Showing papers on "Stress relaxation published in 1968"

Soil creep as a rate process

Abstract: The fundamental equation of the theory of absolute reaction rates has been adapted for use in the study of time-dependent soil deformations. Results of constant stress creep tests have established that the basic form of this equation supports the assumption of a thermally activated creep process, the predicted relationship between experimental activation energy and creep stress, and the predicted stress dependence of creep rate. Some modification of the equation is needed, however, to account for the variation of creep rate with time. Techniques are described for study of deformation mechanisms in soils and test results suggest that interparticle bonding is probably of the primary valence type. Resistance to shear stresses cannot be accounted for in terms of viscous water films, and interparticle contacts must be effectively solid to solid.

Mechanical Properties of a Sand-Ice System

Abstract: The mechanical properties of a saturated frozen sand were studied using constant axial stress creep tests and constant axial strain-rate tests. Observation of the effects on deformational behavior produced by the addition of sand particles to the ice matrix led to an analysis useful in predicting creep rates for a constant stress and stress levels for a constant strain rate. The relationship between strain rate and stress for polycrystalline ice considers a strain dependent hardening term and a strain energy dependent softening term. Parameters of the equation include stress and temperature. Stress factors, dependent on sand volume concentration and friction and dilatancy of the sand, are used in conjunction with the equation for polycrystalline ice to give predictions of the mechanical behavior of the sand-ice system. These are in reasonable agreement with experimental data.

Effects of high hydrostatic pressure on the mechanical behavior of a crystalline polymer–polyoxymethylene

Abstract: The true stress-true strain behavior of polyoxymethylene, n(-CH2O), as an example of a bulk semi-crystalline polymer, has been investigated for constant hydrostatic environmental pressures from 1 atmosphere to 8 kilobars with the principal objectives of elucidating the factors controlling flow and fracture. Experiments were conducted in uniaxial tension at room temperature and constant strain rate. The tensile observations were supplemented by measurements of bulk compressibility and stress relaxation behavior at pressure. In contrast with metals and inorganic compounds, the modulus, yield stress and fracture stress of POM increase strongly with pressure by a factor of approximately three at 8 kilobars. The modulus increase is shown from the stress relaxation measurements to be associated with a pressure-induced increase in the β-transition temperature which points to the potential usefulness of the concept of pressure-temperature super-position of mechanical behavior. The characteristics of the pressure dependence of the yield stress demonstrate that yield criteria based on continum mechanics considerations, including the Mohr or Coulomb-Navier criterion, are not valid for general deformation (non-plane strain) conditions in this polymer. The concept of a critical volume change determining the initiation of yielding is suggested to be applicable to semi-crystalline polymers. Comparison with analogous changes in yield stress with temperature points to an increasing contribution to the control of yielding by the initially disordered regions with increasing pressure or decreasing temperature. The fracture behavior observed at pressure eliminates the concepts of a critical stress as a fracture criterion for POM and of a simple reduction in normal stress at points of stress concentration as the principal effect of the applied pressure on fracture.

A theoretical analysis of creep in fibre reinforced composites

Abstract: A phenomenological analysis is made of the mechanism of creep in a fibre composite. This is done using virtual displacements to demonstrate the usefulness of such an approach. The creep of the composite is found to be governed by the following three processes. (i) Relaxation of shear stresses at fibre ends causing load re-distribution. (ii) Stress relaxation of the matrix causing load transfer to the fibres. (iii) Creep of the fibres. The implications of the combined effect of these processes on the mode of rupture of the composite are briefly examined. Finally, hypothetical composites are analysed to illustrate the application of the theory. Reported observations of the creep behaviour of conventional fibre-reinforced composites are explained by the theory proposed.

Stress Relaxation of Nonlinear Viscoelastic Material under Uniaxial Strain

Abstract: A constitutive equation using a multiple integral functional relationship for stress relaxation of nonlinear viscoelastic material has been investigated for uniaxial stress. The first three integrals were retained and the relaxational functions for constant strain were determined from experiments on polyurethane at constant strain. Using this information the behavior during a multistep strain history was computed using two approximate procedures (a) assuming a product form for the kernel function and (b) employing a modified superposition principle. The latter yielded the more accurate description, although both gave good results.

