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Component failure due to cold dwell fatigue of titanium and its alloys is a long-standing problem which has significant safety and economic implications to the aviation industry. This can be addressed by understanding the governing mechanisms of time dependent plasticity behaviour of Ti at low temperatures. Here, stress relaxation tests were performed at four different temperatures on three major alloy systems: commercially pure titanium (two alloys with different oxygen content), Ti-6Al-4V (two microstructures with differing beta phase fractions) and Ti-6Al-2Sn-4Zr-xMo (two alloys with different Mo content x= 2 or 6, and portion of beta phase). Key parameters controlling the time dependent plasticity were determined as a function of temperature. Both activation volume and energy were found to increase with temperature in all six alloys. It was found that the dwell fatigue effect is more significant by oxygen alloying but is suppressed by the addition of Mo. The presence of the beta phase did not strongly affect the dwell fatigue, however, it was suppressed at high temperature due to the low strain rate and strain rate sensitivity.

A theoretical framework for computation of Burgers vectors from strain and lattice rotation data is presented, as well as implementation into a computer program to automate the process. The efficacy of the method is verified using simulated data of dislocations with known results. A 3D data set retrieved from Bragg coherent diffraction imaging (BCDI) and a 2D data set from high resolution transmission Kikuchi diffraction (HR-TKD) are used as inputs to demonstrate the reliable identification of dislocation positions and accurate determination of Burgers vectors from experimental data. For BCDI data, the results found using our approach show very close agreement to those expected from empirical methods. For the HR-TKD data the predicted dislocation position and the computed Burgers vector showed fair agreement with the expected result, which is promising considering the substantial experimental uncertainties in this dataset. The method reported in this paper provides a general and robust framework for determining dislocation positions and Burgers vectors, and can be readily applied to data from other experimental techniques., Comment: 20 pages, 11 figures. The program created, data used and tests performed are freely available from https://github.com/JacquesCloete/Burgers-Vector-Calculator

Digital image correlation (DIC) and crystal plasticity simulation were utilised to study cold dwell behaviour in a coarse grain Ti-6Al alloy at 3 different temperatures up to 230 C. Strains extracted from large volume grains were measured during creep by DIC and were used to calibrate the crystal plasticity model. The values of critical resolved shear stresses (CRSS) of the two main slip systems (basal and prismatic) were determined as a function of temperature. Stress along paths across the boundaries of two grain pairs, (1) a `rogue' grain pair and (2) a `non-rogue' grain pair, were determined at different temperatures. Load shedding was observed in the `rogue' grain pair, where a stress increment during the creep period was found in the `hard' grain. At elevated temperatures, 120 C was found to be the worst-case scenario as the stress difference at the grain boundaries of these two grain pairs were found to be the largest among the three temperatures. This can be attributed to the fact that the strain rate sensitivity of both prismatic and basal slip systems is at its greatest in this worst-case scenario temperature.

Previous studies demonstrate that grain-boundary sliding could accelerate creep rate and give rise to large internal stresses that can lead to damage development, e.g. formation of wedge cracks. The present study provides more insight into the effects of grain-boundary sliding (GBS) on the deformation behaviour of realistic polycrystalline aggregates during creep, through the development of a computational framework which combines: i) the use of interface elements for sliding at grain boundaries, and ii) special triple point (in 2D) or triple line (in 3D) elements to prevent artificial dilation at these locations in the microstructure with iii) a physically-based crystal plasticity constitutive model for time-dependent inelastic deformation of the individual grains. Experimental data at various scales is used to calibrate the framework and compare with model predictions. We pay particular consideration to effects of grain boundary sliding during creep of Type 316 stainless steel, which is used extensively in structural components of the UK fleet of Advanced Gas Cooled Nuclear Reactors (AGRs). It is found that the anisotropic deformation of the grains and the mismatch in crystallographic orientation between neighbouring grains play a significant role in determining the extent of sliding on a given boundary. Their effect on the development of stress within the grains, particularly at triple grain junctions, and the increase in axial stress along transverse boundaries are quantified. The article demonstrates that the magnitude of the stress along the facets is highly-dependent on the crystallographic orientations of the neighbouring grains and the relative amount of sliding. Boundaries, transverse to the applied load tend to carry higher normal stresses of the order of 100-180 MPa, in cases where the neighbouring grains consist of plastically-harder crystallographic orientations., Comment: Keywords: grain boundary sliding, creep, interface, polycrystalline, triple grain junction, crystal plasticity. 21 Pages, 16 Figures, 2 Tables

