Showing papers on "Stress relaxation published in 2001"

The dynamic competition between stress generation and relaxation mechanisms during coalescence of Volmer–Weber thin films

Abstract: Real-time measurements of stress evolution during the deposition of Volmer–Weber thin films reveal a complex interplay between mechanisms for stress generation and stress relaxation. We observed a generic stress evolution from compressive to tensile, then back to compressive stress as the film thickened, in amorphous and polycrystalline Ge and Si, as well as in polycrystalline Ag, Al, and Ti. Direct measurements of stress relaxation during growth interrupts demonstrate that the generic behavior occurs even in the absence of stress relaxation. When relaxation did occur, the mechanism depended sensitively on whether the film was continuous or discontinuous, on the process conditions, and on the film/substrate interfacial strength. For Ag films, interfacial shear dominated the early relaxation behavior, whereas this mechanism was negligible in Al films due to the much stronger bonding at the Al/SiO2 interface. For amorphous Ge, selective relaxation of tensile stress was observed only at elevated temperatures...

Nonlinear ligament viscoelasticity.

Abstract: Ligaments display time-dependent behavior, characteristic of a viscoelastic solid, and are nonlinear in their stress-strain response. Recent experiments (25) reveal that stress relaxation proceeds more rapidly than creep in medial collateral ligaments, a fact not explained by linear viscoelastic theory but shown by Lakes and Vanderby (17) to be consistent with nonlinear theory. This study tests the following hypothesis: nonlinear viscoelasticity of ligament requires a description more general than the separable quasilinear viscoelasticity (QLV) formulation commonly used. The experimental test for this hypothesis involves performing both creep and relaxation studies at various loads and deformations below the damage threshold. Freshly harvested, rat medial collateral ligaments (MCLs) were used as a model. Results consistently show a nonlinear behavior in which the rate of creep is dependent upon stress level and the rate of relaxation is dependent upon strain level. Furthermore, relaxation proceeds faster than creep; consistent with the experimental observations of Thornton et al. (25) The above results from rat MCLs are not consistent with a separable QLV theory. Inclusion of these nonlinearities would require a more general formulation.

Viscoelastic Properties of an Epoxy Resin during Cure

Abstract: The cure dependent relaxation modulus of an epoxy resin was investigated over the entire range of cure extent. Parallel plate rheometry was used to measure the material behavior below the gel point of the epoxy network. Creep testing in three-point bend was used for specimens cured past gelation. All data were converted to the stress relaxation modulus for comparison of the material behavior among the various cure states and between the two experimental techniques. The data were used to develop a practical model for predicting the cure dependence of the relaxation modulus throughout cure under varying processing conditions.

The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release

Abstract: The molecular stress function theory for polymer melts is extended to include a new, dissipative convective constraint release process. First the Helmholtz free energy of tube segments with strain-dependent tube diameter is established neglecting constraint release, and it is demonstrated that the molecular stress is a function of the average logarithmic stretch under these conditions. Then convective constraint release is introduced as a dissipative process in the energy balance of tube deformation, which leads to a strain-dependent evolution equation for the molecular stress function. Constraint release is considered to be the consequence of different convection mechanisms for tube orientation and tube cross section. Our new, dissipative constraint release model emphasizes that tube kinematics are fundamentally different for rotational and nonrotational flows, and therefore distinguishes explicitly between simple shear and pure shear (planar extension). For the startup of simple shear and extensional flows, the predictions of our set of constitutive equations consisting of a history integral for the stress tensor and a differential evolution equation for the molecular stress function with only two nonlinear material parameters are in excellent agreement with experimental data of a polydisperse high-density polyethylene (HDPE) and a polydisperse low-density polyethylene (LDPE) melt. Also, stress relaxation after step-shear strain is described for both the HDPE and the LDPE melt.

Microscopic theory of convective constraint release

Abstract: We develop a microscopic description of the contribution to stress relaxation in entangled polymer melts of convective constraint release, which is the release of entanglement constraints due to the effects of convective flow on chains surrounding a given chain. Our theory resolves three of the main shortcomings of the Doi–Edwards model in nonlinear rheology, in that it predicts (1) a monotonically increasing shear stress as a function of shear rate, (2) shear stress independent of molecular weight at sufficiently high shear rates, and (3) only modest anisotropies in the single chain scattering function, in agreement with experiment. In addition, our approach predicts that a stress maximum and resulting shear-banding instability would occur for living micelle solutions, as observed.

