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.     

Ageing characteristics of Al-2.5% Li rapidly solidified alloy

The present work was performed on an Al–2.5 wt% Li alloy produced by melt spinning. The ribbons were aged in the temperature range 180 to 310° C for times between 1 min and 120h. The kinetics of coarsening of (Al₃Li) and (AlLi) phase particles were investigated using transmission electron microscopy and hardness measurements. The results show that coarsening of (Al₃Li) follows a simple linear relation with the cube root of Me, whereas coarsening of (AlLi) does not follow the same trend. We believe that the (AlLi) phase nucleates at the (Al₃Li)/matrix interface and grows by the dissolution of the nearby (Al₃Li) particles. The mechanical properties of the powder metallurgy alloy show that a large volume fraction of PFZ contributes to the alloy ductility, 11 %, in the aged condition. Also, the yield strength is greatly improved due to refinement effects enhanced by rapid solidification.     

On the measurement and physical meaning of the cleavage fracture stress in steel

Elastic-plastic two-dimensional (2D) and three-dimensional (3D) finite element models (FEM) are used to analyze the stress distributions ahead of notches of four-point bending (4PB) and three-point bending (3PB) specimens with various sizes of a C-Mn steel. By accurately measuring the location of the cleavage initiation sites, the local cleavage fracture stress _f and the macroscopic cleavage fracture stress _F is accurately measured. The _f and _F measured by 2D FEM are higher than that by 3D FEM. _f values are lower than the _F, and the _f values could be predicted by _f=(0.8––1.0)_F. With increasing specimen sizes (W,B and a) and specimen widths (B) and changing loading methods (4PB and 3PB), the fracture load P _f changes considerably, but the _F and _f remain nearly constant. The stable lower boundary _F and _f values could be obtained by using notched specimens with sizes larger than the Griffiths–Owen specimen. The local cleavage fracture stress _f could be accurately used in the analysis of fracture micromechanism, and to characterize intrinsic toughness of steel. The macroscopic cleavage fracture stress _F is suggested to be a potential engineering parameter which can be used to assess fracture toughness of steel and to design engineering structure.     

Fatigue properties of pure metals

The report considers the stress fatigue limit _D, the fatigue to tensile strength ratio _D/R_m, and the deformation fatigue limit _D of pure metals. For FCC and some HCP metals there exists a linear correlation between fatigue limit and tensile strength. The fatigue limit and the fatigue ratio _D/R_m depend upon the homologous temperature. The fatigue ratios of BCC metals are higher than the fatigue ratios of other metals at room temperature as is also true for metals with nearly the same homologous temperature. The deformation fatigue limit decreases rapidly when T_h - 0.5 and T_h 1. When T_h = 1 then _D = 0, _D = 0 and _D/R_m = 0. The deformation fatigue limits of metals belonging to the same subgroup of the periodic element system and having, similar homologous temperatures at room temperature are very similar.

---

Zusammenfassung Der Artikel behandelt die Dauerfestigkeit _D des Ermuedungskoeffizienten _D/R_m und die Deformation _D, die der Dauerfestigkeit entspricht. Fuer kubisch flachzentrierte Metalle und einige hexagonal Metalle existiert eine lineare Korrelation zwischen Dauerfestigkeit _D and Zugfestigkeit R_m. Die Dauerfestigkeit _D und der Ermuedungskoeffizient _D/R_m koennen als Funktion der homologischen Temperatur betrachtet werden. Der Ermuedungskoeffizient der kubisch raumzentrierten Metalle ist groesser als der der anderen in Raumtemperatur. Dieses stimmt auch fuer Metalle mit aehnlichen hornologischen Temperaturen. Die Deformation _D, die der Dauerfestigkeit entspricht, faellt schnell ab, wenn T_h > 0.5 und T_h 1, Wenn T_h = 1, darn ist _D = 0, _D = 0 und _D/R_m = 0. Die Metalle, die zu derselben Gruppe des periodischen Systems der Elemente gehoeren and aehnliche homologische Temperaturen (in Raumtemperatur) besitzen, haben sehr aehnliche Werte der Deformation _D.

