General model for the kinetics of solute diffusion at solid-solid interfaces

Solute diffusion through solid-solid interfaces is paramount to many physical processes. From a modeling point of view, the discontinuities in the energy landscape at a sharp interface represent difficulties in predicting solute diffusion that, to date, have not been solved in a consistent manner across length scales. Using an explicit finite volume method, this work is the first to derive numerical solutions to the diffusion equations at a continuum level while including discrete variations in the energy landscape at a bicrystal interface. An atomic jump equation consistent with atomistic descriptions is derived and scaled up into a compendium of model interfaces: monolayer energy barriers, monolayer interfacial traps, multilayered traps, and heterogeneous interfaces. These can track solute segregation behavior and long-range diffusion effects. We perform simulations with data for hydrogen diffusion in structural metals, of relevance to the assessment of the hydrogen embrittlement phenomenon, and point defects in electronic devices. The approach developed represents an advancement in the mathematical treatment of solute diffusion through solid-solid interfaces and an important bridge between the atomistic and macroscopic modeling of diffusion, with potential applications in a variety of fields in materials science and physics

Stress orientation dependence for the propagation of stacking faults and superlattice stacking faults in nickel-based superalloys

Superlattice stacking fault propagation dominates the creep deformation behaviour of nickel-based superalloys at intermediate temperatures. These planar defects may appear under many different configurations depending on the dislocation arrangements and their interactions with the precipitates. Whilst these have been spotted and described before, no systematic way to explain their configurations has been provided. The current study quantifies the types of faults in multiple grains within a tensile crept polycrystalline alloy via a combination of scanning transmission electron microscopy and electron backscatter diffraction. A new defect consisting of a superlattice intrinsic stacking fault in the precipitates and an extrinsic stacking fault in the matrix is observed and a mechanism for its formation is proposed. In combination with data from the literature on single crystals, the results are incorporated into a robust framework to discern the orientation dependencies of these faults. A comprehensive analytical model based on a series of one-dimensional force balances on different dislocation configurations is developed first for the case of athermal stacking fault propagation for the cases of cuboidal and spherical precipitates. The model is then extended to include six configurations of superlattice faults and microtwinning. This results in novel mechanistic maps that account for stress, orientation and microstructure, with excellent qualitative agreement with experiments.Consejo Nacional de Ciencia y Tecnologia Cambridge Commonwealth, European and International Trust Rolls-Royce pl

Deformation twinning during high temperature compression tests of the Ni-base superalloy ATI 718Plus®

This study discusses the deformation mechanisms active during high temperature compression tests of the Ni-base superalloy ATI 718Plus R. Deformation twins were observed in deformed grains across a range of temperatures and strain rates by use of transmission electron microscopes (TEM). Even at strain rates as low as 0.01 s-1 and temperatures up to 1025C the microstructure contained of grains which deformed by deformation twinning. It was concluded that the low stacking fault energy of the alloy, which was measured to be 15mJm-2 caused the formation of the deformation twins. In addition, several examples of the early stages of twin formation were captured. The twinning partials were in most cases emitted from grain boundaries. In a second instance cross-slip events from a Frank-Read source lead to the formation of partials which formed stacking faults

Optimisation of the hydrogen bake-out treatment in steels via Gaussian processes

The presence of hydrogen in structural alloys reduces their ductility, a phenomenon called hydrogen embrittlement. Bake-out heat treatments are employed during processing to allow hydrogen trapped in microstructural features to effuse from the samples, but the optimal times and temperatures depend on the kinetics of hydrogen diffusion in the material. In this work, Gaussian process surrogate models are employed to emulate the outputs of microstructure-sensitive diffusion differential equations in steel. Training the models by sequentially increasing the number of dimensions results in better performances and shorter training times. Two main approaches are developed: single output models with experimental design for the prediction of optimal bake-out times, and multi-output principal component analysis models for the prediction of hydrogen concentration evolution. A novel approach is implemented to shorten the training times of multi-trap models by exploiting the symmetry of the equations with respect to different kinds of traps. The resulting models pave the way for the implementation of Gaussian processes on more computationally expensive diffusion simulations for the optimisation of heat treatments and other applications

A multiscale study on the morphology and evolution of slip bands in a nickel-based superalloy during low cycle fatigue

Plastic deformation during low cycle fatigue in fcc materials with low stacking fault energy is accumulated in slip bands, which become preferential sites for crack initiation. Whilst these dislocation structures have been studied before, little has been done to assess the effect and evolution of the individual slip lines within them. In this study, samples of a γ′precipitate strengthened nickel-based superalloy are fatigued at room temperature and 700˚C for 1, 40 and 500 cycles.The resulting dislocation structures are characterised via Electron Channeling Contrast Imaging and Transmission Electron Microscopy. We introduce a new methodology to measure slip band parameters such as the slip line spacing and shear step length by analysing the holes left by sheared precipitates in γ′-etched secondary electron micrographs. Statistics of these parameters are obtained and compared for different conditions. Advantages of this technique include resolution at the scale of individual planes, acquisition of true three-dimensional data and applicability in the bulk of the material. The combination of these techniques provides a unique mechanistic and quantitative insight into the slip band and precipitate morphology evolution.Consejo Nacional de Ciencia y Tecnología Cambridge Commonwealth European and International Trust Roberto Rocca Education Program Royal Academy of Engineering Rolls-Royce plc Engineering and Physical Sciences Research Counci

