F.P.E. Dunne

A systematic study of hcp crystal orientation and morphology effects in polycrystal deformation and fatigue

Elastically anisotropic, physically based, length-scale- and rate-dependent crystal plasticity finite element investigations of a model hcp polycrystal are presented and a systematic study was carried out on the effects of combinations of crystallographic orientations on local, grain-level stresses and accumulated slip in cycles containing cold dwell. It is shown that the most damaging combination is the one comprising a primary hard grain with c-axis near-parallel to the loading direction and an adjacent soft grain having c-axis near-normal to the load and a prismatic slip plane at approximately 70° to the normal to the load. We term such a combination a rogue grain combination. In passing, we compare results with the Stroh model and show that even under conditions of plasticity in the hcp polycrystal, the Stroh model qualitatively predicts some of the observed behaviours. It is shown that under very particular circumstances, a morphological–crystallographic interaction occurs which leads to particularly localized accumulated slip in the soft grain and the penetration of the slip into the adjacent hard grain. The interaction effect occurs only when the (morphological) orientation of the grain boundary in the rogue grain combination coincides (within approximately ±5°) with the (crystallographic) orientation of an active slip system in the soft grain. It is argued that the rogue grain combination and the morphological–crystallographic interaction are responsible for fatigue facet formation in Ti alloys with cold dwell, and a possible mechanism for facet formation is presented. The experimental observations of fatigue facet formation have been reviewed and they provide considerable support for the conclusions from the crystal plasticity modelling. In particular, faceting was found to occur at precisely those locations predicted by the model, i.e. at a rogue grain combination. Some experimental evidence for the need for a crystallographic–morphological interaction in faceting is also presented.

Physically-based model for creep in nickel-base superalloy C263 both above and below the gamma solvus

Abstract The polycrystalline nickel-base superalloy (C263) is used for stationary components in aero-engines such as combustion chambers, casings, liners, exhaust ducting and bearing housings. It is a fine-precipitate strengthened alloy at 800°C, with a precipitate solvus temperature of 925°C. Below the solvus, the precipitate coarsens at elevated temperature. A critical precipitate size exists below which particle cutting is the rate-controlling creep mechanism. Above the critical size, it is dislocation pinning and climb. Once the solvus temperature has been exceeded, however, the rate-controlling mechanism becomes pinning and climb within a dislocation network. This paper presents physically-based constitutive equations for creep deformation in C263. In the presence of the γ′ precipitate, populations of climbing and gliding dislocations are assumed to exist in a similar way to that proposed by Dyson and Osgerby [3] . Climbing dislocations are assumed to be pinned at precipitates. The dependence of steady state glide dislocation flux can then be obtained as a function of precipitate volume fraction. Above the γ′ solvus, the pinning process is different and results from the establishment of a dislocation network, the size of which determines the pinning distance. The physical constants arising in the equations have been determined by the conventional minimisation of errors between experimental and calculated creep curves. They have also been determined quite independently using fundamental data and experiments. Remarkable agreement between the two sets of physical constants is achieved. The constitutive equations have been shown to capture the material’s creep deformation characteristics over a broad range of temperature, both below and above the γ′ solvus. In addition, the effect of precipitate coarsening on creep rate is correctly captured, together with the effect of prior ageing on subsequent creep rate. The damage processes of cavitation and multiplication of mobile dislocation density have been coupled with the constitutive equations and used to predict failure in constant and variable stress creep.

Crystal plasticity analysis of micro-deformation, lattice rotation and geometrically necessary dislocation density

A gradient-enhanced crystal plasticity model is presented that explicitly accounts for the evolution of the densities of geometrically necessary dislocations (GNDs) on individual slip systems of deforming crystals. The GND densities are fully coupled with the crystal slip rule. Application of the model to two distinct and technologically important crystal types, namely hcp Ti and ccp Ni, is given. For the hcp crystals, slip is permitted with a-type slip directions on basal, prismatic and pyramidal planes and c+a-type slip directions on pyramidal planes. First, a single crystal under four-point bending is simulated as the uniform strain gradient expected in the central span provides a good validation of the code. Then, uniaxial deformation of a model near-α Ti polycrystal has been analysed. The resulting distributions of GND densities that develop on the various slip system types have been compared with independent experimental observations. The model predicts that GND density on the c+a systems is approximately an order of magnitude lower than that for a-type systems in agreement with experiment. For the ccp case, slip is considered to take place on the <110>{111} slip systems. Thermal loading of a single-crystal nickel alloy sample containing carbide particles of size approximately 30u2009μm has been analysed. Detailed comparisons are presented between model predictions and results of high-resolution electron backscatter diffraction (EBSD) measurements of the micro-deformations, lattice rotations, curvatures and GND densities local to the nickel–carbide interface. Qualitatively, good agreement is achieved between the coupled and decoupled model elastic strains with the EBSD measurements, but lattice rotations and GND densities are quantitatively well predicted by the coupled crystal model but are less well captured by the decoupled model. The GND coupling is found to lead to reduced lattice rotations and plastic strains in the region of highest heterogeneity close to the Ni matrix/particle interface, which is in agreement with the experimental measurements. The results presented provide objective evidence of the effectiveness of gradient-enhanced crystal plasticity finite element analysis and demonstrate that GND coupling is required in order to capture strains and lattice rotations in regions of high heterogeneity.

