Materials Science Forum Vols. 715-716

Abstract: Recent investigations suggest that general grain boundaries can be categorized into two types: rough (atomically disordered) and faceted (atomically ordered). This paper reports our recent investigations on the migration behaviour of faceted boundaries and its effect on grain growth in polycrystalline ceramics. A model experiment has been performed using bi-layer samples of polycrystals with different average grain sizes and single crystals of BaTiO₃ to study the migration behaviour of faceted boundaries. A non-linear relationship between grain boundary migration and the driving force for migration is revealed. Grain growth behaviour with respect to boundary faceting has also been studied in perovskites. The structural transition of boundaries between rough and faceted can be induced by changing oxygen partial pressure, adding dopants and changing temperature. The fraction of faceted boundaries was changed by changing oxygen partial pressure and donor doping. As the facet fraction decreased, the grain growth behaviour changed from stagnant and abnormal to normal. The different types of growth behaviour observed can be explained by the coupling effect of the maximum driving force for the boundary migration and the critical driving force for appreciable migration of faceted boundaries.

Abstract: Two, high purity, Al-0.1 and 0.3wt%Mn alloys have been cold deformed in plane strain compression to strains of order 1.8 and the kinetics of subsequent recovery by sub-grain coarsening during annealing at 150-300°C measured by high resolution FEG-SEM EBSD. Accurate sub-grain size and misorientation distributions and their evolution with time and temperature have been determined. The average growth rates are then used to estimate the sub-grain boundary mobilities. Growth is analyzed by two well-known growth laws for the average sub-grain size δ (t): i) the standard relation for grain growth: where the exponent n takes values of 2-8 and ii) the relation proposed by Nes for dislocation climb in sub-grain walls: It is shown that the latter relation gives a better fit with the data in terms of the time and temperature dependence of the sub-grain sizes. In particular the activation energies for the logarithmic law are much closer to the values expected for solute-controlled movement of sub-boundaries.

Abstract: The Weighted Burgers Vector (WBV) is defined as the sum, over all types of dislocations, of [(density of intersections of dislocation lines with a map) x (Burgers vector)]. It can be calculated, for any crystal system, solely from orientation gradients in a map view, unlike the full dislocation density tensor, which requires gradients in the third dimension. No assumption is made about gradients in the third dimension and they may be non-zero. The only assumption involved is that elastic strains are small so the lattice distortion is entirely due to dislocations. Orientation gradients can be estimated from gridded orientation measurements obtained by EBSD mapping, so the WBV can be calculated as a vector field on an EBSD map. The magnitude of the WBV gives a lower bound on the magnitude of the dislocation density tensor when that magnitude is defined in a coordinate invariant way. The direction of the WBV can constrain the types of Burgers vectors of geometrically necessary dislocations present in the microstructure, most clearly when it is broken down in terms of lattice vectors. The WBV has five advantages over other measures of local lattice distortion. 1. It is a vector and hence carries more information than any scalar measure of local misorientation. 2. It has an explicit mathematical link to the individual Burgers vectors of dislocations. 3. Since it is derived via tensor calculus, it is not dependent on the map coordinate system, in contrast to existing measures of local misorientation which are not only scalar but dependent on the coordinate system used. 4. Calculation involves no assumptions about energy minimisation. 5. The numerical differentiation involved in calculating the WBV may introduce errors, but there is a direct mathematical link to a contour integral. The net Burgers vector content of dislocations intersecting an area of a map can be simply calculated by an integration round the edge of that area, a method which is fast and complements point-by-point WBV calculations. Errors in orientation measurement will have a much smaller effect here, and dislocations can be detected which are otherwise lost in the noise of any local calculation.

Abstract: Quantitative prediction of grain size and recrystallized volume fraction is still a real challenge for many alloys, and even for simple materials when subjected to complex thermal/mechanical histories, as in multi-pass (industrial) processing. A first step is therefore taken in the direction of multiscale modelling of recrystallization, by considering digital polycrystalline microstructures. These synthetic mesoscopic microstructures are meshed adaptively and anisotropically, with refinement close to the grain boundaries. Crystal plasticity finite element (CPFEM) simulations are combined with a level set framework to model primary recristallization, following plastic deformation. In the level set method, the kinetic equation describing interface motion uses the calculated stored energy field provided by CPFEM calculations, and works on the same mesh. Discontinuous dynamic recrystallization can be modelled within the same approach, effectively coupling plastic deformation with nucleation and growth processes. Parallel to the finite element approach, a mean field model is developed in the general context of multi-pass processing. The model considers categories of grains based on two state variables : grain size and total dislocation density. As opposed to the finite element approach, there is no crystallographic or topological information. It is computationally much cheaper and therefore suitable for direct coupling at the scale of forming processes, for industrial applications. The parameters of the model can be identified from inverse analysis, using experimental stress-strain curves, recrystallized volume fractions, and grain sizes. Mean field and finite element models are compared, and it is shown that the detailed information provided by finite element simulations can be used to calibrate or optimize the mean field method.