Creep Viscosity and Stress Relaxation of Gel‐Derived Silicon Oxycarbide Glasses

Abstract: The temperature dependence of the viscosity and stress-relaxation kinetics of sol–gel-derived SiOC glasses that contain up to 14 at.% carbon have been characterized in the temperature range of 1000°–1400°C. The viscosity, as determined from relaxation experiments, is in good agreement with the creep viscosity and is typically two orders of magnitude higher than the viscosity of vitreous silica. However, materials suffer from partial crystallization at >1150°C, and the precipitation of β-SiC nanocrystals induces a flow-hardening behavior and results in a dynamic increase in viscosity, especially at >1200°C and for glasses with a high carbon content.

Ultraslow Dynamics and Stress Relaxation in the Aging of a Soft Glassy System

Abstract: We use linear rheology and multispeckle dynamic light scattering (MDLS) to investigate the aging of a gel composed of multilamellar vesicles Light scattering data indicate rearrangement of the gel through an unusual ultraslow ballistic motion A dramatic slowdown of the dynamics with sample age t(w) is observed for both rheology and MDLS, the characteristic relaxation time scaling as t(mu)w We find the same aging exponent mu = 078 for both techniques, suggesting that they probe similar physical processes, that is the relaxation of applied or internal stresses for rheology or MDLS, respectively A simple phenomenological model is developed to account for the observed dynamics

Biphasic poroviscoelastic simulation of the unconfined compression of articular cartilage: II--Effect of variable strain rates.

Abstract: This study investigated the abilities of the linear biphasic poroviscoelastic (BPVE) model and the linear biphasic poroelastic (BPE) model to simulate the effect of variable ramp strain rates on the unconfined compression stress relaxation response of articular cartilage. Curve fitting of experimental data showed that the BPVE model was able to successfully account for the ramp strain rate-dependent viscoelastic behavior of articular cartilage under unconfined compression, while the BPE model was able to account for the complete viscoelastic response at a slow strain rate, but only the long-term viscoelastic response at faster strain rates. We concluded that the short-term viscoelastic behavior of articular cartilage, when subjected to a fast ramp strain rate, is primarily governed by a fluid flow-independent (intrinsic) viscoelastic mechanism, whereas the long-term viscoelastic behavior is governed by a fluid flow-dependent (biphasic) viscoelastic mechanism. Furthermore, a linear viscoelastic representation of the solid stress was found to be a valid model assumption for the simulation of ramp strain rate-dependent relaxation behaviors of articular cartilage within the range of ramp strain rates investigated.

Control and elimination of cracking of AlGaN using low-temperature AlGaN interlayers

Abstract: We demonstrate that the insertion of low-temperature AlGaN interlayers is effective in reducing mismatch-induced tensile stress and suppressing the formation of cracks during growth of high-temperature AlGaN directly upon GaN epilayers. Stress evolution and relaxation is monitored using an in situ optical stress sensor. The combination of in situ and ex situ characterization techniques enables us to determine the degree of pseudomorphism in the interlayers. It is observed that the elastic tensile mismatch between AlGaN and GaN is mediated by the relaxation of interlayers; the use of interlayers offers tunability in the in-plane lattice parameters.

Rheology and aging: A simple approach

Abstract: We introduce a rheological model to describe the low-frequency mechanical properties of systems near a fluid/paste transition. We propose a Landau-like expansion for the vicinity of this transition, treating the stress relaxation rate as an order parameter. This leads to a formally simple model that allows us to describe the interplay between aging and non-linearities in the mechanical response of the system. We focus here on systems prepared by fluidification under a strong shear, on which mechanical measurments are performed (oscillatory rheology, stress relaxation, response to a steady shear rate), after a waiting time during which the system evolves on its own.

