On Grain Size Dependence of Minimum Creep Rate

The available experimental results have beensummarized concerning the effect of grain size onminimum creep rate.There are two types of creeprate-grain size relations.One is that there is a criti-cal grain size above which creep rate is independentof grain size,below which creep rate increases withthe decrease of grain size.The other is that there isan intermediate grain size at which creep resistanceis optimum.The first relation usually occurs athigher temperatures(>0.5 T_m),and intermediatestress ranges,while the second relation at interme-diate temperature ranges(0.4-0.5 T_m)and higherstresses.For the two types of creep rate-grain sizerelations,the increase of the creep rates with the de-crease of grain size for small grain sizes is all due tograin boundary sliding.For large grain sizes,a dis-location climb mechanism is dominant in creepdeformation for the first relation,while aHall-Perch grain boundary strengthening effect isbelieved to play an important role by dislocationglide mechanism for the second relation.     

High temperature bending creep of a Sm-α-β Sialon composite

The four-point bending creep behavior of a Sm-- Sialon composite, in which Sm-melilite solid solution (denoted as M) was designed as intergranular phase, was investigated in the temperature range 1260–1350°C and stresses between 85 and 290 MPa. At temperatures less than 1300°C, the stress exponents were measured to be 1.2–1.5, and the creep activation energy was 708 kJ mol^–1, the dominant creep mechanism was identified as diffusion coupled with grain boundary sliding. At temperatures above 1300°C, the stress exponents were determined to be 2.3–2.4, and creep activation energy was 507 kJ mol ^–1, the dominant creep mechanism was suggested to be diffusion cavity growth at sliding grain boundaries. Creep test at 1350°C for pre-oxidation sample showed a pure diffusion mechanism, because of a stress exponent of 1. N^3– diffusing along grain boundaries was believed to be the rate controlling mechanism for diffusion creep. The oxidation and Sialon phase transformation were analyzed and their effect on creep was evaluated.     

Effect of dopants on alumina grain boundary sliding: implications for creep inhibition

We investigate by means of periodic density functional theory the mechanism of grain boundary sliding along the α-alumina Σ11 tilt grain boundary. We identify minimum and maximum energy structures along a preferential sliding pathway for the pure grain boundary, as well as for grain boundaries doped with a series of early transition metals, as well as barium, gadolinium, and neodymium. We predict that the segregation of those dopants results in a considerable increase in the grain boundary sliding barrier. Grain boundary sliding occurs by a series of bond breaking and forming across the grain boundary. Our results suggest that the presence of large cations inhibits the regeneration of bonds during sliding, which results in a decrease in total number of bonds across the grain boundary interface, thereby raising the barrier to sliding. Trends in predicted grain boundary sliding energies are in good agreement with recently measured creep activation energies in polycrystalline alumina, lending further credence to the notion that grain boundary sliding plays a dominant role in alumina creep.     

Creep Behavior of Dispersion-Hardened Aluminum Materials

Dispersion-hardened aluminum materials of pure aluminum with extremely fine oxide and carbide dispersions and very fine grain sizes were creep-deformed under compressive loadings between 573 and 773 K. The creep behavior of the investigated materials is influenced by time, temperature, stress level and microstructure. An increasing content of dispersions causes increasing threshold stresses _thand resistances against creep. The Norton plots of the minimum creep rate versus stress are characterized by extremely high stress exponents n. On the basis of the threshold concept it is demonstrated that the same diffusion process dominates in the dispersion-hardened aluminum materials as in pure aluminum. Their true stress exponents n^*as the slopes of the best fit lines of the are close to 5. The threshold stress decreases considerably with increasing temperature due to the thermally activated recovery of long-range internal back stresses of quasi-planar dislocation structures on the grain boundaries.     

Wedge crack nucleation in Type 316 stainless steel

Type 316 austenitic steel has been heat-treated to produce a range of grain sizes and then creep-tested at 625° C at various stresses so as to examine the nucleation and the factors which effect the nucleation of grain-boundary triple point or wedge cracks. An internal marker technique was used to evaluate the extent of the grain-boundary sliding in relation to the total creep strain. Triple point crack nucleation occurred over the entire range of grain sizes and stresses examined when the product of the stress and grain-boundary displacement reached a critical value; the effective surface energy for grain boundary fracture, estimated using an expression derived by Stroh, was in approximate agreement with the surface free energy value indicating that only limited relaxation occurred by plastic deformation. The first cracks were observed to form along grain boundary facets perpendicular to the applied stress direction and with the sliding grain boundaries at high angles (60 to 80°) to the crack growth direction. Subsequent cracking occurred under conditions which deviated slightly from this initial condition, and the increase in crack density with strain was expressed in terms of geometrical factors which take account of the orientation effects.     

