The effect of extrinsic grain boundary dislocations with unrelaxed and relaxed cores on the state of random boundaries in an austenitic steel

A transmission electron microscopic investigation employing in situ heating of thin foils has been carried out to determine the effect of extrinsic grain boundary dislocations (EGBDs) with unrelaxed as well as relaxed cores on the spreading temperature (T_d) of EGBDs on random grain boundaries in an austenitic stainless steel. The results show that while T_d is not measurably affected by the presence of unrelaxed EGBDs up to a density of a least 5.6 × 10⁷/m, its value is observed to decrease with increasing density of EGBDs with relaxed cores. These changes in T_d are discussed in terms of the possible changes in the structure and the energy of random grain boundaries which may be caused by the presence of these two types of EGBDs. Formerly with the Metallurgical Science Laboratory, The University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada,     

On the spreading of grain boundary dislocations and its effect on grain boundary properties

The effect of dissociation of trapped lattice dislocations (TLDs) on the energy of grain boundaries (GBs) is calculated. Two possible effects are considered. The first is the change of energy of the GBs caused by the presence of TLDs cores. It was shown to be smaller than 5% of the grain boundary energy. The other, more important, is an increase of the energy of the strain fields connected with grain boundaries. Dissociation of TLDs causes an increase of incompatibility strains between plastically deformed grains. The energy of these strains is of the order the GB energy in equilibrium. The EGBDs strain fields provide a driving force for GB sliding and migration. In fact, EGBDs cannot leave the grain boundaries. Recovery of these dislocations can take place only by sliding and migration of grain boundaries.     

The grain size dependence of the yield,flow and fracture stress of commercial purity silver

Heavily cold-rolled sheet material of 99.9 pct purity Ag has been recrystallized at varying temperatures to give average grain diameters,l, in the range between 1 and 60 μ. For this material, the yield stress, flow stress at several strain values, and fracture stress follow the Hall-Petch relation: $$\sigma _\varepsilon = \sigma o_\varepsilon + k_\varepsilon l^{ - 1/2} $$ whereσ _ε is the flow stress at a particular value of strain, ε, ands _{o ε} andk _ε are the experimental constants appropriate to a particular strain value. The range in grain size obtained for this material was sufficiently large to determine that silver can be appreciably strengthened by grain size refinement and that several other relations previously suggested to relate the stress and grain size could be discounted. The finest grain sizes were measured from replicas of etched specimens as viewed with the electron microscope. It is proposed that this type of grain size strengthening may be responsible for the exceptional strength which occurs in certain films of silver fabricated by vapor deposition techniques.     

Interaction of dislocations with grain boundaries in Ni3Al

The interaction between slip dislocations and grain boundaries in hypo-stoichiometric Ni₃Al, with and without boron, has been investigated by using the in situ TEM deformation technique. In both alloys, the slip dislocations were incorporated into the grain boundaries and remained at the point of entry. The difference between the alloys was in the dominant response mode of the grain boundary to the stress concentration associated with a dislocation pileup. In the boron-free material, the stress was relieved primarily by the nucleation and propagation of a crack along the grain boundary. In contrast, in the boron-doped material, relief occurred by the emission of dislocations from the grain boundary. These results are consistent with boron increasing the cohesive energy of the grain boundary. The slip system activated at grain boundaries in the ductile ordered alloy was shown to satisfy the same slip transfer criteria that operate in f.c.c. disordered alloys.     

Roles of dislocations and grain boundaries in martensite nucleation

In order to elucidate roles of dislocations and grain boundaries in martensite nucleation, the transformation temperature (M_s) of specimens austenitized at various temperatures and subjected to prestrain has been measured, using Fe-Ni, Fe-Ni-C, and Fe-Cr-C alloys. It is concluded that the plastic accommodation, in austenite, of the shape strain of the transforming martensite is a vital step in the nucleation event. Any factors impeding such plastic accommodation, such as the lack of dislocations, work hardening, and grain refinement, suppress the transformation. Contrary to the general belief, dislocations themselves do not act as favorable nucleation sites. Grain boundaries provide nucleation site, but only certain types of grain boundaries are qualified to be potential nuclei. A quantitative analysis shows that the increasing difficulty for the plastic accommodation with decreasing grain size is the main factor to depress M_s in fine-grained specimens.     

