Creep mechanisms in beryllium

Observations of beryllium samples which have been creep tested between 922 K and 1422 K indicate that creep behavior is controlled by the relative strengths of the grain boundaries and the matrix. Since creep deformation can occur predominantly by grain boundary sliding or entirely by deformation within the grains, the creep strength was found to be controlled by the weaker of the two features. Low melting phases containing aluminum and silicon which formed along the grain boundaries acted as stress concentrations which favored localized grain boundary deformation, and recrystallization. Creep resistance was found to drop markedly when the BeO content was reduced substantially below 1 pct.     

A model for creep based on the climb of dislocations at grain boundaries

A model for creep based on the climb of dislocations at grain boundaries is presented. It is shown that when a sliding interface or slip band intersects a grain boundary, a traction distribution is established on the boundary. The diffusional flow induced by these tractions results in a steady state creep process. This slip band model predicts an activation energy corresponding to grain boundary self diffusion, with a stress exponent and a grain size dependence which increase and decrease, respectively, as the applied stress increases. The theoretically determined creep rates are in good agreement with the data for metals and alloys which deform by grain boundary sliding and exhibit superplastic flow properties. Other models for creep controlled by grain boundary diffusion are briefly reviewed and compared with the present model. It is concluded that superplastic deformation involves both purely diffusional flow and dislocation motion.     

Characterization of Creep-Damaged Grain Boundaries of Alloy 617

Intergranular cracking and void nucleation occur over extended periods of time in alloy 617 when subjected to stress at high temperatures. Damage occurs inhomogeneously with some boundaries suffering failure, while others are seemingly immune to creep. Crack propagation associated with grain size, and grain boundary character was investigated to determine which types of grain boundaries are susceptible to damage and which are more resistant. Electron backscatter diffraction and a stereological approach to obtain the five-parameter grain boundary distribution were used to measure the proportions of each type of boundary in the initial and damaged structures. The samples were crept at 1273.15 K (1000 °C) at 25 MPa until fracture. It was found that in addition to low-angle and coherent twin boundaries, other low index boundary plane grain boundaries with twist character are relatively resistant to creep.     

Constrained cavity growth models of longitudinal creep deformation of oxide dispersion strengthened alloys

Two models of constrained cavity growth are developed to describe the long-term longitudinal creep behavior of nickel based oxide dispersion strengthened (ODS) alloys. For both models the rupture time is taken as the time for a transverse grain boundary to cavitate fully. A diffusive cavity growth law is assumed to govern cavitation. The applicability of the respective models is determined by the particular grain morphology achieved by thermal-mechanical processing. The first model assumes that longitudinal grain boundaries are unable to slide; hence displacements due to cavitation must be matched by displacements due to dislocation creep in adjoining grains. This model predicts a low stress exponent at the transition from single crystal to cavitation creep behavior, and higher stress exponents at stresses below this transition. Good agreement is found between the model predictions and creep data for MA 754 at 1000 and 1093 °C. A second model considers a grain morphology wherein longitudinal grain boundaries are able to slide by means of deformation of pockets of fine grains. Cavitation of transverse grain boundaries is thus controlled by grain boundary sliding. This model predicts a stress exponent of 1 at low stresses, and serves as an upper bound for the creep rate when a duplex grain morphology is present. Model predictions are in good agreement with creep data for a heat of MA 754 with a duplex grain morphology. Formerly Graduate Research Assistant in the Department of Materials Science and Engineering at Stanford University     

Heterogeneous Creep Deformations and Correlation to Microstructures in Fe-30Cr-3Al Alloys Strengthened by an Fe<Subscript>2</Subscript>Nb Laves Phase

A new Fe-Cr-Al (FCA) alloy system has been developed with good oxidation resistance and creep strength at high temperature. The alloy system is a candidate for use in future fossil-fueled power plants. The creep strength of these alloys at 973 K (700 °C) was found to be comparable with traditional 9 pct Cr ferritic–martensitic steels. A few FCA alloys with general composition of Fe-30Cr-3Al-.2Si-xNb (x = 0, 1, or 2) with a ferrite matrix and Fe₂Nb-type Laves precipitates were prepared. The detailed microstructural characterization of samples, before and after creep rupture testing, indicated precipitation of the Laves phase within the matrix, Laves phase at the grain boundaries, and a 0.5 to 1.5 μm wide precipitate-free zone (PFZ) parallel to all the grain boundaries. In these alloys, the areal fraction of grain boundary Laves phase and the width of the PFZ controlled the cavitation nucleation and eventual grain boundary ductile failure. A phenomenological model was used to compare the creep strain rates controlled by the effects of the particles on the dislocations within the grain and at grain boundaries. (The research sponsored by US-DOE, Office of Fossil Energy, the Crosscutting Research Program).     

