Showing papers on "Stress relaxation published in 2012"

Mechanical characterization of brain tissue in compression at dynamic strain rates.

Abstract: Traumatic brain injury (TBI) occurs when local mechanical load exceeds certain tolerance levels for brain tissue. Extensive research has been done previously for brain matter experiencing compression at quasistatic loading; however, limited data is available to model TBI under dynamic impact conditions. In this research, an experimental setup was developed to perform unconfined compression tests and stress relaxation tests at strain rates≤90/s. The brain tissue showed a stiffer response with increasing strain rates, showing that hyperelastic models are not adequate. Specifically, the compressive nominal stress at 30% strain was 8.83±1.94, 12.8±3.10 and 16.0±1.41 kPa (mean±SD) at strain rates of 30, 60 and 90/s, respectively. Relaxation tests were also conducted at 10%- 50% strain with the average rise time of 10 ms, which can be used to derive time dependent parameters. Numerical simulations were performed using one-term Ogden model with initial shear modulusµ o =6.06±1.44, 9.44±2.427 and 12.64±1.227 kPa (mean±SD) at strain rates of 30, 60 and 90/s, respectively. A separate set of bonded and lubricated tests were also performed under the same test conditions to estimate the friction coefficient µ, by adopting combined experimental-computational approach. The values ofµwere 0.1±0.03 and 0.15±0.07 (mean±SD) at 30 and 90/s strain rates, respectively, indicating that pure slip conditions cannot be achieved in unconfined compression tests even under fully lubricated test conditions. The material parameters obtained in this study will help to develop biofidelic human brainfinite element models, which can subsequently be used to predict brain injuries under impact conditions. c

Atomic-scale relaxation dynamics and aging in a metallic glass probed by x-ray photon correlation spectroscopy.

Abstract: We use x-ray photon correlation spectroscopy to investigate the structural relaxation process in a metallic glass on the atomic length scale. We report evidence for a dynamical crossover between the supercooled liquid phase and the metastable glassy state, suggesting different origins of the relaxation process across the transition. Furthermore, using different cooling rates, we observe a complex hierarchy of dynamic processes characterized by distinct aging regimes. Strong analogies with the aging dynamics of soft glassy materials, such as gels and concentrated colloidal suspensions, point at stress relaxation as a universal mechanism driving the relaxation dynamics of out-of-equilibrium systems.

Micromechanics of brittle creep in rocks

Abstract: In the upper crust, the chemical infuence of pore water promotes time dependent brittle deformation through sub-critical crack growth. Sub-critical crack growth allows rocks to deform and fail at stresses well below their short-term failure strength, and even at constant applied stress (\brittle creep"). Here we provide a micromechanical model describing time dependent brittle creep of water-saturated rocks under triaxial stress conditions. Macroscopic brittle creep is modeled on the basis of microcrack extension under compressive stresses due to sub-critical crack growth. The incremental strains due to the growth of cracks in compression are derived from the sliding wing crack model of Ashby and Sammis [1990], and the crack length evolution is computed from Charles' law. The macroscopic strains and strain rates computed from the model are non linear, and compare well with experimental results obtained on granite, low porosity sandstone and basalt rock samples. Primary creep (decelerating strain) corresponds to decelerating crack growth, due to an initial decrease in stress intensity factor with increasing crack length in compression. Tertiary creep (accelerating strain as failure is approached) corresponds to an increase in crack growth rate due to crack interactions. Secondary creep with apparently constant strain rate arises as an inflexion between those two end-member phases. The minimum strain rate at the inflexion point can be estimated analytically as a function of model parameters, e ective con ning pressure and temperature, which provides an approximate creep law for the process. The creep law is used to infer the long term strain rate as a function of depth in the upper crust due to the action of the applied stresses: in this way, sub-critical cracking reduces the failure stress in a manner equivalent to a decrease in cohesion. We also investigate the competition with pressure solution in porous rocks, and show that the transition from sub-critical cracking to pressure solution dominated creep occurs with increasing depth and decreasing strain rates.

Kinetic model for dependence of thin film stress on growth rate, temperature, and microstructure

Abstract: During deposition, many thin films go through a range of stress states, changing from compressive to tensile and back again. In addition, the stress depends strongly on the processing and material parameters. We have developed a simple analytical model to describe the stress evolution in terms of a kinetic competition between different mechanisms of stress generation and relaxation at the triple junction where the surface and grain boundary intersect. The model describes how the steady state stress scales with the dimensionless parameter D/LR where D is the diffusivity, R is the growth rate, and L is the grain size. It also explains the transition from tensile to compressive stress as the microstructure evolves from isolated islands to a continuous film. We compare calculations from the model with measurements of the stress dependence on grain size and growth rate in the steady state regime and of the evolution of stress with thickness for different temperatures.

