Showing papers on "Stress relaxation published in 1986"

Kinetics of formation of silicides: A review

Abstract: The kinetics of silicide growth are classified into three different categories: (a) diffusion controlled, (b) nucleation controlled, (c) others (reaction rate controlled). These are analyzed with the aim of understanding both the phenomenology of growth and the specific atomic mechanisms of phase formation. Diffusion-controlled growth is discussed with respect to the Nernst-Einstein equation. Stress relaxation is considered as a possible cause of reaction-rate control. The relative merits of two different types of marker experiments are compared. A few silicides are discussed in terms of what can be inferred about diffusion mechanisms. The competition between reaction-rate and diffusion control phenomena is shown to have specific effects on the sequence of phase formation; it is also related to the formation of some amorphous compounds. Reactions between silicon and alloyed metal films are used to illustrate the respective influences of mobility and driving force factors on the kinetics of silicide growth; they can also be used to underline the dominance of nucleation over diffusion in some silicide formation processes.

Yield stress: A time-dependent property and how to measure it

Abstract: This paper reviews the different aspects of the yield stress phenomenon and attempts a synthesis of knowledge. Yield stress can be probed using constant shear stress or shear rate. The magnitude of the result depends on the time allowed to determine whether the sample has developed continuous flow or has ceased flowing. It is closely associated with creep, stress growth and thixotropic breakdown and recovery, and the characteristic times of these transient responses play a part in yield stress measurement. In thixotropic fluids, yield stress is a function of structure and hence of time. In simple thixotropy, the yield stress derived from the equilibrium flow curve is the same as that for the fully built-up structure. But in many materials, the static yield stress obtained after prolonged rest is much higher than the dynamic yield stress from the equilibrium flow curve. This is associated with the phenomenon in which the equilibrium flow curve bends upwards as the shear rate is reduced to very low values. The paper also reviews the many methods that can be used to measure yield stress. It is pointed out that the choice of observation time or shear rate to use should be related to the characteristic time of the flow process to which the result is to be applied. Examples discussed are solids suspension capability of fluids, levelling and sagging, pipeline flow and start-up power requirement of mixers.

Earthquakes in the ductile regime

Abstract: Pseudotachylytes from a crustal scale shear zone in Central Australia have developed in a cyclical manner: once developed, an individual pseudotachylyte is deformed in a ductile manner, only to be overprinted at a later stage by a new generation of pseudotachylytes. Such cyclic generation and deformation of pseudotachylyte has been interpreted in the past as representing conditions at the brittleductile transition; a different interpretation, however, is presented here. It is proposed that psuedotachylytes and associated ultramylonites can develop entirely within the ductile regime as ductile instabilities. Such instabilities are different in nature to those previously discussed at length in the geophysical literature but are identical in principle with the instabilities that develop for velocity-weakening frictional behavior in spring-slider systems. At a given strain rate a critical temperature,T c, is defined, at which the transient work hardening equals the product of stress relaxation due to a thermal fluctuation and the heat generated by shearing. A necessary condition for ductile instability at a given strain rate is that the temperature is belowT c; then the rate of change of stress with respect to strain is negative. An additional requirement is that this rate of change exceeds, in magnitude, the effective elastic stiffness of the loading system. Ductile instabilities are marginally possible at geological strain rates in quartzites but are possible at mid-crustal temperatures in other rock types. On the basis of these observations a new interpretation is presented for the base of the seismogenic zone in crustal regions.

A molecular approach to the spurt effect in polymer melt flow

Abstract: The Doi-Edwards theory of polymer melts, extended to include relaxation processes associated with chain-length equilibration, is used to make quantitative predictions of a discontinuity in the flow curve of a monodisperse melt in a capillary. A fluid interface between regions of high and low deformation rates is found to propagate from the former into the latter. Our results for the “spurt” and its hysteresis compare favorably with experiment using a molecular weight dependence of the ratio of “reptation time” (Td) to “equilibration time” (Teq) in agreement with that determined from nonlinear stress relaxation.

Stress Transfer in Single Fiber/ Resin Tensile Tests

Abstract: Microscale (25 mm gauge length) “dogbone” resin specimens with single carbon fibers embedded through the length of the specimen have been studied as a method for determining the fiber-resin interphase strength. The specimens are pulled in tension until the fiber fragments to a critical length, lc . Evidence is presented here, based primarily on the relaxation of stress birefringence around the fiber fragment, that this test may not be an unambiguous measure of fiber-resin adhesion. Data obtained for various production lots of AS-4, AS-6, and IM-6 fibers indicate an increase in lcd with laminate tensile strength. Although there is theoretical justification for this correlation, it requires that the interphase shear strength is relatively constant. In those instances where interfacial adhesion was expected to be low, i.e., surface contamination or unsurface treated fiber, there was a significant increase in lc/d and usually a distinct difference in stress birefringence compared to “good” adhesion. ...