High temperature creep of a hot-pressed β-sialon

The four-point bending creep properties of a hot-pressed β-sialon with Sm–melilite solid solution (denoted as M′) as intergranular phase have been studied in the temperature range 1250–1350°C in air. Creep rates plotted against stresses gave stress exponents of 1.45, 1.51 and 1.72 at 1250, 1300 and 1350°C, respectively, and Arrhenius plot between creep rate and temperature yielded a creep activation energy of 576 kJ mol⁻¹. Cavities were found to be mainly on the triple grain junctions. Diffusion coupled with grain boundary sliding and accompanied by the formation of wedge-shaped cavities was identified as the dominant creep mechanism.     

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

An evaluation of the grain-boundary sliding contribution to creep deformation in polycrystalline alumina

The occurrence of grain-boundary sliding during creep in fine grained alumina was examined by inscribing marker lines on the tensile surfaces of specimens, prior to testing in four-point bending mode. There was considerable microstructural evidence for the occurrence of grainboundary sliding and grain rotation during creep deformation. Experimental measurements of the offsets in the marker lines at grain boundaries reveal that the grain-boundary sliding contribution to the total strain during creep deformation is 70 ± 6.2%. The extensive grain boundary sliding observed, together with the other mechanical properties, suggests that polycrystalline alumina exhibits superplastic characteristics. Several possible rate controlling mechanisms are examined critically in light of the present results and it is concluded that creep occurs either by an independent grain-boundary sliding mechanism or by an interface controlled diffusion mechanism.     

Microstructure and mechanical characteristics of alpha-alumina-based fibres

The high-temperature mechanical behaviour of alumina-based ceramic fibres has been investigated by the comparison of a dense pure alumina fibre, a porous pure alumina fibre and a zirconia-reinforced dense fibre. Tensile and creep tests have been conducted up to 1300°C in air in parallel with microstructural investigations on the as-received and tested fibres. Room-temperature behaviour of the fibres is close to that of bulk materials having the same microstructure, but the fibre form allows higher failure stresses to be attained. High-temperature deformation of the three fibres is achieved by grain-boundary sliding ( ), and is accompanied by isotropic grain growth. The specific microstructures of each fibre induce differences in the creep threshold levels as a function of temperature and stress and also in creep rates and resistance to damage. Despite better resistance to creep and damage of the zirconia-reinforced fibre, alumina-based fibres are limited to applications below 1100°C. Grain boundaries are the principal cause of mechanical degradation at high temperature with these fibres.     

The tensile and creep behavior of Mg–Zn Alloys with and without Y and Zr as ternary elements

Tensile–creep experiments were conducted in the temperature range 100–200 °C and stress range 20–83 MPa for a series of magnesium–zinc–yttrium (Mg-Zn-Y) and mangnesium-zinc–zirconium (Mg-Zn-Zr) alloys ranging from 0 to 5.4 wt% Zn, 0 to 3 wt% Y, and 0 to 0.6 wt.% Zr. The greatest tensile–creep resistance was exhibited by an Mg–4.1Zn–0.2Y alloy. The room-temperature yield strength increased with increasing Y content for Mg–1.6–2.0Zn alloys. The greatest tensile strength and elongation was exhibited by Mg–5.4Zn–0.6Zr. This alloy also exhibited the finest grain size and the poorest creep resistance. The measured creep exponents and activation energies suggested that the creep mechanisms were dependent on stress. For applied stresses greater than 40 MPa, the creep exponents were between 4 and 8. For applied stresses less than 40 MPa, the creep exponent was 2.2. The calculated activation energies (Qapp) were dependent on temperature where the Q _app values between 100 and 150 °C (65 kJ/mol) were half those between 150 and 200 °C for the same applied stress value (30 MPa). Deformation observations indicated that the grain boundaries were susceptible to cracking in both tension and tension-creep, where at low applied stresses grain boundary sliding was suggested where strain accommodation occurred through grain boundary cracking. Thus grain size and grain boundaries appeared to be important microstructural parameters affecting the mechanical behavior. Microstructural effects on the tensile properties and creep behavior are discussed in comparison to other Mg-based alloy systems.

