Showing papers on "Stress relaxation published in 2011"

Creep, relaxation and viscosity properties for basic fractional models in rheology

Abstract: The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep, relaxation and viscosity properties are considered. The basic models are those that generalize via derivatives of fractional order the classical mechanical models characterized by two, three and four parameters, that we refer to as Kelvin–Voigt, Maxwell, Zener, anti–Zener and Burgers. For each fractional model we provide plots of the creep compliance, relaxation modulus and effective viscosity in non dimensional form in terms of a suitable time scale for different values of the order of fractional derivative. We also discuss the role of the order of fractional derivative in modifying the properties of the classical models.

Basal plane misfit dislocations and stress relaxation in III-nitride semipolar heteroepitaxy

Abstract: This article presents a theoretical analysis of dislocation behavior and stress relaxation in semipolar III-nitride heteroepitaxy, e.g., for AlxGa1−xN and InyGa1−yN layers grown on {hh2−h−m}- or {h0h−m}-type semipolar planes of GaN substrates. We demonstrate that the shear stresses on the unique inclined basal (0001) plane do not vanish for such growth geometries. This leads to the onset of relaxation processes in semipolar III-nitride heterostructures via dislocation glide in the basal slip systems 〈1−1−20〉(0001) and to the formation of misfit dislocations (MDs) with Burgers vectors of (a/3)〈1−1−20〉-type at the semipolar heterointerface. Next we calculate the Matthews-Blakeslee critical thickness for MD formation in semipolar III-nitride layers together with the MD equilibrium spacings for complete misfit relaxation. The component of the MD Burgers vector normal to the film/substrate interface will cause a crystal lattice tilt in the epilayer with respect to the GaN substrate. The calculated magnitudes o...

Depth-resolved residual stress analysis of thin coatings by a new FIB–DIC method

Abstract: A new methodology for the measurement of depth sensitive residual stress profiles of thin coatings with sub-micrometer resolution is presented. The two step method consists of incremental focused ion beam (FIB) ring-core milling, combined with high-resolution in situ SEM-FEG imaging of the relaxing surface and a full field strain analysis by digital image correlation (DIC). The through-thickness profile of the residual stress can be obtained by comparison of the experimentally measured surface strain with finite element modeling using Schajer's integral method. In this work, a chromium nitride (CrN) CAE-PVD 3.0 μm coating on steel substrate, and a gold MS-PVD 1.5 μm on silicon were selected for the experimental implementation. Incremental FIB milling was conducted using an optimized milling strategy that produces minimum re-deposition over the sample surface. Results showed an average residual stress of σ = −5.15 GPa in the CrN coating and σ = +194 MPa in the Au coating. These values are in reasonable agreement with estimates obtained by other conventional techniques. The depth profiles revealed an increasing residual stress from surface to the coating/surface interface for both coatings. This observation is likely related to stress relaxation during grain growth, which was observed in microstructural cross sections, as predicted by existing models for structure–stress evolution in PVD coatings. A correlation between the observed stress gradients and the in-service mechanical behavior of the coatings is proposed. Finally, critical aspects of the technique and the influence of microstructure and elastic anisotropy on stress analysis are analyzed and discussed.

Experimental investigation on mechanical properties of a fiber-reinforced silica aerogel composite

Abstract: Aerogel has been used for thermal insulation because of its extremely low thermal conductivity, but the application has been restricted to non-loading-bearing structures by its low strength properties. Fiber-reinforced aerogel was prepared with higher strength but without sacrificing much of its thermal conductivity. While fiber-reinforced aerogel performs as load-bearing insulation, two behaviors must be investigated: compression and stress relaxation at evaluated temperature. At first, compression test was performed on a fiber-reinforced aerogel composite at both room and evaluated temperature, then the effects of temperature on compression properties of the fiber-reinforced aerogel were analyzed. Stress Relaxation Test was carried out at a constant strain of 0.1 for 1200 s at both room and evaluated temperature. The experimental results show that the stress relaxations increase with the temperature rise from 200 °C to 800 °C. Previous research and Scanning Electron Microscope (SEM) analysis of specimens showed that two time-dependent behaviors: (1) cracks induced by collapse of the pores, and (2) fiber failures subject to interfaces that debond and slide, might be possible reasons for the stress relaxation and the small inelastic strain of specimen tested at 25 °C. While three time dependent phenomena: (1) fusing of aerogel nanoparticles to form nanoparticle clusters, (2) fiber stress relaxation and (3) fiber failures subject to interfaces that debond and slide, would be possible reasons for the remarkable stress relaxation behavior at 800 °C.