Characterization of thermal stresses in through-silicon vias for three-dimensional interconnects by bending beam technique

Abstract: Through-silicon via is a critical element for three-dimensional (3D) integration of devices in multilevel stack structures. Thermally induced stresses in through-silicon vias (TSVs) have raised serious concerns over mechanical and electrical reliability in 3D technology. An experimental technique is presented to characterize thermal stresses in TSVs during thermal cycling based on curvature measurements of bending beam specimens. Focused ion beam and electron backscattering diffraction analyses reveal significant grain growth in copper vias, which is correlated with stress relaxation during the first cycle. Finite element analysis is performed to determine the stress distribution and the effect of localized plasticity and to account for TSV extrusion observed during annealing.

Structure-property relationships in biomedical thermoplastic polyurethane nanocomposites

Abstract: Polyurethanes are excellent potential materials for the construction of implantable medical components due to their exceptional mechanical properties and biocompatibility. Currently, soft silicone materials are employed as insulation for implantable cochlear electrode arrays. Siloxane-based thermoplastic polyurethane (TPU) nanocomposites containing synthetic layered silicates are being investigated as new insulation materials with superior tensile and tear strength and reduced surface tack, potentially allowing for thinner insulation and more intricate electrode designs. In this work, ElastEon E5-325 (Aortech Pty Ltd.) TPU nanocomposites reinforced with 2 and 4 wt % low aspect ratio organo-hectorite and high aspect ratio organo-fluoromica (Lucentite SWN, Somasif ME100, both modified with octadecyltrimethylammonium (ODTMA)) were prepared by a solvent casting technique. The mechanical properties of the resulting nanocomposites were measured by tensile, tear, stress relaxation, and creep testing and morphologically were characterized by DSC, DMTA, XRD, TEM, and strained in situ synchrotron SAXS. We found that the hydrophobic low aspect ratio organohectorite acts as a very potent interfacial compatibilizer. At 2 wt % loading, the resulting nanocomposite displays vastly superior mechanical properties to both soft silicone and ElastEon. In addition to providing 30 nm × 1 nm synthetic nanosilicate reinforcing elements which are readily capable of orientation and reinforcement, these nanosilicates also serve to provide more cohesive hard microdomains and thus creep resistance and dimensional stability. Interestingly, at a higher (4 wt %) loading of organohectorite, gross morphological changes in the TPU microdomain texture are observed, adversely effecting the mechanical properties of the TPU.

Communication: Correlation of the instantaneous and the intermediate-time elasticity with the structural relaxation in glassforming systems

Abstract: The elastic models of the glass transition relate the increasing solidity of the glassforming systems with the huge slowing down of the structural relaxation and the viscous flow. The solidity is quantified in terms of the instantaneous shear modulus G(∞), i.e., the immediate response to a step change in the strain. By molecular-dynamics simulations of a model polymer system, one shows the virtual absence of correlations between the instantaneous elasticity and the structural relaxation. Instead, a well-defined scaling is evidenced by considering the elastic response observed at intermediate times after the initial fast stress relaxation. The scaling regime ranges from sluggish states with virtually pure elastic response on the picosecond time scale up to high-mobility states where fast restructuring events are more apparent.

Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks

Abstract: A 2-D numerical model for brittle creep and stress relaxation is proposed for the time-dependent brittle deformation of heterogeneous brittle rock under uniaxial loading conditions. The model accounts for material heterogeneity through a stochastic local failure stress field, and local material degradation using an exponential material softening law. Importantly, the model introduces the concept of a mesoscopic renormalization to capture the co-operative interaction between microcracks in the transition from distributed to localized damage. The model also describes the temporal and spatial evolution of acoustic emissions, including their size (energy released), in the medium during the progressive damage process. The model is first validated using previously published experimental data and is then used to simulate brittle creep and stress relaxation experiments. The model accurately reproduces the classic trimodal behaviour (primary, secondary and tertiary creep) seen in laboratory brittle creep (constant stress) experiments and the decelerating stress during laboratory stress relaxation (constant strain) experiments. Brittle creep simulations also show evidence of a critical level of damage before the onset of tertiary creep and the initial stages of localization can be seen as early as the start of the secondary creep phase, both of which have been previously observed in experiments. Stress relaxation simulations demonstrate that the total amount of stress relaxation increases when the level of constant axial strain increases, also corroborating with previously published experimental data. Our approach differs from previously adopted macroscopic approaches, based on constitutive laws, and microscopic approaches that focus on fracture propagation. The model shows that complex macroscopic time-dependent behaviour can be explained by the small-scale interaction of elements and material degradation. The fact that the simulations are able to capture a similar time-dependent response of heterogeneous brittle rocks to that seen in the laboratory implies that the model is appropriate to investigate the non-linear complicated time-dependent behaviour of heterogeneous brittle rocks.

