Showing papers on "Stress relaxation published in 2008"

Unexpected power-law stress relaxation of entangled ring polymers.

Abstract: After many years of intense research, most aspects of the motion of entangled polymers have been understood. Long linear and branched polymers have a characteristic entanglement plateau and their stress relaxes by chain reptation or branch retraction, respectively. In both mechanisms, the presence of chain ends is essential. But how do entangled polymers without ends relax their stress? Using properly purified high-molar-mass ring polymers, we demonstrate that these materials exhibit self-similar dynamics, yielding a power-law stress relaxation. However, trace amounts of linear chains at a concentration almost two decades below their overlap cause an enhanced mechanical response. An entanglement plateau is recovered at higher concentrations of linear chains. These results constitute an important step towards solving an outstanding problem of polymer science and are useful for manipulating properties of materials ranging from DNA to polycarbonate. They also provide possible directions for tuning the rheology of entangled polymers.

A thermoviscoelastic model for amorphous shape memory polymers: Incorporating structural and stress relaxation

Abstract: A thermoviscoelastic constitutive model is developed for amorphous shape memory polymers (SMP) based on the hypothesis that structural and stress relaxation are the primary molecular mechanisms of the shape memory effect and its time-dependence. This work represents a new and fundamentally different approach to modeling amorphous SMPs. A principal feature of the constitutive model is the incorporation of the nonlinear Adam–Gibbs model of structural relaxation and a modified Eyring model of viscous flow into a continuum finite–deformation thermoviscoelastic framework. Comparisons with experiments show that the model can reproduce the strain–temperature response, the temperature and strain-rate dependent stress–strain response, and important features of the temperature dependence of the shape memory response. Because the model includes structural relaxation, the shape memory response also exhibits a dependence on the cooling and heating rates.

Microstructure and mechanical properties of Cu–Ni–Si alloys

Abstract: The microstructure and mechanical properties of 0.1 wt.% Mg-added and Mg-free Cu–2.0 wt.% Ni–0.5 wt.% Si alloys aged at 400 °C have been examined. The addition of Mg promotes the formation of disk-shaped Ni2Si precipitates. The Cu–Ni–Si–Mg alloy exhibits higher strength and resistance to stress relaxation than the Cu–Ni–Si alloy. The higher strength or stress relaxation resistance is attributable to the reduction in inter-precipitate spacing by the Mg addition or the drag effect of Mg atoms on dislocation motion. The Cu–Ni–Si alloy with a large grain size of 150 μm shows higher stress relaxation resistance than the alloy with a small grain size of 10 μm because of a lower density of mobile dislocations in the former alloy.

Synthesis and strain relaxation of Ge-core/Si-shell nanowire arrays.

Abstract: Analogous to planar heteroepitaxy, misfit dislocation formation and stress-driven surface roughening can relax coherency strains in misfitting core-shell nanowires. The effects of coaxial dimensions on strain relaxation in aligned arrays of Ge-core/Si-shell nanowires are analyzed quantitatively by transmission electron microscopy and synchrotron X-ray diffraction. Relating these results to reported continuum elasticity models for coaxial nanowire heterostructures provides valuable insights into the observed interplay of roughening and dislocation-mediated strain relaxation.

Effect of low-temperature rolling on the tensile behavior of commercially pure tungsten

Abstract: We have evaluated the tensile behavior of commercially pure tungsten (W) as a function of low-temperature rolling. It is observed that rolling below the nominal recrystallization temperature 1523 K (1250 °C) concomitantly enhances the ductility and strength of W. Strain-rate jump tests and stress-relaxation experiments show that low-temperature rolling also renders reduced strain-rate sensitivity and activation volumes associated with the plastic deformation of W. For W samples rolled at 873 K (600 °C), with a total equivalent strain of ∼2.5 (including a previous rolling strain of 1.7 introduced at 1073 K [800 °C]), the activation volume for plastic deformation is around 10b3 (b is the magnitude of the Burgers vector of W). This is in agreement with a double-kink mechanism with the spreading between the kinks controlled by the forest dislocation density. Fractographic observations indicate that the rolled W exhibits a laminar structure. The layer thickness is a function of rolling temperature, rather than a function of rolling strain introduced.