---

Résumé L'article parle de la contrainte de la limite de fatigue _D le facteur de fatigue _D/R_m et la déformation _D correspondante à la limite de fatigue des métaux pures. Pour les métaux du système cubique aux faces centrées (c. f. c.) et quelques uns du système hexagonale (hex. c.) il existe une correlation linéare entre la limite de fatigue _D et de la résistance a la fraction R_m. La limite de fatigue _D et le facteur de fatigue _D/R_m dependent de la température homologue. Les facteurs de la fatigue des métaux du système cubique centre (c.c.) sort plus grands que ceux des autres métaux dans la température de chambre, aussi por des métaux qui ont presque la même température homologue. La déformation correspondante à la limite de fatigue tombe rapidement quand T_h > 0.5 et T_h 1. Quand T_h = 1, alors _D = 0, _D = 0 et _D/R_m = 0. Cettes déformations _D pour les métaux du même groupe du système périodique des éléments sont proches si les températures homologues dans la température de chambre sont analogues.

     

Residual thermal stresses in the pull-out specimen: A finite element calculation

The residual thermal stress field in the pull-out specimen is calculated in the case of a high properties thermoset system (carbon-bismaleimide). The calculation is performed within the framework of the linear theory of elasticity by means of a finite element method. The specimen is modelled as a three-phase composite (holder-fibre-matrix). The meniscus which forms at the fibre entry is taken into account in order to provide a realistic stress concentration. The latter is far higher than the matrix strength. Evidence that fibre debonding propagates from the fibre end during cooling is then produced.Nomenclature T thermal load - L _e embedded length - r _f fibre radius - _c curvature radius of the meniscus (fibre entry) - r _c radial dimension of the finite element mesh - E _m,E _h matrix and holder moduli - E _A,E _T fibre axial and transverse moduli - _m, _h matrix and holder thermal expansion coefficients - _A, _T fibre axial and transverse thermal expansion coefficients - _rr, , _zz, _rz non-zero components of the residual stress field - _rr ⁱ , ^im , _zz ^im , _rz ⁱ stresses at the interface in the matrix (r=r _f + ) - _rr ⁱ , ^if , _zz ^if , _rz ⁱ stresses at the interface in the fibre (r=r _f–) - _p1 maximum principal stress - _zz ^f mean axial stress over the fibre section - _rupt ^m matrix strength - u _r ,u _z non-zero components of the displacement field     

Evaluation of the true activation enthalpy of superplastic flow including a threshold stress

A new method is suggested for the evaluation of the true activation enthalpy for alloys where the strain rate of the superplastic flow varies with a power of an effective stress _e = -_o, where and _o are the applied stress and a threshold stress, respectively. Some earlier results concerning superplastic AlMgZnCu alloys containing chromium and in which a strongly temperature-dependent threshold stress can be revealed, are reanalysed. The results are in good agreement with the previous ones. It has been shown further that for the alloys investigated the true activation energy increases with increasing chromium content.     

Effect of the temperature dependence of thermal properties on the thermal shock tests of ceramics

Thermal stress generated during a thermal shock is closely related to the fracture of ceramics. An attempt has been made to obtain thermal stress in a specimen by numerical calculation. The temperature dependence of thermal conductivity and diffusivity were introduced to realize the practical thermal conditions. The maximum thermal stress, _max ^* , was recognized at the Fourier number, but differed from the temperature dependence. Correlative equations of _max ^* and _max ^* with the Biot number, _i, under cooling or heating tests, have been proposed. These equations resulted in the exact _max ^* and _max ^* compared with the previous equations, in which temperature dependence was ignored. The thermal shock resistance parameter was expressed by the correlative equations of _max ^* in order to suggest adequate experimental conditions and specimen size. A comparison of the measured and calculated time to failure of the specimen led to confirmation of the fracture criterion. The measured time disagreed with the calculated one, if the fracture by thermal shocking was not predominant. The correlative equations were also useful to select the kind of ceramics subjected to thermal shocking.     