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.     

Modeling of Strain Hardening in the Aluminum Alloy AA6061

In this paper, the evolution of work-hardening and dynamic recovery rates vs the flow stress increase (σ ? σ _y ) in Al-Mg-Si alloys is presented. The experimental data have been extracted from stress–strain curves. All curves show an initial very rapid decrease in slope of the σ–ε curve, which is associated with the elastic–plastic transition. After the elastic–plastic transition, there are typically two distinctive behaviors. For underaged alloys, there is an approximately linear decrease of work-hardening rate as (σ ? σ _y ) increases. However, for overaged alloys after elastic–plastic transition, there is a plateau in the work-hardening rate followed by an almost linear decrease. The maximum work-hardening and dynamic recovery rates are found to be dependent on the aging state. In order to investigate these phenomena, a model has been employed to simulate the work-hardening behavior of Al-Mg-Si alloys. The model is based on a modified version of Kocks–Mecking–Estrin (KME) model, in which there are three main components: (1) hardening due to forest dislocations, grain boundaries, and sub-grains; (2) hardening due to the precipitates; and (3) dynamic recovery. The modeling results are discussed and compared with the experimental data.     

Dislocation and grain boundary interactions in metals

The passage of dislocations through grain boundaries in face centered cubic and body centered cubic polycrystalline metals was studied using dynamic in situ high voltage electron microscopy (HVEM), static transmission electron microscopy (TEM), and anisotropic elastic stress analysis. Several conclusions were reached: (1) when dislocations propagate across grain boundaries, the activated slip system can be predicted from pile-up properties and grain boundary orientation using a combined criterion based on boundary geometric factors and internal stresses; (2) different grain boundaries impede dislocation slip propagation to different degrees, the calculated value of the pile-up obstacle stress varying from 280 to 870 MPa for dislocation transmission through a grain boundary in 304 stainless steel; (3) dynamic in situ straining of miniature tensile specimens reveals additional modes of dislocation and grain boundary interactions that were hidden from static TEM observations. In connection with the last conclusion, simultaneous dislocation transmission and reflection was activated by a stressed pile-up and a complex mechanism involving coordinated movements of four sets of dilocations in and near a grain boundary was observed.     

The effect of grain size and stress upon grain-boundary sliding

Measurements at 293 K have been made of grain-boundary sliding of Pb and a Pb-2.5 pet Tl alloy over a wide range of grain sizes and of stress including conditions which gave superplastic behavior. Steps at grain boundaries(v) were measured on all specimens and marker-line offsets(w) on sufficient specimens to establish a pattern for values ofk2 in the relation to show thatk ₂ depends upon duration of testing,t. The average sliding rates/t, the strain due to sliding ￡ _gb and its contribution γ to the total strain ￡f were derived from the measurements and compared with the predictions of recent theories. Diffusion creep was found to be of minor importance in these tests.     

The effect of grain size and cross-head velocity on the lower yield strength during inhomogeneous discontinuous yielding in iron and steel

The validity of the relation, \(\underline {Ag} \) , has been checked with experimental results on the lower yield strength, σ _aF of various irons and steels determined at room temperature over wide ranges in cross-head velocity,V _c, and grain boundary intercept or grain diameter,l. Good agreement was found with the proposed relation form ^*=4, wherem ^* is the dislocation velocity-effective stress exponent, and α=1/3. σ _i , the internal stress, ranged between 5000 and 13,000 psi andN ^αθK’ between 4.3×10^?15 and 19.3×10^?15. In the original relation, the value of α was one andK’ was given asK, which was assumed to be a material constant. The modification which became necessary indicates that possibly the density of mobile dislocations and/or the resistance of grain boundaries to propagating Lüder’s bands depend on Lüder’s band velocity and strain. The validity of the relation at very high and very low cross-head velocities or strain rates is discussed. The relation should apply in an intermediate range of cross-head or dislocation velocities wherem ^* should remain constant and should show an apparent decrease at both higher and lower velocities. The basis for this prediction is discussed and results are presented at low strain rates.     

