Showing papers on "Stress relaxation published in 1978"

An extension of the self-consistent scheme to plastically-flowing polycrystals

Abstract: T he general formulation of the self-consistent scheme is specified for an isotropic elasto-plastic approximation of the “constraint” tensor. This leads to an explicit interaction law, modified from that of E. k roner (1961), which takes elasto-plastic accommodation into account via a simple scalar “accommodation function”. This model is applied to uniaxial tension tests for fee polycrystals. Both plastic flow and texture development are investigated. Internal stresses are shown to be significantly lowered with respect to the Kroner model predictions, due to the occurrence of plastic stress relaxation. As a result, the specific plastic properties of the material which are studied, as expressed by a single crystal “hardening matrix”, are found to have a significant influence on the final results.

Dynamics of concentrated polymer systems. Part 2.—Molecular motion under flow

Abstract: The primitive chain model presented in Part 1 is extended to the case in which the system is macroscopically deformed. The molecular expression of the stress due to the primitive chain is given, and the stress relaxation after a sudden deformation is calculated as an example.

Creep cavitation by vacancy diffusion in plastically deforming solid

Abstract: The diffusive growth rate of a grain boundary cavity is calculated under conditions where vacancies are created non-uniformly across the boundary. Away from the boundary, power-law creep relaxes the strain due to the diffusive atom plating which occurs preferentially near the cavity and allows increased growth rates. At high stresses the growth rate is proportional to the creep strain rate or stress to a high power and at low stresses the growth rate is proportional to stress.

Stress and Structural Relaxation in Tempering Glass

Abstract: Temper stresses are brought about, primarily, by a partial relaxation of transient stresses generated by rapid cooling of the glass. Stress relaxation under nonisothermal conditions is competently handled by a mathematical tempering model, in which glass is treated as a simple viscoelastic material. However, this model proved inadequate in some respects since the properties of glass depend not only on its instantaneous temperature but also on its prior thermal history. A tempering model was therefore developed that incorporates both stress and structural relaxation. Predictions of this structural model are compared with experimental data on tempering and contrasted with predictions of the viscoelastic model. Such comparisons revealed that, typically, structural relaxation accounts for approximately 24% of the total residual temper stresses.

Experimental study of elongational flow and failure of polymer melts

Abstract: A new and simple instrument for measurement of elongational flow response of polymer melts in constant uniaxial extension rate experiments is described. Quantitative stress development data are presented for a series of low-density polyethylene (LDPE), high-density polyethylene (HDPE), polystyrene (PS), polypropylene (PP), and poly(methyl methacrylate) (PMMA) melts. For small elongation rate E, linear viscoelastic behavior was observed; while for large E, LDPE and PS showed exponential stress growth, while HDPE and PP showed only linear stress growth. Stress relaxation experiments were carried out for several of the same melts in the instrument. Elongation to break and mechanisms of filament failure were studied. HDPE and PP have a tendency to neck and exhibit ductile failure, while at high E, LDPE and PS seem to show cohesive fracture. The elongational flow stress response data were compared to predictions of nonlinear viscoelastic fluid theory, specifically the Bogue-White formulation. The qualitative differences in responses of the melts studied were explained in terms of different dependences of the effective relaxation times on deformation rate and, more specifically, on values of the a parameter in the theory.

The Effect of Water on Stress Relaxation of Faulted and Unfaulted Sandstone

Abstract: A series of stress relaxation experiments have been carried out on faulted and intact Tennessee sandstone to explore the influence of pore water on strength at different strain rates. Temperatures employed were 20, 300 and 400°C, effective confining pressure was 1.5 kb and strain rates as low as 10−10 sec−1 were achieved. Most samples were prefaulted at 2.5 kb confining pressure and room temperature. This is thought to have secured a reproducible initial microstructure.

Three-dimensional numerical simulations of dynamic faulting in a half-space

Abstract: A method is presented for the computation of near-field particle displacements and particle velocities resulting from a dynamic propagating, stress relaxation occurring on a finite fault plane embedded within a three-dimensional semiinfinite medium To check our numerical procedure we compare our results for a circular fault in a full space with Kostrov's (1964) analytic solution for a self-similar propagating stress relaxation We have simulated two bilateral strike-slip earthquakes differing only in hypocentral location and examined the particle motion on the traction-free surface and on the rupture surface Focusing of energy is evident in both ruptures The static displacement on the rupture surface overshoots the theoretical static value by approximately 25 per cent For the rupture that nucleated at depth the free surface almost doubled the particle velocities along the fault trace as compared with the rupture that nucleated at the free surface Our numerical results indicate that for an earthquake occurring on a semi-circular fault with radius of 10 km, an effective stress of 100 bars and a rupture velocity of 09 β in a medium characterized by β = 3 km/sec, α = α = 3 β and a density of 27 gm/cm3 particle velocities can reach 400 cm/sec and displacements 250 cm We also compare our numerical results with the observations made by Archuleta and Brune (1975) for a spontaneous stress relaxation on a semi-circular crack in a prestressed foam rubber block

