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.     

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     

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.     

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.     

Electrical conductivity,thermoelectric power and dielectric constant of NiWO4

The a.c. electrical conductivity ( _ac), thermoelectric power () and dielectric constant () of antiferromagnetic NiWO₄ are presented. _ac and have been measured in the temperature range 300 to 1000 K and in the temperature range 600 to 1000 K. Conductivity data are interpreted in the light of band theory of solids. The compound obeys the exponential law of conductivity = ₀ exp (–W/kT). Activation energy has been estimated as 0.75eV. The conductivity result is summarized in the following equation =2.86 exp (–0.75 eV/kT)^–1 cm^–1 in the intrinsic region. The material is p-type below 660 K and above 950 K, and is n-type between 660 and 950 K.     

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.     

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.     

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.     

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.     

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.     

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     

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     

Coaxial variable-length resonator for determining the electromagnetic parameters of materials at normal and higher temperatures

Conclusions It is possible by means of the above resonator, according to our analysis and in the absence of air gaps between the sample and the line, to evaluate the real components and of permeability and permittivity respectively in the range of 2 to 100 with an error between ±3% and ±10% in the temperature range from room temperature to +400°C, and the imaginary components and (for tan and tan in the range of 0.001 to 2) with an error of 7 to 20% over the same temperature range.     

Types of superplasticm-δ curves of Ti-6Al-4V alloy and their intertransformation

The superplasticm- curves of Ti-6Al-4 alloy have been determined at different temperatures and strain rates; all were of them _L=m _max type, and were of either fundamental, descending or ascending types. The latter two types were transformed from the former through the processes ofm _Lm _O, _LO andm _Lm _F, _LF, respectively. The highest total elongation, _F, was 1150% obtained at 950C and 1.55×10^–3 s^–1. The Chin Liu equation has been applied to all types ofm- curves. The parameters characteristic of all types ofm- curves have been obtained and were found to vary with temperature and strain rate. The total elongation, _F, is determined by the resultant effects of all other parameters, not by a singlem value, theoretically considered to be constant and determined practically by a tensile strain of about 30%–50% (m _30%–50%) as usual.Nomenclature C (=k/k _o ) the normalized slope ofm- curve corresponding to - a material constant corresponding to - m strain-rate sensitivity index corresponding to - m _max maximum on them- curve corresponding to _L - m _min minimum on them- curve corresponding to _L - crosshead speed during the tensile test - the strain of the entire stretching process (has same significance as ordinarily adopted ) - _F total elongation at fracture chosen for the present work - _I intermediate strains including _I1, _I2, _I3, ..., _I(i–1), _Ii , _I(i+1), ..., chosen for the present work - _L limit strain separatingm- curves into sections - _O (=0) starting strain - strain rate - flow stress     

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.     

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.     

Phase transformation and impact properties of type 17-8-2 austenitic weld metals

The influence of stress relieving and ageing treatments in the range 600 to 900° C on the phase transformations and change in room temperature impact properties has been studied for two manual metal arc 17-8-2 weld metals. The transformation of the-ferrite in the range 600 to 800° C was found to conform to a classical Johnson-Mehl equation; the initial precipitates were M₂₃C₆ carbides followed by the intermetallic-phase. At higher temperatures a slower transformation rate was found suggesting a C curve type of behaviour and the dominant intermetallic phase changed to. Room temperature impact toughness values were found to change with ageing time. Below 800° C there was a consistent fall in these values which became very marked when the-phase developed at the/-boundaries, Above 800° C, spherodization of the carbides and intermetallic phases delayed the fall in the impact values, and led to significant increases in the early stages of ageing. Scanning electron microscopy confirmed that the change from ductile to brittle fracture mode was normally associated with the development of the and phases, but at 600° C the fall in impact properties could be atrributed to carbide development.     

The tensile strength and ductility of continuous fibre composites

The plastic instability approach has been applied to the tensile behaviour of a continuous fibre composite. It is shown that the combination of two components with different strengths and degrees of work-hardening produces a new material with a new degree of work-hardening, which may be determined by the present analysis. Expressions for the elongation at rupture and the strength of a composite have been obtained and the results of the calculation are compared with some experimental data.List of symbols V _f volume fraction of fibres in composite - , , true strain of fibre, matrix and composite - s true stress - , , nominal stress on fibre, matrix and composite - _*, _*, _* critical stress of fibre, matrix and composite (ultimate tensile strength) - _*, _* critical strain of separate fibre and matrix - _* critical strain of composite - Q external load - A cross-sectional area - A ₀ initial value of area     

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.     

Methodology for the determination of the interfacial properties of brittle matrix composites

The interfacial properties of a glass-ceramic matrix composite (SiC/CAS) were determined from single-fibre push-out tests using the interfacial test system. The coefficient of friction, , the residual clamping stress, _c, and fibre axial residual stress, _z , were extracted by fitting the experimental stress versus fibre-end displacement curves using the models of Hsueh, and Kerans and Parthasarathy. Using Hsueh's model, the intrinsic interfacial frictional stress (=_c) was found to be 11.1±3.2 MPa, whereas by using Kerans-Parthasarathy's model it was found to be 8.2±1.5 MPa. Comparisons between these models are included, together with a discussion of data analysis techniques.Nomenclature _z Axial fibre residual stress (Pa) - ^* Effective clamping stress (Pa) - _c Residual clamping stress (Pa) - _p Poisson's effect-induced clamping stress (Pa) - _d ⁰ Debond stress in the absence of residual stresses (Pa) - _d Experimental debond stress (Pa) - Compressive applied stress (Pa) - Interfacial shear stress (Pa) - u Fibre-end displacement (m) - h Debond length (m) - r Fibre radius (m) - E _f Fibre Young's modulus (Pa) - E _m Matrix Young's modulus (Pa) - v _f Fibre Poisson's ratio (dimensionless) - v _m Matrix Poisson's ratio (dimensionless) - f Fibre volume fraction (dimensionless) - k Parameter (dimensionless) - D Parameter (dimensionless) - Interfacial coefficient of friction (dimensionless) - G _i Interface toughness (J m^–2) - C _m Load-train compliance (m N^–1)