Cooperative phenomena at grain boundaries during superplastic flow

In situ observations in a scanning electron microscope (SEM) performed on different microstructural scales in Pb—62%Sn specimens, superplastically deformed in single shear and in simple tension, showed sliding of grain groups [cooperative grain boundary sliding (CGBS)], rotation of grain groups (cooperative grain rotation) and cooperative grain boundary migration (correlated migration of sliding grain boundaries). The observed macroscopic pattern of the CGBS surfaces is consistent with predictions of slip-lines field theory. The progress of the sliding of grain blocks at the scale of grain groups can be modeled in terms of cellular dislocations. The micromechanism for such sliding and the migration of sliding grain boundaries at the scale of the individual interface might be interpreted from the viewpoint of grain boundary dislocations.     

Hydrogen detrapping from grain boundaries and dislocations in high purity iron

Hydrogen detrapping in high purity iron was studied by measuring evolution rates of quenched-in hydrogen from 80 to 800 K using a quadrupole mass spectrometer in an ultra high vacuum system. The peak of the evolution rate was observed at 395 K in single crystal specimens and 415 K in polycrystalline specimens with a heating rate of 1 K min⁻¹. Effects of grain size and deformation on the evolution rate was also studied. It was shown that the results are consistent with the evolution rates calculated with the binding energy B = 0.51 ± 0.02 eV and the trap density term γC_{T = (4 ∼ 15) × 10⁻⁵} in polycrystalline iron, and B = 0.47 ± 0.02 eVand γC_T = (2 ∼ 13) × 10⁻⁵ in single crystal iron. The dominant traps are considered to be grain boundaries in polycrystalline specimens and dislocations in single crystal specimens.     

Effect of the lamellar grain size on plastic flow behavior and microstructure evolution during hot working of a gamma titanium aluminide alloy

The kinetics of dynamic spheroidization of the lamellar microstructure and the associated flow-softening behavior during isothermal, constant-strain-rate deformation of a gamma titanium aluminide alloy were investigated, with special emphasis on the role of the prior-alpha grain/colony size. For this purpose, fully lamellar microstructures with prior-alpha grain sizes between 80 and 900 μm were developed in a Ti-45.5Al-2Nb-2Cr alloy using a special forging and heat-treatment schedule. Isothermal hot compression tests were conducted at 1093 °C and strain rates of 0.001, 0.1, and 1.0 s⁻¹ on specimens with different grain sizes. The flow curves from these tests showed a very strong dependence of peak flow stress and flow-softening rate on grain size; both parameters increased with alpha grain/colony size. Microstructures of the upset test specimens revealed the presence of fine, equiaxed grains of γ + α ₂ + β phases resulting from the dynamic spheroidization process that initiated at and proceeded inward from the prior-alpha grain/colony boundaries. The grain interiors displayed evidence of microkinking of the lamellae. The frequency and severity of kinking increased with strain, but were also strongly dependent on the local orientation of lamellae with respect to the compression axis. The kinetics of dynamic spheroidization were found to increase as the strain rate decreased for a given alpha grain size and to decrease with increasing alpha grain size at a given strain rate. The breakdown of the lamellar structure during hot deformation occurred through a combination of events, including shear localization along grain/colony boundaries, microbuckling of the lamellae, and the formation of equiaxed particles of γ + β ₂ + α ₂ on grain/colony boundaries and in zones of localized high deformation within the microbuckled regions.     

Fatigue crack initiation and early propagation in Al 2219-T851

Fatigue crack initiation in Al 2219-T851 for fully reversed loading(R = σ/σ_max =?1) parallel to the material rolling direction is found to occur at intermetallic inclusions at the specimen surface. The inclusions are not involved in crack initiation for fatigue perpendicular to the rolling direction, and for this orientation crack initiation is at grain boundaries and specimens have an increased fatigue life. Except for fatigue at low peak stress, multiple numbers of microcracks are formed and for selected failed specimens the number of cracks has been determined as a function of crack length. Such crack length distribution measurements show that there is significant retardation of microcracks by interaction with grain boundaries. Furthermore it is found that the coalescence of microcracks provides a mechanism for cracking to “jump“ grain boundaries and reduce fatigue lifetime. The effect of relative humidity on this process is to increase the observed mean crack length, and decrease the number of crack initiations apparently due to weakening of the matrix-intermetallic interface at potential initiation sites. The overall result is that no significant dependence of fatigue life on relative humidity is found.     