Sub‐Tg annealing studies of rubber‐modified and unmodified epoxy systems

Abstract: Epoxy network systems based on DGEBA (bisphenol‐A‐diglycidyl ether) and NMA (nadic methyl anhydride) systems modified with the low molecular weight CTBN (carboxyl‐terminated butudiene‐acrylonitrile copolymer) rubbers were prepared and studied. It was found that below the glass transition of the epoxy matrix these materials displayed time‐dependent changes in their mechanical properties; specifically, the strain to break as well as the rate of stress relaxation were observed to decrease in a near‐linear behavior with the logarithm of time at sub‐Tg annealing. Calorimetric methods clearly showed a simultaneous decrease in enthalpy with time that behaved in a similar fashion as the time‐dependent mechanical properties. All the calorimetric and mechanical data are qualitatively related. The importance of this phenomena is considered in view of the widespread use of epoxys. Similar behavior is expected for other network glasses thermally quenched into a nonequilibrium state.

Analysis of non‐linear stress relaxation in polymeric glasses

Abstract: Non-linear stress relaxation data were obtained for polycarbonate and polystyrene as a function of temperature, strain magnitude and thermal history. Data were analyzed according to the previously proposed free volume model to account for the shift of relaxation times with strain and thermal history. The result of the analysis is shown to be in close agreement with the tensile stress-strain data. The yield phenomenon is analyzed as a rate dependent strain-induced glass to rubber transition.

On the use of the stress relaxation testing method in studies of the mechanical behaviour of geological materials

Abstract: Summary. A summary is presented of the use of stress relaxation testing in studies of the mechanical behaviour of materials with emphasis on the underlying assumptions of the method. It is shown that relaxation testing is a powerful experimental method which could profitably be used in future studies of the mechanical properties of geological materials to augment, but not to replace, the more conventional creep and constant strain rate tests. Stress relaxation data can be analysed to determine important parameters in equations describing (a) laws of flow and fracture, and (b) dislocation dynamics. The variation of the first derivative of any stress relaxation curve with stress can be used to establish the applied stress sensitivity to strain rate and the values of activation parameters such as ‘activation volume’. Such parameters may be used to constrain the inference of the dominant deformation mechanism. This account is illustrated by reference to some recent experiments on polycrystalline, synthetic galena (lead sulphide) and prefaulted cylinders of Tennessee sandstone deformed over a wide range of environmental conditions. The accurate sensing of the second derivative of a relaxation curve is required to establish parameters relating to dislocation dynamics, e .g. partition between thermal and athermal components of applied stress, and the stress dependence of dislocation velocity. The determination of such parameters is illustrated with new experiments on single crystals of calcite.

Friction-stress measurements during high-temperature creep of polycrystalline copper

Abstract: A description is given of the high-precision equipment developed to examine the tensile creep behaviour of polycrystalline copper at 686 K. When the dependence of the steady-state creep rate es on applied stress e obeys a power law of the form es ∝ σ4.8 definitive values of the friction stress σ0 can be obtained which allow the creep behaviour to be described as e ∝ (σ−σ0)4. The σ0 values, measured by making consecutive small stress reductions during creep, appear to characterize the long-range back-stresses associated with the dislocation substructures developed under various creep conditions. The deformation behaviour can then be explained in terms of slip resulting from the operation of dislocation sources developed by recovery-controlled growth and rearrangement of the 3-dimensional dislocation network present.

Lamellar separation ,during the deformation of high-density polyethylene

Abstract: Upon tensile straining at low deformation rates (e=2×10−5 sec−1), spherulitic linear polyethylene behaves reversibly for extensions up to 40%. In stress relaxation experiments on unloaded specimens the stress increases with time. Samples kept under constant strain (e = 40%) over four months show macroscopic cracking. Microstructural investigation was performed using low- and wide-angle X-ray diffraction and transmission electron microscopy. These investigations reveal a very inhomogeneous deformation within those lamellar stacks for which the crystalline lamellae lie normal to the tensile axis. The deformation in that case is similar to what has been observed for “elastic hard fibres”. A two-mechanism model to explain the macroscopic observation on the basis of the microscopic observations is developed.

Thermodynamic and kinetic analysis of non elastic deformation in polymeric glasses

Abstract: This paper is aimed at extending to polymeric solids the thermodynamics and kinetics of activated plasticity as it has been used in crystals for about ten years. Application to thermally activated yielding in glassy polymers, due to the uncoiling of chain bonds within crude shear bands, producing an anelastic (pseudo-plastic) strain, is particularly stressed. Definitions of the activation parameters are given based on equilibrium quasi-static thermodynamics, and contributions to the total activation entropy and free energy from the strain induced bond orientation are shown to be generally negligible. The kinetics of barrier overcoming are considered and the operational quantities and experimental procedures are discussed.