Virtual melting as a new mechanism of stress relaxation under high strain rate loading

Abstract: Generation and motion of dislocations and twinning are the main mechanisms of plastic deformation. A new mechanism of plastic deformation and stress relaxation at high strain rates (10(9)-10(12) s(-1)) is proposed, under which virtual melting occurs at temperatures much below the melting temperature. Virtual melting is predicted using a developed, advanced thermodynamic approach and confirmed by large-scale molecular dynamics simulations of shockwave propagation and quasi-isentropic compression in both single and defective crystals. The work and energy of nonhydrostatic stresses at the shock front drastically increase the driving force for melting from the uniaxially compressed solid state, reducing the melting temperature by 80% or 4,000 K. After melting, the relaxation of nonhydrostatic stresses leads to an undercooled and unstable liquid, which recrystallizes in picosecond time scales to a hydrostatically loaded crystal. Characteristic parameters for virtual melting are determined from molecular dynamics simulations of Cu shocked/compressed along the 〈110〉 and 〈111〉 directions and Al shocked/compressed along the 〈110〉 direction.

Thermal relaxation of residual stress in laser shock peened Ti–6Al–4V alloy

Abstract: Laser shock peening (LSP) induced residual stresses in Ti–6Al–4V, and their thermal relaxation due to short-term exposure at elevated temperatures are investigated by an integrated modeling/simulation and experimental approach. A rate and temperature-dependent plasticity model in the form of Johnson–Cook (JC) has been employed to represent the nonlinear constitutive behavior under both LSP and thermal loads. By comparing the simulation results with experimental data, model parameters for Ti–6Al–4V are first calibrated and subsequently applied in analyzing the thermal stability of the residual stress in LSP-treated Ti–6Al–4V. The analysis shows that the magnitude of stress relaxation increases with the increase of applied temperature due to material softening. Most of stress relaxation occurs before 10 min to 20 min exposure in this study, and stress distribution becomes more uniform after thermal exposure. An analytical model based on the Zener–Wert–Avrami formula is then developed based on the simulation results. The activation enthalpy of the relaxation process for laser shock peened Ti–6Al–4V is determined to be in the range of 0.71 eV to 1.37 eV.

Nanoindentation creep of tin and aluminium: A comparative study between constant load and constant strain rate methods

Abstract: Creep properties of polycrystalline Tin (Sn) and single crystal Aluminium (Al) were studied by two nanoindentation methods, i.e., constant load (CL) test and constant strain rate (CSR) test. The indentation strain rate and stress were calculated as the analogies drawn from uniaxial creep analysis. The stress exponent was expressed as the slope of the strain rate–stress curves plotted in the double logarithm scale. Between the two testing methods, the CSR test was clearly shown to be able to detect the creep of Sn in the power-law region, where the grain size had little effect on the creep rate. However, it was found that steady-state creep could not be achieved in the CL test. This has imposed ambiguities in applying the creep analysis developed from conventional creep scheme. The creep displacement from CL test was found unrepeatable for multiple measurements. CL test also has a smaller accessible stress range than that from a CSR test. The gradual variation of the stress exponents, especially for the small grain Sn sample, during holding process in the CL test could be due to the participation of the other rate controlling mechanisms which were closely related to the non-steady-state creep behaviour.

