Showing papers on "Grain boundary strengthening published in 1989"

Theory of plastic deformation: - properties of low energy dislocation structures

Abstract: Work-hardening phenomena are based on the very fundamental principles (i) that at the position of every dislocation axis the respective resolved shear stress cannot exceed the friction stress, including the self-stress of bowing dislocations, and (ii) that always that structure forms which among those accessible by the dislocations minimizes stored energy per unit length of dislocation line. Such dislocation structures have been named LEDSs. The corresponding work-hardening theory, the mesh length theory, is applicable to all materials deforming via gliding dislocations and to all types of deformation. Results previously achieved with the mesh length theory are summarized, and a number of new developments are discussed. Depending on the dislocation structures formed, the work-hardening behavior differs. Easily intersecting glide causes dislocation cell structures with almost dislocation-free cell interiors delineated by dislocation rotation boundaries. Pronounced planar glide causes Taylor lattices characterized by local planar order parallel to the one or perhaps two most highly stressed glide plane(s), no systematic lattice rotations, and overall uniform dislocation density. The most widely observed basic features of work hardening are explained in general terms. Specific applications are indicated for layer-type crystals, h.c.p. single crystals, single-crystal and polycrystalline pure f.c.c. metals and α-brass-type alloys, precipitation-hardened materials and steels. Included are the different stages of work hardening, dynamical effects in low temperature plasticity, the general characteristics of grain boundary strengthening and the Hall-Petch relationship. In addition, proposed explanations for (i) glide system interactions in polyslip resulting in microbands and affecting texture formation, and (ii) creep without stress dependence of dislocation density, are discussed.

Computer simulation on surfaces and [001] symmetric tilt grain boundaries in Ni, Al, and Ni 3 Al

Abstract: We have used “local volume” (embedded atom) type potentials to study the surfaces and grain boundaries of Ni, Al, and Ni3Al. The simulations show that with appropriately fit potentials, the surface and grain boundary structure can be realistically calculated. The surface rippling and relaxation show good agreement with experiments. The energies of most surfaces and grain boundaries also agree with existing data. The structural unit model for grain boundaries in Ni3Al shows the same generic units as in pure metals, but with large variations due to distortions and multiplicity. The utility of the structural unit model is thus more limited for alloys. The grain boundary energies were found to be the highest for Al-rich Ni3Al grain boundaries, and depend significantly on the local composition of the grain boundary. The cusps in the grain boundary energy as a function of misorientation angle are different for different grain boundary stoichiometries. The Ni3Al grain boundaries have approximately the same grain boundary energy and cohesive energy as that of Ni.

Dynamic Grain Growth During Superplastic Deformation of Yttria-Stabilized Tetragonal Zirconia Polycrystals

Abstract: Both static and dynamic grain growth were studied during superplastic deformation of fine-grained yttria-stabilized tetragonal zirconia. It was found that significant grain growth does not take place below 1300°C. Both static and dynamic growth were found to obey a similar equation of the form D3−D30=kt, where D and D0 are the instantaneous and initial grain sizes, respectively, t is the annealing time, and k is the kinetic constant for either static or dynamic grain growth. The activation energies were approximately 580 and 520 kJ/mol for static and dynamic grain growth, respectively.

Effect of grain boundaries on magnetic field penetration in polycrystalline superconductors

Abstract: The magnetic-field penetration at grain boundaries in superconductors is calculated using a model in which the grains and the grain boundaries are treated on an equal basis. The grains are modeled using the London theory, and the grain boundaries as weak-link Josephson junctions in the linear regime. An exact solution is found. Calculations of the overall effective penetration depth are presented for regular laminar arrays of grain boundaries for arbitrary grain size, diagonal grain anisotropy, and grain boundary coupling. Analytical formulas are obtained in several limiting cases, and simple empirically fit formulas are presented that are applicable in most intermediate regimes of grain size and grain coupling. The relevance of the results to the high-temperature oxide superconductors is discussed.

Low-angle tilt grain boundaries in YBa2Cu3O7 superconductors

Abstract: The structure of low-angle tilt boundaries in YBa2Cu3O7 superconductors was studied using high-resolution electron microscopy. The boundaries are shown to consist of arrays of triangular defects which have the spacing predicted by the Read-Shockley formula assuming them to be dislocations with a Burgers vector equal to 1·17 nm, the observed closure failure. It is shown that the structure of the dislocation cores changes as the grain boundary tilt angle is increased to 7·5°, starting out with a structure interpreted to be the result of the dissociation of a perfect || dislocation and at 7·5° having dislocation cores with an amorphous appearance. A stacking fault energy is estimated from the images of the dissociated dislocations to be 0·6-0·7 Jm-2.