Topological origin of stretched exponential relaxation in glass

Abstract: The physical origin of stretched exponential relaxation is considered by many as one of the oldest unsolved problems in science. The functional form for stretched exponential relaxation can be deduced from the axiomatic diffusion-trap model of Phillips. The model predicts a topological origin for the dimensionless stretching exponent, with two “magic” values emerging: β = 3/5 arising from short-range molecular relaxation pathways and β = 3/7 for relaxation dominated by longer-range interactions. In this paper, we report experimental confirmation of these values using microscopically homogeneous silicate glass specimens. Our results reveal a bifurcation of the stretching exponent, with β = 3/5 for stress relaxation and β = 3/7 for structural relaxation, both on macroscopic length scales. These results point to two fundamentally different mechanisms governing stress relaxation versus structural relaxation, corresponding to different effective dimensionalities in configuration space during the relaxation process.

Critical thickness for plastic relaxation of SiGe on Si(001) revisited

Abstract: We have revisited the critical thickness for plastic relaxation hc of SiGe on Si(001). To that end, we have started from prime 200-mm Si(001) wafers and grown (at 20 Torr with SiH2Cl2 and GeH4) various thickness and Ge content SiGe layers in an Epi Centura reduced-pressure–chemical-vapor-deposition chamber. Growth temperature was reduced from 700 °C to 550 °C, as the Ge content increased from 12% to 52%, to minimize surface roughening. X-ray diffraction (XRD) was performed on all samples to determine hc for the various Ge contents probed. Fully strained layers were characterized by: (i) peaks at a constant incidence angle that became narrower and more intense as the thickness increased, and (ii) the presence of numerous thickness fringes on each side of the layers’ peaks. Meanwhile, broader, less intense peaks (without thickness fringes) closer to the Si substrate peak were associated with plastically relaxed SiGe layers. Plastic strain relaxation was more gradual and less complete in higher Ge content layers grown at lower temperatures. We then performed haze and atomic force microscopy (AFM) measurements to have wafer and local scale quantifications of the surface roughening, which occurs when exceeding hc. For 12%, 22%, and 32% Ge, the haze and the surface roughness drastically increased for thicknesses greater than hc. For 42% Ge, the haze and the surface roughness were low for layers that had barely begun to relax, and became much larger for layers that were more plastically relaxed. Finally, for 52% Ge, there was a continuous but less pronounced increase of the haze and surface roughness when getting close to or exceeding hc. The critical thickness for plastic relaxation inferred from XRD was, for Ge content 22% and above, approximately two times higher than predicted by the People and Bean theory [Appl. Phys. Lett. 49, 229 (1986)]. However, some of the thickest SiGe 32%–52%, layers, considered fully strained in XRD, were observed by AFM to have a few “plow” lines, which are the surface signatures of misfit dislocations.

Phase, grain structure, stress, and resistivity of sputter-deposited tungsten films

Abstract: Sputter-deposited W films with nominal thicknesses between 5 and 180 nm were prepared by varying the base pressure prior to film deposition and by including or not including sputtered SiO2 encapsulation layers. X-ray and electron diffraction studies showed that single phase, polycrystalline α-W could be achieved in as-deposited films as thin as 5 nm. The stress state in the as-deposited films was found to be inhomogeneous. Annealing resulted in stress relaxation and reduction of resistivity for all films, except the thinnest, unencapsulated film, which agglomerated. In-plane film grain sizes measured for a subset of the annealed films with thicknesses between 5 and 180 nm surprisingly showed a near constant value (101–116 nm), independent of film thickness. Thick-film (≥120 nm) resistivity values as low as 8.6 μΩ cm at 301 K were obtained after annealing at 850 °C for 2 h. Film resistivities were found to increase with decreasing film thicknesses below 120 nm, even for films which are fully A2 α-W with no metastable, A15 β-W evident. Sputter-deposited W films with nominal thicknesses between 5 and 180 nm were prepared by varying the base pressure prior to film deposition and by including or not including sputtered SiO2 encapsulation layers. X-ray and electron diffraction studies showed that single phase, polycrystalline α-W could be achieved in as-deposited films as thin as 5 nm. The stress state in the as-deposited films was found to be inhomogeneous. Annealing resulted in stress relaxation and reduction of resistivity for all films, except the thinnest, unencapsulated film, which agglomerated. In-plane film grain sizes measured for a subset of the annealed films with thicknesses between 5 and 180 nm surprisingly showed a near constant value (101–116 nm), independent of film thickness. Thick-film (≥120 nm) resistivity values as low as 8.6 μΩ cm at 301 K were obtained after annealing at 850 °C for 2 h. Film resistivities were found to increase with decreasing film thicknesses below 120 nm, even for films which are fully A2 α-W with no...

