M. McLean

A model of solidification microstructures in nickel-based superalloys: predicting primary dendrite spacing selection

Abstract A combined cellular automaton-finite difference (CA-FD) model has been developed to simulate solute diffusion controlled solidification of binary alloys. Constitutional and curvature undercooling were both solved to determine the growth velocity of the solid/liquid interface. A modified decentered square/octahedron (in two or three dimensions) growth technique was implemented in the cellular automaton to account for the effect of crystallographic anisotropy. The resulting model is capable of simulating the growth of equiaxed and columnar dendritic grains in 2D and 3D, with the directions either aligned or inclined with the grid. The algorithm used can also be used on coarser grids, with a concomitant loss in resolution, allowing simulation of sufficiently large numbers of dendrites in 3D to investigate the distribution of spacings, as well as average behavior. Simulations were performed for directional solidification with a range of withdrawal velocities and nucleation conditions, but a constant thermal gradient. The simulations capture the full microstructural development and primary spacing selection by both branching and overgrowth mechanisms. The model illustrates that there is a range of possible stable spacings, and that the final spacing is history dependent. It was also found that a minimum deviation from the steady state dendrite spacing is required before the spacing adjustment mechanisms are activated. The influence of perturbing the withdrawal velocity upon the stability of the spacing was also investigated. It was found that perturbations significantly reduce the range of stable primary dendrite spacing.

Directional and single-crystal solidification of ni-base superalloys : Part I. The role of curved isotherms on grain selection

The development of crystallographic texture during directional solidification has been quantitatively analyzed in columnar castings of the Ni-base superalloys, CMSX4 and CM186LC, produced with a range of cooling rates and liquidus front curvatures. It is proposed that the more diffuse crystallographic texture developed in CMSX4 relative to CM186LC results from a combination of the differing local orientation stability condition and the alloys’ solidification characteristics. The implications of these additional factors on the evolution of the axial grain texture, the grain orientations produced in singlecrystal processing, and the stability of spurious grains in processing CMSX4 are discussed. An experimental method is presented to quantitatively analyze the grain selection process in the case of curved liquidus isotherms by retaining the stereology of the primary 〈001〉 dendrite growth direction and the local thermal gradient vector. This can account for the stability of spuriously nucleated edge grains in a single-crystal matrix.

Morphological aspects of competitive grain growth during directional solidification of a nickel-base superalloy, CMSX4

Quenched directional solidification of specially oriented bi-crystals of the Ni-base superalloy CMSX4, was carried out in an attempt to understand the role of the dendritic morphology in the process of competitive grain growth. For the range of misorientations considered (primary 〈001〉 misoriented by up to 7° from the uniaxial thermal gradient), there was no evidence of overgrowth of the primary misoriented dendrite by the secondary arms on the leading aligned primary. In fact, it was observed that for this range of misorientations, the tip of the retarded primary suppresses the growth of secondaries on its leading neighbour. This subsequently simply restricts the growth of the mis-aligned crystal to its original boundary, rather than reducing its size and is suggested as a possible reason for the range of stable axial orientations encountered during directional solidification of CMSX4.

Modelling of Marangoni effects in electron beam melting

Electron beam melting processes exhibit large thermal gradients in the region where the electron beam intercepts the melt; this leads to variations in the surface energy of the melt close to the beam inducing thermocapillary (Marangoni) flow. During melt processing of many materials the Marangoni contribution can dominate the fluid flow, influencing the trajectories of inclusions within the melt and providing a potential mechanism for controlling the removal and/or distribution of inclusions. A model of the macroscopic fluid flow and heat transfer, incorporating Marangoni effects, during electron beam melting has been developed and validated against surface flow observations during the electron beam button melting (EBBM) of IN718. The model indicates, and experimental observation confirms, that fluid flow in the molten pool is dominated by thermocapillary (Marangoni) forces, for the scale and operating conditions of the EBBM process. It is, therefore, possible to reverse the fluid flow through modification of the surface energy. The effect of altering the concentration of sulphur, which is a highly surface active element, upon the Marangoni flow was determined both experimentally and computationally. The implications of altering this concentration on the effectiveness of inclusion removal and final material quality are discussed.

Directional and single-crystal solidification of Ni-base superalloys: Part II. Coincidence site lattice character of grain boundaries

The development of grain boundary misorientations with an evolving axial texture during directional solidification has been examined using the electron backscattered diffraction (EBSD) technique on the Ni-base superalloys, CMSX4 and CM186LC. A preferred grain boundary misorientation distribution (GBMD) for a sharp 〈001〉 axial texture in CM186LC was associated with a clustering of misorientation axes (MAx) in the proximity of 〈001〉. This is accompanied by an enhanced distribution of coincidence site lattice (CSL) boundaries. The increased distribution of low angle boundaries, Σ1 and Σ5, can be attributed to the existence of a preferred MAx and accommodation by secondary intrinsic grain boundary dislocations. The more diffuse 〈001〉 axial texture in CMSX4 is associated with a significant proportion of MAx deviating from 〈001〉 and a dramatic reduction in the proportion of CSL boundaries.

