Creep of Pb–2·5Sb–0·2Sn alloy at low stresses

Abstract

The creep of a Pb–2·5Sb–0·2Sn alloy has been studied at stresses up to 6·5 MN m^?2 in the temperature range 318–348 K (0·53–0·58T_m) using helical specimens. At 333 K, a transition in the stress exponent from ~1 to 3 occurred at ~3 MN m^?2. The observed good agreements below the transition stress, both for experimental dE/do and predictions for Coble diffusional creep of lead, and for measured activation energy for creep and the activation energy for grain boundary self-diffusion in lead, suggest that grain boundary diffusional creep is the dominant mechanism. at low stresses. The presence of antimony does not seem to affect the magnitude of dE/do appreciably, and the results suggest that the grain boundary self-diffusivity of lead is not influenced by the presence of segregated antimony on the grain boundaries. The diffusional creep occurred above a threshold stress of magnitude ~0·5 MN m^?2, and its temperature dependence was characterised by an activation energy of ~20 kJ mol^?1, similar to the value of 23 ± 7 kJ mol^?1 typical of pure metals in the temperature range investigated. The stress exponent of ~3 observed for the power law regime suggests control by viscous glide of dislocations constrained by dragging of solute atmospheres. Preliminary tests on sagging beam specimens of as-worked material at an applied stress of 2·5 MN m^?2 and a test temperature of 333 K has provided the first direct evidence that anisotropic grain shape affects Coble creep. The specimen with the longest grain dimension along the stress axis underwent slower creep than the specimen with the longest grain dimension perpendicular to the stress axis. This observation is in qualitative agreement with theoretical predictions.

MST/1139     

The role of Coble creep and interface control in superplastic Sn-Pb alloys

The creep behaviour of superplastic Sn-2 wt% Pb and Sn-38.1 wt % Pb is investigated at temperatures between 298 and 403 K and for grain sizes between 2.5 and 260m. In Sn-2 wt% Pb with grain sizes larger than 50 m, diffusion-controlled Coble creep is found and it is experimentally shown that this type of creep is inhibited in smallgrained specimens. Measurements covering low stresses ( 0.1 MPa) and strain rates ( 10^–10 sec^–1) rule out any explanation which relies on a threshold stress for plastic deformation. The observations are explained by a model in which, at low stresses or small grain sizes, Coble creep is rate-limited not by diffusion of vacancies but by the rate of emission and absorption at the curved dislocations in the grain boundaries which are the ultimate sources and sinks of vacancies.     

Enhancement of the diffusional creep of polycrystalline Al2O3 by simultaneous doping with manganese and titanium

The effect of simultaneous doping with manganese and titanium on diffusional creep was studied in dense, polycrystalline alumina over a range of grain sizes (4–80m) and temperatures (1175–1250° C). At a total dopant concentration of 0.32–0.37 cation %, diffusional creep rates were enhanced considerably such that the temperature at which cation mass transport was significant was suppressed by at least 200° C compared to that observed in undoped material. The Mn-Ti (and Cu-Ti) dopant couple was far more effective in enhancing creep rates and suppressing sintering temperatures than the Fe-Ti couple. The enhanced mass transport kinetics are believed to be caused by significant increases in both aluminium lattice and grain-boundary diffusion. When aluminium grain-boundary diffusion is enhanced by increasing the concentration of divalent impurity (Mn²⁺, Fe²⁺) or by creep testing at low temperatures, creep deformation is Newtonian viscous.     

