Cavity growth on a sliding grain boundary

Cavity growth on a sliding grain boundary to which a normal stress is applied is found to be faster than that on a stationary grain boundary. The morphology of the cavity contains an asymmetric crack-like tip which prompts surface diffusion locally when the sliding is dominant, and the growth rate becomes proportional to the third power of the normal stress independent of the sliding rate. Since the sliding rates of all grain boundaries are statistically comparable, only the normal stress dependence remains important. The conditions which favor the present mechanism are examined and shown to be in good agreement with the experimental evidence in creep cavitation.     

An analysis of cavity nucleation in superplasticity

Superplastic alloys possess either a quasi-single phase or a microduplex microstructure: in quasi-single phase alloys, cavities are observed to nucleate predominantly at coarse grain boundary particles whereas in microduplex alloys, cavities tend to form at interphase boundaries and at triple point junctions. A general analysis is presented for cavity nucleation, in both microstructures, under the stress concentrations caused by bursts of grain boundary sliding during superplastic deformation. In quasi-single phase alloys, calculations indicate the cavities nucleate at coarse particles located at grain boundaries because local interphase diffusion creep cannot accommodate the stress concentrations sufficiently rapidly. The analysis demonstrates that it is possible for cavities to nucleate at grain boundary ledges under some limited experimental conditions. It is demonstrated also that the present analysis is in agreement with the available experimental data on a quasi-single phase Cu-based superplastic alloy and a microduplex superplastic Zn-22% Al eutectoid alloy. Calculations show that small pre-existing cavities, if present, are likely to be sintered rapidly prior to superplastic déformation at elevated temperatures.     

On fracture initiation mechanisms and dynamic recrystallization during hot deformation of pure nickel

During hot deformation of pure nickel, three distinctive fracture initiation mechanisms are identified: ductile cavity initiation at high strain rates, wedge type intergranular cracks due to grain boundary sliding at intermediate strain rates, and creep cavitation on the boundaries normal to the maximum principal stress at very low strain rates. Dynamic recrystallization is found to be effective in eliminating such fracture damage in a certain range of temperature and strain rate. By combining the strain rate-temperature conditions for the various fracture initiation mechanisms and effective dynamic recrystallization, a hot-working map is developed for nickel, which displays a safe hot working window in the strain rate-temperature field.     

Numerical models of creep and boundary sliding mechanisms in single-phase, dual-phase, and fully lamellar titanium aluminide

Finite element simulations of the high-temperature behavior of single-phase γ, dual-phase α₂+γ, and fully lamellar (FL) α₂+γTiAl intermetallic alloy microstructures have been performed. Nonlinear viscous primary creep deformation is modeled in each phase based on published creep data. Models were also developed that incorporate grain boundary and lath boundary sliding in addition to the dislocation creep flow within each phase. Overall strain rates are compared to gain an understanding of the relative influence each of these localized deformation mechanisms has on the creep strength of the microstructures considered. Facet stress enhancement factors were also determined for the transverse grain facets in each model to examine the relative susceptibility to creep damage. The results indicate that a mechanism for unrestricted sliding of γ lath boundaries theorized by Hazzledine and co-workers leads to unrealistically high strain rates. However, the results also suggest that the greater creep strength observed experimentally for the lamellar microstructure is primarily due to inhibited former grain boundary sliding (GBS) in this microstructure compared to relatively unimpeded GBS in the equiaxed microstructures. The serrated nature of the former grain boundaries generally observed for lamellar TiAl alloys is consistent with this finding.     

Interface sliding,migration, and cracking during fatigue deformation of a superplastic aluminum-zinc eutectoid alloy

A superplastic aluminum-zinc eutectoid alloy was fatigue tested at 100 °C and 200 °C at different constant plastic strain amplitudes and strain rates. During fatigue deformation, the average peak stress increased with increasing strain rate and grain size and decreasing temperature. It was almost independent of the plastic strain amplitude. To detect interfacial sliding, interphase boundary migration, and intergranular cracking, selected areas on surfaces were examined before fatigue deformation and re-examined after fatigue deformation. Interface sliding, which was almost reversible, occurred on (Al)/(Al) and (Zn)/(Zn) grain boundaries and on (Al)/(Zn) interphase boundaries. Grains appeared to slide in groups. Cracks followed grain and interphase boundaries. Along an intergranular crack, most interfaces were (Zn)/(Zn) grain boundaries and (Al)/ (Zn) interphase boundaries. Grains deformed to accommodate interfacial sliding. The absence of slip lines suggested that diffusional creep made a significant contribution to deformation in grains of the zinc-rich phase. Deformation of the aluminum-rich phase involved the glide and climb of dislocations. J. W. BOWDEN, formerly Graduate Student, Department of Metallurgy and Materials Science, University of Toronto.     

