Showing papers on "Stress relaxation published in 1987"

Linear Viscoelasticity at the Gel Point of a Crosslinking PDMS with Imbalanced Stoichiometry

Abstract: The evolution of linear viscoelasticity during cross‐linking of a stoichiometrically imbalanced polydimethylsiloxane (PDMS) was measured by small amplitude oscillatory shear. At the gel point (GP), stress relaxation was found to follow a power law, St−n, as described by the previously suggested gel equation. However, while stoichiometrically balanced gels (PDMS, polyurethanes) gave the specific exponent value of n=1/2, a higher exponent value, 1/2 Gv′(ω), and a higher rate of stress relaxation. GP was found to occur before the crossover point of the loss and storage moduli, G″(ω0,t), and G′(ω0,t), as measured during the cross‐linking reaction (reaction time, t) at constant frequency, ω0. This suggests new met...

Relaxation of strained-layer semiconductor structures via plastic flow

Abstract: An outstanding puzzle concerning strained‐layer semiconductors is that metastable structures can be grown in which exact coherence with the lattice is apparently conserved in layers much thicker than the equilibrium critical thickness. Using standard descriptions of dislocation dynamics and relaxation via plastic flow, a model for the relaxation of an initially coherent metastable strained layer is developed. This model is applied to relief of mismatch strain in the SiGe/Si(100) system, and good agreement with experimental data is found. Furthermore, the combined effect of relaxation kinetics and finite instrumental resolution on the observed critical thickness was calculated. The results successfully reproduce experimental data on metastable critical thickness in the SiGe/Si(100) system.

Critical stresses for SixGe

Abstract: We have measured the temperature-dependent onset of strain relief in metastable Si/sub x/Ge/sub 1-//sub x/ strained layers grown on Ge substrates. On the basis of these measurements, and physical arguments, we propose that strained-layer breakdown is most directly determined not by thickness and lattice mismatch, but rather by (1) an ''excess'' stress (the difference between that due to misfit strain and that due to dislocation line tension) and (2) temperature. With use of these parameters, observed regimes of stability and metastability are shown to be described within a simple, unified framework.

Stress Buildup and Relaxation During Ion Exchange Strengthening of Glass

Abstract: A soda-lime-silica glass was subjected to an ordinary ion exchange treatment in molten potassium nitrate at temperatures near and substantially below the strain point of the glass. Stress profiles were measured as a function of exchange temperature and time. At all temperatures, the measurements showed rapid relaxation of the surface stress and the development of a pronounced compression maximum in a short period. A simple viscoelastic model with composition-independent parameters was used to analyze the stress profiles. Neither Maxwell's nor Michelson's relaxation expression could satisfy both characteristics of the residual stress development. Reasons for discrepancies are discussed.

Wall relaxation and the driving forces for cell expansive growth.

Abstract: When water uptake by growing cells is prevented, the turgor pressure and the tensile stress in the cell wall are reduced by continued wall loosening. This process, termed in vivo stress relaxation, provides a new way to study the dynamics of wall loosening and to measure the wall yield threshold and the physiological wall extensibility. Stress relaxation experiments indicate that wall stress supplies the mechanical driving force for wall yielding. Cell expansion also requires water absorption. The driving force for water uptake during growth is created by wall relaxation, which lowers the water potential of the expanding cells. New techniques for measuring this driving force show that it is smaller than believed previously; in elongating stems it is only 0.3 to 0.5 bar. This means that the hydraulic resistance of the water transport pathway is small and that rate of cell expansion is controlled primarily by wall loosening and yielding.

Models of viscoplasticity some comments on equilibrium (back) stress and drag stress

Abstract: Phenomenological and microstructural motivations for the terms appearing in the title are found in a literature survey. Although the interpretations differ with various investigators a strong tendency is observed to consider plastic flow as rate dependent. It is stated that plastic strain takes time to develop and the existnce of an equilibrium stress is postulated at which plastic strain is fully developed. It is similar to the back stress used in materials science. The drag stress introduced from microdynamical studies performs the same function as the isotropic variable in plasticity. Most of the theories that describe the transient and steady-state behavior of metallic alloys make the inelastic strain rate a function of the over (effective) stress. It is shown that this concept has considerable advantages in the modeling of changes of viscous (time- or rate-dependent) and plastic (time- or rate-independent) contributions to hardening that are observed in cyclic loading and dynamic plasticity.