Creep behaviour of AZ61 magnesium alloy at low stresses and intermediate temperatures

Abstract

Tensile creep response was investigated for AZ61 alloy (Mg - 6.4Al - 0.9Zn - 0.2Mn, wt-%) of mean linear intercept grain size ~ 25 μm at stresses in the range 0.9 - 4 MPa over the temperature range 250 - 346°C. Bingham behaviour is obtained with strain rate ? under stress σ given by ?∝σ - σ_o with a threshold stress σ_o decreasing from 1.25 MPa at 210°C to ~ 0.5 MPa at 346°C, which is similar to earlier work on pure magnesium. The corresponding Arrhenius plot of log (Td?/d σ) versus T^-1 indicates an activation energy comparable with that expected for the grain boundary self-diffusion coefficient D _B, and values of D _Bδ (where δ is the effective grain boundary thickness) derived from the Coble equation are also similar to those for pure magnesium. Grain elongation in the direction of the tensile stress is also consistent with the key indicative feature of diffusional creep: deposition of material at grain boundaries nearly transverse to the axis of tensile stressing. Strain rates versus stress are shown to be continuous with published results for superplastic flow of AZ61 at comparable temperatures but higher stresses.     

The high temperature creep deformation of Si3N4-6Y2O3-2Al2O3

The creep properties of silicon nitride containing 6 wt % yttria and 2 wt% alumina have been determined in the temperature range 1573 to 1673 K. The stress exponent, n, in the equation ⁿ was determined to be 2.00±0.15 and the true activation energy was found to be 692±25 kJ mol^–1. Transmission electron microscopy studies showed that deformation occurred in the grain boundary glassy phase accompanied by microcrack formation and cavitation. The steady state creep results are consistent with a diffusion controlled creep mechanism involving nitrogen diffusion through the grain boundary glassy phase.     

Creep of polycrystalline alumina,pure and doped with transition metal impurities

Grain size effects were used to evaluate the relative contributions of aluminium lattice and oxygen grain boundary diffusion to the high temperature (1350 to 1550° C) steady state creep of polycrystalline alumina, pure and doped with transition metal impurities (Cr, Fe). Divalent iron in solid solution was found to enhance both aluminium lattice and oxygen grain-boundary diffusion. Large concentrations of divalent iron led to viscous Coble creep which was rate-limited entirely by oxygen grain-boundary diffusion. Nabarro-Herring creep which was rate-limited by aluminium lattice diffusion was observed in pure and chromium-doped material. Chromium additions had no effect on diffusional creep rates but significantly depressed non-viscous creep modes of deformation. Creep deformation maps were constructed at various iron dopant concentrations to illustrate the relative contributions of aluminium grain boundary, aluminium lattice, and oxygen grain-boundary diffusion to the diffusional creep of polycrystalline alumina.     

Transient Creep Associated with Grain Boundary Sliding in Fine-Grained Single-Phase Al2O3

Transient creep data for high-purity polycrystalline alumina are examined at the testing temperature of 1150–1250 °C. The data are analysed in terms of the effect of stress and temperature on the extent of transient time and strain.In order to explain the observed transient creep, a time function of creep strain is proposed from a two-dimensional model based on grain boundary sliding. The grain boundary sliding is assumed to take place by the glide of grain boundary dislocations accommodated by dislocation climb in the neighboring grain boundaries. The time function for a creep strain obtained from the model is given in a form

Low-stress creep behaviour of superplastic Zn-22% Al alloy

Low-stress creep behaviour of microduplex Zn-22% Al alloy was studied using spring specimen geometry. The average phase size in the specimens investigated was 0.87, 1.48 and 1.98 m. Experiments were conducted in the temperature range 393–473 K at stresses below about 1.0 MN m^–2. The present study has established that the stress exponent of the creep rate is unity and, therefore, a viscous creep process dominates the flow in Region I superplasticity. The activation energy corresponds to that for boundary diffusion. However, the phase-size exponent was found to be –2 instead of –3, as predicted by the Coble creep theory. Further, the measured creep rates are three to four orders of magnitude slower than those predicted by the Coble theory. Transmission electron microscopy revealed precipitation, along / grain interfaces, whose inhibiting action on plastic flow should at least be partly responsible for the lower values of measured creep rates. There also exist two other interfaces, namely / and /, whose comprehensive role in diffusion creep is not yet fully understood. Therefore, it seems illogical to describe the creep behaviour of Zn-22% Al by the classical Coble theory, originally developed for single-phase polycrystals.     

