Viscoelastic-plastic behaviour with mean strain changes in polypropylene

The stress-strain curves and stress-relaxation curves of polypropylene are obtained by using a closed-loop, electrohydraulic, servo-controlled testing machine. Effects of mean strain changes on deformation behaviour are examined in a tension-compression mode under strain control at room temperature (18–23 °C). The hysteresis loops of three mean strains show a steady-state response from the stress-strain curves at a strain rate of 1 × 10^–3 s^–1 at a strain width of 5%, at a number of cycles of N=50 and at three mean strains (_m=0, + 1.0 and + 2.0%). The drop of stress at the mean strain of _m= -1.0% is larger in magnitude than that at _m=+1.0%; this is caused by the higher stress level at _m=- 1.0% as compared with the stress level at _m=+1.0%. From the results of stress amplitude and the stress drop behaviour, the magnitude of stress drop is hardly affected by the mean strain.     

Plastic deformation resistance of an indium-lead alloy with strain rates of 10−3–103 sec−1

Nonstandard A vs , N vs , and log vs diagrams were obtained for an indiumlead alloy using a common method together with standard vs diagrams. The strength, deformation, and energy characteristics and their variation coefficient were determined in the _pl.=10^–3–10³ sec^–1 plastic strain rate range. The influence of an increase in _pl on the plastic deformation resistance of the indium-lead alloy is revealed in a significant (up to 100%) increase in the strength and energy characteristics.Translated from Problemy Prochnosti, No. 3, pp. 53–57, March, 1990.     

Decreasing of the initial shear modulus with increasing axial strain explained by means of a plastic-hypoelastic model

Summary The purpose of this work is to examine in detail the possibility to explain the decreasing of the initial shear modulus with increasing axial strain, observed first by Feigen, by means of the plastic-hypoelastic stress-strain relation suggested by Lehmann and by the author of the present paper.Notations _ij components of the infinitesimal strain tensor dilatation - strain deviator - _ij components of the stress tensor - spherical part of the stress tensor - stress deviator - ²= _{ij ij} second invariant of the stress deviator - = ₃₃ axial strain - e= ₁₃ shear component of the strain tensor - =2 ₁₃ shear strain - = ₃₃ axial stress - s= ₁₃ shear stress - T _ij components of Cauchy's stress tensor - F _ij components of the deformation gradient - L _ij components of the velocity gradient (Eulerian coordinates) - components of the rate of deformation tensor - components of the spin tensor - components of the rate of deformations deviator - components of Cauchy's stress deviator - T=T ₃₃ axial Cauchy's stress With 7 Figures     

Thermomechanic behavior of a polymer upon its formation in a crystallization process: Theoretical principles,hypotheses, and mathematical model

A model of thermomechanic behavior of a polymer upon its formation in a crystallization process is proposed. Based on methods of nonequilibrium thermodynamics governing relationships are obtained which make it possible to establish the dependence of the final degree of crystallicity of the material on the history of the crystallization process and to explain the mechanism of formation of the remanent stresses in a polymer article.Notation u translation vector - v velocity vector - acceleration vector - absolute temperature - density - c specific heat capacity - deformation tensor - strain tensor - specific enthropy - U ^* internal energy - z specific free enthalpy - _i internal parameters of state - t time - q heat flux vector - matrix of heat conduction coefficients - W ^* energy dissipation - F vector of mass forces - the 4th rank tensor of elastic pliabilities - matrix of heat expansion coefficients - tensor of contribution of structural variations to deformation - function of equilibrium value ^* - p mean pressure - deviator of the tensor of deformations - spherical part of the deformation tensor - deviator of the tensor of stresses - K volume modulus - unity tensor - Q enthalpy of the crystallization process - Q _eq enthalpy of the equilibrium crystallization process - _g glass transition temperature - ^*() the curve obtained in the equilibrium crystallization process - f final degree of crystallicity Institute of Mechanics of Continuous Media of the Ural Branch of the Russian Academy of Sciences, Perm', Russia. Institute of Technical Chemistry of the Ural Branch of the Russian Academy of Sciences, Perm', Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 479–485, May–June, 1995.     

