reviewed in this paper. For impression creep, analytical solutions and computer simulations for different situations are presented. Materials tested include metals and alloys, superplastic materials, weldments, glasses, ceramics and polymers. Viscosity measurements using indentation techniques and impression creep of thin films are discussed also. For impression fatigue, a steady state per cycle is shown and the power law dependence of maximum stress is presented. Underloading and overloading effects, as well as delayed retardation, are described. Other localized tests, such as nanoindentation, stress relaxation, impression recovery and the adhesion energy determined by impression testing, are briefly discussed also.

Application of nonlinear viscoelastic models to describe ligament behavior

Abstract: Recent experiments in rat medial collateral ligament revealed that the rate of stress relaxation is strain dependent and the rate of creep is stress dependent. This nonlinear behavior requires a more general description than the separable quasilinear viscoelasticity theory commonly used in tissue biomechanics. The purpose of this study was to determine whether the nonlinear theory of Schapery or the modified superposition method could adequately model the strain-dependent stress-relaxation behavior of ligaments. It is shown herein that both theories describe available nonlinear experimental ligament data well and hence can account for both elastic and viscous nonlinearities. However, modified superposition allows for a more direct interpretation of the relationship between model parameters and physical behavior, such as elastic and viscous nonlinearities, than does Schapery's theory. Hence, the modified superposition model is suggested to describe ligament data demonstrating both elastic nonlinearity and strain-dependent relaxation rate behavior. The behavior of the modified superposition model under a sinusoidal strain history is also examined. The model predicts that both elastic and viscous behaviors are dependent on strain amplitude and frequency.

Formation of high-k gate dielectric layers for MOS devices fabricated on strained lattice semiconductor substrates with minimized stress relaxation

Abstract: A semiconductor device is formed by providing a semiconductor substrate comprising a strained lattice semiconductor layer at an upper surface thereof and having a pre-selected amount of lattice therein, forming a thin buffer/interfacial layer of a low-k dielectric material on the upper surface of the semiconductor substrate, and forming a layer of a high-k dielectric material on the thin buffer/interfacial layer of a low-k dielectric material. Embodiments include forming the thin buffer/interfacial layer and high-k layer at a minimum temperature sufficient to effect formation of the respective dielectric layer without incurring, or at least minimizing, strain relaxation of the strained lattice semiconductor layer.

Reversible stress relaxation during precoalescence interruptions of volmer-weber thin film growth.

Abstract: From in situ stress measurements, we have observed that a large component of the precoalescence compressive stress that develops during Volmer-Weber growth of polycrystalline Cu films relaxes reversibly. This phenomenon is similar to the reversible stress relaxation previously observed in the postcoalescence regime. We have also observed that less than a tenth of a monolayer of deposition leads to an instantaneous stress of order 1 GPa. The stress changes in both the precoalescence and postcoalescence regimes of growth are explained by changes in the adatom population during and after deposition.

Strain relaxation of SiGe islands on compliant oxide

Abstract: The relaxation of patterned, compressively strained, epitaxial Si0.7Ge0.3 films transferred to borophosphorosilicate (BPSG) glass by a wafer-bonding and etch-back technique was studied as an approach for fabricating defect-free Si1−xGex relaxed films. Both the desired in-plane expansion and undesired buckling of the films concurrently contribute to the relaxation. Their relative role in the relaxation process was examined experimentally and by modeling. Using x-ray diffraction, Raman scattering and atomic force microscopy, the dynamics of in-plane expansion and buckling of Si0.7Ge0.3 islands for island sizes ranging from 10 μm×10 μm to 200 μm×200 μm for anneal temperatures between 750 and 800 °C was investigated. Lateral relaxation is favored in small and thick islands, and buckling is initially dominant in large and thin islands. Raising the temperature to lower viscosity of the oxide enhances the rate of both processes equally. For very long annealing times, however, the buckling disappeared, allowing l...

Residual stress in thin-film parylene-c

Abstract: This paper reports the influence of thermal annealing on the residual stress in parylene-c thin-films on silicon. Although recently others have used the diaphragm bulge testing method to measure the residual stress in parylene, this is the first extensive study of residual stress in parylene using the load-deflection method and rotating tip strain gages. This paper supports the hypothesis that stress is relaxed in parylene-c films at elevated temperatures (>100/spl deg/C) and that thermal stress accounts for 90% of the residual stress in films that have undergone annealing at these elevated temperatures. It was found that this held true up to 180/spl deg/C which is above the glass transition temperature of the material.