Creep mapping in a polycrystalline ceramic: application to magnesium oxide and magnesiowustite

The construction of deformation mechanism maps for a polycrystalline ionic solid in which anion and cation transport are coupled has been demonstrated. Because of anioncation ambipolar coupling, two regimes of Coble creep are possible in systems where anion grain boundary transport is rapid: (1) rate-controlled at low temperatures and small grain sizes by cation grain-boundary diffusion, and (2) rate-limited at high temperatures and large grain sizes by anion grain-boundary diffusion. A new type of deformation mechanism map was introduced in which the temperature and grain size were primary variables. This map was shown to be particularly useful for materials which deform primarily by diffusional creep mechanisms. Ambipolar diffusional creep theory was used to construct several deformation mechanism maps for polycrystalline MgO and magnesiowustite over wide ranges of stress, grain size, temperature and composition.     

Compressive creep behavior in air of a slightly porous as-sintered polycrystalline α-alumina material

Compressive creep tests in air have been performed on a polycrystalline submicron as sintered and slightly porous α-alumina material. Two different deformation mechanisms, depending on the applied stress and creep temperature, have been identified when the grain size becomes higher than a critical value 〈G ^*〉. For low temperatures and/or low applied stresses, deformation occurs by grain boundary sliding accommodated by an in-series “interface reaction/diffusion of Al³⁺ cations” process, with the limiting step being the interface reaction. In this case increased densification of the samples is observed after creep, compared to the as-sintered ones. In contrast, for high temperatures and/or high-applied stresses, deformation occurs by grain boundary sliding accommodated by the relocation and growth of preexisting cavities, the growth step being also controlled by the diffusion of Al³⁺ cations. In this case, a marked decrease of the relative density is measured on the crept samples compared to the as-sintered ones. Using these results, it is possible to identify the optimal conditions for superplastic forming of previously as-sintered parts, leading to shaped objects with an increased final density.     

Zinc Doping Profile in AlGaAs/GaAs Heteroepitaxial Structures Grown by Metalorganic Chemical Vapor Deposition

The Zn profile in Al _x Ga_{1 – x} As/GaAs (x = 0.2–0.4) quantum-well heteroepitaxial structures doped during growth by metalorganic chemical vapor deposition is modeled with allowance made for the diffusional broadening of the nominal doping profile. Experimentally determined carrier distributions in the heterostructures are used to refine the diffusion coefficient of Zn at a growth temperature of 770°C. The average value of D _Zn is determined to be 6.0 × 10^–14 cm²/s. The position of the p–n junction in Al _x Ga_{1 – x} As/GaAs heterostructures is assessed as a function of the nominal Zn profile and growth rate. The ways of optimizing the doping profile are outlined.     

High-temperature deformation behaviour of YBa2Cu3O7−x

High-temperature compression tests were performed in air for YBa₂Cu₃O_7–x polycrystals with grain sizes of 3 and 7 m at various strain rates between 1.3×10^–5 and 4×10^–4s^–1 and at temperatures between 1136 and 1253 K. Steady state deformation appeared above 1203 K for both samples. A stress exponent of 1.3 and an activation energy of 150 kJ mol^–1 were evaluated. The compression tests and microstructural observations revealed that there was a difference in deformation mechanism above and below 1203 K. The dominant mechanism was diffusional creep associated with grain-boundary sliding above 1203 K, and dislocation glide accompanied with grain-boundary sliding below 1203 K. The growth of anisotropic grains and their preferred arrangement were enhanced by deformation.     