Evolution of rheology during chemical gelation

Abstract: Rheology is a sensitive measure of the evolving molecular structure in a crosslinking polymer. Dynamic mechanical experiments in small amplitude oscillatory shear give the storage modulus G′(ω, p) and the loss modulus G″(ω, p) as a function of frequency ω. The extent of crosslinking, p(t), changes with reaction time. Dynamic mechanical experiments allow detection of the gel point (GP) and give a macroscopic description of the critical gel state (network polymer at GP). This critical gel state is used as a reference for describing the entire evolution of rheology. The most surprising discovery of these experiments was that critical gels exhibit stress relaxation in a power law, i. e. the relaxation modulus is given as G()=St −n. The relaxation exponent, n, depends on network structure. The power law behavior is an expression of mechanical self similarity (fractal behavior). The range of self similarity is defined between an upper and a lower frequency limit. The lower frequency limit (reciprocal of characteristic relaxation time) corresponds to an upper scaling length, the correlation length, which is of the order of the linear size of the largest molecular cluster (of pre-gel) or of the largest remaining percolation cluster (of post-gel). High frequencies probe relaxation within single chains. The upper frequency limit corresponds to a lower scaling length, the glass length, which is given by the dimension of the molecular network units responsible for glassy behavior. The correlation length and, hence, the characteristic relaxation time increase in the approach of the gel point, diverge to infinity at the gel point, and then decrease again with increasing extent of crosslinking. The critical gel has no characteristic length or time scale. All observations are restricted to polymers at a temperature above the glass transition temperature and at frequencies much below the glass frequency.

A model for finite-deformation plasticity

Abstract: We propose a new large deformation viscoplastic model which includes the effects of static and dynamic recovery in its strain rate response as well as the plastic spin in its rotational response. The model is directly obtained from single slip dislocation considerations with the aid of a maximization procedure and a scale invariance argument. It turns out that the evolution of the back stress and the expression for the plastic spin are coupled within the structure of the theory. The model is used for the prediction of nonstandard effects in torsion, namely the development of axial stress and strain as well as the directional softening of the shear stress. The comparisons between the present continuum model and both experiments and self-consistent polycrystalline calculations are very encouraging.

Experimental study of strain-rate dependence and pressure dependence of failure properties of granite

Abstract: Effects of the strain rate and pressure on various brittle properties of granite under compressional loading are studied experimentally. Granite specimens were tested to failure under various constant strain rates at confining pressures of 0.1 to 200 MPa. The strain rates in these tests varied from 10-4 to 10-8s-1. The results show that the strength of granite decreases linearly as the logarithm of the strain rate decreases, and that the strain-rate dependence on the strength is enhanced at high confining pressures. The dilatant strain and elastic wave velocity variations with stress were found to be independent of the strain rate if the stress is normalized by the strength. The dilatant-strain-versus-stress curve is significantly affected by confining pressure but the confining pressure effect on the dilatant strain versus normalized stress is small. The acoustic emission rate is accelerated at a stress level closer to the failure strength as the strain rate decreases. Some of the timedependent properties are explained by a theory based on the concept of subcritical stress-corrosion cracking. But it is also clear that the stress-corrosion cracking theory does not provide reasonable explanations of the variation of acoustic emission rate with stress and the variation of strain with stress at the stage immediately before fracture.

Creep and Stress Relaxation in Solder Joints of Surface-Mounted Chip Carriers

Abstract: When a surface-mounted ceramic chip carrier is subjected to thermal cycling, complex stresses and strains are generated in the solder joints. Using strain gauges along with some simple assumptions, we can indirectly measure the shear strain and shear force during these cycles. The force, the strain, and the temperature are related by a Simple linear equation with calculable coefficients. At any temperature, the solder simultaneously undergoes creep and stress relaxation in a process We call "stress reduction.'' The rate of stress reduction is controlled by the conventional constitutive relation in which the rate of change of shear strain at a given temperature is proportional to the shear stress raised to a constant power. The constitutive relation is used to develop an equation for stress as a function of time during isothermal stress, reduction. Experiments confirm this equation over the ,range of -28 tO 97°C. The measured time to half-stress depends on the initial stress. For typical values it was measured as 10 min to 1 h at 97°C, one month at 33°c, and (by extrapolation) 30 Years at - 28°C. Almost all methods for interpreting metal fatigue involve the strain amplitude during cycling. In temperature cycling the shear strain amplitude can be expressed as (BS/ H) \triang \alpha T, where S is the in-plane distance from the center of the carrier to the solder joint, H is the height of the solder joint, \triang \alpha is the expansivity difference and AT is the temperature amplitude. The parameter B is a solder Compliance factor. For small temperature amplitudes, B approaches unity at high temperatures and is 0.8 at 100°C, · but it is only 0.08 at 0°C Thus the ratio between the strain amplitude and temperature amplitude depends on the temperature, and this must be factored into any theory Which is used to explain thermal cycle, fatigue in solder joints of surface-mounted leadless chip carriers.