Non-volcanic tremor resulting from the combined effect of Earth tides and slow slip events

Abstract: Swarms of non-volcanic tremor in southeastern Japan are associated with slow slip events and tend to occur with a periodicity of 12 or 24 h. This periodicity can be reproduced by a combination of stresses due to Earth tides and transient stress changes caused by slow slip events. Non-volcanic tremors may therefore be useful for understanding stress relaxation at the subduction-zone interface. Slow slip events1 are accompanied by swarms of non-volcanic tremor2,3 along the subduction zone of the Philippine Sea plate in southwest Japan: the swarms often occur with a periodicity of about 12 or 24 h (refs 4, 5). These episodic events are considered to be a manifestation of stress relaxation at the subducting plate interface1,6,7. Here, we analyse seismic data to record the locations and durations of non-volcanic tremor swarms that occurred in May 2005 and February 2006. We evaluate the magnitude of stress changes produced by slow slip events as well as the effective normal stress on the plate interface where slow slip events occur. We find that the observed periodicity in tremor occurrence originates from a combined effect of the periodic stress due to Earth tides and the transient stress due to slow slip events. Our calculations show that non-volcanic tremor is sensitive to stress change. This phenomenon can therefore be effective in monitoring the process of stress relaxation at subducting plate interfaces.

Whisker formation in Sn and Pb–Sn coatings: Role of intermetallic growth, stress evolution, and plastic deformation processes

Abstract: We have simultaneously measured the evolution of intermetallic volume, stress, and whisker density in Sn and Pb–Sn alloy layers on Cu to study the fundamental mechanisms controlling whisker formation. For pure Sn, the stress becomes increasingly compressive and then saturates, corresponding to a plastically deformed region spreading away from the growing intermetallic particles. Whisker nucleation begins after the stress saturates. Pb–Sn layers have similar intermetallic growth kinetics but the resulting stress and whisker density are much less. Measurements after sputtering demonstrate the important role of the surface oxide in inhibiting stress relaxation.

Mechanical properties of Cu–Cr system alloys with and without Zr and Ag

Abstract: The effects of addition of Zr and Ag on the mechanical properties of a Cu–0.5 wt%Cr alloy have been investigated. The addition of 0.15 wt%Zr enhances the strength and resistance to stress relaxation of the Cu–Cr alloy. The increase in strength is caused by both the decrease in inter-precipitate spacing of Cr precipitates and the precipitation of Cu5Zr phase. The stress relaxation resistance is improved by the preferentially forming Cu5Zr precipitates on dislocations, in addition to Cr precipitates on dislocations. The addition of 0.1 wt%Ag to the Cu–Cr and Cu–Cr–Zr alloys improves the strength, stress relaxation resistance and bend formability of these alloys. The increase in strength and stress relaxation resistance is ascribed to the decrease in inter-precipitate spacing of Cr precipitates and the suppression of recovery during aging, and to the Ag-atom-drag effect on dislocation motion. The better bend formability of the Ag-added alloys is explained in terms of the larger post-uniform elongation of the alloys.

Fractional-order viscoelasticity applied to describe uniaxial stress relaxation of human arteries.

Abstract: Viscoelastic models can be used to better understand arterial wall mechanics in physiological and pathological conditions. The arterial wall reveals very slow time-dependent decays in uniaxial stress-relaxation experiments, coherent with weak power-law functions. Quasi-linear viscoelastic (QLV) theory was successfully applied to modeling such responses, but an accurate estimation of the reduced relaxation function parameters can be very difficult. In this work, an alternative relaxation function based on fractional calculus theory is proposed to describe stress relaxation experiments in strips cut from healthy human aortas. Stress relaxation (1 h) was registered at three incremental stress levels. The novel relaxation function with three parameters was integrated into the QLV theory to fit experimental data. It was based in a modified Voigt model, including a fractional element of order alpha, called spring-pot. The stress-relaxation prediction was accurate and fast. Sensitivity plots for each parameter presented a minimum near their optimal values. Least-squares errors remained below 2%. Values of order alpha = 0.1-0.3 confirmed a predominant elastic behavior. The other two parameters of the model can be associated to elastic and viscous constants that explain the time course of the observed relaxation function. The fractional-order model integrated into the QLV theory proved to capture the essential features of the arterial wall mechanical response.