A Constitutive Equation for Grain Boundary Sliding: An Experimental Approach

Although grain boundary sliding (GBS) has been recognized as an important process during high-temperature deformation in crystalline materials, there is paucity in experimental data for characterizing a constitutive equation for GBS. High-temperature tensile creep experiments were conducted, together with measurements of GBS at different strains, stresses, grain sizes, and temperatures. Experimental data obtained on a Mg AZ31 alloy demonstrate that, for the first time, dynamic recrystallization during creep does not alter the contribution of GBS to creep during high-temperature deformation. The experimentally observed invariance of the sliding contribution with strain was used together with the creep data for developing a constitutive equation for GBS in a manner similar to the standard creep equation. Using this new approach, it is demonstrated that the stress, grain size, and temperature dependence for creep and GBS are identical. This is rationalized by a model based on GBS controlled by dislocations, within grains or near-grain boundaries.     

Microstructural changes during wear by plastic deformation of cemented carbide and cermet cutting inserts

The microstructure of one WC-Co and two Ti(C,N)-WC-Co cutting inserts has been studied before and after plastic deformation, caused by high-speed turning. It was found that after deformation, the binder phase had infiltrated some of the grain boundaries and formed lamellae between the hard phase grains. The infiltration of grain boundaries was assumed to occur by a stress-induced dissolution along the grain boundaries of the hard phase grains as a wide front of binder phase, rather than gradually by Co grain boundary diffusion. Some localized dissolution of the hard phase could also be seen as faceting of grains in WC-Co and at triple points in cermets. It was concluded that the plastic deformation occurs by grain boundary infiltration with simultaneous grain boundary sliding. The rate of deformation is controlled by grain boundary infiltration through dissolution of the hard phase grains.     

Role of grain boundary segregation in diffusional creep

The high temperature deformation of polycrystalline materials by the stress directed flow of vacancies is now a well established creep mechanism which operates in two temperature regimes: high temperature, or Nabarro-Herring creep, in which lattice diffusion is rate determining, and low temperature, or Coble creep, in which grain boundary diffusion predominates. Basic studies have been conducted mostly with pure metals for which there exists in general a good correspondence between predicted and observed behavior. Multicomponent engineering alloys will normally experience, as part of their processing history or service lives, the segregation enrichment of interfaces such as grain boundaries by species present in solid solution. The aim of this paper is to evaluate the experimental information and to explore the manner in which this segregation affects the principal forms of diffusional creep. Cases of retarded Herring-Nabarro creep are analyzed in terms of the efficacy of grain boundaries as sources and sinks for vacancies: strongly bound segregant atoms at grain boundaries affect the mobility of defects and hence control the operation of vacancy sources. Recently, observations have been made on the effect of strongly segregating solutes on grain boundary diffusivity. Such behavior influences Coble creep rates, producing in general a retardation. Here we assess the magnitude of the effect induced by various surface active species on grain boundary diffusivity and consequently on Coble creep; predictions show that in general, small amounts of highly surface active impurities induce a remarkable inhibition of this form of creep.     

A theoretical model for creep crack growth

A theory of creep crack growth has been developed with the presumption that the crack growth occurs by the diffusion of vacancies along the grain boundaries. This is consistent with many experimental results that show that creep fracture is generally of intergranular type and the activation energies for crack growth rates fall within the range of grain boundary diffusion energies. The theory is based on the concept that creep crack growth results from a balance of two competing processes-the diffusion of point defects that contributes to the growth and the creep deformation process that retards the growth and causes even its arrest. The present analysis shows that crack growth via grain boundary diffusion occurs within some temperature range. The upper limiting temperature is determined by the bulk diffusion process which disperses the vacancies, that are diffusing to the crack tip, to the plastic zone ahead of the crack front. The lower temperature limit is set by the fact that the grain boundary diffusion rates decrease with the decrease in temperature and thus large stress intensities approaching the fracture toughness value are required to accomplish crack growth by the grain boundary diffusion. Outside these limits creep crack growth occurs via deformation which is significantly slower than growth by the grain boundary diffusion process. The importance of the present analysis rests on the fact that service conditions for many high temperature structural materials fall within the regime wherein creep crack growth occurs via grain boundary diffusion.     