Slow Dynamics of Earth Materials: An Experimental Overview

Abstract: In 1996 Johnson et al. were the first to identify peculiar rate effects in resonant bar experiments on various earth materials. The effects were evident on time scales of minutes to hours. They were also seen in both sedimentary and crystalline rocks, and have since been seen in geomaterials like concrete. Although these effects resemble some aspects of creep and creep recovery, they can be induced by a sinusoidal acoustic drive at strains three orders of magnitude below typical creep experiments. These strains are only a few tenths of a microstrain. Moreover, unlike most creep behavior, the effects have been shown to be macroscopically reversible and repeatable, over hundreds of experiments spanning nearly a year. The unique excitation and character of these rate effects cause them to be called slow dynamics. A review and discussion of slow dynamics is presented, pointing out similarities and differences with ordinary creep and focusing on laboratory experiments. A brief description of some possible mechanisms is included, and a new experiment on a sample of Berea sandstone in ultra high vacuum is shown to point out new research that hopes to help ascertain the role of water as a potential mechanism.

Rheological characterization of styrene-butadiene based medium and its finishing performance using rotational abrasive flow finishing process

Abstract: Finishing of complex shaped components needs advanced finishing processes to produce nano level surface finish. Abrasive flow finishing (AFF) process uses abrasive mixed polymer as a medium to finish complex shapes. The medium should possess three basic properties i.e., better flow ability, self deformability and abrading ability to finish the given surface to nano scale. Various flow and deformation properties of the medium can be investigated by rheological characterization. In the present work, different media are made using specially co-polymered soft styrene butadiene based polymer, plasticizer and abrasives. Static and dynamic rheological properties of these in-house prepared media are evaluated, and it is found that these media follow viscoelastic behavior with shear thinning nature. For a small rise in temperature, the medium starts losing its original properties. In the present work, static (flow test, creep compliance test, stress relaxation test) and dynamic (amplitude sweep and frequency sweep) rheological properties are measured. Finishing experiments are carried out on Al alloy as well as its metal matrix composites using rotational abrasive flow finishing (R-AFF) process. Later, the effect of each rheological parameter such as shear stress, % viscous component, stress relaxation modulus and storage modulus on the change in average surface roughness (ΔR a ) and material removal rate during R-AFF is found.

Thickness-dependent magnetism and spin-glass behaviors in compressively strained BiFeO3 thin films

Abstract: Compressively strained BiFeO3 (BFO) films from 19 to 114 nm are epitaxially grown on LaAlO3 substrates, and their thickness-dependent evolutions of structural and magnetic properties are investigated. Across the morphotropic phase boundary, complex strain relaxation behaviors involving low-symmetry intermediate/bridging phases are observed. The fully strained 38 nm BFO film exhibits a saturation magnetization of ∼28 emu/cm3 at 300 K with a coercivity of 130 Oe while all films show a spin-glass behavior. These findings suggest that tailoring film thickness is effective to suppress the cycloidal magnetic modulation in BFO, leading to magnetic properties different from the bulk counterpart.