Theory of dielectric polarization of a substance. Calculation of dielectric permittivity of water,ammonia, and chlorine

A theory of dielectric polarization of a substance is developed. The theory is verified by experiment and by phenomenological relations that follow from the determination of polarization, molar polarization, and dielectric permittivity.Notation _s static dielectric permittivity - high-frequency dielectric permittivity - _s permittivity perpendicular to the acisC - _s permittivity in the direction of the axisC - a average molecular polarizability - dielectric susceptibility - _i molecular hyperpolarizability - p ⁰ constant dipole moment of a molecule - p dipole moment of a molecule in condensed state - p _add additional dipole moment of a molecule - P polarization of a substance - P _m molar polarization - k Boltzmann constant - T Kelvin temperature - t Celsius temperature - angle between the vectors and - F internal electric field strength - Û internal interaction energy, J·mol^–1 - û internal interaction energy per molecule - N ₀ Avogacro number - V ₀ molar volume - a _t total molecular polarizability - H ⁰ (H) enthalpy as a function of temperature - l(x) Langevin function - n molecular concentration Murmansk State Academy of Fish Fleet. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 5, pp. 767–773, September–October, 1995.     

Analysis of the tensile properties and fractography of as-cast and heat treated 359-SiC-20p composite

An experimental study of the heat treatment of 359-SiC 20p composite and its base alloy was made to determine the strength-ductility characteristics under varying conditions of heat treatment. Microstructural observations revealed that addition of the SiC_p reinforcement to the base alloy produced a more uniform and refined interdendritic microstructure compared to the latter. The tensile data obtained was analysed in terms of the theoretical models existing in the composite literature. Ultimate tensile strength (UTS)-log elongation relationships were obtained to test the applicability of the quality index parameter,Q, to the present composite. From this analysis, it was found that all data points in the ageing temperature range 140–210 °C could be represented by a single line (cf. two lines in the case of 359 alloy), indicating the important fact that the tensile properties of this composite can be predicted/determined over the entire temperature range. The presence of the SiC particles was seen to accelerate the Mg₂Si precipitation kinetics, but not to alter it. Fracture mechanisms were determined from both the fracture surfaces and their longitudinal sections beneath the fracture surface, employing both optical and scanning electron microscopy.Nomenclature a Particle diameter - b Burger's vector - b _ii Numerical constant relating P _ii ^E _m andP ₃₃ ^A - E _c Young's modulus of the composite - E _m Young's modulus of the matrix - E _p Young's modulus of SiC particles - El Elongation (%) - f _p SiC volume fraction - P ₃₃ ^A Applied stress - P _ii ^E Long range back stress developed by elastic misfit - P _m ^F Change in matrix flow stress - <P _ii ^P >_m Back stresses due to plastic deformation - P _c ^ps Proof strain of a composite - q _ii Plastic misfit - Q Quality index - R Statistical correlation coefficient - RE Rockwell E hardness value - S SiC particle aspect ratio - S _c Critical aspect ratio for the SiC particles - UTS Ultimate tensile strength of the alloy or composite - YS Yield strength of the alloy or composite - Critical misfit strain - Constant, 1.25 for aluminum alloys - Plastic strain - ^ps Plastic strain at whichP _c ^ps is required - Work hardening rate at a given plastic strain - Work hardening rate as a function of total strain - Shear modulus - Dislocation density - _c ^O Yield stress of the composite - _CTE Increase in yield stress due to coefficient of thermal expansion (CTE) - _m ^O Yield stress of the matrix - _p Particle strength - _i Interfacial shear strength     

