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.     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

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     

Transport results from untwinned YBCO: Washboard frequency of the vortex lattice,and the quasiparticle mean free path

The washboard frequency of the moving vortex lattice in untwinned YBa₂ Cu₃ O_6.93 may be observed through mode-locking to an externally applied ac current of frequency _ext. The interference between and _ext results in jumps in the dc current-voltage characteristics when and _ext are harmonically related¹. The interference effect disappears in the vortex liquid state. The Hall conductivity _xy below T_c in YBCO contains contributions² from a positive quasiparticle (qp) term (H) and a negative vortex term (1/H). The qp term is surprisingly large well below T_c and implies a large gap anisotropy and a long qp mean free path (mfp). The thermal Hall effect³ _xy is closely related to the qp _xy; _xy is produced by asymmetric scattering of qp by pinned vortices. The qp mfp at H = 0, extracted from _xy and extended to low T by _xy, increases remarkably from 90 Å at T_c to more than 0.5m at 22 K.     

Pyramidal yield criteria for epoxides

The tensile, compressive and shear yield strengths of two epoxides were measured under superposed hydrostatic pressure extending to 300 MN m^–2. For both materials, the ratio of the moduli of the tensile, _T, to compressive, _C, yield stress at atmospheric pressure was approximately 34, as has been reported previously for a number of thermoplastics. The ₂= ₃ envelope in stress space was plotted according to these two-parameter ( _C and _T) yield criteria: conical, paraboloidal and pyramidal; the best correlation was with the last. The experimental tensile and compressive data for tests under pressure, however, fit slightly better two straight lines which are consistent with a three-parameter single hexagonal pyramidal yield surface. For plane stress and shear under pressure yield envelopes of these surfaces, the correlation with experimental data is again best for the pyramidal criteria, except for biaxial or triaxial tension when these resins are brittle. The third independent parameter employed in the pyramidal criterion was the equi-biaxial compressive yield stress, determined by tensile experiments under appropriate superposed hydrostatic pressure; alternatively plane strain compressive yield stress, _PC, may be used.     

The influence of antimony-additions on the creep behaviour of a 25wt% Cr-20wt% Ni austenitic stainless steel

The effect of antimony on the creep behaviour (dislocation creep) of a 25 wt% Cr-20 wt% Ni stainless steel with ~ 0.005 wt% C was studied with a view to assessing the segregation effect. The antimony content of the steel was varied up to 4000 ppm. The test temperature range was 1153 to 1193 K, the stress range, 9.8 to 49.0 MPa, and the grain-size range, 40 to 600m. The steady state creep rate, , decreases with increasing antimony content, especially in the range of intermediate grain sizes (100 to 300m). Stress drop tests were performed in the secondary creep stages and the results indicate that antimony causes dislocations in the substructure to be immobile, probably by segregating to them, reducing the driving stress for creep.Nomenclature _a Creep stress in a constant load creep test without stress-drop - _A Initial applied stress in stress-drop tests - Stress decrement - ( _A-) Applied stress after a stress decrement, - t _i Incubation time after stress drop (by the positive creep) - _C Strain-arrest stress - _i Internal stress - _{s s}-component (= _i- _c) - Steady state creep rate (average value) in a constant load creep test - Strain rate at time,t, in a constant load creep test - New steady state creep rate (average value) after stress drop from _A to ( _A-) - Strain rate at time,t, after stress drop.     

Interfacial debonding and fibre pull-out stresses

Based on a theoretical model developed previously by the authors in Part II of this series for a single fibre pull-out test, a methodology for the evaluation of interfacial properties of fibre-matrix composites is presented to determine the interfacial fracture toughness G _c, the friction coefficient , the radial residual clamping stress q _o and the critical bonded fibre length z _max. An important parameter, the stress drop , which is defined as the difference between the maximum debond stress _d ^* and the initial frictional pull-out stress _fr, is introduced to characterize the interfacial debonding and fibre pull-out behaviour. The maximum logarithmic stress drop, In(), is obtained when the embedded fibre length L is equal to the critical bonded fibre length z _max. The slope of the In()-L curve for L bigger than z _max is found to be a constant that is related to the interfacial friction coefficient . The effect of fibre anisotropy on fibre debonding and fibre pull-out is also included in this analysis. Published experimental data for several fibre-matrix composites are chosen to evaluate their interfacial properties by using the present methodology.On leave at the Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong.     