Deformation of a carbon-epoxy composite under hydrostatic pressure

This paper describes the behaviour of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures. The composite consisted of 36% by volume of continuous fibres of Modmur Type II embedded in Epikote 828 epoxy resin. When deformed under pressures of less than 100 MPa the composite failed by longitudinal splitting, but splitting was suppressed at higher pressures (up to 500 MPa) and failure was by kinking. The failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant. This suggests that the pressure effects were introduced by fracture processes. Microscopical examination of the kinked structures showed that the carbon fibres in the kink bands were broken into many fairly uniform short lengths. A model for kinking in the composite is suggested which involves the buckling and fracture of the carbon fibres.List of symbols d diameter of fibre - E _f elastic modulus of fibre - E _m elastic modulus of epoxy - G _m shear modulus of epoxy - k radius of gyration of fibre section - l length of buckle in fibre - P confining pressure (= ₂ = ₃) - R radius of bent fibre - V _f volume fraction of fibres in composite - _t, _c bending strains in fibres - angle between the plane of fracture and ₁ - ₁ principal stress - ₃ confining pressure - _c strength of composite - _f strength of fibre in buckling mode - _n normal stress on a fracture plane - _m strength of epoxy matrix - shear stress - tangent slope of Mohr envelope - slope of pressure versus strength curves in Figs. 3 and 4.     

Fracture stress difference of notched polycarbonate between atmospheric pressure and a hydrostatic pressure

Experimental data on fracture stress of polycarbonate (PC) with and without various artificial notches have been obtained at atmospheric pressure and a high hydrostatic pressure (400 MPa). The difference in fracture stress, _F, between both pressures was directly proportional to the intensity of pressure,P, and was inversely proportional to the stress concentration factor of the notch,K _n such that _F following the form of the Kaieda-Oguchi formula, _F. By using the combined stress concentration factor,K _nc, of superposed notch and craze, and by considering the change in elastic modulus due to pressure, the experimental data agreed with the modified Kaieda-Oguchi formula. The stress concentration factor of the craze was calculated by using the Dugdale model.     

Influence of threshold parameters on cleavage fracture predictions using the Weibull stress model

This study explores applications of three-parameter Weibull stress models to predict cleavage fracture behavior in ferritic structural steels tested in the transition region. The work emphasizes the role of the threshold parameters (_th and _{w – min}) in cleavage fracture predictions of a surface crack specimen loaded predominantly in tension for an A515-70 pressure vessel steel. A recently proposed procedure based upon a toughness scaling methodology using a modified Weibull stress (^* _w) extends the calibration scheme for the Weibull modulus, m, to include the threshold parameters. The methodology is applied to calibrate the Weibull stress parameter for the tested material and then to predict the toughness distribution for the surface crack specimen. While the functional relationship between ^* _w and m suggests a strong effect of the threshold stress, _th, on the calibrated m-parameter, the results show a remarkably weak dependence of fracture predictions on _th as does the dependence of fracture predictions on _w–min for this specimen.     

Ionic and electronic conductivity in some simple lithium salts

The electrical conductivity () and thermoelectric power (S) of Li₃VO₄, Li₃PO₄ and Li₃BO₃ solidified melts are presented in the temperature range from 415 K to the melting point of each solid. The ionic ( _i,) and electronic ( _e) contributions to have been separated over the entire temperature range with the help of a time-dependence study of the d.c. electrical conductivity. Superionic phases in all three solids have been observed below their melting points in which the conductivity is almost purely ionic. The value of the phase transition temperature below which the solid transforms from superionic to normal phase has been obtained. It has been shown that in the normal phase, these solids are mixed conductors. Data for the temperature variations of both _i, and _e are also presented and discussed.     