Transient Behavior of Liquid Crystalline Solutions of Poly(benzylglutamate)

Abstract: A solution of poly‐γ‐benzyl‐L‐glutamate (PBLG) in m‐cresol has been investigated. Viscoelastic properties during steady state shear flow and in oscillatory flow are presented. The existence of a stable negative first normal stress difference is confirmed. The dynamic Newtonian viscosity is considerably smaller than the corresponding steady state shear value. The transient behavior after cessation of flow is studied in detail using dynamic measurements. After cessation of flow, the dynamic moduli change over a time scale which is much larger than that for stress relaxation. Effects of frequency, temperature and previous shear rate are analyzed. The structural interpretation of the data is discussed. Available models for polymeric liquid crystals have to be developed further before a comparison with the present results becomes possible.

Volume Relaxation Far from Equilibrium

Abstract: Narayanaswamy's model of structural relaxation is applied to the data of Hara and Suetoshi on volume relaxation in plate glass. Both the Adam-Gibbs and Arrhenius equations are used to represent the relaxation time. Equally good fits are obtained with both equations, but only the Adam-Gibbs model gives Physically meaningful fitting parameters. The exponent b describing the shape of the relaxation time spectrum decreases at small values of reduced time, as it does for stress relaxation Discrepancies between calculated and measured densities at 350°C are not resolved by allowing for a nonlinear driving force or thermorheological complexity.

Creep crack growth under non-steady-state conditions

Abstract: The problem of characterizing crack growth under small scale creep and transition conditions is of great practical significance. This paper defines a crack tip parameter C, for characterizing creep crack growth behavior under wide range creep conditions from small scale creep to steady-state creep. Under steady-state creep conditions, C, is shown to reduce to the familiar C*-integral. The physical basis for the C, parameter is also provided. Wide range creep crack growth data on A470 Class 8 steel using two specimen geometries were obtained and correlated with the C, parameter in the temperature regime of 482 to 538°C. The levels of creep deformation in the various specimens tested to obtain the crack growth rate data ranged from small scale creep to essentially steady-state creep conditions.

Creep and fracture of a vitreous-bonded aluminium oxide

Abstract: Creep and creep-rupture behaviour of a commercial grade of glass-bonded, 96% aluminum oxide was characterized as a function of temperature and applied stress. The creep data were fitted to the classical empirical relation usually used to describe this phenomenon. The apparent activation enthalpy, ΔH = 926 kJ mol−1, and the stress exponent,n = 4.8, lie at the high end of the range reported for two-phase materials, primarily as a result of structural modifications that occur during creep. A stress-modified Monkman-Grant relationship was fitted to the creep-rupture data to give a stress exponent of −4.2. None of the available theories of creep rupture provided a satisfactory description of the present set of data. Analytical electron microscopy was used to characterize the composition and structure of this material. In the as-received material the intergranular phase was a glass of nearly uniform composition. During high-temperature exposure, devitrification of the glass resulted in the formation of various crystalline phases within the intergranular region of the material. Devitrification depended on both the proximity to the surface, where it was most pronounced, and on the state of stress. In this regard, flexural creep samples exhibited extensive crystallization within the tensile region of the flexural specimens, but little crystallization within the compressive cross-section. From the composition of the retained glass, estimates of the viscosity of the glass at the grain boundaries were made and used, in combination with microstructural information, to compare the creep behaviour with available theories of creep. The results of this paper are consistent with percolation and solution precipitation mechanisms of creep deformation. By contrast, cavitation did not seem to play a major role in the creep deformation process.