The influence of a threshold stress for grain boundary sliding on constitutive response of polycrystalline Al during high temperature deformation

A continuum polycrystal plasticity model was used to estimate the influence of a threshold stress for grain boundary sliding on the relationship between macroscopic flow stress and strain rate for the aluminum alloy AA5083 when subjected to plane strain uniaxial tension at 450 °C. Under these conditions, AA5083 deforms by dislocation glide at strain rates exceeding 0.001 s⁻¹, and by grain boundary sliding at lower strain rates. The stress–strain rate response can be approximated by , where A and n depend on grain size and strain rate. We find that a threshold stress less or equal to 4 MPa has only a small influence on flow stress and stress exponent n in the dislocation creep regime (a threshold stress of 2 MPa increases n from 4.2 to 4.5), but substantially increases both flow stress and stress exponent in the grain boundary sliding regime (a threshold stress of 2 MPa increases n from 1.5 to 2.7). In addition, when the threshold stress is included, our model predicts stress versus strain rate behavior that is in good agreement with experimental measurements reported by Kulas et al. [M.A. Kulas, W.P. Green, E.M. Taleff, P.E. Krajewski, T.R. McNelley, Metall. Mater. Trans. A 36 (2005) 1249].     

High-temperature fracture and diffusional deformation mechanisms in Si-Al-O-N ceramics

A comparison has been made of hot-pressed Si-Al-O-N ceramics, with different impurity sintering aids (MgO and Mn₃O₄), in relation to microstructure, high-temperature creep and fracture. The Mn-containing ceramic exhibits a mechanism for creep of grainboundary sliding accompanied by cavitation at triple junctions, nucleated within an impurity silicate residue. The measured non-integral stress exponent (n∼1.5) and activation energyQ in the creep equation = const. σ ⁿ exp (-Q/kT) are typical of commercial silicon nitrides. A similar cavity-interlinkage is the principal mechanism for sub-critical crack growth, characterized by a low value for the stress-intensity exponent (n) in the relationV (crack velocity)=const.K ₁ ⁿ determined on double-torsion test specimens. Triple-junction silicate, and hence cavitation, is absent in the Mg-containing ceramic, which exhibits a Coble diffusional creep mechanism (stress exponentn=1). Sub-critical crack growth occurs only over a narrow range of stress intensity, near toK _lC withn∼13 in theV-K ₁ ⁿ relation. A grain-boundary de-segregation caused mainly by extraction of impurities into an oxide film results in further improvement in creep and resistance to sub-critical crack growth.     

Transient and steady state creep behaviour of polycrystalline MgO

Stress change experiments during compressive creep tests at high stresses on polycrystalline MgO at 1596 K have shown that the creep rate at any instant during transient and steady state creep is predicted by the ratio,r/h, wherer is the rate of recovery (=??σ/t6t) andh is the coefficient of strain hardening (=?σ/?ε). Over most of transient and steady state creep, whenh is constant and the decrease in creep rate, \(\dot \in\) , is a direct result of a decrease inr, the variation of the creep strain,ε, with time,t, is accurately described as $$ \in = \in _0 + \in _T (1 - e^{ - mt} ) + \dot \in _s t$$ whereε ₀ is the instantaneous strain on loading,ε _T the transient creep strain,m relates to the rate of exhaustion of transient creep and \(\dot \in _s\) is the steady creep rate. Deviations from this equation occur during the initial 10 to 15% of the transient creep life, whenh increases rapidly. The variations in \(\dot \in\) ,r andh during transient and steady state creep are explained in terms of a model for creep in which the rate-determining process is the diffusion controlled growth of the three-dimensional dislocation network within subgrains to form dislocation sources allowing slip to occur.     