Abstract: Since the properties of the bulk ceramics are dependent on the grain size the ceramic materials with nanoscale grain size is of interest. Sintering of nanosized powder compacts to full density with minimum grain growth is a difficult task to achieve due to its high surface energy. Two step sintering methode was developed to enhance densification with minimum grain growth for silicon nitride ceramics with liquid phase. Starting with nano-sized silicon nitride powder two step sintering methode gives rise to a very fine-grained b-Si₃N₄ matrix with large agglomerated Si₂N₂O grains due to its high surface oxygen content. Addition of Y₂O₃ shifts the composition point to a primary phase field with no Si₂N₂O, gives rise to b-Si₃N₄ with nano scale grain size and near full density. Carbothermal reduction method was employed to reduce the oxygen content in nano-sized silicon nitride powder to give nanocrystalline dense silicon nitride ceramics without Si₂N₂O formation. Use of SPS was effective to suppress the grain growth and to give near full density. Microstructural development and mechanical properties will be reported.

Abstract: A three dimensional phase field model has been developed to simulate the texture formed during the static recrystallisation of FCC metals with medium or high stacking fault energy, such as aluminium, copper and nickel. Before recrystallisation the deformation texture as well as the stored energy was simulated using a three dimensional crystal plasticity finite element model. This output calculated on the distorted finite element mesh was first mapped onto the regular grid of the phase field model using a linear interpolation method and then used as initial condition for the subsequent recrystallisation texture modelling. This model has successfully predicted the typical recrystallisation texture components: cube {001}<100>, R {124}<211> in the aluminium alloy. In addition, the softening fraction and three dimensional microstructure produced during static recrystallisation have also been simulated by this model.

Abstract: The Zener drag force exerted by M₂₃C₆ carbides, Fe₂(W,Mo) Laves phase and M(C,N) particles for migration of different grain boundaries in P92-type and P911+3%Co heat-resistant steels was calculated. In particular, the prior austenite grain boundaries (PAGB), boundaries of packets and blocks, which are mainly high-angle boundaries (HAGB), were addressed. Zener pinning pressures were determined for each type of dispersoids separately taking into account that the M₂₃C₆ carbides, Fe₂(W,Mo) Laves phase are inhomogeneously distributed such that they are mainly located at the boundaries, and the M(C,N) dispersoids are uniformly distributed throughout the metallic matrix. In the both steels, the pinning pressure from the second phase particles located at grain boundaries is about an order of magnitude higher than that caused by homogeneously distributed MX precipitates. In spite of numerous second phase particles precipitated during tempering, grain growth (although rather moderate) occurred during the creep tests of the studied materials. The driving pressure for grain boundary motion might be mostly associated with high dislocation density retained in the tempered martensite structure. The resulting pressure for grain growth in the P92-type steel under creep conditions at 600 and 650°C is somewhat higher than that for the P911 steel.

Abstract: In recent past, a linear regression model to predict the activation energy (Qrex) and kinetics of static recrystallisation for hot-deformed austenite was developed based on stress relaxation test results of over 40 different carbon steels. The model is able to predict satisfactorily the static recrystallisation (SRX) kinetics of common carbon steel grades (including microalloyed steels) and also several special steel grades. In this study, the main effects of seven alloying elements, viz., C, Mn, Cr, Ni, Mo, Nb and V, on the activation energy of recrystallisation were further examined by using eight experimental steels based on an orthogonal Taguchi L8 matrix. All steels contained constant additions of B, Ti and Si. Even though originally intended for studies on phase transformation characteristics and hardenability under direct quenching conditions, the L8 matrix steels were suitably employed for further validation of the SRX regression model. In addition, the SRX characteristics and kinetics of a set of new steel compositions including C-Mn, C-Mn-Nb and C-Mn-Nb-Ti types were examined in the light of model equations, which further confirm the suitability of the regression model.

Abstract: Eight years ago recrystallization of OFE (oxygen-free electronic) copper was examined in detail using various techniques. In 2008 exactly the same material was measured using EBSD microscopy. The deformed state and fully recrystallized state have been analyzed and compared with data obtained eight years ago. The stored energy (SE) estimated by Image Quality (IQ) analysis was compared in these two cases. A significant amount of recovery took place in the sample, but only in some texture components. Some others present more or less the same SE as eight years ago. The textures of recrystallized samples were compared. We observed that the difference in SE distribution between the two deformed state has an influence on the final textures after recrystallization. Our study confirms the hypothesis that if a grain (orientation) has distinctly lower SE than other orientations - it has the highest growth preference (threshold hypothesis). Such grains (orientations) are dominant in the recrystallization texture.

Abstract: Modelling the evolution of structures in polycrystalline materials with distributions of fine particles requires integration of multiple length scales. Grain boundaries interact with particles on the scale of the particle diameters. The particle pinning force controls the kinetics of grain growth. Grain diameters can be several orders of magnitude larger than particles. In this work, a methodology is proposed to combine two sets of phase field models at different length scales. At the smaller scale, the effect of particles on movement of a single grain boundary is modelled in a small domain with a high grid resolution. The interface moves in an array of particles with specified shape and size distributions. The average pinning force exerted by the particles, is calculated from the interface velocity. Then, an effective driving force model is developed to incorporate the obtained pinning force into the large scale where grain growth simulations are preformed. In this model, the particle pinning force is subtracted from the driving force in the phase field formulation. In this effective formulation, particles are not resolved in the calculation grid. Therefore, with the larger numerical mesh, modelling of larger systems is possible. Kinetics of grain growth was studied with 2 dimensional simulations. Keywords: Phase field modelling, particle pinning, grain growth