The nonlinear mechanical response of the red blood cell.

Abstract: We measure the dynamical mechanical properties of human red blood cells. A single cell response is measured with optical tweezers. We investigate both the stress relaxation following a fast deformation and the effect of varying the strain rate. We find a power-law decay of the stress as a function of time, down to a plateau stress, and a power-law increase of the cell's elasticity as a function of the strain rate. Interestingly, the exponents of these quantities violate the linear superposition principle, indicating a nonlinear response. We propose that this is due to the breaking of a fraction of the crosslinks during the deformation process. The soft glassy rheology model accounts for the relation between the exponents we observe experimentally. This picture is consistent with recent models of bond remodeling in the red blood cell's molecular structure. Our results imply that the blood cell's mechanical behavior depends critically on the deformation process.

Investigating load relaxation mechanics in tendon

Abstract: Tendons are hierarchical fibre composite materials, designed for the efficient transfer of force from muscles to the skeleton. As such, they exhibit high tensile strength, as well as complex viscoelastic and anisotropic characteristics. Although the viscoelastic behaviour has received considerable attention, the mechanisms by which the tendon structure facilitates this behaviour are less well understood. This study examines viscoelasticity within isolated tendon fascicles, using stress relaxation tests to examine how the matrix acts to dissipate load during the relaxation period. The fascicle behaviour during incremental and direct load relaxation tests was examined, using mechanical testing and confocal microscopy to assess the load and structural responses of the tendon, respectively. Results provide further evidence of the highly viscoelastic nature of tendon, and also demonstrate that relaxation behaviour within isolated tendon fascicles is dominated by fibre sliding mechanisms. These data indicate an important functional role for proteoglycans, in controlling the viscoelastic behaviour and the mechanisms of strain transfer within tendon.

Mechanics of grain-size reduction in fault zones

Abstract: [1] Recent observations of nanometer-scale particles in the cores of exhumed fault zones raise questions about how such small particles are formed and how they survive, especially if significant shear heating is produced during an earthquake. Commercial crushing and grinding operations encounter a grind limit near 1 mm below which particles deform plastically rather than fracturing. A fragmentation model and low-temperature plasticity mechanics indicate that it is not possible to produce under compressive loading and short timescale significantly smaller particles at any strain rate. However, shock loading and subcritical crack growth can produce nanometer-scale fragments in compression. Under tensile loading the fragment size is determined by a competition between the nucleation of cracks and stress relaxation in their neighborhoods. Therefore higher tensile strain rates produce smaller fragments. The ultimate limit is determined by the availability of elastic strain energy, which does not place a significant constraint on the minimum grain size. Grain growth kinetics suggests that survivability of grains is very temperature sensitive. A 10 nm quartz fragment will double its size in 0.1 s at 1000C, in 20 s at 800C, in 14 h at 600C, and in 10 years at 400C. The observation of grains smaller than 10 nm places meaningful constraints on the dynamic fields and permeability of the fault zone during a large earthquake. Microstructural analysis of the grains and rock damage may be used to infer whether fragmentation occurred under macroscopic tension or compression.

Constitutive framework for biodegradable polymers with applications to biodegradable stents.