Microstructure-based creep modelling of a 9%Cr martensitic steel

Abstract Martensitic 9 –12%Cr steels can undergo significant changes in their microstructure during thermal/mechanical exposure. Four elements of their microstructure seem to be of particular importance: (i) strain-dependent coarsening of subgrains within the initial tempered martensitic lath microstructure; (ii) an accompanying proportionate decrease in the density of subgrain network dislocations; (iii) Ostwald ripening of MX carbo-nitrides within the subgrains; and (iv) depletion of subgrain matrix-strengthening solid solution elements (Mo/W) due to low density precipitation of large, strength-benign particles of Laves phase. A body of data now exists within the literature on the evolution kinetics of each of these processes but this can only be utilised for life prediction by one or two of the many creep models developed over the decades. In the present work, a microstructure-based Continuum Creep Damage Mechanics (CDM) model has been used to generate strain trajectories by incorporating previously published evolution kinetics for (iii) and (iv) into the kinetic creep equation as well as introducing strain-dependent coarsening of subgrains and network dislocations in a novel way. Using data specific to 9Cr –1Mo–V,Nb steel, the CDM calculations demonstrate that although subgrain-coarsening dominates tertiary creep trajectories (as Blum has long suggested), lifetimes may be significantly reduced further both by solid-solution depletion of Mo and coarsening of MX carbo-nitrides, depending upon stress/temperature.

Processing defects in hot extrusion reaction synthesis

Abstract Experiments were conducted on a miniature and a larger extrusion press to simultaneously form and extrude nickel aluminides (Ni3Al, NiAl) and nickel aluminide composites from elemental powders using a novel process called hot extrusion reaction synthesis. An overview of macroscopic and microscopic processing defects that can arise in this process is presented as well as strategies for overcoming these defects. Extrusion cracking was found to significantly increase with increased nickel content. Higher extrusion die exit temperatures promoted both a reaction converting elemental powders to the desired intermetallic or intermetallic composites and reduced cracking of NiAl extrusions. Processing defects in the form of matrix micro-cracking and reaction layers between intermetallic matrix and SiC reinforcements were also present in the composite material. The reaction always occurs seconds after the material had been extruded, thus bypassing the consolidation stage of extrusion resulting in the presence of reaction induced porosity. A novel high temperature transient window has been identified for the production of pore-free intermetallic and intermetallic composite rods and wires.

Integrated model for tracking defects through full manufacturing route of aerospace discs

Abstract Process models simulating the various stages of gas turbine disc manufacture have been integrated to simulate defect tracking throughout the entire manufacturing route: vacuum induction melting, vacuum arc remelting (VAR), homogenisation heat treatment, cogging, forging, final heat treatment and machining. An integrated complete manufacturing route model allows intrinsic or extrinsic defects entrained within the material during the initial VAR stage to be tracked through the subsequent processes. This enables determination of the motion of these defects during hot deformation stages as well as calculation of whether they might be removed during machining. If they remain in the final component, they may potentially serve as initiation sites for in service failure. The model was applied to a generic disc geometry and it was found that intrinsic defects formed (such as freckles and discrete white spots) during VAR at mid-radius spots are undesirable as they have a high probability of remaining in the final disc. Inclusions in the central region or near edge, such as solidification or dendritic white spot and extrinsic particles, are frequently removed during final machining. Further, it was demonstrated that the technique can also be used for diagnosing the origins of defects found in the final machined disc by tracking their motion in reverse to obtain their initial location in the upstream processes, thus providing a tool to help optimise quality control through process design.

Scalable, continuous variable, cellular automaton model for grain growth during homogenisation of vacuum arc remelted Inconel* 718

Abstract A scalable, continuous variable, cellular automaton (CA) model for the quantitative simulation of normal grain growth is presented. The CA model is based on a discrete solution of the classical Turnbull rate equation for grain boundary motion on a mesoscopic scale. The domain is discretised using a regular cubic lattice considering the first and second nearest neighbourhoods. CA rules were usedto determine the state of each cellbased on the local driving force. The effects of both the boundary curvature and the misorientation of grains were incorporated. The driving force was used to determine the direction of the movement of each boundary cell, forming the basis of a continuous variable cell transition rule. The use of experimental grain boundary characteristics (e.g. energy and mobility) allows one to make predictions on industrially applicable spatial and temporal scales. The model was applied to quantitatively predict grain growth during the homogenisation heat treatment of vacuum arc remelted Inconel 718.

Preliminary evaluation of hot extrusion miniaturization

Experiments were conducted to examine the feasibility of hot extruding metals on a miniature scale thus providing a quick and cheap method of studying extrusion in general. Aluminium was successfully extruded using a new miniature hot extrusion rig, producing aluminium wires (maximum diameter 2.6 mm) as opposed to rods. A preliminary comparison of extrusion pressures on the miniature rig and on a larger extrusion press was conducted. The effects of temperature, extrusion speed and extrusion ratio on the extrusion pressure were examined for both miniature and larger scale extrusions. Extrusion speed had little effect on extrusion pressure, because the range of speeds examined was too small (due to speed limitations on the larger extrusion press). Both extrusion sizes generally displayed similar dependencies on temperature and extrusion ratio. However, the extrusion pressures for miniature extrusions were found to be always lower than for the larger scale extrusions. This may have been due the evaluation of parameters in the expression used for strain rate in the comparison. Finite element analysis may prove useful in gaining a fuller understanding of the miniaturization process.