Calibrating and verifying crystal plasticity material models is a significant challenge, particularly for materials with a number of potential slip and twin systems. Here we use digital image correlation on coarse-grained $\alpha$-uranium during tensile testing in conjunction with crystal plasticity finite element simulations. This approach allows us to determine the critical resolved shear stress, and hardening rate of the different slip and twin systems. The constitutive model is based on dislocation densities as state variables and the simulated geometry is constructed from electron backscatter diffraction images that provide shape, size and orientation of the grains, allowing a direct comparison between virtual and real experiments. An optimisation algorithm is used to find the model parameters that reproduce the evolution of the average strain in each grain as the load is increased. A tensile bar, containing four grains aligned with the load direction, is used to calibrate the model with eight unknown parameters. The approach is then independently validated by simulating the strain distribution in a second tensile bar. Different mechanisms for the hardening of the twin systems are evaluated. The latent hardening of the most active twin system turns out to be determined by coplanar twins and slip. The hardening rate of the most active slip system is lower than in fine-grained $\alpha$-uranium. The method developed in the present research can be applied to identify the critical resolved shear stress and hardening parameters of other coarse-grained materials.

There is a long-standing technological problem in which a stress dwell during cyclic loading at room temperature in Ti causes a significant fatigue life reduction. It is thought that localised time dependent plasticity in soft grains favourably oriented for easy plastic slip leads to load shedding and an increase in stress within a neighbouring hard grain poorly oriented for easy slip. Quantifying this time dependent plasticity process is key to understand the complex cold dwell fatigue problem. Knowing the effect of operating temperature and oxygen content on cold dwell fatigue will be beneficial for future alloy design to address this problem. In this work, synchrotron X-ray diffraction during stress relaxation experiments was used to characterise the time dependent plastic behaviour of two commercially pure titanium samples (grade 1 and grade 4) with different oxygen content at 4 different temperatures (room temperature, 75C, 145C and 250C). Lattice strains were measured by tracking the diffraction peak shift from multiple crystallographic plane families (21 diffraction rings) as a function of their orientation with respect to the loading direction. Critical resolved shear stress, activation energy and activation volume were established for both prismatic and basal slip as a function of temperature and oxygen content by fitting a crystal plasticity finite element model to the lattice strain relaxation responses measured along the loading axis for five strong reflections. Higher strain rate sensitivity was found to lead to higher plasticity during cold dwell.

Coupling of nano-indentation and crystal plasticity finite element (CPFE) simulations is widely used to quantitatively probe the small-scale mechanical behaviour of materials. Earlier studies showed that CPFE can successfully reproduce the load-displacement curves and surface morphology for different crystal orientations. Here, we report the orientation dependence of residual lattice strain patterns and dislocation structures in tungsten. For orientations with one or more Burgers vectors close to parallel to the sample surface, dislocation movement and residual lattice strains are confined to long, narrow channels. CPFE is unable to reproduce this behaviour, and our analysis reveals the responsible underlying mechanisms.

In this paper, we investigate the residual deformation field in the vicinity of nano-scratch tests using two orientations of a Berkovich tip on an (001) Cu single crystal. We compare the deformation with that from indentation, in an attempt to understand the mechanisms of deformation in tangential sliding. The lattice rotation fields are mapped experimentally using high-resolution electron backscatter diffraction (HR-EBSD) on cross-sections prepared using focused ion beam (FIB). A physically-based crystal plasticity finite element model (CPFEM) is used to simulate the lattice rotation fields, and provide insight into the 3D rotation field surrounding nano-scratch experiments, as it transitions from an initial static indentation to a steady-state scratch. The CPFEM simulations capture the experimental rotation fields with good fidelity, and show how the rotations about the scratch direction are reversed as the indenter moves away from the initial indentation.

There is a long standing technological problem in which a stress dwell during cyclic loading at room temperature in Ti causes a significant fatigue life reduction. It is thought that localised time dependent plasticity in soft grains oriented for easy plastic slip leads to load shedding and an increase in stress within a neighbouring hard grain poorly oriented for easy slip. Quantifying this time dependent plasticity process is key to successfully predicting the complex cold dwell fatigue problem. This work uses a novel approach of in situ synchrotron X-ray diffraction during stress relaxation tests, to quantify the time dependent plasticity. Measured lattice strains from multiple lattice families (21 diffraction rings) were compared with simulated lattice strains from crystal plasticity finite element (CPFE) simulations. The prism slip parameters were found to show stronger strain rate sensitivity compared to basal slip, and this has a significant effect on stress redistribution to hard grain orientations during cold creep.