Tangent modulus tensor in plasticity under finite strain

Summary The tangent modulus tensor, denoted as , plays a central role in finite element simulation of nonlinear applications such as metalforming. Using Kronecker product notation, compact expressions for have been derived in Refs. [1]–[3] for hyperelastic materials with reference to the Lagrangian configuration. In the current investigation, the corresponding expression is derived for materials experiencing finite strain due to plastic flow, starting from yield and flow relations referred to the current configuration. Issues posed by the decomposition into elastic and plastic strains and by the objective stress flux are addressed. Associated and non-associated models are accommodated, as is plastic incompressibility. A constitutive inequality with uniqueness implications is formulated which extends the condition for stability in the small to finite strain. Modifications of are presented which accommodate kinematic hardening. As an illustration, is presented for finite torsion of a shaft, comprised of a steel described by a von Mises yield function with isotropic hardening.Notation B strain displacement matrix - C=F ^T F Green strain tensor - compliance matrix - D=(L+L ^T )/2 deformation rate tensor - D fourth order tangent modulus tensor - tangent modulus tensor (second order) - d VEC(D) - e VEC() - E Eulerian pseudostrain - F, F _e ,F _p Helmholtz free energy - F=x/X deformation gradient tensor - f consistent force vector - residual function - G strain displacement matrix - h history vector - h time interval - H function arising in tangent modulus tensor - I, I ₉ identity tensor - i VEC(I) - k ₀,k ₁ parameters of yield function - K _g geometric stiffness matrix - K _T tangent stiffness matrix - k _k kinematic hardening coefficient - J Jacobian matrix - L=v/x velocity gradient tensor - m unit normal vector to yield surface - M strain-displacement matrix - N shape function matrix - n unit normal vector to deformed surface - n ₀ unit normal vector to undeformed surface - n unit normal vector to potential surface - r, R, R ₀ radial coordinate - s VEC() - S deformed surface - S ₀ undeformed surface - t time - t, t ₀ traction - t VEC() - VEC( ) - t VEC() - t _r reference stress interior to the yield surface - t t–t _r - T kinematic hardening modulus matrix - u=x–X displacement vector - U permutation matrix - v=x/t particle velocity - V deformed volume - V ₀ undeformed volume - X position vector of a given particle in the undeformed configuration - x(X,t) position vector in the deformed configuration - z, Z axial coordinate - vector of nodal displacements - =(F ^T F–I)/2 Lagrangian strain tensor - history parameter scalar - , azimuthal coordinate - elastic bulk modulus - flow rule coefficient - twisting rate coefficient - elastic shear modulus - iterate - Second Piola-Kirchhoff stress - Cauchy stress - Truesdell stress flux - deviatoric Cauchy stress - Y, Y yield function - residual function - plastic potential - X, Xe, Xp second order tangent modulus tensors in current configuration - X, Xe, Xp second order tangent modulus tensors in undeformed configuration - (.) variational operator - VEC(.) vectorization operator - TEN(.) Kronecker operator - tr(.) trace - Kronecker product     

Coefficients of mass transfer between a fluidized bed and the surface of a capillary-porous body

Results are presented from a theoretical determination of coefficients of mass transfer between a fluidized bed of porous particles and a capillary-porous body.Notation a particle radius - F area of contact of particles with the surface of the body - f percentage of area of surface of product in contact with the bubble phase - g acceleration due to gravity - i flow of liquid mass from a unit area of the surface - N number of fluidizations - n number of particles coming into contact with a surface of unit area per unit of time - p_p, p_b capillary potentials of particles and product - R₂, R₁ radii of narrow and broad pores inside the product - r radius of capillaries in the particles - S area of the surface being treated - T temperature of the bed - t time of treatment - u percentage content of liquid in the specimen - V volume of the product being treated - v mean square component of the fluctuation velocity of the particles in the direction normal to the surface - , * standard and corrected mass-transfer coefficients determined from (5) and (9) - _b, _b, _p porosities of product determined for all and for only the small pores and the porosity of the material of the particles - _d, _m porosity of the dense phase and the porosity of the bed in the state of minimum fluidization - _b, _p angles of wetting of the materials of the product and particles, respectively, by the liquid binder - , viscosity and density of the liquid - ₀ density of the dry product - surface tension coefficient of the liquid - characteristic time of contact of particles with the surface - Re_m Reynolds number corresponding to particle radius and minimum-bed-fluidization velocity [6] Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 460–465, March, 1981.     

Rejuvenation procedures to recover creep properties of nickel-base superalloys by heat treatment and hot isostatic pressing techniques