Domain formation in epitaxial Pb(Zr, Ti)O3 thin films

Abstract: Ferroelectric twin-domain structures in epitaxial Pb(Zr, Ti)O3 (PZT) thin films grown on various single-crystal substrates such as MgO(001), KTaO3(001), and SrTiO3(001) were investigated by two-dimensional reciprocal space mapping using synchrotron x-ray diffraction. Each system showed a characteristic domain structure. PbTiO3 thin films grown on MgO(001) showed highly c-axis oriented domain structures consisting of a periodic array of 90° twinlike domains. Perfectly c-axis oriented films were obtained on SrTiO3(001), while the films grown on KTaO3(001) showed a-domain dominant structures with a small amount of c domains embedded in matrix a domains. Contributions of net elastic strain stored in each heteroepitaxial layer and its relaxation to the final domain structures were evaluated considering thermodynamic equilibrium relief of coherency strain by misfit dislocation generation at the film growth temperature. A comparison between theoretical consideration and experimental results clearly demonstrates that the nature of effective misfit strain and its relaxation during film growth play a critical role in the formation of domain structures in epitaxial PZT thin films. Moreover, it was verified that the control of such critical strain factors by changing film composition could modify dominant domain structures in a drastic way. In addition, it was found that the crystalline quality of the films is closely correlated to the tilting nature of the domain structure in each system and coherency strain across the 90° domain boundary is accommodated mainly by the domain tilt of the minor domain.

Strain relaxation of pseudomorphic heterostructures after hydrogen or helium ion implantation for virtual substrate fabrication

Abstract: Strain relaxed Si1−xGex layers on Si(1 0 0) are used as virtual substrates for the growth of e.g. Si/Si1−xGex quantum well structures. We investigated the effects of H+ and He+ ion implantation and subsequent annealing on pseudomorphic Si 1−x Ge x / Si (1 0 0) heterostructures grown by molecular beam epitaxy (MBE). A narrow defect band is generated by ion implantation slightly underneath the interface inducing the formation of strain-relieving misfit dislocations (MDs) during subsequent thermal annealing. Using H+ ion implantation, nearly complete strain relaxation of Si1−xGex layers with Ge fractions up to 22 at.% was obtained at temperatures as low as 800°C and the samples appeared free of threading dislocations (TDs) within the SiGe layer to the limit of transmission electron microscopy (TEM) analysis. Efficient strain relaxation was demonstrated even for Si1−xGex layers with Ge fractions up to 30 at.% using He+ ion implantation. We have thus developed a method for producing high-quality, thin, relaxed Si1−xGex films on Si(1 0 0) with TD densities well below 10 7 cm −2 by standard techniques as MBE and ion implantation. The heterostructures were analyzed using X-ray diffraction (XRD), Rutherford backscattering/channeling spectrometry and TEM. We propose a model of strain relaxation in which dislocations generated in conjunction with the formation of H or He filled overpressurized cavities glide to the interface where they form strain-relieving misfit segments. On the basis of this assumption, the conditions for efficient strain relaxation are discussed.

A new vogel-like law: ionic conductivity, dielectric relaxation, and viscosity near the glass transition.

Abstract: A model is developed that describes temperature and pressure dependence of dielectric relaxation, ionic conductivity, and viscosity of glass-forming liquids near the glass transition temperature. The expressions for ionic conductivity are compared with experimental results for two polymer electrolytes. Those for dielectric relaxation are compared with data for poly(propylene oxide) and poly(vinyl acetate). The theoretical viscosity law is compared with experiment for propylene carbonate.

A Viscoelastic Model for Predicting Isotropic Residual Stresses in Thermosetting Materials: Effects of Processing Parameters:

Abstract: The isotropic residual stresses in a composite subjected to three-dimensional constraints are calculated by extending a thermo-viscoelastic model developed previously by Simon et al. [1] to describe the time, temperature, and conversion dependence of the shear modulus for a commercial thermosetting material during cure. Experimental residual stress data as a function of cure time are fit to obtain limiting values for the rubbery and glassy bulk moduli. The effects of cure history on isotropic residual stresses are then investigated via simulations using the bulk moduli, a model of the cure kinetics, the relationship beween T g and conversion, and the stress relaxation function obtained in the thermo-viscoelastic model which includes the dependence of the shift factor on temperature and conversion. The isotropic residual stresses at room temperature can be directly related to the cure temperature at which gelation occurred for cases when vitrification does not occur during cure.