Modeling cross-hatch surface morphology in growing mismatched layers

Abstract: We propose and investigate a model for the development of cross-hatch surface morphology in growing mismatched layers. The model incorporates two important elements: (i) strain relaxation due to dislocation glide in the layer (film) interior that is also associated with misfit dislocation formation at the film/substrate interface and (ii) lateral surface transport that eliminates surface steps that originated from dislocation glide. A combination of dislocation-assisted strain relaxation and surface step flow leads to the appearance of surface height undulations during layer growth. A Monte Carlo simulation technique was applied to model dislocation nucleation events in the course of strain relaxation. The simulation was used to model the influence of dislocations on film surface height profiles. The surface height displacement was calculated from the analytic elasticity solutions for edge dislocations near a free surface. The results of the modeling predict that the average amplitude of the surface undulations and their apparent wavelength both increase with increasing film relaxation and film thickness. The developed cross-hatch pattern is characterized by an atomically smooth but mesoscopically (lateral dimensions ∼0.1–10 μm) rough surface morphology. The conclusions of the model are in agreement with atomic force microscopy observations of cross-hatch surface relief in In0.25Ga0.75As/GaAs samples grown well beyond the critical thickness for misfit dislocation formation.

Structural and optical properties of InGaN/GaN layers close to the critical layer thickness

Abstract: In this work, we investigate structural and optical properties of metalorganic chemical vapor deposition grown wurtzite InxGa1−xN/GaN epitaxial layers with thicknesses that are close to the critical layer thickness (CLT) for strain relaxation. CLT for InxGa1−xN/GaN structures was calculated as a function of the InN content, x, using the energy balance model proposed by People and Bean [Appl. Phys. Lett. 47, 322 (1985)]. Experimentally determined CLT are in good agreement with these calculations. The occurrence of discontinuous strain relaxation (DSR), when the CLT is exceeded, is revealed in the case of a 120 nm thick In0.19Ga0.89N layer by x-ray reciprocal space mapping of an asymmetrical reflection. The effect of DSR on the luminescence of this layer is clear: The luminescence spectrum shows two peaks centered at ∼2.50 and ∼2.67 eV, respectively. These two components of the luminescence of the sample originate in regions of different strain, as discriminated by depth-resolving cathodoluminescence spectroscopy. DSR leads directly to the emergence of the second, lower-energy, peak. Based on this experimental evidence, it is argued that the appearance of luminescence doublets in InGaN is not evidence of “quantum dotlike In-rich” or “phase separated” regions, as commonly proposed.

Rheology of Three-Arm Asymmetric Star Polymer Melts

Abstract: We present experimental and theoretical results for the linear rheology of melts of entangled, three-arm asymmetric polyisoprene stars. Asymmetric three-arm stars, in which two arms have the same length and the third is shorter, cross over from starlike to linear-like stress relaxation as the length of the third arm varies. We combine recent theories of stress relaxation in symmetric stars and in linear melts to predict the dynamic modulus of the asymmetric stars. For stars with short arm molecular weights of a few entanglement lengths, our theory underestimates the effective drag caused by the short arm, even when polydispersity effects are included. This unexplained discrepancy does not appear in a recent comparison of a related theory with measurements on polyisoprene H-polymers.

On measuring creep behaviour in granular materials through triaxial testing

Abstract: The first part of the paper describes the precision and long-term stability that are required in triaxial stress-strain measurements and in stress-path control systems to obtain reliable information on creep in granular media. It is shown that membrane penetration and sample end compliance must be accounted for and that lubricated ends and local strain measurements are essential. The temperature sensitivity of each transducer also needs to be assessed, even when working in a temperature-controlled laboratory. The second part of the paper presents illustrative data that were obtained in tests on sand and Ballotini® glass beads. Considerable creep deformations were observed under both isotropic and anisotropic effective stress conditions, even at relatively low pressures where particle breakage was unlikely to be significant. The experiments show how creep depends on the stress conditions imposed, how the strain increment directions change during creep, and how the creep rates stabilize with time.Key words:...

A generalized model for the uniaxial isothermal deformation of a viscoelastic body

Abstract: Using the notion of a fractional derivative we formulate a new model for a uniaxial deformation of a visco-elastic body. The basic assumption is that all derivatives σ(γ) with respect to time of the stress depend (with specified weighting factor) on all derivatives e(γ) with respect to time of the strain (multiplied with another weighting factor), for 0≤γ≤1. In this respect our model is a generalization of the Zener model, i.e., it is a Zener fractional model with infinitely many terms. The relation between stress and strain is given in explicit form. For two specific choices of parameters the behavior of the model under suddenly applied stress (creep) and suddenly applied strain (stress relaxation) are examined.

Rheology and flow-birefringence from viscoelastic polymer-clay solutions

Abstract: The shear orientation of viscoelastic clay-polymer solutions was investigated by means of rheology and flow birefringence (Δn). The polymer chains are in dynamic adsorption/desorption equilibrium with the clay particles to form a “network”. The elastic behavior of the network was characterized by constant stress, oscillatory shear, and stress relaxation experiments. Constant stress experiments indicated a yield stress upon which shear flow started and no strain recovery could be observed. Oscillatory shear experiments showed a broad elastic region followed by flow when a critical strain was reached. Stress relaxation experiments showed several relaxation times when the same critical strain was reached. Experiments under steady flow characterized the transient behavior of the network. With increasing steady shear rate a pronounced minimum in birefringence was observed at a critical shear rate. The shear rate dependent viscosity showed near power law behavior and no corresponding critical feature. While birefringence detects orientational effects on a microscopic length scale, rheology averages over macroscopic changes in the sample. The same degree of orientation could be achieved under constant shear rate or constant stress conditions.