Rayleigh-taylor instability of two viscoelastic superposed fluids

Abstract: The stability of the plane interface separating two viscoelastic superposed fluids of uniform densities has been studied. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. It is found that the system is stable for stable configuration and unstable for unstable configuration. The behaviour of growth rates with respect to stress relaxation time and strain retardation time parameters are examined analytically.

The absence of instantaneous plastic strain upon stress changes during creep of some solid solutions

Abstract: The apparent instantaneous strain associated with sudden stress change has been measured during creep of alloys in which mechanical behaviour indicates that the glide motion of dislocations is viscous. Measurements were made on Cu-10·4at.% Al alloy (800 K, 30·0 MPa), Fe-1·8at.%Mo alloy (1124 K, 13·7 MPa), and Al-5·5at.% Mg alloy (573 K, 25·0 MPa). The amount of stress change was limited to 5 to 20% of the base (creep) stress. The elongation and the contraction associated with equal positive and negative stress changes were the same and no instantaneous plastic strain could be observed in accord with theoretical considerations.

Combined constant strain rate and stress relaxation test for linear viscoelastic studies

Abstract: The strain history of the combined test is formed by a constant strain rate during the period 0 t1. This test includes as limiting cases the relaxation test (t1 → 0), the constant strain rate or stress growth experiment (t1 → ∞), and the stress relaxation after cessation of constant strain rate flow (t1 sufficiently large). The constant t1 can be chosen arbitrarily such that the test conditions of the combined test can be adjusted according to the problem investigated and to the capability of the testing device. From this, practical advantages follow for linear viscoelastic studies of polymeric solids and liquids, e.g., the zero shear viscosity η0 for unstable polymer melts can be determined at least approximately. In order to obtain linear viscoelastic material functions from the measured stress record, a simple procedure is given which avoids the difficulties with the “factor-of-10 rule” for short relaxation times.

Fracture Characteristics of Solids Containing Doubly-Periodic Arrays of Cracks

Abstract: The stress relaxation process from the tips of doubly-periodic (rectangular and diamond-shaped) arrays of slit-like cracks contained in an infinite elastic solid is studied under both plane and anti-plane strain conditions. The displacement discontinuities due to slit-like cracks are represented by distributions of suitable dislocations. The latter are determined from singular integral equations resulting from the satisfaction of the traction-free conditions at the crack faces. In the absence of a closed form solution, these equations are solved numerically after expanding the non-singular part of the kernel in a series of Chebyshev polynomials. Results are presented for the extent of spread of plasticity from each of the cracks and for the crack-tip opening displacement as functions of the horizontal and vertical crack spacings and the externally applied stress and discussed from the point of fracture initiation from an array of stress concentrations. It is shown that an array of cracks can have a detrimental or beneficial effect on the fracture characteristics of the solid depending on the far-field state of stress. Moreover, the crack-tip opening displacement is practically independent of the horizontal separation of cracks for small values of the distance of vertical separation and depends only on the latter.

Distribution of temperature, strain rate and strain in plastically deforming metals at high strain rates

Abstract: A method of calculating the distribution, and its time dependence, of temperature, strain rate and strain in plastically deforming metals is presented. It is assumed that the strain rate y depends on stress T and temperature T as γ = (const) Tm exp (-E/RT) where m, E and R are constants. It is found that the heat generated by deformation causes a significant inhomogeneous plastic deformation associated with the inhomogeneous temperature distribution in a specimen at high strain rates. The flow stress decrease arising from the inhomogeneous deformation is calculated; it is greater at lower temperatures, at higher strain rates and for longer specimens. The temperature rise in slip bands is also considered. Calculations are carried out for aluminium at temperatures above 100°C. Some of the results are compared with experimental observations.

Viscoelasticity of ABS samples differing in thermal history

Abstract: An important parameter in the various molding techniques used in polymer processing is the rate of cooling the object. The effect of the thermal history on the linear viscoelastic properties was studied, mainly by means of stress relaxation experiments on ABS samples in which the influence of other process variables was eliminated. In agreement with recent literature data, it appeared that the time dependence of the stress can be represented by a universal formula, provided that no perceptible change in temperature or relaxation of volume takes place during the experiment. The position of the momentary relaxation curve along the time scale can therefore be described by one characteristic mechanical relaxation time tr. The value of tr is affected by the temperature T, but even more by the thermal history, i.e., by the rate of cooling, q, and the annealing time, ta, at the measuring temperature previous to recording of the relaxation curve. In the case of very rapidly quenched samples, exact proportionality was found to exist between tr and ta at temperatures below Tg −15°C. In slowly cooled samples tr can be longer by a factor of ten than in quenched samples, at the same T and at annealing times of about 1 h. The difference decreases with increasing ta, but remains substantial up to ta values much longer than the total cooling time.