Predicting the dramatic changes in material properties caused by irradiation damage is key for the design of future nuclear fission and fusion reactors. Self-ion implantation is an attractive tool for mimicking the effects of neutron irradiation. However, the damaged layer of implanted samples is only few microns thick, making it difficult to estimate macroscopic properties. Here we address this challenge using a combination of experimental and modelling techniques. We concentrate on self-ion-implanted tungsten, the front-runner for fusion armour components and a prototypical bcc material. To capture dose-dependent evolution of properties, we experimentally characterise samples with damage levels from 0.01 to 1 dpa. Spherical nano-indentation of <001> grains shows hardness increasing up to a dose of 0.032 dpa, beyond which it saturates. AFM measurements show pile-up increasing up to the same dose, beyond which large pile-up and slip-steps are seen. Based on the observations we develop a crystal plasticity (CPFE) model for the irradiated material. It captures irradiation-induced hardening followed by strain-softening through interaction of irradiation-defects and gliding dislocations. Shear resistance of irradiation-defects is derived from TEM observations of similarly irradiated samples. Nano-indentation of pristine and implanted tungsten of doses 0.01, 0.1, 0.32 and 1 dpa is simulated. Two model parameters are fitted to the experimental results of the 0.01 dpa sample and are kept unchanged for all other doses. Peak load, indent surface profiles and damage saturation predicted by the CPFE model closely match experimental observations. Predicted lattice distortions and dislocation distributions around indents agree with corresponding measurements from HR-EBSD. Finally, the CPFE model is used to predict the macroscopic stress-strain response of similarly irradiated bulk tungsten material.

We study the mechanisms of slip transfer at a grain boundary, in titanium, using Differential Aperture X-ray Laue Micro-diffraction (DAXM). This 3D characterization tool enables measurement of the full (9-component) Nye lattice curvature tensor and calculation of the density of geometrically necessary dislocations (GNDs). We observe dislocation pile-ups at a grain boundary, as the neighbor grain prohibits easy passage for dislocation transmission. This incompatibility results in local micro-plasticity within the slipping grain, near to where the slip planes intersect the grain boundary, and we observe bands of GNDs lying near the grain boundary. We observe that the distribution of GNDs can be significantly influenced by the formation of grain boundary ledges that serve as secondary dislocation sources. This observation highlights the non-continuum nature of polycrystal deformation and helps us understand the higher order complexity of grain boundary characteristics., Comment: 30 pages, 9 figures, 2 tables

The influence of hydrogen on dislocation junctions was analysed by incorporating a hydrogen dependent core force into nodal based discrete dislocation dynamics. Hydrogen reduces the core energy of dislocations, which reduces the magnitude of the dislocation core force. We refer to this as hydrogen core force shielding, as it is analogous to hydrogen elastic shielding but occurs at much lower hydrogen concentrations. The dislocation core energy change due to hydrogen was calibrated at the atomic scale accounting for the nonlinear inter-atomic interactions at the dislocation core, giving the model a sound physical basis. Hydrogen was found to strengthen binary junctions and promote the nucleation of dislocations from triple junctions. Simulations of microcantilever bend tests with hydrogen core force shielding showed an increase in the junction density and subsequent hardening. These simulations were performed at a small hydrogen concentration realistic for bcc iron.

A literature review of studies investigating the topography of nano-indents in ion-implanted materials reveals seemingly inconsistent observations, with report of both pile-up and sink-in. This may be due to the crystallographic orientation of the measured sample point, which is often not considered when evaluating implantation-induced changes in the deformation response. Here we explore the orientation dependence of spherical nano-indentation in pure and helium-implanted tungsten, considering grains with <001>, <110> and <111> out-of-plane orientations. Atomic force microscopy (AFM) of indents in unimplanted tungsten shows little orientation dependence. However, in the implanted material a much larger, more localised pile-up is observed for <001> grains than for <110> and <111> orientations. Based on the observations for <001> grains, we hypothesise that a large initial hardening due to helium-induced defects is followed by localised defect removal and subsequent strain softening. A crystal plasticity finite element model of the indentation process, formulated based on this hypothesis, accurately reproduces the experimentally-observed orientation-dependence of indent morphology. The results suggest that the mechanism governing the interaction of helium-induced defects with glide dislocations is orientation independent. Rather, differences in pile-up morphology are due to the relative orientations of the crystal slip systems, sample surface and spherical indenter. This highlights the importance of accounting for crystallographic orientation when probing the deformation behaviour of ion-implanted materials using nano-indentation.