Creep and fatigue in polymer matrix composites

Abstract: Part 1 Viscoelastic and viscoplastic modelling: Viscoelastic constitutive modeling of creep and stress relaxation in polymers and polymer matrix composites Time-temperature-age superposition principle for predicting long-term response of linear viscoelastic materials Time-dependent behaviour of active/intelligent polymer matrix composites incorporating piezoceramic fibers Predicting the elastic-viscoplastic and creep behaviour of polymer matrix composites using the homogenization theory Measuring fiber strain and creep behaviour in polymer matrix composites using Raman spectroscopy Predicting the viscoelastic behaviour of polymer nanocomposites Constitutive modelling of viscoplastic deformation of polymer matrix composites Creep analysis of polymer matrix composites using viscoplastic models Micromechanical modeling of viscoelastic behaviour of polymer matrix composites undergoing large deformations. Part 2 Creep rupture: Fiber bundle models for creep rupture analysis of polymer matrix composites Micromechanical modelling of time-dependent failure in off-axis polymer matrix composites Time-dependent failure criteria for lifetime prediction of polymer matrix composite structures. Part 3 Fatigue modelling, characterisation and monitoring: Testing the fatigue strength of fibers used in fiber-reinforced composites using fiber bundle tests Continuum damage mechanical modelling of creep damage and fatigue in polymer matrix composites Accelerated testing methodology for predicting long-term creep and fatigue in polymer matrix composites Fatigue testing methods for polymer matrix composites The effect of viscoelasticity on fatigue behavior of polymer matrix composites Characterization of vicoelasticity, viscoplasticity and damage in composites Structural health monitoring of composite structures for durability.

Syndeformational antigorite dehydration produces stable fault slip

Abstract: We conducted deformation experiments in which temperature was increased above the thermal stability of antigorite to directly test the dehydration embrittlement hypothesis and its potential link to intermediate-depth earthquakes. The experiments were designed to maximize the possibility for instability: pore pressure was undrained, pre-dehydration stress was high, and deformation was localized prior to initiation of reaction. However, stick-slip instabilities (or unstable fault behavior) did not develop. Rather, we find that weakening occurs stably at a rate that depends on the ratio of the temperature ramp rate to the strain rate (), resulting in laboratory slow slip or stress relaxation events.

Transport and strain relaxation in wurtzite InAs–GaAs core-shell heterowires

Abstract: Indium-arsenide–gallium-arsenide (InAs–GaAs) core-shell, wurtzite nanowires have been grown on GaAs (001) substrates. The core-shell geometries (core radii 11 to 26 nm, shell thickness >2.5 nm) exceeded equilibrium critical values for strain relaxation via dislocations, apparent from transmission electron microscopy. Partial axial relaxation is detected in all nanowires increasing exponentially with size, while radial strain relaxation is >90%, but undetected in nanowires with both smaller core radii <16 nm and shell thicknesses <5 nm. Electrical measurements on individual core-shell nanowires show that the resulting dislocations are correlated with reduced electron field-effect mobility compared to bare InAs nanowires.

Reassessing the Mechanisms of Negative-Bias Temperature Instability by Repetitive Stress/Relaxation Experiments

Abstract: A major intrinsic limitation of the reaction-diffusion (R-D) model for negative-bias temperature instability (NBTI) is revealed through dynamic stress experiments. We found no evidence of self-limiting recovery, one of the key features of the transport-based R-D model, after repeating the stress and relaxation cycles alternately for many times. The amount of recovery per cycle of the parameter of interest (e.g., threshold voltage shift, change in the charge-pumping (CP) current, etc.) is shown to remain constant, independent of the number of stress/recovery cycles. Under repeated cycling of the test device between stress and recovery, it is also found that the amount of parametric shift induced by the stress cycle becomes nearly identical to that recovered during the relaxation cycle, i.e., the parametric evolution under a fixed set of stress and recovery intervals is cyclic in nature. In conjunction with the thermal activation result, this cyclic behavior of the dynamic NBTI is ascribed to an ensemble of switching hole traps having broad spectra of characteristic trapping and detrapping time constants. The same group of traps responds under a fixed set of experimental conditions, giving rise to the cyclic behavior. The interface state generation was also investigated using a CP current measurement and is found to be permanent within the range of timing examined. It is also shown that the variation in the power-law exponent of the as-measured change in the CP current with temperature could be consistently explained by considering the different thermal activation of the hole trapping and interface state components. In view of these new evidences, previous claims of consistency between the generation/recovery of the interface states and the R-D model or its dispersive counterpart must be reviewed.