Initiation of dynamic recrystallization under inhomogeneous stress states in pure copper

Abstract The initiation of dynamic recrystallization (DRX) in 99.9% pure copper has been investigated for the case of homogeneous and inhomogeneous deformation. Tests were conducted at 400°C on conventional cylindrical test specimens and on specially designed truncated cone specimens in which strain, strain rate, and stress vary spatially. A range of interrupted tests was carried out in order to identify the strain to initiation of DRX for the case of homogeneous deformation, and to track the motion of the “recrystallization front” for the case of inhomogeneous deformation. A material model implemented into finite element software, and employing the initiation criterion of Poliak and Jonas is presented. The model is calibrated using the homogeneous test data, and is used to predict deformation, initiation of DRX, and microstructural change in the truncated cone specimens. The computed results are compared with experiments, and the model is shown to be capable of tracking the motion of “recrystallization fronts” through the deforming material under conditions of inhomogeneous stress. It is also demonstrated that one truncated cone specimen test can replace several tests using conventional cylindrical specimens to study the relationship between dynamic recrystallized grain size and saturated stress.

Interface effects during consolidation in titanium alloy components locally reinforced with matrix-coated fibre composite

Abstract An investigation has been made of diffusion bonding at the interface between a local reinforcing metal matrix composite and a monolithic engineering material. Diffusion bonding occurs during the consolidation of the composite during component manufacture. In this study, the composite is made up from Ti–6Al–4V titanium alloy coated SiC fibres, and the monolithic engineering material is also Ti–6Al–4V, but with a different microstructure. An interface model is presented which takes account of diffusion bonding and which is able to describe the deformation behaviour at the interface between composite and monolithic material during composite consolidation. The model is developed from an existing diffusion bonding theory, and is implemented into finite element software. The finite element simulations, and results of experiments, show that diffusion bonding can lead to localised deformation, the inhibition of consolidation, and a resulting inhomogeneous distribution of consolidated and unconsolidated regions during component manufacture. A further effect of the diffusion bonding is to increase the level of component distortion which results from the constraint imposed on the consolidating composite. The interface model presented enables the simulation of practical forming processes so that process variables such as temperature and pressure can be chosen to ensure appropriate finished component properties.

Fibre re-arrangement and matrix softening phenomena in matrix-coated fibre (MCF) composites during vacuum hot pressing consolidation

Experiments were carried out under constant load with increasing temperature during uniaxial constrained compression (vacuum hot pressing) to investigate the consolidation behaviour of matrix-coated fibres (MCFs). Regular fibre arrays were achieved in the consolidated specimen by a fine control of the die assembly from which the matrix deformation behaviour was extracted. The results indicate that there exists a softening temperature at which the MCFs start to deform rapidly, which leads to a high densification rate. The mechanisms involved are discussed. This observation is of significant consequence to the design of the composite fabrication process.

Dynamic recrystallisation in a copper/stainless steel pseudo-two-phase material

The initiation and development of dynamic recrystallisation in a pseudo-two-phase material have been investigated to study the effect of area fraction and distribution of the pseudo-second phase. Hot compression tests have been conducted at 400°C on specially fabricated pseudo-two-phase copper test specimens and single-phase copper test specimens. A material model has been implemented into finite element software coupled with the recently proposed criterion for initiation of dynamic recrystallisation in single-phase materials. Micro-mechanical models have been employed to predict deformation, the initiation of dynamic recrystallisation and microstructural change in the pseudo-two-phase specimens. Good agreement is observed between the experimental results and the model predictions. It is found that an increase in area fraction of pseudo-second phase accelerates the initiation of dynamic recrystallisation but reduces the spatial development of recrystallisation. Furthermore, the intensity of localised deformation and the constraint imposed by different configurations of rigid pseudo-second phase influence the initiation of dynamic recrystallisation and its spatial development. A distribution with lower intensity of localised deformation and less constraint has a later initiation of dynamic recrystallisation and a larger spatial development of recrystallisation. The bonding condition between matrix/fibre interfaces influences the nominal strain to initiation, locations where dynamic recrystallisation first occurs and the spatial development of recrystallisation.