Hardening and Strain Localisation in Helium-Ion-Implanted Tungsten

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

Crystal plasticity finite element simulations of cast α-uranium

α-uranium, the stable phase of uranium up to 670◦C, has a base-centred orthorombic crystal structure. This crystal structure gives rise to elastic and thermal anisotropy, meaning α-uranium exhibits complex deformation and fracture behaviour. Understanding the relationship between the microstructure and mechanical properties is important to prevent fracture during manufacture and usage of components. The lattice of α-uranium corresponds to a distorted close-packed-hexagonal crystal structure and it exhibits twins of both the 1st and 2nd kind. Therefore, detailed examination of the behaviour of α-uranium can also contribute to the general understanding of the interaction between plasticity, twinning and fracture in hcp crystals. Plastic deformation in α-uranium can be accommodated by 4 slip systems and 3 twin systems, previously identified by McCabe et al. These deformation modes are implemented into a crystal plasticity finite element (CPFE) material model. A temperature dependent, dislocation density based law is implemented to describe the critical resolved shear stress on the different slip/twin systems. The strong anisotropic thermal expansion behaviour is taken into account to simulate the development of internal residual stresses following casting of the material. During cooling, the internal stresses in α-uranium are sufficient to induce plasticity. This effect is quantified using polycrystal simulations, in which first the temperature is decreased, then plastic relaxation takes place, followed by application of a mechanical load. The asymmetry between mechanical properties in tension and compression, due to the presence of twins, is investigated. The model is calibrated using stress strain curves and the lattice strain found from published neutron diffraction experiments carried out on textured samples at ISIS. The strength of the slip systems is found to be lower than in fine grained material, while the strength of the twin system is similar to single crystals. The CPFE method allows the heterogeneity of the strain between neighbouring grains and its influence on the evolution of the internal stress state to be investigated

Orientation-dependent indentation response of helium-implanted tungsten

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 , and 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 grains than for and orientations. Based on the observations for 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

Coupling a discrete twin model with cohesive elements to understand twin-induced fracture

The interplay between twinning and fracture in metals under deformation is an open question. The plastic strain concentration created by twin bands can induce large stresses on the grain boundaries. We present simulations in which a continuum model describing discrete twins is coupled with a crystal plasticity finite element model and a cohesive zone model for intergranular fracture. The discrete twin model can predict twin nucleation, propagation, growth and the correct twin thickness. Therefore, the plastic strain concentration in the twin band can be modelled. The cohesive zone model is based on a bilinear traction-separation law in which the damage is caused by the normal stress on the grain boundary. An algorithm is developed to generate interface elements at the grain boundaries that satisfy the traction-separation law. The model is calibrated by comparing polycrystal simulations with the experimentally observed strain to failure and maximum stress. The dynamics of twin and crack nucleation have been investigated. First, twins nucleate and propagate in a grain, then, microcracks form near the intersection between twin tips and grain boundaries. Microcracks appear at multiple locations before merging. A propagating crack can nucleate additional twins starting from the grain boundary, a few micrometres away from the original crack nucleation site. This model can be used to understand which type of texture is more resistant against crack nucleation and propagation in cast metals in which twinning is a deformation mechanism. The code is available online at https://github.com/TarletonGroup/CrystalPlasticity

Modified deformation behaviour of self-ion irradiated tungsten : A combined nano-indentation, HR-EBSD and crystal plasticity study

Predicting the dramatic changes in mechanical and physical properties caused by irradiation damage is key for the design of future nuclear fission and fusion reactors. Self-ion irradiation provides an attractive tool for mimicking the effects of neutron irradiation. However, the damaged layer of self-ion implanted samples is only a 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 frontrunner for fusion reactor 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 grains shows hardness increasing up to a dose of 0.032 dpa, beyond which it saturates. Atomic force microscopy (AFM) measurements show pile-up increasing up to the same dose, beyond which large pile-up and slip-steps are seen. Based on these observations we develop a simple crystal plasticity finite element (CPFE) model for the irradiated material. It captures irradiation-induced hardening followed by strain-softening through the interaction of irradiation-induced-defects and gliding dislocations. The shear resistance of irradiation-induced-defects is physically-based, estimated from transmission electron microscopy (TEM) observations of similarly irradiated samples. Nano-indentation of pristine tungsten and implanted tungsten of doses 0.01, 0.1, 0.32 and 1 dpa is simulated. Only two model parameters are fitted to the experimental results of the 0.01 dpa sample and are kept unchanged for all other doses. The peak indentation load, indent surface profiles and damage saturation predicted by the CPFE model closely match our experimental observations. Predicted lattice distortions and dislocation distributions around indents agree well with corresponding measurements from high-resolution electron backscatter diffraction (HR-EBSD). Finally, the CPFE model is used to predict the macroscopic stress-strain response of similarly irradiated bulk tungsten material. This macroscopic information is the key input required for design of fusion armour components.Peer reviewe

Evaluation of local stress state due to grain-boundary sliding during creep within a crystal plasticity finite element multi-scale framework

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 Table

A robust and efficient hybrid solver for crystal plasticity

Conventional crystal plasticity (CP) solvers are based on a Newton-Raphson (NR) approach which use an initial guess for the free variables (often stress) to be solved. These solvers are limited by a finite interval of convergence and often fail when the free variable falls outside this interval. Solution failure results in the reduction of the time increment to be solved, thus convergence of the CP solver is a bottleneck which determines the computational cost of the simulation. The numerical stability of the slip law in its inverted form offers a solver that isn't vulnerable to poor pre-conditioning (initial guess) and can be used to progress to a solution from a stable starting point (i.e., from zero slip rate γ˙pk=0 s−1). In this paper, a novel formulation that enables the application of the slip law in its inverted form is introduced; this treats all slip systems as independent by approximating the Jacobian as a diagonal matrix, thus overcomes ill-defined and singular Jacobians associated with previous approaches. This scheme was demonstrated to offer superior robustness and convergence rate for a case with a single slip system, however the convergence rate for extreme cases with several active slip systems was relatively poor. Here, we introduce a novel ‘hybrid scheme’ that first uses the reverse scheme for the first stage of the solution, and then transitions to the forward scheme to complete the solution at a higher convergence rate. Several examples are given for pointwise calculations, followed by CPFEM simulations for FCC copper and HCP Zircaloy-4, which demonstrated solver performance in practise. The performance of simulations using the hybrid scheme was shown to require six to nine times fewer increments compared to the conventional forward scheme solver based on a free variable of stress and initial guess based on a fully elastic increment

Orientation dependence of the nano-indentation behaviour of pure tungsten

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