Effect of impurity type on boundary sliding behavior in the superplastic Zn-22 pct Al alloy

The effect of impurity type on boundary sliding behavior in the superplastic Zn-22 pct Al alloy was investigated using two grades of the alloy: Zn-22 pct Al-0.13 pct Cu (grade Cu) and Zn-22 pct Al-0.14 pct Fe (grade Fe). In the investigation, boundary sliding offset measurements in both grades were made at strain rates ranging from 5×10⁻⁷/s to 10⁻¹/s. This range of strain rate covered region I (the low strain rate region), region II (the intermediate strain rate region), and region III (the high strain rate region) of the sigmoidal plot between stress and strain rate that was previously reported for grade Fe. The experimental results show that the contributions of boundary sliding to the total strain, ξ, in the two grades of Zn-22 pct Al are about 20 and 52 pct at high (region III) and intermediate (region II) strain rates, respectively. By contrast, the experimental data reveal that ξ in grade Cu at low strain rates (52 pct) is essentially equal to that at intermediate strain rates (region II), while ξ in grade Fe at low strain rates (24 pct) is considerably lower than that at intermediate strain rates (56 pct). It is demonstrated that the difference in sliding behavior between grade Fe and grade Cu at low strain rates corresponds well with the difference in superplastic behavior between the two grades. In addition, consideration of the present and earlier data on sliding behavior in Zn-22 pct Al provides a correlation between two roles played by boundaries during superplastic deformation: the ability of boundaries to contribute to deformation through the process of boundary sliding and their ability to serve as favorable sites for the accumulation of impurities, i.e., boundary segregation.     

Grain boundary sliding,and the effects of particles on its rate

Grain boundary sliding can be conveniently studied by loading helical springs wound of wire with a “bamboo” structure. Such tests on pure silver coils show that identically-stressed boundaries slide at widely different rates, and that the sliding rate in any one boundary is very anisotropic. A grain boundary precipitate of hard particles (SiO₂ or A1₂O₃) slows down the sliding, and renders all boundaries identical, and isotropic (as far as grain boundary sliding is concerned). This can be understood if the grain boundary particles are thought of as hard pegs, around which silver must diffuse if sliding is to continue.     

Nanometer grain boundary sliding in Cu: [011] symmetric tilt boundaries,misorientation dependence and anisotropy

Sliding on [011] symmetric tilt boundaries in Cu has been studied between 323 and 584 K, using an electron microscope technique and bicrystals of an aged Cu-1.05%Fe-0.45%Co alloy. The b.c.c. FeCo particles formed by aging on boundaries suppress the sliding so that it amounts to less than 1 nm. The sliding has been detected by observing a change in the direction of Moiré fringes formed by the matrix {111} and the particle {110}. Finely dispersed f.c.c. FeCo particles in grains abutting boundaries completely prevent crystal dislocations playing any role in boundary sliding. The sliding increases with increasing temperature and saturates to a value determined by the size and distribution of the boundary particles and the applied shear stress. A boundary with a higher energy can slide at a lower temperature, as low as 350 K. A curve showing the ease of sliding against the misorientation angle is similar, with cusps, to the energy vs misorientation angle curve. The sliding parallel to the tilting axis, [011], occurs at lower temperatures than that in the direction normal to the tilting axis.     

Cavitation at grain and phase boundaries during superplastic flow of an aluminum bronze

Cavities have been observed to form at grain and phase boundaries under certain strain rate conditions during superplastic tensile deformation of a Cu-9.5 pct Al-4 pct Fe aluminum-bronze. The cavities form preferentially at α-β interfaces or triple junctions involving both phases. The process of cavitation is associated with grain boundary sliding and cavity nucleation probably occurs at points of stress concentration in the sliding interfaces. The ductility is not markedly impaired by the cavities because the high strain-rate sensitivity of the material inhibits the interlinkage of cavities at high strains. A range of strains and strain rates for superplastic forming processes has been determined at which the volume fraction of cavities present was tolerable.     