Analysis of steady state shearing and stress relaxation in the Maxwell orthogonal rheometer

Abstract: A nonlinear, integral viscoelastic model is used to predict the stresses in the Maxwell orthogonal rheometer The resulting expressions indicate that the instrument yields data on material functions not heretofore measured, and also show how the data may be analyzed to get the complex viscosity Expressions are given for stress relaxation after cessation of shearing Some experimental data are analyzed to give model parameters

High‐Temperature‐Creep Mechanism of TiNi

Abstract: Polycrystalline specimens of the intermetallic compound TiNi were tested in tension in the temperature range 700°–1000°C. The specimens were observed to deform uniformly over the gage length until the very end of deformation, when it failed by necking. It was noted that the steady‐state flow stress was independent of the strain and was a function only of the temperature and strain rate. The shear strain rate γ was given by γ∝τn where n=3.0±0.2, r was the shear stress, and n was independent of temperature. The apparent activation energy for creep was found to be 60.0±3.0 kcal/mole and was independent of stress. The result strongly suggests that a viscous creep process, as first formulated by Weertman, is probably the rate‐controlling mechanism for this compound in the stress and temperature range investigated.

Prediction of Uniaxial Stress Relaxation from Creep of Nonlinear Viscoelastic Material

Abstract: A method is described for predicting nonlinear stress relaxation from nonlinear creep data under constant uniaxial stress. This method utilizes as a first approximation an inversion of the function obtained from the multiple integral equation describing creep at constant stress. A correction procedure accounts for the variable stress during relaxation by employing the general multiple integral function with an assumption that the kernel functions containing mixed time parameters may be taken as products. The results computed from creep data with only one stage of corrections are in good agreement with relaxation experiments on a polyurethane tube.

Relation between nylon fiber mechanical properties and dye diffusion behavior

Abstract: The mobility of polymer chain segments is shown to play a major role in the diffusion of dyes in nylon 66. The rate of dye diffusion has been related to the time-dependent mechanical properties, such as creep and stress relaxation, which are controlled by the mobility of the chain segments. The theoretical relations derived by Fujita et al. relating the diffusion of small molecules in amorphous polymers to other properties are shown to be applicable for the dyeing of semicrystalline nylon. Data showing the effects of surface area, temperature, and the amount of dye absorbed at saturation on the dyeing rate are presented and discussed.

Dynamic Mechanical Properties of Cross‐Linked Rubbers. IV. Dicumyl Peroxide Vulcanizates of Styrene‐Butadiene Rubber

Abstract: The viscoelastic properties of three samples of a random styrene‐butadiene co‐polymer with 23.5 wt‐% styrene, cross‐linked by dicumyl peroxide to different extents, have been studied by dynamic shear and shear creep measurements, and the unvulcanized precursor has been studied in creep. The frequency and temperature ranges were 0.2 to 3600 cps and −30 to 55°C. The creep data were converted to the corresponding dynamic viscoelastic functions at very low frequencies. All data were reduced to T0=298°K by shift factors calculated from the equation log aT=−4.57(T−T0)/(113.6+T−T0). By fitting the creep to a modification of the empirical equation of Thirion and Chasset, values of the equilibrium compliance and relaxation parameters were obtained in good agreement with results of those authors from stress relaxation in extension. All the viscoelastic functions displayed two principal regions of frequency dependence as found for other rubberlike polymers. The high‐frequency dispersion, near 105 on the radian frequ...

Study of Erythrocyte Aggregation by Blood Viscometry at Low Shear Rates Using a Balance Method

Abstract: Abalance method was used to investigate the viscometric behavior and aggregation properties of blood at very low shear rates. The system was essentially a parallel-plate viscometer, consisting of a thin brass plate suspended by a fine wire from one end of an analytical beam balance. The yield shear stress of a sample was obtained directly by recording stress relaxation curves. Results were obtained for homogeneous Newtonian and non-Newtonian fluids and for blood and various red cell suspensions. It was found that human and canine blood behave as fluids exhibiting a yield stress. Suspensions of red cells in saline had much smaller values of yield stress, which is consistent with greatly diminished erythrocyte aggregation when fibrinogen is lacking. Measured values of the yield stress were in the range of 0.001 to 0.1 dynes/cm2.