Development of grain misorientation texture, in terms of coincident site lattice structures, as a function of thermomechanical treatments

Abstract: Microtexture (i.e. grain-specific) measurements have been made from grains both before and after grain growth in an austenitic stainless steel. Such measurements allow computation of grain misorientation texture in terms of the proportions of coincident site lattice (CSL) boundaries. After 2% postrecrystallization strain the grain growth is surface initiated in this alloy, and so, during the grain growth incubation period to, data were acquired just from those grains contiguous with the free surface. A clear trend emerged that the proportion and clustering of CSLs (particularly ‘special’ types which tend to have higher than average mobilities) increased both during to and after to when grains were actually growing. The CSL fractions were consistently greater for surface than for interior grains. It is therefore proposed that firstly the clustering of CSLs at surface grains is instrumental in the initiation of anomalous grain growth and secondly the nature of the grain misorientation texture after...

Microstructural refinement and associated strength of copper alloys obtained by mechanical alloying

Abstract: Several dispersoid-containing copper alloys have been produced by ball milling mixtures of copper and other powders followed by hot extrusion of the milled powders. In all cases the added material is quickly dispersed to very fine size within the copper. This dispersion forms more quickly at lower dispersoid fractions and for slightly soluble additions, such as chromium and niobium, and less rapidly for stable boride additions. Particle stability, both during extrusion as well as during subsequent heat treatments, is controlled by a volume diffusion coarsening process. The grain size is determined uniquely by grain boundary pinning by the particles. The strengths of the materials obtained are completely explained by an Orowan-type dislocation model, and the grain size dependence of strength is shown to be a consequence of the interdependence of particle distribution and grain size.

Effect of grain size on substructural evolution and plastic behaviour of copper

Abstract: Previous study has established that close correlations exist in copper single crystals between dislocation cells and active slip systems. In grains of a polycrystalline sample, comparison between cells and slip systems may indicate the level of intragranular stress field. In order to reach a better understanding of cell development in polycrystalline metals, tensile tests were performed on copper sheets with different grain sizes (between 20 and 250 μm). Transmission electron microscopy observations have shown that for a 250 μm grain size the dislocation substructure in similar to that which has been observed in single crystals; in some grain orientations only one family of parallel dislocation walls is observed. For grain sizes equal to or lower than 65 μm the plastic behaviour is strongly influenced by the interaction between grains; closed cells are present whatever the grain orientation. Such observations may be explained through a composite model taking into account the statistical and geometrical dislocation densities. However, a strain limit value appears in the applicability of this model; the limit is dependent on the grain size. For large strain amounts the accomodation between dislocation cells seems to control the stress-strain curves.

Control of intergranular fatigue cracking by slip homogeneity in copper II: Effect of loading mode

Abstract: Recent studies of long-life fatigue in polycrystalline copper have shown fractures to initiate primarily at grain boundaries. This is considered surprising in the light of early work where crack nucleation in persistent slip bands seemed to be the rule. To investigate the causes of this behavior, studies habe been carried out on polycrystalline copper with emphasis on the following factors: grain size (Part I), method of starting the test, frequency and mode of test control (Part II). The results show that the cyclic plasticity is the controlling factor in grain boundary initiation and propagation of fatigue cracks. It was found that transgranular cracking can be produced by factors which promote strain localization, and reducing the grain size of the specimens in constant-amplitude tests is one of them. In small-grain-sized metals, most of the applied plastic strain is concentrated in a few persistent slip bands, some of which develop into cracks with continued cycling. Use of coarse-grained structures causes strain homogenization and therefore intergranular cracking. For coarse-grained copper, a step is gradually built up at a sensitive grain boundary as a result of the “homogeneous” cyclic slip, at which point the cracking occurs in the same manner as proposed by Kim and Laird for high strain fatigue.

Evolution of Microstructure and Grain Growth in ZrO2–Y2O3 Alloys

Abstract: The microstructure evolution and grain growth during high-temperature heat treatment in ZrO2–4 and 8mol%Y2O3 alloys were examined. ZrO2–8mol%Y2O3 alloy was of single cubic phase (c-ZrO2), while ZrO2–4mol%Y2O3 alloy consisted of mixed grains of c-ZrO2 and tetragonal phase (t-ZrO2) with the equilibrium yttria contents after a certain period of heating. This structure was different from the microstructure containing precipitates in grain interior, and was referred to be the dual-phase structure. The grain growth of dual-phase structure was much slower than that of single c-ZrO2. The grain growth kinetics of dual-phase structure under the equilibrium partitioning of yttria between c-ZrO2 and t-ZrO2 grains could be described by the rate equation which was derived by assuming the growth of individual grains limited by grain-boundary diffusion of yttrium ions.