The rejuvenation procedures to recover the creep properties of nickel-base superalloys by atmospheric pressure heat treatment and hot isostatic pressing techniques have been reviewed in detail. It is very important that such treatments be applied at an optimum stage in the service life of a turbine blade. In other words, the rejuvenation procedures must be applied early enough to prevent catastrophic failures or irreparable damage and late enough to give a cost-effective benefit. The optimum stage at which to undertake a rejuvenation procedure to extend the creep lives of superalloys is immediately prior to the tertiary stage. By using these techniques it is not possible to extend the creep lives of superalloys indefinitely because of the accumulation of some permanent damage incurred during service conditions.Nomenclature ERF Economic repair factor - P _r Price of repaired and rejuvenated part - P _n Price of new part - L _n Potential operational life of new part - L _r Potential operational life of repaired/rejuvenated part - N Cavity density or number of cavities per unit area (mm^–2) - n _v Number of cavities per unit volume (mm^–3) - Creep strain - ₁ Maximum principal stress (MPa) - ¯ von Mises effective shear stress (MPa) - t _f Time to failure - t _t Time to commencement of tertiary creep - Creep damage tolerance parameter - _f Strain at fracture (or failure) - T _m Absolute melting temperature - ₀ Friction stress - r Spherical radius of cavities - 2x Intercavity spacing - Grain boundary width - P _I Cavity gas pressure - P _H External hydrostatic pressure - Atomic volume - k Boltzmann constant - T Absolute temperature - Surface energy of the cavity - D _b Grain boundary diffusion coefficient - _d Ductility recovery parameter - Strain to reach the same acceleration after recovery annealing - ₀ Strain necessary for standard material to reach a given acceleration of the secondary-creep rate in the tertiary region - _t Strain needed to have produced the reduced cavity volume after rejuvenation annealing - Creep rate - Secondary or minimum creep rate - ₁ Strain previous to the regenerative annealing period - n Total number of strain/regenerative anneal cycles - _v Recovery parameter for cavity volume - V ₀ Original total cavity volume at the start of the recovery - V _t Cavity volume after recovery annealing for a timet     

Features of reaction stress generation in alloys based on titanium nickelide

Generation of reaction stresses is studied in relation to the magnitude of prior strain _pr, the part of it recovered, shape memory strain _SME, and method of assigning it in alloys based on titanium nickelide exhibiting different kinetic development of the shape memory effect, structural type, and phase transition temperatures. It is shown that curves for the dependence of maximum reaction stresses on shape memory strain _SME may either almost agree, independent of the method of assigning _pr and the nature of martensitic transformation, or be placed much lower than the tensile diagram for material in the austenitic condition.Translated from Problemy Prochnosti, No. 3, pp. 60–63, March, 1990.     

The effect of ionizing radiation on dielectric properties of bovine achilles tendon collagen in the temperature range of thermal denaturation

The effect of -irradiation, with doses from 10²–2×10³ kGy, on the dielectric properties of solid-state collagen was studied. The temperature dependence of the constants and ' revealed a decrease in the denaturation temperature with increasing dose of irradiation. Dielectric dispersion observed in the frequency range 10 Hz to 10 kHz was suggested to be due to Maxwell-Wagner-Sillars polarization. In addition, an increase in the irradiation dose resulted in increasing activation energy of bovine achilles tendon collagen.     

Slip flow past an approximate spheroid

Summary Creeping axisymmetric slip flow past a spheroid whose shape deviates slightly from that of a sphere is investigated. An exact solution is obtained to the first order in the small parameter characterizing the deformation. As an application, the case of flow past an oblate spheroid is considered and the drag experienced by it is evaluated. Special well-known cases are deduced and some observations made.Notation A _n, B_n, C_n, D_n, E_n, F_n, b₂, d₂ Constants - a, b radii of spheres - coefficient of sliding fraction - D drag - , _m parameters characterizing the deformation of the sphere - c a(1+) - viscosity coefficient - - dimensionless coordinate - I _n Gegenbauer function - P _n Legendre function - Stream function - U stream velocity at infinity     

Effect of intermittent polishing on low-cycle fatigue of pure aluminium

Low-cycle fatigue tests of aluminium were interrupted in order to remove surface roughening and superficial cracks produced by prior loading. Depending on the frequency of intermittent polishing and the strain level considerable increases in endurance life were observed.Nomenclature _t total strain range - _p plastic strain range - _e elastic strain range - N _p the number of cycles at which the intermittent polishing is carried out (single-step tests) - N _mp the number of cycles at which the last intermittent polishing action is performed in addition to preceding ones in every 50 cycles (multi-step tests) - N _pf the endurance life in the case of intermittent polishing (single- or multi-step tests) - N _f the endurance life without intermittent polishing     

Superconducting alloys containing paramagnetic impurities with local states within the gap. Effect of a magnetic field

The effect of a uniform magnetic field on a superconductor containing magnetic impurities has been investigated by treating the scattering of conduction electrons by magnetic impurities exactly (within the Shiba-Rusinov model). Our generalized equations defining the single-particle Green function reduce to earlier known results in appropriate limits. As an application of our equations we have calculated the transition temperature T _c. For fixed values of the parameter ₀ (the normalized position of the bound state within the BCS gap), the parameter p (the normalized magnetic field), and the parameter (=S _z ²/S²), the detailed dependence of T _c on the normalized impurity concentration ovc has been shown. The dependence of T _c on p for fixed values of ₀, ovc, and has also been shown. Our results are significantly different from the earlier known results.Work supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.     