Stress relaxation of monodisperse poly‐α‐methylstyrene

Abstract: The viscoelastic properties of monodisperse poly-α-methylstyrenes of molecular weights of 4 × 104 to 50 × 104 were studied by the tensile stress-relaxation method. The relaxation-time spectra as well as the steady-flow viscosity, the steady-state compliance, the maximum relaxation time, and the modulus associated with the maximum relaxation time were determined. The molecular weight dependences of these quantities were compared with the theory of Rouse and Bueche as modified by Ferry, Landel, and Williams, as well as with data on other polymers reported in the literature.

Rheological Properties of Hydrogels of Agar-agar. III. Stress Relaxation of Agarose Gels

Abstract: A stress relaxation experiment on hydrogels of agarose isolated from agar-agar was made by means of a chainomatic balance relaxometer for the purpose of investigating the mechanism of gelation. The measurements were made on the agarose gels of the concentration range from 1.2 to 2.0 wt%, and also on agar-agar gels for the comparison, at various temperatures from 25 to 55°C. The relaxation curves obtained were represented approximately by a mechanical model consisting of three Maxwell models in parallel. The apparent activation energy, ΔH, which was calculated from the temperature dependence of the longest relaxation time, τ1 was about 5 kcal/mol for all gels treated in this study, which was nearly the same magnitude as that for agar-agar gels. It was observed in the curves obtained that the relaxation curves for agarose gels had quite similar characteristics to those for agar-agar gels of the same concentration and was observed that the total instantaneous modulus of the former gels amounted to about 80% ...

Experimental Approach to a Theory of Plasticity at Elevated Temperatures

Abstract: The problem of providing an experimental basis for an isothermal theory of plasticity of metals at elevated temperatures has been examined. The key objectives are considered to be the establishment of a steady‐state function and the discovery of a nonsteady deformation law. Constant stress and constant strain rate are judged the best loading conditions for both of these tasks since they provide paths, under the simplest thermomechanical histories, to the steady‐state deformation. The use of plots of strain rate and its time derivative for constant stress tests and plots of stress and its time derivative for constant strain rate tests is advocated as a means of best displaying the transient nonsteady behavior. It is even suggested that the functions represented by such plots may be independent of the loading history prior to the period of constant stress or constant strain rate applications. Constant stress and constant strain rate tests are limited in the early (nonsteady) period by lack of control of structure on initial loading, and generally in the later period by the nonuniformity of deformation. It is suggested that the former difficulty may be overcome by employing loading rates sufficiently rapid to permit sensible constancy of structure. Nonuniformity of deformation imposes a severe restriction on the examination of steady‐state deformation.

Viscoelasticity of oriented poly(ethylene terephthalate)

Abstract: Time–temperature superposition can be successfully applied to both the stress relaxation and dynamic mechanical properties of oriented PET fibers. Two curves result; one is the time dependence of the modulus at constant temperature, while the other is the shift, log aT, of this curve along the time scale as a function of temperature. This temperature dependence is less than that for both unoriented PET and typical amorphous polymers above Tg. It is about the same as that for oriented nylon 66 and unoriented glassy poly(methyl methacrylate). The isothermal modulus has the same time dependence as that of the unoriented PET; however, it is a factor of 3.3 larger. The modulus curve is almost identical in both shape and magnitude with that of oriented nylon 66. However, a temperature of 82°C. is required to place the viscoelastic dispersion region of PET at the same time scale as nylon 66 at 25°C. This temperature increase is the major difference in viscoelasticity between these two oriented polymers.

X-ray diffraction study of residual macrostresses in shot-peened and fatiqued 4130 steel

Abstract: A study has been made of the effects of shot peening and fatigue cycling on the residual macrostresses determined by X-ray methods in an austenitized and tempered AISI 4130 steel (150–170 ksi). The results show that the effect of shot peening is to produce a residual compressive macrostress layer 0.014-in. deep. The residual-stress profile (stress vs. depth) exhibits a small negative stress gradient at and near the surface and a large positive stress gradient in the interior. Stress relaxation (due to fatique cycling) which occurred early in the fatigue history of the specimen was found greater at the surface than in the subsurface layers. Stress gradients of the stress profile increased with continued cycling and varied with depth. A correlation appears to exist between stress relaxation and stress gradients at the surface.

On the propagation of transient pulses in linearly viscoelastic media

Abstract: A general procedure is developed for predicting the way in which transient pulses propagate through an arbitrary, linearly viscoelastic, medium characterized by creep or stress relaxation functions. By use of the Laplace transform, differential operations in transform space, and some asymptotic methods, the boundary-value problem in question is reformulated in terms of a Volterra integral equation, with the space variable playing the role of a parameter. This equation is readily resolved numerically, and results obtained by this procedure compare very well with solutions available in the literature.