A Combined Model for Hardening, Softening, and Damage Processes in Advanced Heat Resistant Steels at Elevated Temperature

Abstract: Phenomenological constitutive equations that describe inelastic behavior of advanced steels at elevated temperature are developed. To characterize hardening, recovery, and softening processes, a composite model with creep-hard and creep-soft constituents is applied. The volume fraction of the creep-hard constituent is assumed to decrease toward a saturation value. This approach reproduces well the primary creep as a result of stress redistribution between constituents and tertiary creep as a result of softening. To describe the whole tertiary creep stage, a damage variable in the sense of continuum damage mechanics is introduced. The material parameters and the response functions in the model are calibrated against experimental creep curves for X20CrMoV12-1 steel. For the verification, simulations of the inelastic response are performed and the results compared with experimental data including creep under stress change conditions and stress-strain response under constant strain rate. Furthermore, the life...

A viscoelastic model for the compaction of fibrous materials

Abstract: Fibrous materials experience compression in many important industrial and technical applications. They are known to undergo a viscoelastic response in such circumstances, exhibiting phenomena such as dependence on compaction velocity, stress relaxation and stress–strain hysteresis. In this paper, a model has been developed for the stress in compacting fibrous materials. The model is based on the multiplicative decomposition of the stress into a function of the strain and a second function of the strain‐rate. The model is applicable to that class of materials whose stress–strain responses at different compaction velocities can be collapsed onto a single master curve when the stress is normalised appropriately. The model parameters can be determined using a least‐squares fitting to a select number of test data. The model has been tested for two materials of different architectures over a range of compaction speeds and maximum volume fractions; the match to experimental data is excellent.

A Nonlinear Model of Passive Muscle Viscosity

Abstract: The material properties of passive skeletal muscle are critical to proper function and are frequently a target for therapeutic and interventional strategies. Investigations into the passive viscoelasticity of muscle have primarily focused on characterizing the elastic behavior, largely neglecting the viscous component. However, viscosity is a sizeable contributor to muscle stress and extensibility during passive stretch and thus there is a need for characterization of the viscous as well as the elastic components of muscle viscoelasticity. Single mouse muscle fibers were subjected to incremental stress relaxation tests to characterize the dependence of passive muscle stress on time, strain and strain rate. A model was then developed to describe fiber viscoelasticity incorporating the observed nonlinearities. The results of this model were compared with two commonly used linear viscoelastic models in their ability to represent fiber stress relaxation and strain rate sensitivity. The viscous component of mouse muscle fiber stress was not linear as is typically assumed, but rather a more complex function of time, strain and strain rate. The model developed here, which incorporates these nonlinearities, was better able to represent the stress relaxation behavior of fibers under the conditions tested than commonly used models with linear viscosity. It presents a new tool to investigate the changes in muscle viscous stresses with age, injury and disuse.

The orthotropic viscoelastic behavior of aortic elastin.

Abstract: In this paper, we studied the viscoelastic behaviors of isolated aortic elastin using combined modeling and experimental approaches Biaxial stress relaxation and creep experiments were performed to study the time-dependent behavior of elastin Experimental results reveal that stress relaxation preconditioning is necessary in order to obtain repeatable stress relaxation responses Elastin exhibits less stress relaxation than intact or decellularized aorta The rate of stress relaxation of intact and decellularized aorta is linearly dependent on the initial stress levels The rate of stress relaxation for elastin increases linearly at stress levels below about 60 kPa; however, the rate changes very slightly at higher initial stress levels Experimental results also show that creep response is negligible for elastin, and the intact or decellularized aorta A quasi-linear viscoelasticity model was incorporated into a statistical mechanics based eight-chain microstructural model at the fiber level to simulate the orthotropic viscoelastic behavior of elastin A user material subroutine was developed for finite element analysis Results demonstrate that this model is suitable to capture both the orthotropic hyperelasticity and viscoelasticity of elastin

Quantifying the stress relaxation modulus of polymer thin films via thermal wrinkling.

Abstract: The viscoelastic properties of polymer thin films can have a significant impact on the performance in many small-scale devices. In this work, we use a phenomenon based on a thermally induced instab...