Showing papers on "Stress relaxation published in 2006"

A structural kinetics model for thixotropy

Abstract: A general structural kinetics model is presented to describe the flow behaviour of thixotropic systems based on inelastic suspending media. The total stress is divided in structure-dependent elastic and viscous contributions. The kinetic equation for the structure parameter takes into account the effect of shear on structure breakdown and build-up, as well as the effect of Brownian motion on build-up. The relaxation and deformation of the flocs is also included. Both the kinetic and the relaxation equations contain a distribution of time constants. The predictions of this model, as well as those of two representative models from the literature, are compared with experimental data using an objective method for parameter estimation. Model validation is based on stress transients resulting from sudden changes in shear rate, including both structure build-up and breakdown. The predictions of the viscous and elastic components are evaluated separately using stress jump experiments with steady and non-steady state starting conditions.

High-Frequency Stress Relaxation in Semiflexible Polymer Solutions and Networks

Abstract: We measure the linear viscoelasticity of sterically entangled and chemically cross-linked networks of actin filaments over more than five decades of frequency. The high-frequency response reveals rich dynamics unique to semiflexible polymers, including a previously unobserved relaxation due to rapid axial tension propagation. For high molecular weight, and for cross-linked gels, we obtain quantitative agreement with predicted shear moduli in both amplitude and frequency dependence.

Flat GaN epitaxial layers grown on Si(111) by metalorganic vapor phase epitaxy using step-graded AlGaN intermediate layers

Abstract: In this work, we report on the growth by metalorganic vapor phase epitaxy (MOVPE) of GaN layers on AlN/Si(111) templates with step-graded AlGaN intermediate layers. First, we will discuss the optimization of the AlN/Si(111) templates and then we will discuss the incorporation of step-graded AlGaN intermediate layers. It is found that the growth stress in GaN on high-temperature (HT) AlN/Si(111) templates is compressive, although, due to relaxation, the stress we have measured is much lower than the theoretical value. In order to prevent the stress relaxation, step-graded AlGaN layers are introduced and a crack-free GaN epitaxial layer of thickness >1 µm is demonstrated. Under optimized growth conditions, the total layer stack, exceeding 2 µm in total, is kept under compressive stress, and the radius of the convex wafer bowing is as large as 119 m. The crystalline quality of the GaN layers is examined by high-resolution x-ray diffraction (HR-XRD), and the full-width-at-half maximums (FWHMs) of the x-ray rocking curve (0002) ω-scan and (−1015) ω-scan are 790 arc sec and 730 arc sec, respectively. It is found by cross-sectional transmission electron microscopy (TEM) that the step-graded AlGaN layers terminate or bend the dislocations at the interfaces.

Stress relaxation effect on transport properties of strained vanadium dioxide epitaxial thin films

Abstract: A stress relaxation effect on the transport properties of strained vanadium dioxide epitaxial thin films grown on $\mathrm{Ti}{\mathrm{O}}_{2}$ (001) single crystal was investigated. When varying the film thickness ranging from $10\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}30\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, there were no significant changes on the crystal structures identified by x-ray diffraction, i.e., no observable stress relaxation effects. On the other hand, increasing the film thickness resulted in the drastic changes on the transport properties including emerging the multisteps of the metal-insulator transition and also increasing the resistivity. The discrepancy between the observed crystal structure and the transport properties was related to the presence of the nanoscale line cracks due to thermal stress. Thus controlling thermal stress relaxation rather than the stress due to the lattice mismatch is critical to investigate the intrinsic nature on the transport properties of strained vanadium dioxide epitaxial thin films.

Brittle creep, damage and time to failure in rocks

Abstract: We propose a numerical model based on static fatigue laws in order to model the time-dependent damage and deformation of rocks under creep. An empirical relation between time to failure and applied stress is used to simulate the behavior of each element of our finite element model. We review available data on creep experiments in order to study how the material properties and the loading conditions control the failure time. The main parameter that controls the failure time is the applied stress. Two commonly used models, an exponential tfexp (bs/s0) and a power law function tfsb0 fit the data as well. These time-to-failure laws are used at the scale of each element to simulate its damage as a function of its stress history. An element is damaged by decreasing its Young's modulus to simulate the effect of increasing crack density at smaller scales. Elastic interactions between elements and heterogeneity of the mechanical properties lead to the emergence of a complex macroscopic behavior, which is richer than the elementary one. In particular, we observe primary and tertiary creep regimes associated respectively with a power law decay and increase of the rate of strain, damage event and energy release. Our model produces a power law distribution of damage event sizes, with an average size that increases with time as a power law until macroscopic failure. Damage localization emerges at the transition between primary and tertiary creep, when damage rate starts accelerating. The final state of the simulation shows highly damaged bands, similar to shear bands observed in laboratory experiments. The thickness and the orientation of these bands depend on the applied stress. This model thus reproduces many properties of rock creep, which were previously not modeled simultaneously.