Refractive index, relaxation times and the viscoelastic model in dry‐grown SiO2 films on Si

Abstract: Inert thermal anneals were performed at various temperatures to determine annealing kinetics of dry thermally grown SiO2 films on Si. Two stages of relaxation are demonstrated. The film relaxes quickly to an intermediate level, and then progresses more slowly toward full relaxation. The relaxation times to attain the fully relaxed refractive index, 1.460, and full ≤3% swelling were found to fall below typical oxidation times at T≥1150 °C, in concurrence with the experimentally observed breakpoint in the refractive index versus growth temperature data. It is concluded that the linear viscoelastic model is sufficient to quantitatively explain the breakpoints in refractive index for both wet and dry thermally grown oxide.

Transient Rheological Behaviour of A Lyotropic Polymeric Liquid Crystal

Abstract: The stress transients resulting from step-wise changes in shear rate have been investigated for a liquid crystalline solution of PBLG in m-cresol In step-up experiments these transients display a complex profile which includes multiple maxima, even in the Newtonian region To a first approximation the curves scale with strain A stepwise decrease in shear rate also causes a stress pattern with multiple maxima The initial decay is related to the stress relaxation upon cessation of flow Many of these features are not described by the existing theories They are explained in terms of supermolecular structures such as domains

Stress variations due to microcracks in GaAs grown on Si

Abstract: Luminescence studies of thick (≥5 μm) GaAs epitaxial layers grown on Si substrates reveal regions of nonuniform stress associated with the presence of microcracks. Using cathodoluminescence spectroscopy as a tool for microcharacterization, the magnitude of the stress, derived from the peak positions of the luminescence spectra, is shown to increase gradually as a function of distance from the intersection of two microcracks. The greatest degree of stress relief was found at this intersection.

A model for the oxide growth stress and its effect on the creep of metals

Abstract: A mathematical model is developed for the effect of the oxide growth stress upon the high temperature deformation of metal. The growth stress is modeled as a volumetric strain calculated from a modified Pilling-Bedworth ratio. The model is three-dimensional and allows the metal and the oxide scale to undergo both elastic and creep deformation during oxidation. The problems of oxidizing a flat plate, a solid rod, and a curved plate are formulated and solved. Experimental results for these geometries in the Ni-NiO system at 1000 °C are well predicted, both with and without an external load. The creep properties and the stress distribution in the NiO scale are calculated.

Theory of mobile dislocation density: Application to the deformation of 304 stainless steel

Abstract: Tensile and creep deformation of 304 stainless steel have been studied at room temperature in a soft tensile machine. The strain-stress curve shows a long inelastic transient, over nearly two hundred megapascals, in which the slope and the strain rate increase by about a factor of 3. Creep is characterized by large creep strain, transient strain rate, and a weak stress dependence. The stress rate applied during loading, on the other hand, has a strong effect on the subsequent creep. These results, in combination with earlier studies, have suggested a new model for the evolution of mobile dislocation density. Mobile dislocations are injected into the sample as a consequence of the increase of stress; the dislocations move under the influence of an effective stress over a statistical mean free path and then are trapped in a network. The effects of trapping are reduced mobile density, strain hardening, and a decrease in the effective stress. Application of the model provides a quantitative prediction of the principal experimental results.

Stress relaxation in short jute fiber‐reinforced nitrile rubber composites

Abstract: Stress relaxation measurements in tension have been made on nitrile rubber vulcanizates containing short jute fibers. The effects of strain level, bonding system (silica-resorcinol-hexa), fiber orientation, fiber content, temperature, and prestraining on the rate of stress relaxation have been investigated. Existence of a relaxation mechanism within the first 200 s is reported.