Creep and intergranular cracking of Ni-Cr-Fe-C in 360 °C argon

The influence of carbon and chromium on the creep and intergranular (IG) cracking behavior of controlled-purity Ni-xCr-9Fe-yC alloys in 360 °C argon was investigated using constant extension rate tension (CERT) and constant load tension (CLT) testing. The CERT test results at 360 °C show that the degree of IG cracking increases with decreasing bulk chromium or carbon content. The CLT test results at 360 °C and 430 °C reveal that, as the amounts of chromium and carbon in solution decrease, the steady-state creep rate increases. The occurrence of severe IG cracking correlates with a high steady-state creep rate, suggesting that creep plays a role in the IG cracking behavior in argon at 360 °C. The failure mode of IG cracking and the deformation mode of creep are coupled through the formation of grain boundary voids that interlink to form grain boundary cavities, resulting in eventual failure by IG cavitation and ductile overload of the remaining ligaments. Grain boundary sliding may be enhancing grain boundary cavitation by redistributing the stress from inclined to more perpendicular boundaries and concentrating stress at discontinuities for the boundaries oriented 45 deg with respect to the tensile axis. Additions of carbon or chromium, which reduce the creep rate over all stress levels, also reduce the amount of IG fracture in CERT experiments. A damage accumulation model was formulated and applied to CERT tests to determine whether creep damage during a CERT test controls failure. Results show that, while creep plays a significant role in CERT experiments, failure is likely controlled by ductile overload caused by reduction in area resulting from grain boundary void formation and interlinkage. Thomas M. Angeliu, formerly Graduate Student Research Assistant, Department of Materials Science and Engineering, the University of Michigan, Ann Arbor, MI,.     

Creep deformation of TD-nickel chromium

The creep behavior of thoria dispersed nickel-chromium (TD-NiCr) was examined at 1093°C (2000°F). Major emphasis was placed on 1) the effects of the material and the test related variables (grain size, temperature, stress, strain and strain rate) on the deformation characteristics, and 2) the evaluation of single crystal TD-NiCr material produced by a directional recrystallization technique. Creep activation enthalpies were found to increase with increasing grain size reaching maximum values for the single crystal TD-NiCr. Stress exponent of the steady state creep rate was also significantly higher for the single crystal material as compared to that determined for the polycrystalline TD-NiCr. The elevated temperature deformation of TD-NiCr was analyzed in terms of two parallel-concurrent processes: 1) diffusion controlled grain boundary sliding and 2) dislocation motion. The characteristics of the dislocation motion deformation mode (as observed in the single crystal TD-NiCr) suggest that strong particle-dislocation interactions are present. The relative contributions of dislocation motion and grain boundary sliding in TD-NiCr were estimated. In creep, grain boundary sliding was found to predominate for the small, equiaxed grain structures, whereas the dislocation deformation mode became significant for only the large grain TD-NiCr and the single crystal material. Formerly Graduate Assistant, Case Western Reserve University, Cleveland, Ohio 44106.     

Deformation mechanisms of a rapidly solidified Al-8.8Fe-3.7Ce alloy

The mechanisms of deformation of a rapidly solidified and compacted Al-8.8Fe-3.7Ce (wt pct) alloy were investigated in the stress range 20 to 115 MPa and temperature range 523 to 623 K. The stress dependence of the steady state strain rates indicated a transition from diffusional creep to power law creep, the transition stress decreasing with increasing temperature from 70 MPa (σ/G = 3.1 × 10^-3) at 523 K to 40 MPa (σ/G = 1.9 × 10^-3) at 623 K. The activation energy in the power law creep regime was close to that of bulk self-diffusion in aluminum, while the activation energy in the diffusional creep regime was close to that of grain boundary self-diffusion in Al. The creep strain rates in the power law creep regime were found to be predicted much better by the substructure-invariant creep law (Sherby, 1981) than by the semi-empirical Dorn equation for Al, with the inclusion of a “threshold” stress. In the Coble creep regime, it was found that the cell/subgrain boundaries are inefficient vacancy sources/sinks and that their contribution to Coble creep is totally suppressed in this alloy. The Coble creep rates could be explained by using the average diameter of the powder particles as the effective grain size in the Coble creep equation.     

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.     

Deformation mechanisms during low-and high-temperature superplasticity in 5083 Al-Mg alloy

The controlling deformation mechanisms and grain boundary sliding behavior during low-, medium-, and high-temperature superplasticity (LTSP, MTSP, and HTSP) in fine-grained 5083 Al-Mg base alloys are systematically examined as a function of strain. Grain boundary sliding was observed to proceed at temperatures as low as 200 °C. With increasing LTSP straining from the initial (ε<0.5) to later stages (ε>1.0), the strain rate sensitivity m, plastic anisotropy factor R, high-angle grain boundary fraction, grain size exponent p, and grain boundary sliding contribution all increased. During the initial LTSP stage, there was little grain size dependence and the primary deformation mechanisms were solute drag creep plus minor power-law creep. At later stages, grain size dependence increased and grain boundary sliding gradually controlled the deformation. During MTSP and HTSP, solute drag creep and grain boundary sliding were the dominant deformation mechanisms.     