Improved algorithm for efficient and realistic creep analysis of large creep-sensitive concrete structures

Abstract: Recent compilation of data on numerous large-span prestressed segmentally erected box girder bridges revealed gross underestimation of their multi-decade deflections. The main cause has been identified as incorrect and obsolete creep prediction models in various existing standard recommendations and is being addressed in a separate study. However, previous analyses of the excessive deflections of the Koror-Babeldaob (KB) Bridge in Palau and of four Japanese bridges have shown that a more accurate method of multi-decade creep analysis is required. The objective of this paper is to provide a systematic and comprehensive presentation, appropriate not only for bridges but also for any large creep-sensitive structure. For each time step, the solution is reduced to an elastic structural analysis with generally orthotropic elastic moduli and eigenstrains. This analysis should normally be three-dimensional (3-D). It can be accomplished with a commercial finite element code such as ABAQUS. Based on the Kelvin chain model, the integral-type creep law is converted to a rate-type form with internal variables, which account for the previous history. For time steps short enough to render aging during each step to be negligible, a unique continuous retardation spectrum for each step is obtained by Laplace transform inversion using simple Widder's formula. Discretization of the spectrum then yields the current Kelvin chain moduli. The rate-type creep analysis is computationally more efficient than the classical integral-type analysis. More importantly, though, it makes it possible to take into account the evolution of various inelastic and nonlinear phenomena such as tensile cracking, cyclic creep, and stress relaxation in prestressing tendons at variable strain, as well as the effects of humidity and temperature variations, and the effect of wall thickness variation on drying creep and shrinkage. Finally, the advantages compared to the existing commercial programs, based on step-by-step integration of memory integrals, are pointed out and illustrated by a simple example.

Inhomogeneous shear flows in soft jammed materials with tunable attractive forces.

Abstract: We perform molecular dynamics simulations to characterize the occurrence of inhomogeneous shear flows in soft jammed materials. We use rough walls to impose a simple shear flow and study the athermal motion of jammed assemblies of soft particles in two spatial dimensions, both for purely repulsive interactions and in the presence of an additional short-range attraction of varying strength. In steady state, pronounced flow inhomogeneities emerge for all systems when the shear rate becomes small. Deviations from linear flow are stronger in magnitude and become very long lived when the strength of the attraction increases, but differ from permanent shear bands. Flow inhomogeneities occur in a stress window bounded by the dynamic and static yield stress values. Attractive forces enhance the flow heterogeneities because they accelerate stress relaxation, thus effectively moving the system closer to the yield stress regime where inhomogeneities are most pronounced. The present scenario for understanding the effect of particle adhesion on shear localization, which is based on detailed molecular dynamics simulations with realistic particle interactions, differs qualitatively from previous qualitative explanations and ad hoc theoretical modeling.

Geomechanical modeling of stresses adjacent to salt bodies: Part 1—Uncoupled models

Abstract: We compare four approaches to geomechanical modeling of stresses adjacent to salt bodies. These approaches are distinguished by their use of elastic or elastoplastic constitutive laws for sediments surrounding the salt, as well as their treatment of fluid pressures in modeling. We simulate total stress in an elastic medium and then subtract an assumed pore pressure after calculations are complete; simulate effective stress in an elastic medium and use assumed pore pressure during calculations; simulate total stress in an elastoplastic medium, either ignoring pore pressure or approximating its effects by decreasing the internal friction angle; and simulate effective stress in an elastoplastic medium and use assumed pore pressure during calculations. To evaluate these approaches, we compare stresses generated by viscoelastic stress relaxation of a salt sphere. In all cases, relaxation causes the salt sphere to shorten vertically and expand laterally, producing extensional strains above and below the sphere and shortening against the sphere flanks. Deviatoric stresses are highest when sediments are assumed to be elastic, whereas plastic yielding in elastoplastic models places an upper limit on deviatoric stresses that the rocks can support, so stress perturbations are smaller. These comparisons provide insights into stresses around salt bodies and give geoscientists a basis for evaluating and comparing stress predictions.

Creep deformation and rupture behaviour of 9Cr–1W–0.2V–0.06Ta Reduced Activation Ferritic–Martensitic steel

Abstract: This paper presents the creep deformation and rupture behaviour of indigenously produced 9Cr–1W–0.2V–0.06Ta Reduced Activation Ferritic–Martensitic (RAFM) steel for fusion reactor application. Creep studies were carried out at 773, 823 and 873 K over a stress range of 100–300 MPa. The creep deformation of the steel was found to proceed with relatively shorter primary regime followed by an extended tertiary regime with virtually no secondary regime. The variation of minimum creep rate of the material with applied stress followed a power law relation, έ m = Aσ n , with stress exponent value ‘ n ’ decreasing with increase in temperature. The product of minimum creep rate and creep rupture life was found to obey the modified Monkman–Grant relation. The time to onset of tertiary stage of deformation was directly proportional to rupture life. TEM studies revealed relatively large changes in martensitic sub-structure and coarsening of precipitates in the steel on creep exposure as compared to thermal exposure. Microstructural degradation was considered as the prime cause of extended tertiary stage of creep deformation, which was also reflected in the damage tolerance factor λ with a value more than 2.5. In view of the microstructural instability of the material on creep exposure, the variation of minimum creep rate with stress and temperature did not obey Dorn's equation modified by invoking Lagneborg and Bergman's concepts of back stress.