Tungsten is the main candidate material for plasma-facing armour components in future fusion reactors. In-service, fusion neutron irradiation creates lattice defects through collision cascades. Helium, injected from plasma, aggravates damage by increasing defect retention. Both can be mimicked using helium-ion-implantation. In a recent study on 3000 appm helium-implanted tungsten (W-3000He), we hypothesized helium-induced irradiation hardening, followed by softening during deformation. The hypothesis was founded on observations of large increase in hardness, substantial pile-up and slip-step formation around nano-indents and Laue diffraction measurements of localised deformation underlying indents. Here we test this hypothesis by implementing it in a crystal plasticity finite element (CPFE) formulation, simulating nano-indentation in W-3000He at 300 K. The model considers thermally-activated dislocation glide through helium-defect obstacles, whose barrier strength is derived as a function of defect concentration and morphology. Only one fitting parameter is used for the simulated helium-implanted tungsten; defect removal rate. The simulation captures the localised large pile-up remarkably well and predicts confined fields of lattice distortions and geometrically necessary dislocation underlying indents which agree quantitatively with previous Laue measurements. Strain localisation is further confirmed through high resolution electron backscatter diffraction and transmission electron microscopy measurements on cross-section lift-outs from centre of nano-indents in W-3000He.

In an attempt to bridge the gap between atomistic and continuum plasticity simulations of hydrogen in iron, we present three dimensional discrete dislocation plasticity simulations incorporating the hydrogen elastic stress and a hydrogen dependent dislocation mobility law. The hydrogen induced stress is incorporated following the formulation derived by Gu and El-Awady (2018) which here we extend to a finite boundary value problem, a microcantilever beam, via the superposition principle. The hydrogen dependent mobility law is based on first principle calculations by Katzarov et al. (2017) and was found to promote dislocation generation and enhance slip planarity at a bulk hydrogen concentration of 0.1 appm; which is typical for bcc materials. The hydrogen elastic stress produced the same behaviour, but only when the bulk concentration was extremely high. In a microcantilever, hydrogen was found to promote dislocation activity which lowered the flow stress and generated more pronounced slip steps on the free surfaces. These observations are consistent with the hydrogen enhanced localized plasticity (HELP) mechanism, and it is concluded that both the hydrogen elastic stress and hydrogen increased dislocation mobility are viable explanations for HELP. However it is the latter that dominates at the low concentrations typically found in bcc metals., Comment: 24 pages 20 figures

The use of Nye's dislocation tensor for calculating the density of geometrically necessary dislocations (GND) is widely adopted in the study of plastically deformed materials. The curl operation involved in finding the Nye tensor, while conceptually straightforward has been marred with inconsistencies and several different definitions are in use. For the three most common definitions, we show that their consistent application leads to the same result. To eliminate frequently encountered confusion, a summary of expressions for Nye's tensor in terms of elastic and plastic deformation gradient, and for both small and large deformations, is presented. A further question when estimating GND density concerns the optimization technique used to solve the under-determined set of equations linking Nye's tensor and GND density. A systematic comparison of the densities obtained by two widely used techniques, L1 and L2 minimisation, shows that both methods yield remarkably similar total GND densities. Thus the mathematically simpler, L2, may be preferred over L1 except when information about the distribution of densities on specific slip systems is required. To illustrate this, we compare experimentally measured lattice distortions beneath nano-indents in pure tungsten, probed using 3D-resolved synchrotron X-ray micro-diffraction, with those predicted by 3D strain-gradient crystal plasticity finite element calculations. The results are in good agreement and show that the volumetric component of the elastic strain field has a surprisingly small effect on the determined Nye tensor. This is important for experimental techniques, such as micro-beam Laue measurements and HR-EBSD, where only the deviatoric strain component is measured., Comment: 66 pages, 15 figures, 7 appendices

Focussed Ion Beam (FIB) milling is a mainstay of nano-scale machining. By manipulating a tightly focussed beam of energetic ions, often gallium (Ga+), FIB can sculpt nanostructures via localised sputtering. This ability to cut solid matter on the nano-scale has revolutionised sample preparation across the life-, earth- and materials sciences. For example FIB is central to microchip prototyping, 3D material analysis, targeted electron microscopy sample extraction and the nanotechnology behind size-dependent material properties. Despite its widespread usage, detailed understanding of the functional consequences of FIB-induced structural damage, intrinsic to the technique, remains elusive. Here, we present nano-scale measurements of three-dimensional, FIB-induced lattice strains, probed using Bragg Coherent X-ray Diffraction Imaging (BCDI). We observe that even low gallium ion doses, typical of FIB imaging, cause substantial lattice distortions. At higher doses, extended self-organised defect structures appear, giving rise to stresses far in excess of the bulk yield limit. Combined with detailed numerical calculations, these observations provide fundamental insight into the nature of the damage created and the structural instabilities that lead to a surprisingly inhomogeneous morphology., Comment: 35 pages total, 12 figures total. Main text 16 pages 3 figures. Supplementary information 19 pages 9 figures