High temperature creep damage in steels and superalloys

The nucleation and growth of cavities was examined in steel bicrystals (Fe-3%-Si, X 8 CrNiNb 16 13) and in the ODS superalloy Inconel MA 754 (Inconel MA 754 (78% Ni; 20% Cr; 0.5% Ti; 0.3% Al; 0.6% Y₂O₃). Cavity density distributions were measured on metallographic sections and on cleaved grain boundaries as a function of time, strain, temperature and stress. Nucleation and growth laws were obtained by evaluating the distributions with appropriate models. For the fcc and bcc bicrystals, it was found that cavities nucleated continuously at sulfide and carbide particles during creep. They grew by grain boundary diffusion. But the growth rate was delayed with increasing creep strain due to cavities which nucleated in the surroundings of existing cavities. For the ODS alloy, however, many round cavities preexisted on quasi-boundaries consisting of the aggregate of coarse oxide and carbide particles. They grew initially by diffusion, but with increasing creep time (cavity size), the growth mechanism switched from growth controlled by grain boundary diffusion to growth controlled by power law creep. Implications for life predictions are discussed.     

The role of coincidence-site-lattice boundaries in creep of Ni-16Cr-9Fe at 360 °C

The objective of this study is to understand and quantify the role of the coincidence-site-lattice boundary (CSLB) population on creep deformation of Ni-16Cr-9Fe at 360 °C. It is hypothesized that an increase in the CSLB population decreases the annihilation rate of dislocations in the grain boundary, leading to an increase in the internal stress and a decrease in the effective stress. The result is a reduction in the creep strain rate. The role of CSLBs in deformation is, thus, to increase the internal stress by trapping run-in lattice dislocations at the grain boundaries as extrinsic grain boundary dislocations (EGBDs), creating backstresses on following dislocations rather than annihilating them, as in the case of high-angle boundaries (HABs). The hypothesis was substantiated by showing (1) that dislocation absorption kinetics differ substantially between a CSLB and an HAB, and (2) that the CSLB fraction strongly affects the internal stress in the solid. Dislocation absorption kinetics were measured by comparing EGBD density in transmission electron microscopy (TEM). Results showed that CSLBs contain an EGBD density which is 3 times higher than HABs at 1.25 pct strain. Internal stress was measured by the stress dip test and was found to be ≈ 30 MPa higher in the CSLB-enhanced sample. Steady-state creep rates of Ni-16Cr-9Fe in 360 °C argon were also found to be strongly affected by the grain boundary character distribution. Increasing the CSLB fraction by approximately a factor of 2 resulted in a decrease in steady-state creep rates by a factor of 8 to 26 in coarse-grain (330 μm) samples and a factor of 40 to 66 in small-grain (35 μm) samples. It is postulated that annihilation of EGBDs only occurs at triple lines where at least two HABs intersect. By using a geometric relationship to evaluate the probability of EGBDs annihilating at a triple line, the model predicts a non-linear dependence of the creep rate with CSLB fraction, yielding excellent correlation with measurement. The model provides a physical basis for measurements which show that increasing the CSLB fraction by only moderate amounts can greatly reduce the steady-state creep rate in Ni-16Cr-9Fe.     

Compositional effects on the creep ductility of a low alloy steel

The role which P plays in determining the creep ductility of 2.25Cr-1Mo steel is examined by notched bar creep rupture tests on high purity material selectively doped with combinations of Mn, Si and P. The impurity concentrations, hardness and grain size were carefully controlled. The ductility of as-tempered samples containing dopants was found to be higher than those without dopants; however the ductility of step cooled samples containing Mn and P was found to be lower than as-tempered samples. It is suggested that P, when segregated to the prior austenite grain boundaries, enhances the nucleation of grain boundary cavities while retarding their growth. Mechanisms for each process are proposed. Formerly a Postdoctoral Research Fellow at the University of Pennsylvania formerly a Visiting Scientist at the University of Pennsylvania Formerly a Graduate Student at the University of Pennsylvania     

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.     

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.     

Mechanisms of strain accumulation and damage development during creep of prestrained 316 stainless steels

The effects of prestraining at room temperature and at the creep temperature of 848 K, as well as the responses to stress reductions during creep, have been studied for 316 stainless steels varying in composition and initial microstructure. The results are analyzed by contrasting the strengthening effects achieved by introducing high dislocation densities prior to creep exposure with the deleterious effects, which can occur when prestraining causes premature void nucleation at grain boundaries. In addition, by recognizing the differing contributions made by the grain interiors and the grain boundary zones to the overall rates of creep strain accumulation, a consistent explanation is provided for the diverse creep behavior patterns reported for different metals and alloys after various prestraining treatments.