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.     

Convection in a shallow laterally heated cavity with conducting boundaries

Shallow cavity flows driven by horizontal temperature gradients are analysed over a range of Rayleigh numbersR and Prandtl numbers , whereR is comparable in size to the aspect ratioL(1). Eigenvalue calculations show the existence of a critical Prandtl number R > R _c (), below which the parallel core-flow structure is destroyed for Rayleigh numbersR>R _c(). For other Rayleigh numbers and Prandtl numbers the horizontal scale of influence of the end walls of the cavity is determined.     

Examining the temperature dependence of the mechanical properties for materials in large-diameter tubes

Measurements have been made on the mechanical properties of largediameter tubes made of 09G2S, 14G2SAF, and 17G1S steels and on welded joints in them at strain rates of 200 sec^–1 and 113–293 K. Fivefold microspecimens 1.2 mm in diameter have been employed. The parameters have been determined in the temperature-rate dependence of the Yaroshevich yield point, lower brittleness temperature, and fracture resistance as affected by the ferrite diameter. A method is proposed for predicting the brittleness range from the dependence of the notch bottom narrowing B on the generalized parameter = S_f/_y — _t/_i for a Menaget specimen.Translated from Problemy Prochnosti, No. 4, pp. 43–50, April, 1994.     

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.     

Experimental investigation of the effects of stress rate and stress level on fracture in polystyrene

The effects of stress rate and stress level on fatigue crack propagation in compression-moulded single-edge notched specimens (0.25 mm in thickness) of polystyrene are reported. Values of the stress rate are obtained from the formula = 2v(_max – _max),, wherev is the frequency and _max, _min are the maximum and minimum stresses of the fatigue cycle. Different levels of are achieved by changing the frequency while keeping _max, _min at fixed values. The effect of the stress level is investigated by keeping and _min constant and varying _max andv. The results show that when the kinetic data are plotted as l/t against the energy release rateG ₁, a relatively small effect of the stress rate is observed. If the same data are treated as l/N againstG ₁, a decrease in l/N with test frequency is seen. The increase in the level of _max results in a higher crack speed. The critical crack length is found to be practically the same for all stress-rate experiments. A decrease in the critical crack length is observed with the increase in stress level. Analysis of craze distribution around the crack path shows that the extent of crazing decreases with the increase in stress rate and increases with the increase in stress level. For all experimental conditions, the ratio of the second moment to the square root of the fourth moment of the histograms of craze density along directions normal to the crack path is found to be constant throughout the slow phase of crack propagation. This result supports a self-similarity hypothesis of damage evolution proposed in the crack layer model.     

Fatigue of metallic glasses

The fatigue behaviour of Ni₄₉Fe₂₉P₁₄B₆Si₂, Ni₄₈Fe₂₉P₁₄B₆Al₃ and Pd_77.5Cu₆Si_16.5 metallic glasses is examined. In the finite lifetime regime the relationship between stress amplitude ( _a), fracture stress ( _f), mean stress ( _m) and cycles to failure (N _f) is _a=A( _f–_m) (2N _f) ^b , whereA andb are 16.9 and –0.40 respectively for reduced gauge section Ni₄₉ strips (for _m 140 kg mm^–2) and 27.0 and –0.44 for Pd base wires. These results are unusual in thatA 1. Consequently, a sharp discontinuity exists near _a( _f– _m) –1. In a simple tensile test failure occurs at _f(=_y) and 2N_f=1; for peak stresses only a percent or so less than _f the sample will withstand hundreds of cycles of stress. For uniform cross-section glassy metal filaments, a fatigue limit is observed at stress ratios ( _a/ _f) in the vicinity of 0.07 to 0.15. The fatigue limit for reduced section specimens is a factor of 2 higher. Fatigue failure of the Ni-Fe strips may occur under partially or fully plane stress or plane strain conditions, depending on sample thickness and stress. Final failure of the Pd_77.5Cu₆Si_16.5 wires always occurs by general yielding of the remaining section.     

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.     

