Environmental stress cracking of glassy polymers and solubility parameters

The use of solubility parameters to predict critical stress ( _c ^* ) or strains (_c) for environmental cracking/crazing in several glassy polymers (e.g. PMMA, PPO, PS, PVC, PSF and PC) is re-examined. It is shown that the enthalpic component ( _H ) of the Flory-Huggins semi-interaction parameter () does not always give a good correlation between _c and _H even though solvent molar volume and polymer-solvent molecular interactions have already been considered. Re-analysis of available experimental data using Gent's theory shows that there is a general trend for _c ^* (or _c) to increase with . These results, therefore, support Gent's proposed mechanism of environmental stress crazing/cracking. It is finally concluded that unless a definite relationship can be established between _c or _c ^* with _H it is not possible to predicta priori _c or _c ^* , given the empirical solubility parameters of a solvent. Unfortunately, there are not many such relationships as discovered in this paper.     

The anomalous thermal boundary resistance in superfluid4He near Tλ

The anomalous thermal boundary resistance R of superfluid⁴He near the lambda point T was studied in a cell with parallel copper faces and with various fluid layer thicknesses. The study was made as a function of the heat current Q and reduced temperature (T — T)/T = . In all cases, R tends to a maximum value R_itmax at T = T. This value is independent of Q, and is reproducible for various experiments. This contrasts with the regular boundary resistance which can vary considerably between successive experiments. Near T, the limiting slope dR/d¦¦ is found to be proportional to Q^–1, and this leads to a scaled representation of the data. This analysis is extended to data of similar experiments with gold plated copper surfaces by Duncan and Ahlers and by Zhong et al. The measurements of R over the whole range of¦¦ where it is observable are discussed and compared with previous experiments.     

Brittle matrices reinforced with polyalkene films of varying elastic moduli

The inclusion of polyalkene films of different moduli in a cement-based matrix has shown the benefits to be gained, in terms of increased stress at a given strain, from the use of films of high elastic modulus. Further, the concept of load-bearing cracks is used to explain the transition region between the limit of proportionality and the bend-over point on the tensile stress-strain curve, which is found to exist with high film modulus composites. This transition region could be an important factor affecting the choice of film to be used in a commercial composite.Nomenclature E _c uncracked composite modulus - E _m matrix modulus - E _f film modulus - V _m matrix volume-fraction - V _t film volume-fraction - V _f(crit) (E _{c mu})/ _fu - A _c cross-sectional area of composite - (E _m V _m/E _fV_f) - _m matrix strain - _mu matrix cracking strain - _mu average matrix cracking strain, (#x03C3;_co)/E _c - _mc strain at end of multiple cracking - _fu ultimate fibre stress - _cu ultimate composite stress - _co average composite cracking stress (assumed at a strain of _mc/2) - S4 81 draw ratio polypropylene film - S8 181 draw ratio polypropylene film - E3H polyethylene film - LOP limit of proportionality (stress at first crack, assumed to be a departure from linearity of the tensile stress-strain curve of a perfectly straight and uniform test specimen. However, this point cannot be reliably determined from the stress-strain curve because of the clamping strains induced in warped specimens) - BOP bend-over point (stress at which the approximately horizontal portion of multiple cracking region commences. The BOP is generally higher than the LOP and is a much more reliable point to determine experimentally than the LOP)     

Direct and inverse heat-conduction problems for a semiinfinite rod for a partial outflow of heat through the surface

Analytical solutions of the direct and inverse problems of nonstationary heat conduction in a thin semiinfinite rod are given for the case of radiative heat fluxes at the lateral surfaces and a partial outflow of heat by convection and radiation through the end of the rod.Notation thermal diffusivity - x₁ coordinate along the length of the rod - t₁ time - t=t₁/d² dimensionless time (Fourier number) - x=X₁/d relative coordinate - T_o initial temperature - Boltzmann constant - Sk=aT_c ³d/ Stark number - Bi=d/ reduced Biot number - emissivity Translated from Inzhenero-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 148–153, July, 1984.     