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The Measurement of Compressive Creep Deformation and Damage Mechanisms in a Single-Phase Alumina Part I Grain boundary sliding

Grain boundary sliding (GBS) has been hypothesized to act as the primary driving force for the nucleation and growth of grain boundary cavities in ceramics undergoing creep. In addition, GBS is often a major mode of deformation during high-temperature creep. This paper demonstrates the importance of GBS with mode II GBS measurements performed using a stereoimaging technique on a single-phase alumina tested under constant compressive stresses of 70 and 140 MPa at 1600 °C. Measurements were taken at constant time intervals during creep. The results support previous observations that GBS is stochastic and history independent. GBS displacements at given time intervals are shown to fit a Wiebull distribution. During steady-state creep, GBS displacements increased linearly with time at a constant sliding rate of 6.0 × 10–5 m s–1 at 70 MPa and 1.3 × 10–4 m s–1 at 140 MPa. Also, an average of 67% of the grain boundaries exhibited measurable sliding throughout the creep life of the 140 MPa test. Results of the GBS measurements are used to modify an existing creep model describing stochastic GBS. In part II of this paper [1], the GBS measurements reported are related to the associated creep cavitation measured in specimens tested under identical conditions.     

The role of grain boundary sliding and reinforcement morphology on the creep deformation behaviour of discontinuously reinforced composites

In this study, the role of grain boundary sliding behaviour on the creep deformation characteristics of discontinuously reinforced composites is investigated numerically together with the other influencing parameters: reinforcement aspect ratio, grain size and interfacial behaviour between the reinforcement and the matrix. The results obtained for the composites are compared with results obtained for a polycrystalline matrix material having identical grain size and morphology. The results indicate that, with sliding grain boundaries, the stress enhancement factor for the composites is much higher than the one observed for the matrix material and its value increases with increasing reinforcement aspect ratio, reduction in the matrix grain size and sliding interfacial behaviour between the reinforcement and the matrix. In the composites, the contribution of the grain boundary sliding to overall steady state creep rates occurs in a larger stress range in comparison to the matrix material. Experimentally observed higher creep exponent values or stress dependent creep exponent values for the composites could not be explained solely by the mechanism of grain boundary sliding. However, experimentally observed large scale triple point grain boundary cavitation in the composites could occur due to large grain rotations resulting from grain boundary sliding.     

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].     

Creep deformation mechanism of magnesium-based alloys

Two heat-resistant magnesium alloys AJC421 and Mg-2Nd were prepared. Both as-cast Mg-2Nd and AJC421 alloys exhibited good creep resistance in comparison with commonly used magnesium alloys. The improvement in creep properties through Nd addition to pure magnesium is attributed to both solid solution and precipitation hardening. The stress exponents of 4.5–5.5 and activation energies of 70.0–96.0 kJ/mol obtained from the as-cast Mg-2Nd alloy at low temperatures and low stresses indicate the five power law can be used for predicting the creep mechanism. The additions of alkaline earth elements Sr and Ca into Mg–Al alloys suppress the discontinuous precipitation of Mg₁₇Al₁₂ and form thermal-stable intermediate phases at grain boundaries, leading to effective restriction to grain boundary sliding and migration. However, the mechanism responsible for creep deformation of Mg–Al based alloys with Ca and Sr additions is not consistent with the results of microstructure observations performed on the alloys before and after creep tests.     

Grain Boundary Sliding at Serrated Grain Boundaries

A constitutive model is developed for grain boundary sliding (GBS) at serrated grain boundaries. Based on a previously developed GBS model, using the dynamics of grain boundary dislocation pile-up, the present model takes the average of the sliding rate over the characteristic dimensions of grain boundary serrations. Thus, a geometric factor is introduced to account for the effects of serration wave length and amplitude on the GBS rate, as compared to the GBS rate at planar boundaries. By considering the role of grain boundary shear stress in stress balancing, the proposed model removes the singularity at planar boundaries which exists in the diffusion-controlled GBS model at serrated grain boundaries. The modified model describes very well the transient creep of complex Ni-base superalloys with and without grain boundary serrations and should be suitable for other engineering alloys (with the exception of columnar grained and single crystal alloys).     