The physics and mechanics of fibre-reinforced brittle matrix composites

This review compiles knowledge about the mechanical and structural performance of brittle matrix composites. The overall philosophy recognizes the need for models that allow efficient interpolation between experimental results, as the constituents and the fibre architecture are varied. This approach is necessary because empirical methods are prohibitively expensive. Moreover, the field is not yet mature, though evolving rapidly. Consequently, an attempt is made to provide a framework into which models could be inserted, and then validated by means of an efficient experimental matrix. The most comprehensive available models and the status of experimental assessments are reviewed. The phenomena given emphasis include: the stress/strain behaviour in tension and shear, the ultimate tensile strength and notch sensitivity, fatigue, stress corrosion and creep.Nomenclature a _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - a _o Length of unbridged matrix crack - a _m Fracture mirror radius - a _N Notch size - a _t Transition flaw size - b Plate dimension - b _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - c _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - d Matrix crack spacing - d _s Saturation crack spacing - f Fibre volume fraction - f _l Fibre volume fraction in the loading direction - g Function related to cracking of 90 ° plies - h Fibre pull-out length - l Sliding length - l _i Debond length - l _s Shear band length - m Shape parameter for fibre strength distribution - m _m Shape parameter for matrix flaw-size distribution - n Creep exponent - n _m Creep exponent for matrix - n _f Creep exponent for fibre - q Residual stress in matrix in axial orientation - s _ij Deviatoric stress - t Time - t _p Ply thickness - t _b Beam thickness - u Crack opening displacement (COD) - u _a COD due to applied stress - u _b COD due to bridging - v Sliding displacement - w Beam width - B Creep rheology parameter _o/ _o ⁿ - C _v Specific heat at constant strain - E Young's modulus for composite - E _o Plane strain Young's modulus for composites - Unloading modulus - E _* Young's modulus of material with matrix cracks - E _f Young's modulus of fibre - E _m Young's modulus of matrix - E _L Ply modulus in longitudinal orientation - E _T Ply modulus in transverse orientation - E _t Tangent modulus - E _s Secant modulus - G Shear modulus - G Energy release rate (ERR) - G _tip Tip ERR - G _tip ^o Tip ERR at lower bound - K Stress intensity factor (SIF) - K _b SIF caused by bridging - K _m Critical SIF for matrix - K _R Crack growth resistance - K _tip SIF at crack tip - I _o Moment of inertia - L Crack spacing in 90 ° plies - L _f Fragment length - L _g Gauge length - L _o Reference length for fibres - N Number of fatigue cycles - N _s Number of cycles at which sliding stress reaches steady-state - R Fibre radius - R R-ratio for fatigue (_max/_min) - R _c Radius of curvature - S Tensile strength of fibre - S _b Dry bundle strength of fibres - S _c Characteristic fibre strength - S _g UTS subject to global load sharing - S _o Scale factor for fibre strength - S _p Pull-out strength - S _th Threshold stress for fatigue - S _u Ultimate tensile strength (UTS) - S _* UTS in the presence of a flaw - T Temperature - T Change in temperature - t Traction function for thermomechanical fatigue (TMF) - t _b Bridging function for TMF - Linear thermal coefficient of expansion (TCE) - _f TCE of fibre - _m TCE of matrix - Shear strain - _c Shear ductility - _c Characteristic length - Hysteresis loop width - Strain - _* Strain caused by relief of residual stress upon matrix cracking - _e Elastic strain - _o Permanent strain - _o Reference strain rate for creep - Transient creep strain - _s Sliding strain - Pull-out parameter - Friction coefficient - Fatigue exponent (of order 0.1) - Beam curvature - Poisson's ratio - Orientation of interlaminar cracks - Density - Stress - _b Bridging stress - ¯_b Peak, reference stress - _e Effective stress = [(3/2)s _ijs_ij]^1/2 - _f Stress in fibre - _i Debond stress - _m Stress in matrix - _mc Matrix cracking stress - ^o Stress on 0 ° plies - _o Creep reference stress - _rr Radial stress - ^R Residual stress - _s Saturation stress - _s ^* Peak stress for traction law - Lower bound stress for tunnel cracking - ^T Misfit stress - Interface sliding stress - _f Value of sliding stress after fatigue - _o Constant component of interface sliding stress - _s In-plane shear strength - ¯_c Critical stress for interlaminar crack growth - _ss Steady-state value of after fatigue - ^R Displacement caused by matrix removal - _p Unloading strain differential - _o Reloading strain differential - Fracture energy - _i Interface debond energy - _f Fibre fracture energy - _m Matrix fracture energy - _R Fracture resistance - _s Steady-state fracture resistance - _T Transverse fracture energy - Misfit strain - _o Misfit strain at ambient temperature     