Analysis of the hysteresis loops of a martensitic steel: Part I: Study of the influence of strain amplitude and temperature under pure fatigue loadings using an enhanced stress partitioning method

Abstract: In order to identify the microstructural mechanisms leading to the softening effect usually presented by martensitic steels under cyclic loadings (with or without hold times), a study of the cyclic stress partition is presented. As the usual stress partitioning methods were found to be inadequate in the present case, a new method based both on Cottrell's method and on the Statistical Process Control principles, is proposed. This new method is used to distinguish between the kinematic, the isotropic and the viscous parts of the cyclic stress. The evolutions of these different stresses are evaluated for several strain amplitudes and temperatures under pure fatigue loading in this first part. It is shown that the softening effect is mainly due to a decrease of the backstress: the higher the strain amplitude, the stronger and the faster the softening effect. The isotropic stress is found to be independent of the strain amplitude, but increases when the temperature decreases. Whereas the viscous stress represents a large part of the total stress at 823 K, it becomes almost negligible below 673 K. These results are finally linked to the microstructural coarsening previously observed and modelled. Therefore, the decrease of the kinematic stress can be related to grain size effect.

Rubber friction on smooth surfaces

Abstract: We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.

Crystallization and stress relaxation in highly stretched samples of natural rubber and its synthetic analogue

Abstract: Vulcanizates of natural rubber (NR) and its synthetic analogue (IR) were quickly stretched to 6 times the original length. The post stretch relaxation of tensile stress and the development of strain-induced crystallization (SIC) were studied by simultaneous measurements of the stress and the diffraction intensities using the synchrotron X-ray source. In the range of 8 s, NR crystallized much faster than IR. Accordingly, the origin of the superior toughness of NR was thought to come from the ability of rapid SIC. Time constants of the post-stretch crystallization were estimated from the X-ray study. Then the crystallization time constants were used to decompose the contribution of SIC from the total magnitude of the post-stretch relaxation. The contribution of SIC was dominant for the total magnitude of the post-stretch relaxation during several seconds.

Rheology of active filament solutions.

Abstract: We study the viscoelasticity of an active solution of polar biofilaments and motor proteins. Using a molecular model, we derive the constitutive equations for the stress tensor in the isotropic phase and in phases with liquid crystalline order. The stress relaxation in the various phases is discussed. Contractile activity is responsible for a spectacular difference in the viscoelastic properties on opposite sides of the order-disorder transition.

Melt rheology of long-chain-branched polypropylenes

Abstract: Rheological properties of long-chain-branched isotactic polypropylene (PP) via copolymerization with a very small amount of nonconjugated α,ω-diene monomer using metallocene catalyst system in both linear and nonlinear regions were investigated, comparing with conventional linear and long-chain-branched PP modified at postreactor. Although comonomer incorporation was equal to 0.05 mol% or less, it caused high molecular weight, broad molecular weight distribution, and long-chain branching. A detailed study on the effect of diene incorporation on the polymer properties was conducted, comparing with modified PP in postreactor. Polymer chain microstructures were characterized by gel permeation chromatography with multiangle laser light scattering (MALLS), differential scanning calorimetry, and rheological means: dynamic viscoelasticity, step-strain, uniaxial elongational flow measurements, and large amplitude oscillatory shear. The PP, which incorporated a small amount of diene monomer, showed significantly improved viscoelastic behaviors. The diene-propylene copolymer containing long-chain branches showed extremely long relaxation mode under shear and outstanding viscosity increase under elongational flow, so-called strain hardening. The difference in microstructure of diene-propylene copolymer with modified PP with long-chain branches is investigated by MALLS and rheological characterizations.

Effects of fatigue and fretting on residual stresses introduced by laser shock peening

Abstract: The effects of fatigue and fretting fatigue on the distribution of residual stresses in shot and laser shock peened Ti–6Al–4V samples have been investigated. Residual elastic strains have been determined using high-energy synchrotron X-ray diffraction. Laser shock peening introduces a considerable compressive residual stress, the compressive zone extending 1.5 mm below the surface. The effects of fatigue loading have been investigated using a notched three-point bend geometry. The residual stress field was found to be largely insensitive to fatigue cycling, at least for the applied stress range studied. For fretting fatigue, while the residual stresses at depth were little affected, within 0.5 mm of the surface significant stress relaxation was observed; the extent of relaxation being greatest in the direction parallel to the fretting direction. The states of residual stress have been quantified using the concept of eigenstrain, which quantifies the retained plastic misfit resulting from peening. Finite element modeling has been used to determine the eigenstrain profiles causing the measured elastic strain profiles, and the changes to these eigenstrain profiles due to fretting. Our results suggest laser shock peening confers much greater fretting fatigue resistance than traditional shot peening alone due to the much deeper compressive zone.