Microstructural modelling of creep crack growth from a blunted crack

The effect of crack tip blunting on the initial stages of creep crack growth is investigated by means of a planar microstructural model in which grains are represented discretely. The actual linking-up process of discrete microcracks with the macroscopic crack is simulated, with full account of the underlying physical mechanisms such as the nucleation, growth and coalescence of grain boundary cavities accompanied by grain boundary sliding. Results are presented for -controlled mode I crack growth under small-scale damage conditions. Particular attention is focused on creep constrained vs. unconstrained growth. Also the effect of grain boundary shear stresses on linking-up is investigated through shear-modified nucleation and growth models. The computations show a general trend that while an initially sharp crack tends to propagate away from the original crack plane, crack tip blunting reduces the crack growth direction. Under unconstrained conditions this can be partly rationalized by the strain rate and facet stress distribution corresponding to steady-state creep. This revised version was published online in August 2006 with corrections to the Cover Date.     

Creep in a Cu-14at.%Al solid solution alloy at intermediate temperatures and low stresses

The helicoid spring specimen technique was applied to investigate creep of a Cu-14at.%Al solid solution alloy at homologous temperatures from 0.54 to 0.65 and stresses ranging from 0.2 to 5.0 MPa. At stresses lower than about 1 MPa, Coble-type creep was found to dominate, associated with a threshold stress apparently independent either of grain size or of temperature. At stresses above about 1 MPa, another creep mechanism obviously contributes to the measured creep rate. This mechanism operating in parallel with Coble creep is characterized by the fact that the steady state creep rate is proportional to the second power of stress and inversely proportional to the third power of grain size and is most probably grain boundary diffusion controlled. This mechanism, called the non-viscous mechanism in the present work, is similar to that considered by Gifkins and Kaibyshev et al. to result from the motion of grain boundary dislocations (grain boundary sliding) accomodated by slip of lattice dislocations in thin layers along grain boundaries, although these workers assumed the creep rate to be inversely proportional not to the cube but to the square of the grain size.     

Simulation of microfracture process of brittle polycrystals: Microcracking and crack propagation

Microcracking and crack propagation behavior are simulated for 2-dimensional alumina polycrystals which have thermal anisotropy within a grain. Microcracks are generated by thermally induced residual stresses at the grain boundary. Stress redistribution due to microcracking and stress intensity factors at the microcrack tip are obtained numerically by the body force method. The location at which microfracture occurs is determined by a competition between microcracking and crack propagation under external stresses. The microfracture stress increases with the progress of fracture and decreases after the maximum indicating a fracture strength. In many cases, the extension of microcracks induces an unstable fracture. With both increasing grain size and decreasing grain boundary toughness, the number of microcracks prior to the unstable state increases and the stress concentration due to the microcracks plays a significant role in the stable crack extension, resulting in lower strengths than the fracture-mechanical predictions.     

The influence of temperature cycling on the creep properties of Nickel 201 and Inconel 600 in combustion gas

The effect of temperature cycling on the creep behaviour of Nickel 201 and Inconel 600 in combustion gas has been studied. Specimens were tested both at constant temperature, 900° C, and at 900° C interrupted by temperarature drops down to 510° C. The creep straining has been analysed with respect to a weighted time parameter which includes the creep contribution during the lower temperatures of each cycle. With respect to this compensated time parameter, the temperature variations were generally observed to result in a strong acceleration in creep. The effect seemed to increase with increasing frequency of temperature drops, increasing grain size and decreasing stress. Thus, at low stress levels, large-grained specimens of both alloys experienced an acceleration even inabsolute creep rate upon cycling. The grain size dependency indicates that the destructive effect of the cycles is caused by crack formation. Surface cracking associated with grain boundary oxidation seemed to be the dominant cracking mode. It is suggested that, during creep in oxidizing environments, repeated periods of cooling might strongly accelerate the growth of surface creep cracks due to the difference in thermal expansion between metals and oxides. This difference causes high tensile stresses to arise in the metal in front of the grain boundary oxides, and the stresses are assumed to be high enough to nucleate microcracks along the boundary.