Abstract: Biodegradable polymeric stents must provide mechanical support of the stenotic artery wall up to several months while being subjected to cyclic loading that affects the degradation process. To understand the applicability and efficacy of biodegradable polymers, a two-pronged approach involving experiments and theory is necessary. This article addresses the second aspect, the development of a theoretical framework within which the behavior of such materials can be studied. We present a constitutive model for polymers that undergo deformation induced-degradation. For our purpose, degradation is the scission of chemical bonds of the backbone chain, results in molecular weight reduction, and consequently in the commonly observed softening. A model of a solid capable of degradation, which in its absence responds like an elastic solid, is developed. We assume the existence of a scalar field that reflects the local state of degradation and changes the properties of the material. A rate equation for the measure of degradation that depends on strain is coupled with the balance of linear momentum. Uniaxial extension of a body, which in the absence of degradation behaves as a neo-Hookean elastic solid, exhibits stress relaxation, creep, and hysteresis, due to degradation.

Constitutive modeling of solid propellant materials with evolving microstructural damage

Abstract: Solid propellants are composite materials with complex microstructure. In a generic form, the material consists of polymeric binder, crystal oxidizer (e.g., ammonium perchlorate), and fuel particles (e.g., aluminum). Severe stressing and extreme temperatures induce damage which is manifested in particle cracking, dewetting along particle/polymer interfaces, void nucleation and growth. Damage complicates the overall constitutive response of a solid propellant over and above the complexities associated with the differing constitutive properties of the particle and binder phases. Using rigorous homogenization theory for composite materials, we propose a general 3-D nonlinear macroscopic constitutive law that models microstructural damage evolution upon straining through continuous void formation and growth. The law addresses the viscous deformation rate within the framework of additive decomposition of the deformation rate and the concept of back stress is used to improve the model performance in stress relaxation. No restriction is placed on the magnitude of the strains. Experimental data from the standard relaxation and uniaxial tension tests are used to calibrate the model parameters in the case of a high elongation solid propellant. It is emphasized that the model parameters are descriptors of individual phase constitutive response and criticality conditions for particle decohesion which can systematically be determined through experiment. The model is used to predict the response of the material under more complex loading paths and to investigate the effect of crack tip damage on the mechanical behavior of a compact tension fracture specimen.

Plastic behavior of some yield stress fluids: from creep to long-time yield

Abstract: The yielding of several reversible yield stress fluids is studied during scissometric-like creep experiments. The temporal evolution of the apparent deformation is recorded for applied stresses close and below the usual yield stress. Similarly to solids, three main creep regimes are observed. First, a primary creep regime displaying a temporal power law evolution of the deformation rate occurs, followed by a temporal minimum, which leads to an apparent flow of the material. This local minimum, defined as the “transition time,” and the subsequent fluidization can be observed at long times. The evolution of this time as a function of the applied stress appears to follow a universal law reminiscent of fracture behavior in hard solids.

Laboratory study of the frictional rheology of sheared till

Abstract: [1] Deformation of till produces power law creep for low strain at stresses high enough to cause permanent deformation but below the shear strength. Experiments were conducted on till (a mixed size granular material) from Matanuska Glacier, Alaska, and the Scioto (Ohio) Lobe of the Laurentide Ice Sheet (Caesar till). We deformed till in double direct shear under fixed shear velocity or shear stress (creep). Normal stress ranged from 50 kPa to 5 MPa at shearing rates ranging from 1 to 300 μm/s for 1 cm thick samples. Creep was induced via small step perturbations in stress. Fabric development within till layers was investigated by varying shear strain prior to creep tests. In velocity-controlled experiments, till deforms as a nearly Coulomb plastic material with slight velocity strengthening, corresponding to a stress exponent, n > 60. Creep experiments conducted well below the shear strength indicate lower n values, increasing as shear stress increases. With increasing initial strain and inferred fabric development, the creep strain rate decreases while n increases. Experiments at a normal stress of 1 MPa and no initial strain show n = 6.8, increasing to n = 17.5 at higher shear strains; however, strain rate was still decreasing and thus these values represent maximum estimates. Our data show that in the absence of dilatant hardening till exhibits rate sensitivity at strain of order 1 or less. At low strains, n likely depends on consolidation state, permeability, and dilation. Deformation is nearly rate insensitive (Coulomb plastic) at shear stress near the shear strength or at high strain.