Stress-strain behaviour of nitrogen bearing austenitic stainless steels in the temperature range 298–473 K

The stress-strain behaviour of three nitrogen-bearing low-nickel austenitic stainless steels has been investigated via a series of tensile tests in the temperature range 298–473 K at an initial strain rate of 1.6×10^–5s^–1. Experimental stress-strain data were analysed employing Rosenbrock's minimization technique in terms of constitutive equations proposed by Hollomon, Ludwik, Voce and Ludwigson. Ludwigson's equation has been found to describe the flow behaviour accurately, followed by Voce's equation. The resultant strain-hardening parameters were analysed in terms of variations in temperature. A linear relationship between ultimate tensile stress and the Ludwigson parameters has been established. The influence of nitrogen on the Ludwigson modelling parameters has also been explained.Nomenclature True stress - _t True strain - _f True fracture strain - Strain rate - T Temperature - K _H, n _H Hollomon parameters - K _L, n _L Ludwik parameters - K _1L, k _2L, n _1L, n _2L Ludwigson parameters - _s, K _V, n _V Voce parameters - _{u relation} Uniform strain computed from a particular relation - _L Transient strain - ₀ Flow stress at zero plastic strain (Ludwik) - _L Transient stress - _y Yield stress - _u Ultimate tensile stress     

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     

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     

Morphological investigations of a textured black copper selective coating

The microstructural investigations of a textured black copper selective coating are reported. These surfaces possess remarkably high initial absorptance 0.97 to 0.98 and emittance ₁₀₀ 0.2 ± 0.02. These surfaces reveal a new sponge-like, porous, layered microstructure. They are made of loosely packed long and fine grains which appear randomly distributed. The copper grains are dispersed in a semiconductor oxide matrix. The spacing between these grains is of the order of solar wavelength. Also, these surfaces possess opulent solar selectivity and structural stability up to 250° C in air and under vacuum conditions.     

A mathematical programming approach to a problem in variance penalised Markov decision processes

In this paper we present three algorithms for solving a problem in which it is required to get an optimal compromise between the average expected reward per unit time and the variance of the reward per unit time. The algorithms lead to an-optimal solution, where>0 is arbitrary.     

High-frequency dielectric behaviour of polycrystalline zinc substituted cobalt ferrites

The dielectric constant () and complex dielectric constant () of zinc substituted cobalt ferrites have been measured at room temperature in the high frequency range 100 kHz to 1 MHz. The values of dielectric loss tangent (tan ) have been computed from and . Plots of dielectric constant () versus frequency show a normal dielectric behaviour of the spinel ferrites. The frequency dependence of dielectric loss tangent (tan ) is found to be abnormal, giving a peak at certain frequency for all the ferrites under investigation. A qualitative explanation is given for the composition and frequency dependence of the dielectric constant and dielectric loss tangent. The dielectric constant for these mixed ferrites is approximately inversely proportional to the square root of the resistivity. A plot of dielectric constant versus temperature shows a transition near the Curie temperature. An attempt is made to explain the possible mechanism for this observation.     

Low endurance fatigue in metals and polymers

The fatigue behaviour of commercially pure aluminium and of nylon under sequentially varying strain amplitudes is compared with a damage law of the type suggested by Miner. Aluminium obeys such a law for both cyclic and uniaxial prestrains but the behaviour of nylon is significantly affected by microcracking, which produces a marked effect of loading sequence.Appendix N Number of strain cycles at a given time - N _f Value of N at failure - True tensile stress - True stress range for a strain cycled specimen - _h Value of at half the life of the specimen - True tensile strain - Total true strain range - _p True plastic strain range (= the breadth of the hysteresis loop at = 0) - _d True diametral strain range - E Young's modulus - Linear strain hardening rate when tested at a particular value of _p - D Damage due to cycling - D _p Damage due to prestrain - _p Prestrain. C, K, K₁, , are constants     

High-field electrical conduction in m Hgl2

The electrical and dielectric properties of illuminated Hgl₂ were studied at room temperature under various a.c.-signal amplitudes in the frequency range 1 Hz to 10 kHz. Below 40 H, We real part of the dielectric constant, ,was found to vag slightly with voltege for low electric fields (E < 10³V cm^–1, above which it showed a steady increase with the applied voltage. At higher frequencies, no voltage dependence of (or the geometrical capacitance) of the crystal was observed. On the other hand, the imaginary part of the dielectric constant, or the a.c. conductivity, (=_o) was found to decrease considerably with the applied voltage forE < 10³V cm^–1 at all frequencies. For higher fields (E > 10³V cm^–1), exp [C(E/)^1/2], whereC is e constant. Above 40 Hz, this variation was in good agreement with the behaviour of the bulk, resistance of the crystal. Such behaviour is discussed in the view of Richardnon-Schottky and Poole-Frenkel conduction mechanisms, which seem to be operative in Hgl₂ at room temperature.     

