On the prediction of martensite formation in metals

A new approach to predict athermal martensite formation in metals is presented. It is based on computing the driving force of the transformation including a strain energy term induced by atomic shear displacements and energy terms due to substitutional and interstitial lattice distortions. The model is applied to prescribe the martensite and austenite start temperatures in Fe-, Ti- and Co-based alloys with no adjustable parameters. Expressions for Ms variations with composition are derived for multicomponent systems. The transformation temperature hysteresis is predicted in Co alloys showing that this approximation can be used to design alloys with the shape memory effect.The author would like to acknowledge the Royal Academy of Engineering for his research fellowship funding and to Prof. Mark Blamire for the provision of laboratory facilities

Accelerating off-lattice kinetic Monte Carlo simulations to predict hydrogen vacancy-cluster interactions in α–Fe

We present an enhanced off-lattice kinetic Monte Carlo (OLKMC) model, based on a new method for tolerant classification of atomistic local-environments that is invariant under Euclidean-transformations and permutations of atoms. Our method ensures that environments within a norm-based tolerance are classified as equivalent. During OLKMC simulations, our method guarantees to elide the maximum number of redundant saddle-point searches in symmetrically equivalent local-environments. Hence, we are able to study the trapping/detrapping of hydrogen from up to five-vacancy clusters and simultaneously the effect hydrogen has on the diffusivity of these clusters. These processes occur at vastly different timescales at room temperature in body-centred cubic iron. We predict the diffusion pathways of clusters/complexes without a priori assumptions of their mechanisms, not only reproducing previously reported mechanisms but also discovering new ones for larger complexes. We detail the hydrogen-induced changes in the clusters’ diffusion mechanisms and find evidence that, in contrast to mono-vacancies, the introduction of hydrogen to larger clusters can increase their diffusivity. We compare the effective hydrogen diffusivity to Oriani’s classical theory of trapping, finding general agreement and some evidence that hydrogen may not always be in equilibrium with traps, when the traps are mobile. Finally, we compute the trapping atmosphere of meta-stable states surrounding non-point traps, opening new avenues to better understand and predict hydrogen embrittlement in complex alloys

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

The Portevin-Le Chatelier Effect in Nickel-Base Superalloys: Origins, Consequences and Comparison to Strain Ageing in Other Alloy Systems

Dynamic Strain Ageing (DSA) has reached widespread acceptance since its proposal in the 1940’s as the mechanism behind the Portevin-Le Chatelier effect in ferritic steels. However, it remains an open question as to whether the classical mechanism can be extended to Face-Centred Cubic (FCC) alloys, including nickel-based superalloys, as often implicitly assumed. Given the historical link between serrated flow and loss of ductility in steels, understanding such consequences in superalloys used in key components of a jet engine demands attention. This review compares plastic instabilities in superalloys to those in ferritic steels, including the effects of temperature, strain rate, compositional, microstructural and extrinsic testing parameters on the extent of serrated flow and consequences on mechanical properties. Outstanding issues are discussed in detail, relating both to the lack of a complete experimental argument depicting the origins of serrated flow and different serration ‘Types’, as well as the inability of current predictive models to fully account for multiscale experimental observations. Proposed explanations for plastic instabilities in FCC alloys are discussed, including but not limited to classical DSA, with the aim to guide future experiments to elucidate the origins of serrated flow across length scales and improve key properties such as fatigue life

Understanding martensite and twin formation in austenitic steels: A model describing TRIP and TWIP effects