In situ stress evolution during magnetron sputtering of transition metal nitride thin films

Abstract: Stress evolution during reactive magnetron sputtering of TiN, ZrN, and TiZrN layers was studied using real-time wafer curvature measurements. The presence of stress gradients is revealed, as the result of two kinetically competing stress generation mechanisms: atomic peening effect, inducing compressive stress, and void formation, leading to a tensile stress regime predominant at higher film thickness. No stress relaxation is detected during growth interrupt in both regimes. A change from compressive to tensile stress is evidenced with increasing film thickness, Ti content, sputtering pressure, and decreasing bias voltage.

A time and hydration dependent viscoplastic model for polyelectrolyte membranes in fuel cells

Abstract: Ionomers are co-polymers with ionic groups. One of the interesting applications of ionomer membranes is as electrolytes in proton exchange membrane (PEM) fuel cells. The most commonly used membranes in PEM fuel cells are perfluorosulfonic acid (PFSA) membranes, e.g., Nafion® from DuPontTM. Besides its dependency on temperature and hydration due to phase inversion and cluster formation, Nafion® as a polymer, exhibits strong time and rate effects. In this work, the stress–strain behavior of Nafion® at different strain rates has been obtained in an environmental chamber for various temperatures and hydrations. After a certain strain was reached in each test, stress relaxation was performed for an hour to observe the relaxation behavior of Nafion®. We attempted to use a nonlinear, time-dependent constitutive model to predict the hygro-thermomechanical behavior of Nafion®. Because a substantial component of the response is unrecoverable, a viscoplastic model was employed. The proposed two-layer viscoplasticity model consisted of an elastoplastic network that was in parallel with an elastic-viscous network (Maxwell model) which separates the rate-dependent and rate-independent behavior of the material. After obtaining the necessary parameters for different hydrations, this model showed reasonably accurate success in predicting the stress–strain behavior at different strain rates, and matched the relaxation test results. Finite element simulations based on the proposed two-layer viscoplasticity model were in good agreement with test results and can be used to study the stress–strain state of the ionomer membranes in fuel cell configurations.

Effect of strain rate on properties of superelastic NiTi thin wires

Abstract: This study deals with the effect of strain rate on tensile and energy absorbing properties of superelastic NiTi thin wires. It also attempts to gain an understanding of the interplay of the ductile behavior, temperature and strain rate effects, energy storage and cycling. The wires are in austenite condition at room temperature and above. The strain rates imposed during testing range from 0.2 to 180%/min (i.e., 0.06x2013;54 mm/min) corresponding to a frequency of 2.77 xD7; 10x2212;4 to 0.25 Hz for strain amplitudes of 6%. The corresponding frequency for 8% strain amplitude is 2.08 xD7; 10x2212;4 to 0.18 Hz. It is shown that NiTi SMAs exhibit ductility at both low and high strain rates. This is also true for the cold worked and heat treated conditions both below Mf and above Af. During tensile testing the stress-induced martensite (SIM) plateau increases in length and translates upwards with increase in strain rate up to a certain value. Similarly, the onset of elastic yield stress also increases with strain rate. At high strain rates the SIM segment and elastically deformed SIM segment overlap. The SIM formation is not able to cope with the externally imposed higher strain rates. This is also the reason for the reduction of hysteresis loop at the high strain rates as observed in the cyclic tests.13; The dissipated strain energy density (Ed) increases with increasing strain rate up to a certain value beyond which the Ed decreases. It is clear that the mean point of the superelastic loop shifts to the right and upwards (higher stress and higher strain region) for cyclic testing with increase in strain rates. However, it shifts to the right and downwards (lower stress/higher strain regime) for both the 6 and 8% strain amplitude cycling at constant strain rate. The stabilization of residual strain and Ed is based on the same underlying mechanism relating to SIM formation and occurs at the same numbers of cycles.