Studies on the Transient Shear Flow Behavior of Liquid Crystalline Polymers

Abstract: An understanding of the flow behavior of liquid crystalline polymers (LCP's) is of immense practical value because of the potential to form high modulus materials from these polymers. These fluids exhibit a high degree of structure even in the quiescent state, as evidenced by their ability to transmit polarized light. In an effort to understand how the structure changes during flow, we have carried out a study on the transient shear flow properties of two thermotropic copolyesters of 60‐ and 80‐mole % para‐hydroxybenzoic acid (PHB) and polyethyleneterephthalate (PET) and a lyotropic system of poly‐p‐phenyleneterephthalamide (PPT) in 100% sulfuric acid. In one of the first theories concerned with the flow behavior of liquid crystalline fluids, which was proposed by Ericksen, the transient flow properties are all predicted to be due to changes in orientation of a director which describes the orientation of packets of rod‐like molecules. Stress growth, interrupted stress growth, and stress relaxation experiments are carried out on the three LCP's and at first sight are in qualitative agreement with the predictions of Ericksen's theory. However, wide angle X‐ray scattering analysis of quenched samples subjected to shear flow along with annealing experiments on oriented samples indicate that these materials do not orient readily in shear flow. Furthermore, orientation generated during extensional flow relaxes at a rate much faster than is indicated by the interrupted stress growth experiments. It is concluded that the stress growth response of LCP's is due to a disruption of a domain structure which exists within the fluid rather than to orientation changes of the domains of rod‐like molecules.

A New Nonlinear Viscoelastic Constitutive Equation for Predicting Yield in Amorphous Solid Polymers

Abstract: A new constitutive equation has been developed for describing the nonlinear viscoelastic properties, including yield, of polymer solids. The nonlinear viscoelastic constitutive equation is the logical extension of the standard three‐dimensional linear viscoelastic constitutive equation to include the effects of deformation‐induced changes in the thermodynamic state of the polymer on the rate of viscoelastic relaxation. The rate of viscoelastic relaxation depends upon the fraction of unoccupied lattice sites (i.e., holes) in the Simha‐Somcynsky statistical thermodynamic equation of state, and the hole fraction is a known function of the temperature, pressure, and specific volume. The nonlinear viscoelastic yield and postyield behavior are a direct consequence of the deformation‐induced dilation. All material constants contained in the constitutive equation can be determined from independent elastic, linear viscoelastic, and pressure‐volume‐temperature measurements—there are no adjustable constants. The con...

X‐ray study of misfit strain relaxation in lattice‐mismatched heterojunctions

Abstract: High‐resolution x‐ray diffraction measurements have been carried out in AlxGa1−xAs and InxGa1−xAs grown by the molecular beam epitaxy method on (001) GaAs substrates The thin epitaxial layers in these lattice‐mismatched semiconductor single heterojunctions are uniformly distorted and there is an elastic limit for large x The epitaxial layer is affected by a thick substrate even over the elastic limit, ie, the epitaxial layer still shows a strained state beyond the elastic limit The relationship between the misfit strain and the lattice distortion is discussed

Study of the α and β relaxations on a commercial poly(vinyl chloride) by thermally stimulated creep and depolarization current techniques

Abstract: Thermally stimulated creep and depolarization current measurements have been carried out in a temperature range between −180 and 120 °C, on a pure commercial poly(vinyl chloride). Mechanical and dielectric relaxation times involved in α and β relaxations are obtained by fractional stresses/polarizations procedure. The distribution of the Arrhenius‐like kinetic parameters, deduced from the relaxation times, is interpreted in terms of compensation laws. From the obtained results, a same molecular origin can be assumed for the mechanical and dielectric behavior in both α and β relaxations. Moreover, the compensation law analysis leads to two different relaxations modes, likely associated to two kinds of thermally activated molecular motions, in β relaxation. In the α region, the values of found kinetic parameters point out a high degree of cooperativeness of the involved molecular motions. Depolarization curve in this region shows a high temperature peak, not found in the mechanical one, whose evolution with the poling field allows us to assign it to a nondipolar process associated to the movement of free charge carriers.

Transient crack growth under creep conditions

Abstract: Transient crack growth in an elastic/power-law creeping material is investigated under antiplane shear loading and small-scale-yielding conditions. At time t = 0 the solid is suddenly loaded far from the crack by tractions that correspond to the elastic crack-tip stress distribution. At that time the crack begins to propagate at a constant velocity. The stress fields evolve in a complex manner as the crack propagates due to the competing effects of stress relaxation due to constrained creep and stress elevation due to the instantaneous elastic material response to crack growth. From detailed finite element calculations it is shown that these fields can be approximated by a simple matching of three asymptotic singular crack-tip solutions. A characteristic stress, distance and time are defined for this problem which provide a normalization that accounts for any crack velocity, loading and all material properties for a given creep exponent n . Results are presented for crack-tip stresses, strains, crack opening displacements and creep zones.