Laminar thermal boundary layer on a continuous accelerated sheet extruded in an ambient fluid

Summary Exact boundary layer similarity solutions are developed for flow, friction and heat transfer on a continuously accelerated sheet extruded in an ambient fluid of a lower temperature.Melt-spinning, polymer and glass industries and the cooling of extruded metallic plates are practical applications of this problem.Results for skin-friction and heat-transfer coefficients are given. Larger acceleration is accompanied by larger skin-friction and heat-transfer coefficients. Rapid cooling of the sheet is accompanied by a larger Nusselt number.Nomenclature sheet width - c dimensionless constant - c _f local skin friction coefficient - F dimensionless transformed stream function - G dimensionless transformed temperature - local heat transfer coefficient - fluid thermal conductivity - length of deformation zone - m exponent of surface speed variation - q exponent of surface temperature variation - T dimensionless temperature - sheet surface temperature - solidification temperature - ambient temperature - sheet thickness - u velocity component along the sheet - u _s sheet surface velocity - wind up velocity - v velocity component normal to the sheet - x dimensionless coordinate along the sheet - y dimensionless coordinate normal to the sheet - Nu Nusselt number, - Pr Prandtl number, - Re Reynolds number, - =Re^–0.5 - dimensionless similarity coordinate - dynamic viscosity - kinematic viscosity - fluid mass density - sheet mass density - wall shear stress - dimensionless stream function With 3 Figures     

Measurement of temperature in a non-steady-state gas flow

A method is described for measuring the temperature of a non-steady-state gas flow with a thermocouple which is an inertial component of the first order.Notation T*_f non-steady-state gas flow temperature - T_t thermosensor temperature - thermal inertia factor of thermosensor - time - C total heat capacity of thermosensor sensitive element - S total heat-exchange surface between sensitive element and flow - heat-liberation coefficient - temperature distribution nonuniformity coefficient in sensitive element - Re, Nu, Pr, Bi, Pd hydromechanical and thermophysical similarity numbers - P^* total flow pressure - P static flow pressure - T^* total flow temperature - d_t sensitive element diameter - w gas flow velocity - flow density - flow viscosity - _f flow thermal conductivity - k gas adiabatic constant - R universal gas constant - M Mach number - T thermodynamic flow temperature - _o, _o and values at T=288°K - A, m, n, p, r coefficients - _c heat-liberation coefficient due to colvection - _r heat-liberation coefficient due to radiation - _b emissivity of sensitive element material - Stefan-Boltzmann constant - T_e temperature of walls of environment - _c, _r, _tc thermosensor thermal inertia factors due to convective, radiant, and conductive heat exchange - L length of sensitive element within flow - a thermal diffusivity of sensitive element material - _t thermal conductivity of sensitive element material Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 59–64, July, 1984.     

Dynamic scaling and ultrasonic attenuation in 4He near the superfluid transition point

Attenuation of first sound has been measured in ⁴He under saturated vapor pressure near the lambda temperature T at frequencies /2 ranging from 10.2 to 271 MHz. The frequency dependence of the critical part of the attenuation is determined and the dynamic scaling hypothesis is examined. Above the lambda point, it is found that the critical attenuation is described by a scaling function (, ) = ^1+y F(), where = ₀^–x and = T/T – 1, with the results x = 1.02±0.05 and y = 0.33±0.03. The characteristic frequency of the order-parameter fluctuation with the wave number k equal to the inverse correlation length is then proportional to ^x , which is in an excellent agreement with the prediction of dynamic scaling. Below the lambda point, a characteristic relaxation time or times shorter than previously expected at lower frequencies appears to exist in the present frequency range.Based on a Ph.D dissertation submitted by K. Tozaki to the University of Tokyo (1977).     