Cyclic deformation behavior of a super-vacuum die cast magnesium alloy

Abstract: Magnesium alloy as a lightweight structural material has recently kindled considerable interest in the automotive and aerospace industries, since lightweighting is considered as one of the salient strategies in reducing fuel consumption and anthropogenic greenhouse gas emissions. The structural applications of magnesium alloys inevitably involve fatigue resistance. This study was aimed at evaluating cyclic deformation behavior and fatigue life of a super-vacuum die cast (SVDC) AM60B alloy using strain-controlled low cycle fatigue tests at two strain ratios of R s = −1 and R s = 0.1. The SVDC AM60B alloy exhibited a superior fatigue resistance to the conventional die cast AM60 alloy especially in the high-cycle fatigue region. Fatigue life was longer at R s = −1 than at R s = 0.1 at lower strain amplitudes. With increasing total strain amplitude, cyclic stress amplitudes increased, hysteresis loops exhibited a clockwise rotation despite the symmetry in tension and compression at R s = −1, and fatigue life and psuedoelastic modulus decreased at both strain ratios. Cyclic hardening increased with increasing strain amplitude and strain ratio due to the formation of more twins and their interaction with dislocations. Two types of twins (wider lenticular extension twins and narrower banded contraction twins) were observed in some favorably oriented large α-Mg cells near the fracture surface. Mean stress relaxation occurred mainly within the initial 10–30% of fatigue life. Cyclic hardening exponent was higher than monotonic hardening exponent. Fatigue crack initiation occurred from the specimen surface or near-surface defects, and crack propagation was mainly characterized by fatigue striations coupled with some secondary cracks and tear ridges.

Stress Relaxation via Addition–Fragmentation Chain Transfer in High Tg, High Conversion Methacrylate-Based Systems

Abstract: To reduce shrinkage stress which arises during the polymerization of cross-linked polymers, allyl sulfide functional groups were incorporated into methacrylate polymerizations to determine their effect on stress relaxation via addition–fragmentation chain transfer (AFCT). Additionally, stoichiometrically balanced thiol and allyl sulfide-containing norbornene monomers were incorporated into the methacrylate resin to maximize the overall functional group conversion and promote AFCT while also enhancing the polymer’s mechanical properties. Shrinkage stress and reaction kinetics for each of the various functional groups were measured by tensometry and Fourier-transform infrared (FTIR) spectroscopy, respectively. The glass transition temperature (Tg) and elastic moduli (E′) were measured using dynamic mechanical analysis. When the allyl sulfide functional group was incorporated into dimethacrylates, the polymerization-induced shrinkage stress was not relieved as compared with analogous propyl sulfide-containin...

Reentanglement Kinetics of Freeze-Dried Polymers above the Glass Transition Temperature

Abstract: Rheology experiments were performed to monitoring the kinetics of the entanglement recovery process of freeze-dried polystyrene. Complete reentanglement time requires unexpected long time, which does not monotonically reduce with the concentration of precursor solution. The entanglement recovery was treated as the complementary process of stress relaxation in Doi–Edwards model and was found to agree well with the exponential law. We clarified that freeze-drying is an effective way to achieve disentanglement for polymer chains. The correlation between recovery time and the concentration of precursor solution is in good agreement with previous results from molecular dynamics (MD) simulations.

Resistance to dynamic deformation and fracture of tantalum with different grain and defect structures

Abstract: This paper presents the results of measurements of the strength properties of technically pure tantalum under shock wave loading. It has been found that a decrease in the grain size under severe plastic deformation leads to an increase in the hardness of the material by approximately 25%, but the experimentally measured values of the dynamic yield stress for the fine-grained material prove to be less than those of the initial coarse-grained specimens. This effect has been explained by a higher rate of stress relaxation in the fine-grained material. The hardening of tantalum under shock wave loading at a pressure in the range 40–100 GPa leads to a further increase in the rate of stress relaxation, a decrease in the dynamic yield stress, and the disappearance of the difference between its values for the coarse-grained and fine-grained materials. The spall strength of tantalum increases by approximately 5% with a decrease in the grain size and remains unchanged after the shock wave loading. The maximum fracture stresses are observed in tantalum single crystals.