A unified description for the evolution of ε– and α ′ – martensite, and twinning in austenitic steels is presented. The formation of micron—scale ε and twin bands is obtained by considering the evolution of hierarchically arranged nano–sized ε and twins (embryos). The critical size and applied stress when these structures form is obtained by minimising their free energy of formation. The difference between forming an ε plate or a twin lies in the number of overlapping stacking faults in their structure. A nucleation rate criterion is proposed in terms of the critical embryo size, resolved shear stress and embryo number density. Based on Olson and Cohen's classical α ′ –martensite transformation model, the nucleation rate of α ′ is considered proportional to that for ε. These results, combined with dislocation–based approximations, are employed to prescribe the microstructure and flow stress response in steels where transformation–induced–plasticity (TRIP) and/or twinning–induced–plasticity (TWIP) effects operate; these include austenitic stainless and high–Mn steels. Maps showing the operation range of ε, α ′ and twinning in terms of the stacking fault energy at different strain levels are defined. Effects of chemical composition in the microstructure and mechanical response in stainless steels are also explored. These results allow identifying potential compositional scenarios when the TRIP and/or TWIP effects are promoted in austenitic steels

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

Modelling deformation-induced martensite transformation in high-carbon steels

The transformation behaviour of retained austenite in steels is known to differ according to chemical composition and other microstructural attributes. Earlier research indicated that austenite in high-carbon steels transforms into martensite only when the applied stress exceeds a critical value, contrary to low-carbon steels where transformation occurs in the early stages of deformation. Although transformation models have been proposed, most are optimised for low-carbon steels. Here, we propose physics-based models applied to high-carbon steels to overcome previous limitations. The models have fewer free parameters (4) compared to previous approaches (6), exhibiting improvements in the numerical and physical interpretation of the austenite transformation process. We envision the use of these models as tools for alloy design, also highlighting their scientific and technological value

Hydrogen transport in metals: Integration of permeation, thermal desorption and degassing

A modelling suite for hydrogen transport during electrochemical permeation, degassing and thermal desorption spectroscopy is presented. The approach is based on Fick's diffusion laws, where the initial concentration and diffusion coefficients depend on microstructure and charging conditions. The evolution equations are shown to reduce to classical models for hydrogen diffusion and thermal desorption spectroscopy. The number density of trapping sites is found to be proportional to the mean spacing of each microstructural feature, including dislocations, grain boundaries and various precipitates. The model is validated with several steel grades and polycrystalline nickel for a wide range of processing conditions and microstructures. A systematic study of the factors affecting hydrogen mobility in martensitic steels showed that dislocations control the effective diffusion coefficient of hydrogen. However, they also release hydrogen into the lattice more rapidly than other kind of traps. It is suggested that these effects contribute to the increased susceptibility to hydrogen embrittlement in martensitic and other high-strength steels. These results show that the methodology can be employed as a tool for alloy and process design, and that dislocation kinematics play a crucial role in such design

A unified model for plasticity in ferritic, martensitic and dual-phase steels

Unified equations for the relationships among dislocation density, carbon content and grain size in ferritic, martensitic and dual-phase steels are presented. Advanced high-strength steels have been developed to meet targets of improved strength and formability in the automotive industry, where combined properties are achieved by tailoring complex microstructures. Specifically, in dual-phase (DP) steels, martensite with high strength and poor ductility reinforces steel, whereas ferrite with high ductility and low strength maintains steel’s formability. To further optimise DP steel’s performance, detailed understanding is required of how carbon content and initial microstructure affect deformation and damage in multi-phase alloys. Therefore, we derive modified versions of the Kocks–Mecking model describing the evolution of the dislocation density. The coefficient controlling dislocation generation is obtained by estimating the strain increments produced by dislocations pinning at other dislocations, solute atoms and grain boundaries; such increments are obtained by comparing the energy required to form dislocation dipoles, Cottrell atmospheres and pile-ups at grain boundaries, respectively, against the energy required for a dislocation to form and glide. Further analysis is made on how thermal activation affects the efficiency of different obstacles to pin dislocations to obtain the dislocation recovery rate. The results are validated against ferritic, martensitic and dual-phase steels showing good accuracy. The outputs are then employed to suggest optimal carbon and grain size combinations in ferrite and martensite to achieve highest uniform elongation in single- and dual-phase steels. The models are also combined with finite-element simulations to understand the effect of microstructure and composition on plastic localisation at the ferrite/martensite interface to design microstructures in dual-phase steels for improved ductility.</jats:p