Microcracking in polycrystalline ceramics: elastic isotropy and thermal anisotropy

Abstract: A hexagonal grain array model is used to study grain boundary microcracking of a polycrystalline aggregate due to residual stress. Each grain is assumed to be elastically isotropic but thermally anisotropic. The axes of thermal anisotropy for each grain are arbitrary. An explicit analytic solution is obtained for the entire residual stress field. This solution is used to give a detailed description of the grain boundary stress fields. Further, explicit algebraic formulae are given for stress intensity factors associated with grain boundary microcracks. The results are used to predict the critical grain size for the occurrence of spontaneous microcracking. Agreement between theory and experiment is good.

The effect of grain size on fracture toughness

Abstract: The problem of dislocations emitted from a semi-infinite crack in mode II or III loading and blocked by a penetrable barrier (grain boundary), or many such equally spaced barriers, is studied. Analytical solutions for the continuous distribution of dislocations between the crack tip and a barrier is obtained. The case of multiple barriers is studied by computer simulation. The results are used to understand the effect of grain size on fracture toughness. For the same applied stress intensity factor, the toughness is found to increase with increasing grain size. By using a power-law relation, the exponent varies between 0 and 1.5 depending on the ratio of the lattice friction for dislocation motion to the grain-boundary strength. Together with the Petch relation for the dependence of grain size on fracture stress, a relation is suggested between the grain size and the critical stress intensity factor for crack propagation.

The microstructures of strip-cast low-carbon steels and their response to thermal processing

Abstract: The as-cast microstructure and its modification when subjected to heat treatment is examined for strip-cast low carbon steels. The local solidification rate in the twin-roll strip casting process is estimated to. be 590 to 850 °C/s, and the primary and secondary dendrite arm spacings are approximately 17 to 25 and 10 μm, respectively. The as-cast structure is predominantly Widmanstatten ferrite and, thereby, differs from the conventional hot-rolled sheet. It is suggested that the as-cast morphology is a result of the large initial austenite grain size and the cooling rate and is not a unique characteristic of rapid solidification of strip casting. By restricting the austenite grain size and cooling rate, polygonal ferrite morphology probably can be produced during strip casting. The response to heat treatment depends on the presence of aluminum; with a moderate amount of aluminum, the A1N precipitates in the as-cast structure inhibit the subsequent grain boundary movement and may affect the subsequent recrystallization behavior.

Strengths of grain boundaries in pure metals

Abstract: The relative surface energies for brittle fracture along grain boundaries or along crystal planes, at low temperatures, are estimated and used in a criterion for the relative strengths of boundaries and cleavages. It is concluded that the boundary is weaker than the crystal in a wide range of metals; that it becomes weaker as the ratio of shear modulus to bulk modulus increases; and that brittle pure metals, such as iridium and molybdenum, fracture preferentially on grain boundaries. The critical modulus ratio is in all cases lower than that for the ductile–brittle cleavage transition.MST/1154

On the onset of low-energy dislocation substructures in fatigue: Grain size effects

Abstract: It has long been known that grain boundaries are effective sources and traps for dislocations. It is also known that geometrically necessary dislocations that have formed during cycling can rearrange into low-energy structures. Such structures have been evaluated in polycrystalline high-strength low-alloy steels of two grain sizes. A selected area channeling pattern technique was used in conjuction with transmission electron microscopy to follow dislocation structure evolution. With accumulated plastic strain, the coarsegrained (approximately 85 μm) microstructure developed more misorientations within single grains, while the fine-grained (approximately 6 μm) structure showed more homogeneous slip. This could be explained by considering two factors. The first is that coarse grains do not develop as much constraint during deformation as fine grains do. Therefore, multiple slip processes accommodate strain in coarse grains more easily, whereas whole grain rotations occur in fine-grained materials. The second factor is that the dislocation density was initially higher in the fine-grained structure. This would reduce the dislocation mean free path from the start of deformation, thereby reducing the ability to form lower-energy structures. Implications of these findings on fatigue crack initiation will also be discussed.

The effect of small plastic deformation and annealing on the properties of polycrystals: Part II. Theoretical model for the transformation of nonequilibrium grain boundaries

Abstract: The nonequilibrium grain boundary state which has a high energy state is the result of absorption of a certain density of extrinsic grain boundary dislocations (EGBD’s). The equilibrium of such a boundary occurs by annealing at higher temperatures. A model has been proposed in this paper which assumes that the equilibrium of a nonequilibrium grain boundary involves the annihilation of EGBD’s by climbvia lattice diffusion of vacancies at the triple points. Due to the stress field of the EGBD’s, there is a vacancy concentration gradient around the triple points. The profile of the vacancy concentration gradient is derived by assuming a steady state flux of vacancies. Using this vacancy concentration profile, the expressions for the rate of climb of EGBD’s are derived. The proposed model predicts that the time required for the equilibration of nonequilibrium grain boundaries is dependent not only on the annealing temperature but also on the initial density of EGBD’s and the boundary length (which is related to the grain size). It has also been shown that the equilibrium behavior predicted by our model is in good agreement with the experimental results obtained for 316L stainless steel.