Distribution characteristics of mechanical properties and correlation between the respective properties on S35C carbon steel

Mechanical properties of tensile strength, , upper yield stress, _SU, lower yield stress, _SL elongation, , area reduction, , Vickers hardness, H _v, and impact absorbed energy, E, were examined using 50 specimens of S35C carbon steel, which were machined from two bars supplied from the same charged and heat-treated material. Distribution characteristics of these properties are discussed, and the correlation between each pair of them is investigated from a statistical viewpoint. The main conclusions obtained are summarized as follows; distribution characteristics of _B, _SL, , , H _v and E are well approximated by a normal distribution, but those of asu are not approximated as well by this type of distribution. In the latter case, a Weibull distribution is preferable to represent the distribution pattern. No significant correlation was observed between each pair of the above mechanical properties. Consequently, individual properties have the inherent distribution characteristics independent of the other properties.     

Studies in the cold drawing of Pd77.5Cu6Si16.5 metallic glass and 316 stainless steel crystalline wires

The stress necessary to draw Pd_77.5Cu₆Si_16.5 metallic glass wires has been measured using a tensile machine, and compared with that of 316 stainless steel crystalline wires. To assess the elastic back-pull of a drawn material, variable static back-stresses have been loaded on a drawing wire. In the case of the metallic glass wires, the draw stress, _d, under different applied back-pulls, _ab, increases linearly with the reduction in area, R _a, up to 23% and then increases less rapidly. This tendency of the curve _d versus R _a is also the same in 316 crystalline wires. On the other hand, the elastic back-pull of the glassy wires is 2.05 kg mm^–2 at zero applied back-pull and then decreases monotonically with _ab, while that of the 316 crystalline wires is 6.62 kg mm^–2 at _ab=0 and decreases linearly with the increase in _ab. The empirical maximum reduction in Pd_77.5Cu₆Si_16.5 metallic glass wire for one-pass drawing is measured to be 40% at _ab=0 and it then decreases with increasing _ab. The resultant curves of drawing stress versus reduction in area are discussed in the light of plastic theory. The theoretical curves calculated under the assumption of small strain-hardening fits quite well with the experimental curves of Pd_77.5Cu₆Si_16.5 glassy wires.     

Steady-state creep in a 25 wt % Cr-20 wt % Ni austenitic stainless steel

Steady-state creep behaviour of a 25 wt % Cr-20 wt % Ni stainless steel without precipitates was studied in the stress range 9.8 to 39.2 MPa at temperatures between 1133 and 1193 K. The results of stress-drop tests indicate that, in the steady-state creep region, diffusion-controlled recovery creep is dominant. Such recovery creep can be accounted for in terms of the composition of the internal stress, _i=_s+_c, except in the case of fine-grained specimens where d<80 m, whered is the mean grain diameter, _s is possible to reduce easily and is comparable to the driving stress for creep, and _c is the persistent stress field due to metastable substructure. In the fine-grained specimens, it is suggested that the steady-state creep is dominantly controlled by grain boundaries.     

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.     

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.     

Effect of shot peening on the fatigue and fracture behaviour of two titanium alloys

The fatigue and fracture behaviour of two titanium alloys, the near-alpha IMI-685 and alpha-beta IMI-318, were studied in the machined and polished (MP) as well as the machined, polished and shot (glass-bead) peened (MPS) conditions. Glass-bead peening reduced the room-temperature as well as the high-temperature (450°C) fatigue life of alloy IMI-685 at high stress amplitudes, _a, approaching the proof stress, _ps, of the material (LCF region). When the applied stress amplitude (0–770 MPa, HCF region) was comparable to the peen-induced peak longitudinal residual stress, _LP, i.e. (_LP/a)=0.92, an improvement in the room-temperature fatigue life of IMI-685 was observed. When the (_LP/a) ratio was less than this value, decreases in the fatigue life were seen. The room-temperature fatigue behaviour of IMI-318 at high stress amplitudes was similar to that of IMI-685. The decrease in the fatigue life of this alloy, at a stress amplitude (770 MPa) where improvement was observed for IMI-685, could be attributed to the higher relaxation of peen-induced residual stresses in IMI-318 compared with IMI-685. Glass-bead peening improved the hightemperature (450°C) fatigue life of IMI-685 at a low stress amplitude (465 MPa; (_a/PS)=0.87). The crack-initiation sites in the MP and the MPS conditions were at the surface for both the alloys. However, fracture in the surface layers of the alloys appeared more brittle in the peened (MPS) rather than in the unpeened (MP) condition.