Effect of magnesium content on the stress exponent and effective stress in the steady state creep of Al-Mg alloys

The stress exponent of steady state creep,n, and the internal ( _i) and effective stresses ( _e) have been determined using the strain transient dip test for a series of polycrystalline Al-Mg alloys creep tested at 300° C and compared with previously published data. The internal or dislocation back stress, _i, varied with applied stress,, but was insensitive to magnesium content of the alloy, being represented by the empirical equation _i=1.084 ^1.802. Such an applied stress dependence of _i can be explained by using an equation for _i of the form _i (dislocation density)^1/2 and published values for the stress dependence of dislocation density. Values of the friction stress, _f, derived using the equation _e/=(1–c) (1– _f/), indicate that _f is not dependent on the magnesium content. A constant value of _f can best be rationalized by postulating that the creep dislocation structure is relatively insensitive to the magnesium content of the alloy.On leave from Engineering Materials Department, University of Windsor, Windsor, Ontario N9B 3P4, Canada.     

Stress relaxation in hot-drawn low density polyethylene

The tensile stress relaxation behaviour of hot-drawn low density polyethylene, (LDPE), has been investigated at room temperature at various draw ratios. The drawing was performed at 85° C. The main result was an increase in relaxation rate in the draw direction, especially at low draw ratios when compared to the relaxation behaviour of the isotropic material. This is attributed to a lowering of the internal stress. The position of the relaxation curves along the log time axis was also changed as a result of the drawing, corresponding to a shift to shorter times. The activation volume, , varied with the initial effective stress ₀ ^* according to ₀ ^* 10kT, where ₀ ^* =₀ — _i, is the difference between the applied initial stress, ₀, and the internal stress _i. This result supports earlier findings relating to similarities in the stress relaxation behaviour of different solids.     

Bending of square aluminium extrusions with aluminium foam filler

Summary An experimental programme consisting of 24 tests was carried out to study the three-point-bending behavior of square AA6060 aluminium extrusions filled with aluminium foam under quasi-static loading conditions. The outer cross section width and span of the beams were kept constant at 80 mm and 800 mm, respectively. The main parameters investigated were the foam density, the extrusion wall strength and the extrusion wall thickness. The experiments showed that the foam filler significantly altered the local deformation pattern of the beams. Simple design formulae were developed in order to predict the load bearing capacity of the foam filled beams.Notation d load cell displacement - total beam rotation - ₀₂ total beam rotation at extrusion flange yielding (non-filled beam) - ₁, ₂ beam end rotations - b outer component cross section width - h component wall thickness - L total beam span length - s central load section of beam - A _e extrusion cross sectional area - A _f foam cross sectional area - P load cell force - M total cross section moment - M _e extrusion moment - M ₀₂ maximum elastic moment capacity of extrusion - M _pl perfect plastic moment capacity of extrusion - M _f foam core moment - M _sf maximum foam core moment - M _s total initial peak moment - M _sa total moment capacity after foam failure - M _u ultimate extrusion moment capacity - M _se calculated moment resistance of extrusion at foam failure - stress, engineering - ₀₂ extrusion wall stress at 0.2% plastic strain - _U extrusion wall ultimate stress - ₀ extrusion wall characteristic stress, 0.5(₀₂+ _U ) - _f foam plateau stress - _s foam tensile failure stress - strain, engineering - ₀₂ extrusion strain corresponding to yield stress ₀₂ - _u extrusion strain corresponding to ultimate stress _U - _s foam tensile failure strain - beam curvature - ₀₂ beam curvature at extrusion flange yielding - _u beam curvature at extrusion ultimate stress - _s beam curvature at foam tensile failure strain - f extrusion section shape factor - k elastic bending stiffness ratio between foam core and extrusion - E extrusion Young's modulus - E _t extrusion tangential modulus - n extrusion material hardening constant - _f foam density - _i foam batch density,i=1, 2, 3 - x, y, z coordinate reference system (x-beam axis) - x _c distance from beam end (change in formula for curvature)     