Thermal boundary resistance in superfluid4He nearT λ

New measurements of the boundary resistivity in superfluid⁴He (2ppb³He) nearT are reported as a function of ¦¦ ( =T/T (Q) — 1) and of heat flux Q in a cell with parallel polished copper surfaces. Here we call T(Q) the temperature where the superfluid state abruptly disappears. In this design, the sidewall gaps between the copper pieces and the stainless steel spacer were eliminated. In contrast to several previous experiments but in agreement with those of Li and Lip a, no largeQ-dependent boundary resistivity anomaly was detected. However, as ¦¦ 0 the small weakly divergent resistivity was observed and its dependence onQ over the experimental range 1 <Q < 80 W/cm² was found to be very small. These new results are compared with previous experiments and predictions. An explanation of the previously observed anomalous transport phenomena is presented in terms of a heat flow through the sidewall gaps in these cells, and its limitation by a critical flow value _c. This phenomenological model can be fit satisfactorily to the observations. In the appendix we calculate _c from mutual friction.     

A micromechanical method for predicting the precipitation hardening response of particle strengthened alloys hardened by ordered precipitates

Summary A micromechanical method was developed for predicting the precipitation hardening response of particle strengthened alloys hardened by ordered precipitates based on the microstructure, composition, and heat treatment, and utilizing a minimum number of experimental tests to evaluate the microstructural constants of the overall model. The overall approach was based on incorporating the dislocation particle interaction mechanics, particle growth and coarsening theory, thermodynamics, and particle strengthening mechanisms applicable to precipitation hardened alloys as part of the overall micromechanical method. The method/model evaluates, from a minimum number of experimental tensile tests, microstructural constants necessary in determining the precipitation srengthening response of a particle strengthened alloy. The materials that were used as vehicles to demonstrate and evaluate the model were precipitation hardenable aluminium-lithium-zirconium and nickel-aluminum alloys. Utilizing these demonstration alloys, the method used a total of four tensile tests to evaluate the necessary microstructural constants and thus predict the variation in strength as a function of aging time, aging temperature, and composition, for the underaged, the peak-aged, and the overaged conditions. Predictions of the precipitation strengthening response were made incorporating the Wagner particle distribution model to evaluate the size distributions of particles in the microstructures. The predicted variation of strength with aging practice and composition using the Wagner distribution model compared well with the corresponding experimental yield strength results.Notation b Burgers vector - average particle size diameter for a particle distribution - d _loop particle looping diameter for dislocation bypassing by Orowan looping - f _v volume fraction of precipitates - h() Wagner particle size distribution function - n _total total number of precipitate particles per unit area on a given microstructural plane - average particle size radius for a particle distribution - average planar particle size radius on a given microstructural plane - t aging time, in hours - average planar particle cross sectional area - G _t total shear modulus of the material - K _c particle growth rate constant - texture or Taylor grain orientation factor - N _v total number of precipitate particles per unit volume - Q _A activation energy for diffusion - R universal gas constant - T aging temperature - the interparticle separation or spacing - _y yield strength - _q as-quenched strength - _i intrinsic lattice strength - _c critical resolved shear strength - _loop critical resolved shear strength for dislocation particle bypassing via. Orowan looping - _particle total critical resolved shear strength for particle strengthening - _shear critical resolved shear strength for dislocation particle shearing, in underaged state     

On internal stress and activation volume in polymers

The two-site model is developed for the analysis of stress relaxation data. It is shown that the product of d In (– )/d and (- _i) is constant where is the applied stress, _i is the (deformation-induced) internal stress and = d/dt. The quantity d In ( )/d is often presented in the literature as the (experimental) activation volume, and there are many examples in which the above relationship with (- _i) holds true. This is in apparent contradiction to the arguments that lead to the association of the quantity d In (– )/d with the activation volume, since these normally start with the premise that the activation volume is independent of stress. In the modified theory presented here the source of this anomaly is apparent. Similar anomalies arise in the estimation of activation volume from creep or constant strain rate tests and these are also examined from the standpoint of the site model theory. In the derivation presented here full account is taken of the site population distribution and this is the major difference compared to most other analyses. The predicted behaviour is identical to that obtained with the standard linear solid. Consideration is also given to the orientation-dependence of stress-aided activation.