A composite model for the grain-size dependence of yield stress of nanograined materials

Based on the observation that, in a nanograined material, a significant portion of atoms resides in the grain-boundary region and grain-boundary activity plays a key role for its plastic behavior, a micromechanics-based composite model is developed to calculate the transition of yield stress as the grain size decreases from the coarse grain to the nanograin regime. The development makes use of a generalized self-consistent scheme in conjunction with the secant moduli of the constituent phases and a field-fluctuation approach. The constituent grains are modeled by inclusions with a grain-size-dependent plastic property and, in order to reflect the atomic sliding inside the grain boundaries observed in molecular dynamic simulations, the grain-boundary phase is modeled as a soft, ductile material with a pressure-dependent property. Applications of the developed model to a high-density copper showed the distinctive—some experimentally observed—features: (1) the yield stress initially increases following the Hall-Petch equation, but as the grain size reduces to the nanorange, it will depart and decrease; (2) when the grain size drops to a critical value (called the critical equicohesive grain size), the slope turns negative, (3) there is a tension-compression asymmetry (or strength-differential effect) in the yield stress, and (4) parametric calculations for materials whose grains deform only elastically indicate that the Hall-Petch plot will exhibit a continuously decreasing negative slope over the entire range of grain size. Further application of the theory to palladium in the nanorange shows a continuous decrease of the yield strength with decreasing grain size. It can be generally concluded that the range following the Hall-Petch equation is dominated by the deformation of the grains, and the range with a negative slope is controlled by the plasticity of the grain boundaries. During the transitional stage, both grains and grain boundaries deform competitively.     

A composite model for the grain-size dependence of yield stress of nanograined materials

Based on the observation that, in a nanograined material, a significant portion of atoms resides in the grain-boundary region and grain-boundary activity plays a key role for its plastic behavior, a micromechanics-based composite model is developed to calculate the transition of yield stress as the grain size decreases from the coarse grain to the nanograin regime. The development makes use of a generalized self-consistent scheme in conjunction with the secant moduli of the constituent phases and a field-fluctuation approach. The constituent grains are modeled by inclusions with a grain-size-dependent plastic property and, in order to reflect the atomic sliding inside the grain boundaries observed in molecular dynamic simulations, the grain-boundary phase is modeled as a soft, ductile material with a pressure-dependent property. Applications of the developed model to a high-density copper showed the distinctive—some experimentally observed—features: (1) the yield stress initially increases following the Hall-Petch equation, but as the grain size reduces to the nanorange, it will depart and decrease; (2) when the grain size drops to a critical value (called the critical equicohesive grain size), the slope turns negative, (3) there is a tension-compression asymmetry (or strength-differential effect) in the yield stress, and (4) parametric calculations for materials whose grains deform only elastically indicate that the Hall-Petch plot will exhibit a continuously decreasing negative slope over the entire range of grain size. Further application of the theory to palladium in the nanorange shows a continuous decrease of the yield strength with decreasing grain size. It can be generally concluded that the range following the Hall-Petch equation is dominated by the deformation of the grains, and the range with a negative slope is controlled by the plasticity of the grain boundaries. During the transitional stage, both grains and grain boundaries deform competitively.     

The absence of relative grain translation during superplastic deformation of an Al-Li-Mg-Cu-Zr alloy

The deformation of AA8090 Al-Li-Mg-Cu-Zr alloy at elevated temperature and slow strain rates has been investigated in uniaxial tension. Under suitable conditions, this material exhibited a high strain-rate sensitivity of the flow stress and was superplastic. This superplastic behavior was obtained in material with an initially elongated grain structure combined with a distribution of similarly oriented grains and low-angle grain boundaries that was not conducive to boundary sliding. Observations of the development of microstructure and of the crystallographic preferred orientation indicated that no significant rigid body translation and little rotation of grain interiors occurred up to strains of about 0.4 and that the probability of relative translation of grain interiors up to strains of at least 1 was low. The changes of structure observed could be accounted for by a combination of grain growth and grain rotation. The consequence of these observations on the grain switching and grain boundary sliding mechanisms generally assumed to operate during superplastic deformation is discussed, with the conclusion that those mechanisms may not be wholly appropriate for explaining high rate sensitivity in this material over the range of strain rates investigated.     