Effect of confining pressure on dilatation, recrystallization, and flow of rock salt at 150°C

Abstract: Microstructural evidence for fluid-assisted dynamic recrystallization (FADRX) is widespread in naturally deformed rock salt. However, the principal experimental evidence for FADRX in salt has been obtained from stress relaxation experiments, and it is unclear whether the process occurs during steady state dislocation creep and what its effect might be. Here we report deformation experiments performed on natural rock salt at a constant strain rate of 3.5×10−7 s−1, 150°C, and confining pressures Pc of 3–30 MPa. Samples deformed at Pc = 3 MPa showed continuous work hardening and minor dilatation. Microstructurally, they exhibited intergranular cracking plus slip band and subgrain structures indicative of dislocation glide/creep. Electron backscatter diffraction analysis revealed a high frequency of boundaries with low-angle misorientations in the range 5°–10°. In contrast, samples deformed at Pc ≥ 6.5 MPa showed work hardening followed by steady state flow at strains >6–7%. These samples compacted slightly, and crystal plastic deformation was accompanied by extensive FADRX, with a predominance of high-angle boundaries (30°–50°) over low-angle boundaries. We infer that FADRX is suppressed by dilatation at low pressures as a result of grain boundary disruption. At pressures high enough to prevent dilatation, however, FADRX acts as a “recovery” mechanism counteracting work hardening. The results offer a possible explanation for rheological variability seen in previous experiments conducted at pressures up to 30 MPa. A simple rate model for diffusion- and interface-controlled FADRX indicates that FADRX should become increasingly important toward natural halokinetic conditions, although the effect on flow stresses is likely to be small.

Effects of Strain Level and Proteoglycan Depletion on Preconditioning and Viscoelastic Responses of Rat Dorsal Skin

Abstract: The mechanical response of rat dorsal skin was experimentally studied under cyclic uniaxial ramp stretches to various strain levels. Special emphasis was paid to the effects of the preconditioning protocol on the stress-strain relationship, and to the effects of ramp strain level and proteoglycan (PG) depletion, on viscoelasticity and preconditioning responses. The results show that preconditioning significantly reduced both the slope of the low strain stress-strain relationship, and the stress levels at consecutive stretch cycles. Following a short rest there was a significant partial recovery. Stress decay due to preconditioning was significant at all strain levels, and increased with strain. Stress relaxation was significant at all strain levels, but varied little with strain. Recovery following a 10 min rest was minor at all strain levels and varied little with strain. PG-depleted samples manifested similar response patterns. These results are consistent with the following notion: (1) skin consists of three mechanical components: elastin and proteoglycan which dominate the low strain response and are effected by preconditioning and (PG) depletion, and collagen which dominates the high strain response and is unaffected by preconditioning and PG depletion; (2) that the viscoelasticity of elastin and PG vs that of collagen are similar, so that rat dorsal skin can be regarded quasilinear viscoelastic.

Strain profiles in pyramidal quantum dots by means of atomistic simulation

Abstract: The minimum energy configurations of the atomic structure of a Ge island on a Si(001) substrate are calculated by using the conjugate gradient minimization of the potential energy of the system. The island is assumed to be covered or uncovered by a Si layer and assumed to be of pyramidal shape with the sidewalls of {110} or {105} facets; the base length of the island ranges from 5.43 to 10.9 nm. Two empirical potentials, the Keating and Stillinger–Weber potentials, are used. At the interfaces between the regions occupied by the atoms of different species, the potential parameters for such bondings are properly adopted. The strain profiles along the three selected paths within the structure and along the cap surface are calculated. While the profiles of the normal strain component exx obtained by the two potentials are in good agreement with each other except within the substrate and at the edges of the island in the uncovered structures, the two profiles of the normal strain component ezz show a considerable difference in their magnitude, and the use of the Stillinger–Weber potential is recommended for the islands of the small sizes below 10 nm. The validity of the valence force field model with the Keating potential for such small islands is questionable although this model is widely recognized to be applicable to the calculation of strains in the quantum dot structures. The strain relaxation in the uncovered island is discussed through the comparison with that in the covered island. The strain profile along the cap surface explains vertical self-organization of stacked dots.