Interactions between lattice dislocations and grain boundaries in Ni3Al investigated by means of in situ TEM and computer modelling experiments

The interaction between lattice dislocations and grain boundaries in Ni₃Al has been investigated by means of in situ TEM deformation experiments. The interaction between screw dislocations and a coherent twin boundary could be analyzed in detail. The interaction mechanism found experimentally was compared to the results of a computer modelling study. In the computer modelling study, many-body potentials representing Ni₃Al were used. The results of the in situ straining indicate that 〈110〉 screw dislocations impinging on a Σ = 3 coherent twin boundary that have a Burgers vector that is parallel to the grain boundary plane can be transmitted to the symmetric slip plane in the other grain under influence of an applied stress. A one-to-one comparison with the results of a computer modelling study of exactly the same system in Ni₃Al can be made and the experiment agrees with the simulations. Also, observations were made of superlattice intrinsic stacking faults (SISF) that were formed as a result of the interaction between gliding dislocations and the dislocations of a low angle grain boundary (cell wall). The creation of jogs in the line of the gliding dislocation may be the cause of the SISF formation.     

Constraint induced stresses and the hard surface-soft surface question in fatigue

Cu, 80-20 α-brass and 70-30 α-brass single crystals were cycled in a strain controlled tension-compression mode. Chemical polishing over the entire gage length of specimens in the grips at zero load and zero strain and reloading indicated no detectable difference in flow stress, or equivalently no significant difference in the resolved shear stress on the slip system. When half the gage length was electrolytically polished in specimens unloaded from tension to zero load, bending occurred in a manner indicating that the residual σ_zz stress was higher at the interior than at the surface. Unloading from compression to zero load indicated a reversal in residual σ_zz stress distribution. Finite element method (FEM) analysis, taking into account the slip behavior of a single crystal and the effect of end constraints occurring in the test, confirmed that there was little difference between the resolved shear stress on the slip system at the surface and the interior during deformation. The FEM calculations also indicated that the residual σ_zz stress was nonuniform, in agreement with the bending experiments. These results, therefore, indicate that a difference in flow stress between surface and interior is not necessary for bending to take place when half the gage length is electropolished.     

Theory of coble creep for irregular grain structures

Coble creep occurs by the diffusion of matter along grain boundaries. Under the action of an externally applied stress, matter diffuses from grain boundaries in compression to those in tension. Individual grains elongate and macroscopic creep ensues. To date, Coble creep has been derived only for simple periodic grain structures. In this work we show how to solve the Coble creep problem for irregular, two-dimensional grain structures consisting of straight grain boundary segments connected by triple points. Since the normal stress distributions at the grain boundaries are represented by cubic polynomials, 4n_gb constants have to be determined for a two-dimensional grain structure consisting of n_gb grain boundary segments. We show how the corresponding system of 4n_gb equations can be set up for freely chosen boundary conditions at the grain boundary-surface intersections. Several calculated examples with clusters consisting of 25 grains illustrate the power of the technique.     

Investigation of grain boundary diffusion in polycrystals by means of extrinsic grain boundary dislocations spreading rate

The spreading rate of extrinsic grain boundary dislocations (EGBDs) was used to study the diffusivity on grain boundaries in austenitic steel for a range of temperatures. The distribution function of the grain boundary diffusivity as well as the activation energy for grain boundary diffusion may be obtained by this method. This is an important characteristic of polycrystals. It is especially suited for investigating changes of distribution functions of grain boundary properties after various thermomechanical treatments or changes of grain boundary chemical composition as well as for studying the effect of grain boundaries on polycrystal properties. The optimal averaging methods of such distribution functions to a single diffusion coefficient were discussed. It was concluded, that EGBD spreading rate measurements provide a very sensitive method of grain boundary diffusion determination.