Small-angle neutron scattering study of creep cavity nucleation and growth in sintered alumina

The early stages of creep cavitation in sintered alumina are characterized using small-angle neutron scattering (SANS). It is found that the initial cavity density is of the order of 10¹¹ cm^–3, and that the average initial pore is approximately 60 nm in radius. The incubation time for nucleating additional pores during subsequent creep is extremely short, in agreement with the theory based on the precipitation of grain-boundary diffusing vacancies. Pore density at constant stress and temperature is a linearly increasing function of time, as predicted by classical nucleation theory. However, a local stress of 10^–2 E is required to achieve the measured nucleation rate. Cavities are observed to lie primarily on two-grain junctions in linear arrays, with an average cavity radius of approximately 60 nm. It is hypothesized that the cavities nucleate at grain boundary ledges which provide the necessary local stress concentrations. Calculation of the individual cavity growth rate yields a zero or near zero value. This suggests a rapid transient growth period following nucleation which quickly decreases to a negligible growth rate.     

Comparative creep damage assessments using the various models

The creep fracture characteristics of a conventionally cast (CC) MARM-002 superalloy were studied for creep conditions of 1173 K/200–400 MPa using different approaches including the Kachanov-Rabotnov type continuum damage mechanics, grain boundary damage accumulation, and Chen-Argon diffusional cavity growth. A rapid improvement in creep rupture life can be achieved by reducing the Kachanov-Rabotnov damage rate () below a critical value of this rate. It is possible that a large improvement in creep resistance would be made by decreasing grain boundary damage rate rather than continuum damage rate since the minimum creep rate (_m) accelerates rapidly without changing the parameter .     

A study of grain-boundary structure in rare-earth doped aluminas using an EBSD technique

Oversized rare-earth dopant ions such as Y³⁺, Nd³⁺, and La³⁺ segregate to grain boundaries and reduce the tensile creep rate of -Al₂O₃ by 2-3 orders of magnitude. It has been speculated that these dopant ions can modify the grain boundary structure in alumina by promoting the formation of special grain boundaries. If this were indeed the case, it would provide a possible explanation for the aforementioned creep rate retardation. In order to test this hypothesis, electron backscatter diffraction (EBSD) has been used to assess both the proportion of coincidence-site lattice boundaries, and the grain boundary misorientation distribution, in aluminas doped with various ions (Zr, Y, Nd, La, Nd/Zr). The results show that the grain boundary structure in alumina is not significantly altered by the addition of the above dopants, implying that the change in grain boundary chemistry is primarily responsible for the observed creep behavior.     

High temperature creep of ultrafine-grained Fe-doped MgO polycrystals

Creep deformation in ultrafine-grained (0.1 to 1μm) Fe-doped magnesia polycrystals is studied in compression, at temperatures of 700 to 1050° C, and constant loads of 50 to 140 MPa. The stress exponent observed to be nearly unity and the strong grain size sensitivity (ė∼d ^−2.85) suggest that diffusional creep mechanisms dominate the deformation. In the grain size range of the present study the grain boundary diffusion contribution is significantly more important than lattice diffusion. Magnesium is tentatively identified as the rate-controlling species along grain boundaries from an analysis of the diffusivities inferred from the present work and from other authors for Fe-doped magnesia. Associated with the CNRS.     

Deformation mechanisms in an austenitic stainless steel (25Cr-20Ni) at elevated temperature

The creep behaviour at elevated temperature of an austenitic stainless steel (25Cr-20Ni), both with and without antimony additions, has been reanalysed. Formerly, the creep behaviour was interpreted by considering creep mechanisms based on diffusional (Coble) creep and threshold stresses. In the present paper, it is proposed that an alternative mechanism of grain boundary sliding, accommodated by slip in grain boundary mantle regions, can in fact be used to describe more accurately the creep behaviour. Quantitative predictions, based on phenomenological equations for describing creep controlled by grain boundary sliding, are made of the influences of grain size, stress and antimony addition on creep rates, and of the influence of grain size on the activation energy for creep of 25Cr-20Ni stainless steel. Comparison of these predictions with those based on creep models incorporating only diffusional flow are made. Furthermore, the existence of a threshold stress in creep of single-phase, massive materials is strongly questioned.