电子束悬浮熔炼钼铼合金铸锭的热加工方法

电子束悬浮熔炼钼铼合金铸锭晶粒粗大,致使热加工性能变差,锻造过程出现开裂,文章分析了锻造过程材料的受力状态,认为是垂直晶界的拉应力导致沿晶开裂,据此提出了热轧开坯的工艺方法,且规定第1道次平行铸锭轴向喂料,轧制过程中材料产生剪切滑移变形,滑移面与晶界成一定夹角,不产生垂直晶界的拉应力,避免了拉应力作用下的沿晶开裂,获得优质热轧板。     

High temperature creep cavitation mechanisms in a continuously cast high purity copper

Continuously cast high purity copper was used to study intergranular high temperature creep fracture mechanisms. With the help of an internal marker system due to impurity segregation, grain boundary sliding, GBS, was found to have occurred to a similar extent on cavitated and uncavitated boundaries. To explain this phenomenon a void nucleation model involving small nonwetting shearable particles is suggested. Metallographic observations and the apparent activation energy derived from fracture time data indicate the operation of the vacancy condensation mechanism at the lower temperatures and higher stresses. At the higher temperatures and lower stresses void growth is enhanced by GBS. This cavitation mechanism obtains strong support from measurements of the distribution of voids on grain boundaries as a function of the boundary angle with respect to the tensile direction. Computer analysis of these distributions, in terms of a model which properly accounts for the distribution of potential nuclei, yields bimodal curves exhibiting peaks at grain boundaries oriented for high shear stress (peak I), and for high normal stress (peak II). A phenomenological equation is proposed for the dependence of peak I on test conditions. Peak II is thought to be caused by nucleation by local GBS and growth by vacancy condensation under locally enhanced normal stress. A. RUKWIED, formerly Physicist, Engineering Metallurgy Section, Metallurgy Division, National Bureau of Standards, U. S. Department of Commerce, Washington, D. C.     

Denuded zones, diffusional creep, and grain boundary sliding

The appearance of denuded zones following low stress creep in particle-containing crystalline materials is both a microstructural prediction and observation often cited as irrefutable evidence for the Nabarro-Herring (N-H) mechanism of diffusional creep. The denuded zones are predicted to be at grain boundaries that are orthogonal to the direction of the applied stress. Furthermore, their dimensions should account for the accumulated plastic flow. In the present article, the evidence for such denuded zones is critically examined. These zones have been observed during creep of magnesium, aluminum, and nickel-base alloys. The investigation casts serious doubts on the apparently compelling evidence for the link between denuded zones and diffusional creep. Specifically, denuded zones are clearly observed under conditions that are explicitly not diffusional creep. Additionally, the denuded zones are often found in directions that are not orthogonal to the applied stress. Other mechanisms that can account for the observations of denuded zones are discussed. It is proposed that grain boundary sliding accommodated by slip is the rate-controlling process in the stress range where denuded zones have been observed. It is likely that the denuded zones are created by dissolution of precipitates at grain boundaries that are simultaneously sliding and migrating during creep. This article is based on a presentation made in the workshop entitled “Mechanisms of Elevated Temperature Plasticity and Fracture,” which was held June 27–29, 2001, in Dan Diego, CA, concurrent with the 2001 Joint Applied Mechanics and Materials Summer Conference. The workshop was sponsored by Basic Energy Sciences of the United States Department of Energy.     

Processing and superplastic properties of fine-grained iron carbide

Fine-grained iron carbide material (80 vol pct iron carbide and 20 vol pct of an iron-base second phase) was prepared using two different powder metallurgy procedures: (1) hot isostatic pressing followed by uniaxial pressing and (2) hot extrusion followed by uniaxial pressing. Both procedures yield materials that are superplastic at elevated temperature with low values of the stress exponent (n = 2 to 1) and tensile elongations as high as 600 pct. The strain rate in then = 2 region is inversely proportional to approximately the cube of the grain size with an activation energy for superplastic flow between 200 and 240 kJ/mol. It is postulated that superplastic flow in the iron carbide material, in then = 2 region, is grain-boundary sliding accommodated by slip controlled by iron diffusion along iron carbide grain boundaries. The flow stress in compression is about 2 times higher than in tension in the region where grain-boundary sliding is the rate-controlling process. It is believed that the difference in flow stress is a result of the greater ease of grain-boundary sliding in tension than in compression. Tensile elongations were observed to increase with a decrease in stress and a decrease in grain size. These effects are quantitatively explained by a fracture mechanics model that has been developed to predict the tensile ductility of superplastic ceramics.     