Prediction of long‐term ABS relaxation behavior

Abstract: The applicability of time–temperature superposition to tensile stress relaxation of ABS plastics has been verified at strains from 0.5 to 5% for temperatures in the range of 10–50°C. Master curves have been compiled to predict the long-term stress relaxation at 23°C. and a stress–strain–reduced time surface has been constructed. A comparison of relaxation times and activation energies has confirmed that a strain increase facilitates stress relaxation up to yield. The decay of relaxation modulus at linear viscoelastic strains was shown to be equivalent to that of tensile creep modulus. By normalizing the master curves to originate at yield stress and then converting them into multiaxial from the strain which gives the best data fit with long-term hydrostatic pipe-burst strength was shown to be at yield or beyond. The ABS yield-strain master curves at 23°C. were shown to match satisfactorily the long-term pipe-rupture data. Activation energies for ABS relaxation have been compared below and above the rigid matrix Tg, to assess the degree of stiffening of the polymer in the solid state.

Stress Relaxation in Single Crystals of Copper and α-Brasses

Abstract: Stress relaxation at constant strains has been studied in crystals of copper and α-brasses containing 10, 20, or 30 at.-% zinc at 77,200, and 291° K after consecutive small plastic deformations. Close to the yield point the relaxation was generally within 1% of the applied stress, but at large deformations, notably within the third stage of work-hardening, it attained ∼ 10%. Any given relaxation was observed for ∼ 1000 sec, over most of which period the decay of the stress was logarithmic in time. Energy barriers of the activated process were from ∼ 0.08 eV for copper and 0.2–0.3 eV for brasses. Their significance is discussed in terms of a model in which unpinning of dislocations from rows of solute atoms is the principal process determining the relaxation rate.

The Design and Calibration of a Stress Relaxation Ball Indentation Penetrometer

Abstract: A stress relaxation ball indentation penetrometer was designed and constructed with the intent of measuring the time‐dependent stress relaxation modulus of materials incapable of supporting their own weight. An equation is derived to relate the modulus to the geometry of a deformation by a sphere into a plane. The relevance of this equation to creep experiments is discussed.

Stress relaxation of anhydrous gelatin rubbers

Abstract: Anhydrous gelatin–glycerol compositions exhibit rubbery behavior in the temperature region −40 to +40°C. and in the gelatin weight fraction range 0.1–0.4. These rubbers are capable of sustaining considerable stress over several decades of time at room temperature or below but flow rapidly in the region 45–60°C. Stress relaxation moduli at 25°C. appear to be insensitive to the substitution of glycerol with water but shear viscosity data indicate that gelatin–glycerol rubbers flow at temperatures about 15°C. higher than their aqueous counterparts.

Stress Relaxation in Nickel Single Crystals between 77°−350°K

Abstract: Stress‐relaxation tests were conducted in compression with nickel single crystals of various orientations and purities The experiments were performed at five temperatures, 77°, 153°, 198°, 298°, and 350°K The data are fit by the semilogarithmic equation, Δτ(kT/B) (In A′t+1), based on reaction rate theory Crystals oriented to produce glide on intersecting slip planes exhibited no relaxation at the three lower test temperatures This absence of relaxation is believed to be a result of the high activation enthalpy necessary to produce dislocation motion across the intersecting glide dislocations which would markedly reduce the rate of thermal activation Crystals oriented to produce slip on a single set of planes had only one relaxation curve at low temperatures; no subsequent relaxation after the initial one could be induced At higher temperatures, after relaxation had ended, new relaxation was easily initiated by increasing the stress slightly The activated volumes obtained were almost independent of

The Strain-Rate and Temperature Dependence of Effective Flow Stress in Pure Iron and Some Iron Alloys

Abstract: The strain-rate sensitivity of the flow stress in iron and iron alloys was studied over wide range of strain rate below room temperature. The main results obtained are as follows. (i) The experimental method to decompose the flow stress into the effective stress and the internal stress was shown (ii) Both the Johnston-type power low and the rate equation were well satisfied if described in terms of the effective stress. (iii) Such a decomposition of flow stress was found to be very useful in analysis of such effects as solution hardening and work hardening.