Towards Enhancing Hot Tooling to Form High-γ′ Superalloys

Ni-superalloys are well-established for use in high temperature applications in aerospace, power generation, and automotive sectors, yet, are seldom considered as materials for hot tooling. The operational conditions of hot forming dies potentially exceed those experienced by aircraft turbine discs. Fortunately, new disc alloys have pronounced elevated temperature capabilities and the current study focuses on implementing two advanced alloys, VDM 780 and Haynes 282 (H282) as hot tool materials. There is, however, inadequate evidence of their life-limiting properties and mechanisms in the in-service temperature regime of 700–900 ºC. Thus, realistic operating conditions were replicated by combining interrupted short and long-term thermal-mechanical tests. Initially, isothermal ageing in the furnace was used to compare the extent of γ′ coarsening between the alloys, and subsequent in-situ ageing and compression testing measured the accompanying loss in strength. Compression creep testing at stresses near the yield points (250–750 MPa) revealed accelerated creep rates at high temperatures. The results indicated that even as exposure duration, temperature, and applied stress all influence microstructural evolution, the exposure temperature was pivotal in determining the effective life of these γ′ strengthened alloys. Dissolution kinetics of γ′ around near-solvus temperatures was crucial and was governed by elemental additions. As a result, the research paves the way for a better understanding and design of superalloys with improved thermal integrity for hot tooling

Stress response and microstructural evolution of nickel-based superalloys during low cycle fatigue: Physics-based modelling of cyclic hardening and softening

Low cycle fatigue is one of the main life limiting factors in gas turbine discs. The plastic deformation behaviour that leads to crack initiation is not fully understood, and phenomenological descriptions fail to explain the stress response typical of nickel-based superalloys, which consists of cyclic hardening followed by cyclic softening. In this study, samples of nickel-based superalloy 718Plus with different ageing heat treatments are fatigued for 500 cycles at room temperature, their microstructures characterised and their slip localisation behaviour quantified via electron channeling contrast imaging (ECCI). A physics-based mesoscopic model is developed to investigate the effects of ageing and loading conditions on cyclic deformation behaviour. The formation of slip bands and evolution of the local dislocation density are used to describe cyclic hardening, while continued precipitate shearing from the accumulation of slip irreversibilities is modelled as the source of cyclic softening. Both mechanisms are then coupled via a parameter for the volume fraction of slip bands. The model successfully reproduces the trends observed for the different conditions, with overaged samples eventually surpassing the cyclic stress of the peak-aged specimens due to a slower softening rate. Curves from the literature for superalloy Nimonic PE16 are also reproduced for different ageing conditions and strain amplitudes. Further electron microscopy near surface cracks reveals the presence of precipitate-free deformation bands only in the underaged condition, which is explained in terms of a saturation point for the shearing process.F.D. León-Cázares is grateful for funding from CONACyT, the Cambridge Trust and the Roberto Rocca Education Program. E.I. Galindo-Nava acknowledges funding from RAEng for his research fellowship. We also acknowledge Rolls-Royce plc and the Engineering and Physical Sciences Research Council (EPSRC) for financial support under the Strategic Partnership, Grant Numbers EP/H022309/1 and EP/H500375/1, and thank Rolls-Royce Deutschland for supplying the material

A stress orientation analysis framework for dislocation glide in face-centred cubic metals

Plastic deformation in metals is heavily influenced by the loading direction. Studies have explored its effects on multiple mechanisms by analysing individual dislocations, but there is currently no systematic way of rationalising the cooperative behaviour of the different slip systems for arbitrary stress tensors. The current study constitutes the foundation of a new orientation analysis framework for face-centred cubic crystals by introducing “stress orientation maps”, graphical tools to simultaneously analyse the effects of loading orientation on the stress state of the a 2 ⟨ 1 1 ¯ 0 ⟩ { 111 } and a 6 ⟨ 112 ⟩ { 111 } slip systems in a comprehensive, yet intuitive way. Relationships between the Schmid and Escaig stresses are described from geometrical constraints of the slip systems in the crystal structure, linking the dislocation behaviour on a slip plane with the stress tensor via a one parameter description. The case of uniaxial loading along different orientations within the fundamental sector of the unit cell is explored to describe the physical basis, properties and capabilities of this framework. The stress normal to the slip plane is then considered in the analysis via an extension of the Mohr’s circles. The orientation dependence of two twin nucleation mechanisms from the literature are examined as examples of how the stress orientation maps can be used.Cambridge Commonwealth European and International Trust Rolls-Royce plc Consejo Nacional de Ciencia y Tecnologí