Ligament creep behavior can be predicted from stress relaxation by incorporating fiber recruitment

Abstract: Structural modeling and morphological crimp analysis were used to investigate if collagen fiber recruitment could account for our previous finding, that ligament creep behavior cannot be predicted using inverse stress relaxation behavior directly. Ligament creep behavior was accurately predicted using our simple nonlinear structural model that incorporated collagen fiber creep and collagen fiber recruitment. Collagen fiber creep was modeled using the inverse stress relaxation function and estimated fiber modulus. Collagen fiber recruitment was modeled with a linear variation in crimp over an idealized rectangular ligament cross section. Concomitantly, significant differences in collagen crimp patterns were observed as a result of creep testing; however; no significant changes were observed as a result of relaxation testing. This morphological evidence supported the model assumptions that fiber recruitment occurs during creep and that stress relaxation behavior results from the viscoelastic response of an unchanging group of fibers. Not only was the prediction improved compared to the inverse stress relaxation behavior alone, the model demonstrated that fiber recruitment increased the load-bearing area of the ligament over time and correspondingly stress was redistributed, reducing stress on the fibers initially loaded. These findings may have important implications for both models and experiments on ligament structure and function at low loads.

Strain relaxation in AlGaN/GaN superlattices grown on GaN

Abstract: Lattice relaxation of strained AlxGa1−xN/GaN superlattices grown on thick GaN buffer layers is investigated using optical microscopy, x-ray diffraction, and photoluminescence spectroscopy. The results are compared to strained bulk AlxGa1−xN layers particularly with regard to the impact of the superlattice period and the Al content. A relaxation process which keeps the coherency between AlxGa1−xN barriers and GaN wells in the superlattice is found and it is attributed to misfit dislocations at the buffer/superlattice interface. Additionally, the AlxGa1−xN barriers relax via crack channels which form beyond a critical Al content and limit the additional strain energy compared to a free-standing superlattice to a maximum value. Cracks relieve tensile plane stress to an extent similar as in bulk layers, i.e., they do not put the GaN wells of the superlattice under additional plane compression. This is explained by misfit dislocations which nucleate at crack faces and glide into the superlattice at the well/barrier interfaces. The onset of cracking is found to shift to higher tensile stresses in the AlxGa1−xN barriers when increasing the superlattice period which is discussed in view of edge cracks being the starting point of crack channels.

Thermal stability of the strained-Si/Si0.7Ge0.3 heterostructure

Abstract: Thermal stability of the strained-Si/Si0.7Ge0.3 heterostructure was investigated by secondary-ion mass spectroscopy, Raman spectroscopy, and atomic force microscopy. Ge atoms diffused out through the strained-Si layer during heat treatment of 1000 °C for 1 h. The activation energy of Ge diffusion in strained Si was 3.3 eV, which was lower than the value in unstrained Si (4.7–5.3 eV). Strain in the strained-Si layer did not change after thermal treatment at 950 °C or less for 1 h. Slip lines due to strain relaxation formed at the surface of the strained-Si layer for the samples treated at 950–1000 °C for 1 h. For practical application of the strained-Si/Si0.7Ge0.3 heterostructure to electron devices, the maximum thermal budget should be made less than that equivalent to 900 °C annealing for 1 h.

Stresses and first-order dislocation energetics in equilibrium Stranski-Krastanow islands

Abstract: We numerically determine the state of stress in two-dimensional Stranski-Krastanow islands having equilibrium shape. These calculations reveal important generic characteristics and quantitative details of the stress state in equilibrium islands, including stress relaxation and stress concentration. We also use the stresses to determine the first-order energy of introducing dislocations of different Burgers vectors into Stranski-Krastanow islands. These results characterize the ``energy wells'' sought by dislocations to relieve the misfit stress, and suggest that misfit dislocations in islands segregate according to the orientation of their Burgers vector. This segregation allows for more efficient relief of the nonuniform strain in misfitting islands.

Deviations from dynamic dilution in the terminal relaxation of star polymers.

Abstract: We present a "slip-link" model for relaxation of entangled star polymers that accounts for chain-end fluctuations and constraint release and that explains deviations from the "dynamic dilution" equation observed in recent dielectric and stress relaxation data. In the terminal regime where tube expansion fails to keep up with chain relaxation, relaxation is controlled by rare events in which newly created entanglements near the branch point draw the chain end towards the last remaining old entanglement, where a shallow fluctuation releases it.