The mechano-sorptive creep susceptibility of two softwoods and its relation to some other materials properties

Abstract: This paper describes a new design of bending creep machine for accurate measurements of mechano-sorptive creep. Tests on two species of pine showed that at low stresses bending and tension gave similar results. It is shown that the mechano-sorptive creep susceptibility correlates with the mean microfibrillar angle of the S2 layer in a continuous relation that includes two species of pine, including one which showed evidence of compression wood; thus giving further evidence of the importance of inter-microfibril stresses in the S2 layer in mechano-sorptive creep. Accordingly, mechano-sorptive creep susceptibility also correlated continuously with elastic compliance; thus encouraging the possibility of the selection of non-susceptible material by machine stress grading. These two correlations also diminish the main obstacle to research on mechano-sorptive creep, the excessive variability of the material and the consequent difficulty of matching of samples.

The effect of molecular weight on the rheological properties of poly(dimethylsiloxane) filled with fumed silica

Abstract: The viscometric, stress relaxation, and stress growth rheological properties were measured for various molecular weight PDMS fluids filled with fumed silica. The stress growth function exhibited significant overshoot, when the continuous phase molecular weight was slightly greater than the entanglement molecular weight; however, significant overshoot peaks were not observed, when the continuous phase molecular weight was less than or much greater than the molecular weight between entanglements. The experimentally observed transient rheological properties are rationalized in terms of a molecular model, where interparticle interactions occur via entanglements of the polymer adsorbed on the silica surface. When the molecular weight of the adsorbed polymer is greater than the entanglement molecular weight, the strength of the interparticle interaction will increase substantially and the particle diffusivity will substantially decrease.

Negative creep and recovery during high-temperature creep of MgO single crystals at low stresses

Abstract: High-temperature creep equipment with very high precision has been used to measure the creep of MgO single crystals above 1948 K and stresses lower than 4 MPa A transition in exponent,n, from 3 at stresses higher than 2 MPa to almost unity at lower stress region was observed Since in a single crystal deformation can only occur by the generation and movement of dislocations, the transition in stress exponent from high to low stress region cannot be interpreted in terms of a change from dislocation to diffusional creep processes Decreasing the stress by a small amount during steady-state creep resulted in an incubation period of zero creep rate before creep commenced at lower stress However, large stress reduction led to a period of negative creep during which the dislocation substructure coarsens and the subgrain cell boundaries straighten On the basis of dislocation substructure studies, it is proposed that the kinetics of backflow are thought to be based on the local network refinement caused by the reverse movement of dislocations and that recovery is necessary before further movement of dislocation can occur It is shown that the network theory proposed by Davis and Wilshire can satisfactorily account for all stress reduction observed during forward creep

Viscoelastic constitutive model for determining in-situ stress magnitudes from enelastic strain recovery of core

Abstract: A new, 3-D viscoelastic model is developed to describe the inelastic-strain-recovery (ASR) process. Measured ASR data are curve-fit to the model using a least-squares algorithm and viscoelastic material properties are calculated. The stress state at depth can then be determined given some additional information. Examples and comparisons with measured stresses are given. 20 refs., 10 figs., 5 tabs.

Nucleation and Growth of Stress Relief Patterns in Sputtered Molybdenum Films

Abstract: Stress relief patterns in sputtered molybdenum films were studied by Nomarski differential interference contrast microscope. As a result of the very large biaxial compressive stress in the film plane, ranging from E/16 to E/130 (where E is Young's modulus), the films were partially buckled and detached from the substrate, exhibiting one of two modes of stress relief pattern, wrinkled spots or wavy ridges. The former mode is a nucleation pattern and the latter a growth pattern. The transition between the two can be interpreted in terms of the stress intensity factor K1 at the head of the gap formed due to stress between the film and the substrate. K1 can be regarded as measure of the bond strength between the film and the substrate.

Linear viscoelastic behavior of frankfurters

Abstract: Normal creep and stress relaxation experiments were performed on seven commercial brands of frankfurters. A nonlinear procedure was used to determine the model best fitting the data for each test. Re assumption of linear viscoelasticity was tested by the equivalence of model parameters. Results showed fankfurters to be linear viscoelastic materials at strain levels up to 3.8%.

Stress development in supported polymer films during thermal cycling

Abstract: A simple and in-situ bending-beam technique has been used to investigate the stress-temperature relationships for three different polymer coatings (viz, poly(methyl methacrylate), FR-4 epoxy resin, and an amide-imide polymer) during thermal cycling. With this technique, we were able to detect stress relaxation near the polymer's glass transition or caused by cracking of the polymer. Knowing the Poisson's ratio and Young's modulus for the polymer, this technique also allows calculation of the polymer's thermal expansion coefficient from measured thermal stress data. The calculated thermal expansion coefficient of poly(methyl methacrylate) (7 × 10−5/°C) is in good agreement with literature values (5 to 9 × 10−5/°C).