A note on the resistance to brittle fracture in various ceramic materials

The square of the ratio of the abraded bending strength, _d, to the unabraded bending strength, , is proposed as a measure of the resistance to crack propagation in ceramic materials. Data for various porcelains, glass-ceramics, and glasses showed that _d is essentially constant and that (_d/)² decreased rapidly with increase of the unabraded strength.     

Conventional Electronic Structure of MgB2 and ZrB2: LDA vs. de Haas-v. Alphen & ARPES Data

We compare full potential LDA band calculations of the Fermi surfaces areas and band masses of MgB₂ and ZrB₂ previously reported and new dHvA data. Discrepancies in areas in MgB₂ can be removed by a small shift of bands relative to bands. Comparison of effective masses lead to orbit averaged el-ph coupling constants =1.3 and =0.5, whereas for ZrB₂ only weak el-ph coupling with <0.3 is found. The ARPES data can be also well described by the LDA showing the presence of surface states.     

Inhomogeneous shear flows of linear polymers

Solutions of a system of equations of nonlinear viscoelastic fluid motion describing inhomogeneous shear flows of linear polymers are indicated.Notation _ij stress tensor - p pressure - F_i mass force vector - _ij Kronecker delta - coefficient of shear viscosity - relaxation time - _ij inner parameter - _ij=vi/x_j velocity gradient tensor - ₀ initial value of the shear viscosity coefficient - ₀ initial value of the relaxation time - D dimensionless first invariant of the additional stress tensor - A, B, C constants of integration - f(D) universal function characterizing the material - r, , z cylindrical coordinates - u=v_z axial component of the velocity vector - v=v circumferential component of the velocity vector - ₁, ₂ first and second differences of the normal stress - Q volume mass flow rate - R radius of a circular tube - R₁, R₂ radii of the inner and outer cylinders, respectively - M moment per unit length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 449–456, September, 1981.     

Quantum statistical foundation to the fermi liquid model and Ginzburg-Landau wave function

An energy eigenvalue equation for a quasi-particle is derived, starting with the Heisenberg equation of motion for an annihilation operator. An elementary derivation of the Fermi liquid model having a sharply defined Fermi surface in thek-space is given, starting with a realistic model of a metal including the Coulomb interaction amongand between electrons and lattice-ions. The Ginzburg-Landau wave function (r), where represents the superconducting pairon (Cooper-pair) state, is shown to be connected with the one-pairon density operatorn by (r) = r¦_n ^1/2¦. A close analogy between supercurrent and laser is indicated.On sabbatical leave from Department of Physics and Astronomy, State University of New York at Buffalo, Buffalo, New York.     

Transport property and battery discharge characteristic studies on 1−x(0.75Agl∶0.25AgCl)∶ xAl2O3 composite electrolyte system

Various experimental studies on a new fast Ag⁺ ion-conducting composite electrolyte system: (1–x) (0.75Agl0.25AgCl)xAl₂O₃ are reported. Undried Al₂O₃ particles of size <10 m were used. The conventional matrix material Agl has been replaced by a new mixed 0.75Agl0.25AgCl quenched and/or annealed host compound. Conductivity enhancements 10 from the annealed host and 3 times from the quenched host obtained for the composition 0.7(0.75Agl0.25AgCl)0.3Al₂O₃, can be explained on the basis of the space charge interface mechanism. Direct measurements of ionic mobility as function of temperature together with the conductivity were carried out for the best composition. Subsequently, the mobile ion concentration n values were calculated from and a data. The value of heat of ion transport q* obtained from the plot of thermoelectric power versus 1/T supports Rice and Roth's free ion theory for superionic conductors. Using the best composition as an electrolyte various solid state batteries were fabricated and studied at room temperature with different cathode preparations and load conditions.