On grain boundary sliding and diffusional creep

The problem of sliding at a nonplanar grain boundary is considered in detail. The stress field, and sliding displacement and velocity can be calculated at a boundary with a shape which is periodic in the sliding direction (a wavy or stepped grain boundary): a) when deformation within the crystals which meet at the boundary is purely elastic, b) when diffusional flow of matter from point to point on the boundary is permitted. The results give solutions to the following problems. 1) How much sliding occurs in a polycrystal when neither diffusive flow nor dislocation motion is possible? 2) What is the sliding rate at a wavy or stepped grain boundary when diffusional flow of matter occurs? 3) What is the rate of diffusional creep in a polycrystal in which grain boundaries slide? 4) How is this creep rate affected by grain shape, and grain boundary migration? 5) How does an array of discrete particles influence the sliding rate at a grain boundary and the diffusional creep rate of a polycrystal? The results are compared with published solutions to some of these problems.     

The Effect of Solute Atoms on Aluminum Grain Boundary Sliding at Elevated Temperature

Grain boundary sliding (GBS) is an important deformation mechanism for elevated temperature forming processes. Molecular dynamics simulations are used to investigate the effect of solute atoms in near grain boundaries (GBs) on the sliding of Al bicrystals at 750 K (477 °C). The threshold stress for GBS is computed for a variety of GBs with different structures and energies. Without solute atoms, low-energy GBs tend to exhibit significantly less sliding than high-energy GBs. Simulation results show that elements which tend to phase segregate from Al, such as Si, can enhance GBS in high-energy GBs by weakening Al bonds and by increasing atomic mobility. In comparison, intermetallic forming elements, such as Mg, will form immobile Mg-Al clusters, decrease diffusivity, and inhibit GBS.     

Creep at very low rates

The creep rate in a land-based power station must be less than 10⁻¹¹ s⁻¹. At these low rates of deformation the transport of matter occurs by the migration of vacancies rather than by the glide of dislocations. A quantitative understanding of these diffusional processes is, therefore, important. First type of diffusional creep (Nabarro-Herring (N-H)): the sources and sinks of vacancies are grain boundaries. The vacancies may diffuse through the bulk of the grain or along the grain boundaries (Coble (C)). Second type (Harper-Dorn (H-D)): the vacancies diffuse from edge dislocations with their Burgers vectors parallel to the major tensile axis to those with Burgers vectors perpendicular to this axis. The coherence of the polycrystalline aggregate is maintained by sliding along the grain boundaries. The three mechanisms of vacancy migration, grain boundary sliding, and dislocation glide may all interact. The theories of N-H and C creep in pure metals are established and confirmed, but H-D creep and grain boundary sliding are less well understood. Practical engineering materials are usually strengthened by precipitates that accumulate on grain boundaries and slow down creep in complicated ways. This article is based on a presentation made in the workshop entitled “Mechanisms of Elevated Temperature Plasticity and Fracture,” which was held June 27–29, 2001, in Dan Diego, CA, concurrent with the 2001 Joint Applied Mechanics and Materials Summer Conference. The workshop was sponsored by Basic Energy Sciences of the United States Department of Energy.     

Effect of Recovery and Recrystallization on the Hall–Petch Relation Parameters in Submicrocrystalline Metals: II. Model for Calculating the Hall–Petch Relation Parameters

A model is developed to calculate the Hall–Petch relation parameters for the submicrocrystalline (SMC) metals fabricated by severe plastic deformation (SPD) methods. The model is based on the assumption that the flow stress in SMC metals includes both conventional contributions (caused by lattice dislocations, impurity atoms, etc.) and a contribution related to the long-range internal stress fields created by the SPD-induced defects distributed over grain boundaries. Equations are derived to calculate the Hall–Petch relation parameters as functions of the strain and the strain rate. The results calculated by the derived equations agree well with the experimental data. The low resistance of grain boundaries to the motion of grain boundaries in SMC materials (see part I of this work) is found to be related to a violation of the Hall–Petch relation in SMC metals.