Creep at low stresses: An evaluation of diffusion creep and Harper-Dorn creep as viable creep mechanisms

Abstract: High-temperature creep experiments often reveal a transition at very low stresses to a region where the stress exponent is reduced to a value lying typically in the range of ∼1 to 2. This region is generally associated with the occurrence of a new creep mechanism, such as grain-boundary sliding, diffusion creep, and/or Harper-Dorn creep. Several recent reports have suggested that diffusion creep and Harper-Dorn creep may not be viable creep mechanisms. This article examines these two processes and demonstrates that there is good evidence supporting the occurrence of both creep mechanisms under at least some experimental conditions.

Effect of helium ion implantation and annealing on the relaxation behavior of pseudomorphic Si1−xGex buffer layers on Si (100) substrates

Abstract: The influence of He implantation and annealing on the relaxation of Si0.7Ge0.3 layers on Si (100) substrates is investigated. Proper choice of the implantation energy results in a narrow defect band ≈100 nm underneath the substrate/epilayer interface. During annealing at 700–1000 °C, He-filled bubbles are created, which act as sources for misfit dislocations. Efficient annihilation of the threading dislocations is theoretically predicted, if a certain He bubble density with respect to the buffer layer thickness is maintained. The variation of the implantation dose and the annealing conditions changes density and size of spherical He bubbles, resulting in characteristic differences of the dislocation structure. Si1−xGex layers with Ge fractions up to 30 at. % relax the initial strain by 70% at an implantation dose of 2×1016 cm−2 and an annealing temperature as low as 850 °C. Simultaneously, a low threading dislocation density of 107 cm−2 is achieved. The strain relaxation mechanism in the presence of He fi...

Electromigration-induced plastic deformation in passivated metal lines

Abstract: We have used scanning white beam x-ray microdiffraction to study microstructural evolution during an in situ electromigration experiment on a passivated Al(Cu) test line. The data show plastic deformation and grain rotations occurring under the influence of electromigration, seen as broadening, movement, and splitting of reflections diffracted from individual metal grains. We believe this deformation is due to localized shear stresses that arise due to the inhomogeneous transfer of metal along the line. Deviatoric stress measurements show changes in the components of stress within the line, including relaxation of stress when current is removed.

Intermediate length scale dynamics of polyisobutylene

Abstract: We report on a neutron spin echo investigation of the intermediate scale dynamics of polyisobutylene studying both the self-motion and the collective motion. The momentum transfer (Q) dependences of the self-correlation times are found to follow a Q(-2/beta) law in agreement with the picture of Gaussian dynamics. In the full Q range of observation, their temperature dependence is weaker than the rheological shift factor. The same is true for the stress relaxation time as seen in sound wave absorption. The collective times show both temperature dependences; at the structure factor peak, they follow the temperature dependence of the viscosity, but below the peak, one finds the stress relaxation behavior.

Constitutive model of the TWIP effect in a polycrystalline high manganese content austenitic steel

Abstract: The TEM study of our steel with a high manganese content reveals that mechanical twining (TWIP effect) occurs during the deformation at room temperature. Microtwins are organised into parallel stacks and two systems are sequentially activated in each grain. They participate to the deformation and they are strong obstacles for the dislocations and for other twins, leading to the decrease of the effective grain size. Thus, TWIP provides our alloy a very good ductility and a high hardening rate. Our constitutive modelling deduced from a model proposed by Bouaziz and Guelton [4] integrates this typical organisation of microtwins. Twinning is quantified in each grain by the partial volume fraction of twins in each system. A nucleation law for the microtwins is introduced which depends on the local stress and the stress relaxation due to pre-existing twins. The flow stress is deduced from the dislocation density, which evolves with the dynamical recovery and the decrease of the mean free path (MFP). The MFP takes into account the grain and twin boundaries and the forest dislocations. The strain is calculated by adding the contributions of dislocation glide and twinning accounting the orientation of the grain. To treat the polycristal, the behaviours of different grain orientations are mixed by assuming at each strain step that the increment of elastic energy stored is the same in each grain. The model was successfully applied to describe the mechanical properties of our alloy, for two different grain sizes. Some microstructural parameters are yet fitted. This leads to an insufficient prediction of the evolution of the microstructure. In further developments, we expect to introduce numerical simulation results on local characteristics of microtwins (thickness, critical resolved shear stress for twinning) and experimental results on the rate of twin nucleation.