Longitudinal dielectric function and collective surface oscillations in superconductors

The electrodynamic approach to the problem of collective oscillations in superconductors is considered. The kinetic equation for quasiparticles is used to find the longitudinal dielectric function ₁ (, k) of a pure superconductor at ( is the collision frequency). With the help of the evaluated ₁ (, k) the existence of collective oscillations localized near the boundary of the superconductor is investigated.     

Universal simulation of degenerating homogeneous turbulence

The problem of universal simulation of the dynamics of a turbulent velocity field (universal in the sense of arbitrary values of the Reynolds turbulence number) is treated on the basis of the moment model in the second approximation.Notation ¯q² _i ² double the kinetic turbulence energy - _u ² =5v¯q²/_u Taylor turbulence scale squared - _u=v1/x_k)²> kinetic-energy dissipation function - N_Re,=¯q²_u / Reynolds turbulence number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 46–52, January, 1982.     

Investigation into the growth and electromechanical properties of Pb(Mg1/3Nb2/3)O3 thin films

Pulsed laser deposition (PLD) has been used to fabricate relaxor thin films and thin film capacitors based on the Pb(Mg_1/3Nb_2/3)O₃ system. Best capacitor structures show dielectric constants (_r) of 1000 and losses (tan ) 0.02 at 1 kHz at 300 K. Electromechanical investigations show that tensile longitudinal strains of up to 0.2% can be achieved in these films.     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

The surface of liquid 4He,based on the idea that π i<j f(r ij) describes a droplet

We argue that the wave function f(r _ij) describes the ground state of a droplet of liquid ⁴ He. With this wave function, expressions for the surface energy and the surface tension of liquid ⁴ He at T = 0 are derived. Choosing particular f(r) and density profile, and the simplest pair correlation function, we plot the variation of and with surface thickness t. For slow variation of density at the surface, becomes proportional to t. The surface thickness is found to be about 4 ». The inclusion of phonon zero-point motion correlations in the wave function leads (at T = 0) to a –R ² log R term in the energy of a droplet of radius R, implying a logarithmic divergence in both and . At T > 0 the phonon correlations give a log T dependence of and and a negative bulk specific heat. Suggestions as to the reason for these problems are explored, but no definite conclusions are reached.     

Submillimeter surface impedance and relaxation: A case study of quasi-two-dimensional YBa2Cu3Ox

Surface impedance measurements in the normal and superconducting state are an excellent method to study the conduction electron dynamics in metals. This holds especially in the relaxation range, i.e., for distances traveled in one r.f. periods= _F/(_f is the Fermi velocity) being smaller or of the order of the penetration depth and mean free pathl. For materials with _F<-10⁷ cm/sec the relaxation range is easily accessible forf>0.1 THz. Then, in the normal state, relaxation defines the surface impedance with a penetration depth approaching the London penetration depth _L, andR _0l/2 as surface resistance allowing a measure of _L and relaxation time (T, ). In the superconducting state the photon interaction scales with _F/_L=l/ ( _f is the dimension of Cooper pairs for l) and causes at low frequencies an absorption rate growing with, which is decreasing with _F/l. The rate increase proportional to turns to a decrease above 0.1 THz, being accompanied by a decrease of with frequency which is stronger for large and small _F/l. These characteristic dependences allow a measurement of material parameters, anisotropy, and dynamics of electrons. To evaluate the consequences of theâ, b, and-direction anisotropy, the integral kernels for normal and superconducting surface impedances in its nonintegrated, angle-dependent form are presented, analyzed, and compared with impedance measurements above 0.1 THz of YBa₂Cu₃O_x.     

Effect of cobalt oxide on the a.c. conduction mechanism of copper tellurite glasses

Electrical measurements on binary and ternary glasses of compositions 65TeO₂-35CuO and 65TeO₂-34CuO-1CoO (mol%) are reported at temperatures between 293–458 K in the frequency range up to 10^–6 Hz. The measured conductivity shows a frequency dependence obeying the equation () =A ^s withs <1 but taking different values at different temperatures. The capacitance of the glasses shows an increase in value with increase in temperature at low frequencies. The tangent of the loss angle (tan ) and dielectric loss factor _r were found to increase with the increase in temperature and decrease in frequency but the usual Debye loss peaks were absent even at high temperatures. The relative dielectric constant _r was unexpectedly high, approximately 10³, and was found to decrease very slightly with increasing frequency. Overall the effect of a small amount of CoO (ã 1 mol%) is found to have a dominant effect on the dielectric properties of copper tellurite glasses.     

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