Quasi-static internal deformation due to a dislocation source in a multilayered elastic/viscoelastic half-space and an equivalence theorem

Abstract: SUMMARY We have obtained general expressions for quasi-static internal deformation fields due to a dislocation source in a multilayered elastic/viscoelastic half-space under gravity by applying the correspondence principle of linear viscoelasticity to the associated elastic solution (Fukahata & Matsu'ura 2005). The use of the upgoing propagator matrix for the region below the source and the downgoing propagator matrix for the region above the source in the derivation of mathematical expressions guarantees the numerical stability of the obtained viscoelastic solution over the whole region. The viscoelastic deformation fields due to a dislocation source tend to a certain steady state with the progress of viscoelastic stress relaxation. The completely relaxed viscoelastic solution can be directly obtained from the associated elastic solution by taking the rigidity of the elastic layer corresponding to a Maxwell viscoelastic layer to be zero. We gave an explicit mathematical proof of this theoretical relationship, which we named the equivalence theorem, on the basis of the correspondence principle of linear viscoelasticity and the limiting value theorem of the Laplace transform. The equivalence theorem is applicable not only to the elastic-viscoelastic stratified medium but also to general elastic and linear-viscoelastic composite media. As numerical examples we show the quasi-static internal displacement fields due to strike-slip motion on a vertical fault and dip-slip motion on a subduction plate boundary in an elastic surface layer overlying a viscoelastic half-space. The temporal variation of the computed deformation fields shows that the effective relaxation time of the elastic-viscoelastic system is much longer than the Maxwell relaxation time defined by the ratio of viscosity to rigidity in the viscoelastic layer.

A Finite-Deformation Constitutive Model of Bulk Metallic Glass Plasticity

Abstract: A constitutive model of bulk metallic glass (BMG) plasticity is developed which accounts for finitedeformation kinematics, the kinetics of free volume, strain hardening, thermal softening, rate-dependency and non-Newtonian viscosity. The model has been validated against uniaxial compression test data; and against plate bending experiments. The model captures accurately salient aspects of the material behavior including: the viscosity of Vitreloy 1 as a function of temperature and strain rate; the temperature and strain-rate dependence of the equilibrium free-volume concentration; the uniaxial compression stress-strain curves as a function of strain rate and temperature; and the dependence of shear-band spacing on plate thickness. Calculations suggest that, under adiabatic conditions, strain softening and localization in BMGs is due both to an increase in free volume and to the rise in temperature within the band. The calculations also suggest that the shear band spacing in plate-bending specimens is controlled by the stress relaxation in the vicinity of the shear bands.

A Finite-Deformation Constitutive Model of Bulk Metallic

Abstract: A constitutive model of bulk metallic glass (BMG) plasticity is developed which accounts for finite- deformation kinematics, the kinetics of free volume, strain hardening, thermal softening, rate-dependency and non-Newtonian viscosity. The model has been vali- dated against uniaxial compression test data; and against plate bending experiments. The model captures accu- rately salient aspects of the material behavior including: the viscosity of Vitreloy 1 as a function of temperature and strain rate; the temperature and strain-rate depen- dence of the equilibrium free-volume concentration; the uniaxial compression stress-strain curves as a function of strain rate and temperature; and the dependence of shear-band spacing on plate thickness. Calculations suggest that, under adiabatic conditions, strain softening and localization in BMGs is due both to an increase in free volume and to the rise in temperature within the band. The calculations also suggest that the shear band spacing in plate-bending specimens is controlled by the stress relaxation in the vicinity of the shear bands.

Stress analysis of spontaneous Sn whisker growth

Abstract: Spontaneous Sn whisker growth is a surface relief phenomenon of creep, driven by a compressive stress gradient. No externally applied stress is required for the growth, and the compressive stress is generated within, from the chemical reaction between Sn and Cu to form the intermetallic compound Cu6Sn5 at room temperature. To obtain the compressive stress gradient, a break of the protective oxide on the Sn surface is required because the free surface of the break is stress-free. Thus, spontaneous Sn whisker growth is unique that stress relaxation accompanies stress generation. One of the whisker challenging issues in understanding and in finding effective methods to prevent spontaneous Sn whisker growth is to develop accelerated tests of whisker growth. Use of electromigration on short Sn stripes can facilitate this. The stress distribution around the vicinity and the root of a whisker can be obtained by using the micro-beam X-ray diffraction utilizing synchrotron radiation. A discussion of how to prevent spontaneous Sn whisker growth by blocking both stress generation and stress relaxation is given.