Examining deformation localization of irradiated tungsten under uniaxial compression with crystal plasticity

Highlights

• Stress-strain response related with irradiated microstructure is predicted under compression with crystal plasticity..

• Lognormal distribution of strain is quantitatively captured and is linked to the damage dose..

• The predicted strain localization matches well with the optical micrograph image from the corresponding experiment.

Abstract

In this work, the deformation behavior of irradiated tungsten at elevated service temperatures is examined using mechanism-based crystal plasticity finite element framework by considering multiple mechanisms, including thermal softening and irradiation hardening. The previously developed mechanism-based crystal plasticity model is first utilized to assess the yield stress of unirradiated and irradiated tungsten upon low-temperature irradiation. The engineering stress-strain response under uniaxial compression is then predicted by considering the effect of irradiation-induced defect clusters on the motion of deformation-induced dislocations, and the predicted results agree well with the experimental measurements. More importantly, the formation and evolution of plastic strain localization zones in the form of shear bands are qualitatively captured, and the maximal principal strain distribution is quantitatively linked to the dose of irradiation damage. Finally, the deformation-induced shear band as a result of plastic instability in the compressed tungsten specimen is discussed.

Introduction

Tungsten, a primary candidate of plasma-facing material for the first wall of fusion reactors, has excellent physical properties such as high melting temperature and superior thermal conductivity. However, its ductile-to-brittle transition temperature (e.g., 550 °C for pure tungsten plate [1]) is much higher than other metallic materials (e.g., −81 °C for Eurofer97 steel [2]), reducing its ductility and fracture toughness at elevated service temperatures. More seriously, the extreme service environment can also accelerate the degradation of mechanical properties of tungsten due to the generation of irradiation defects [3,4]. Therefore, fundamental understandings on the deformation mechanisms of irradiated tungsten and predictive capabilities on the interplays between irradiation-induced defect clusters and deformation-induced dislocations at service temperature must be established before the engineering application of tungsten as plasma-facing material in a fusion reactor.

On the microscopic scale, many prior studies have elucidated different types of irradiation defects for tungsten. While some defect clusters (e.g., small loops) are considered as weak obstacles to dislocation gliding, others (e.g., voids and bubbles) act as strong obstacles to impede the dislocation movement. On the one hand, the moving dislocations generate point defects, and the migration point defects promote the formation of short-range orders. On the other hand, the irradiation-induced short-range orders can be annihilated/destructed by the dislocation movement [5]. As a result of such interplay, dislocation channeling was often observed in the deformed metal after irradiation, and it occurred even at low dose since irradiation-induced defect clusters are present in sufficient density [6]. Transmission electron microscopy (TEM) studies confirmed that defect clusters are absent in the channels, and whilst defect clusters are clearly visible outside the channels [7]. However, the interaction between deformation-induced dislocations and irradiation-generated defect clusters can be quite complex. For example, the high internal stress around the precipitates caused by dislocation accumulation in bcc iron could contribute to the cross-slipped dislocations overcoming irradiation-induced defect clusters [8].

Previously, the dynamic interactions of irradiation defects under external loading have been examined with various modeling and simulation approaches at atomic level [[9], [10], [11], [12]]. For example, the absorption and retention of irradiation-induced interstitial loops after edge dislocation gliding were captured by molecular dynamics (MD) simulations, and it was found that the Burgers vector of residual loop can either transform or remain unchanged, depending on the loop characteristics (e.g., size and mobility) [12]. Discrete dislocation dynamics (DDD) simulation on a single copper crystal [13] showed the unpinning of irradiation-induced defects are swept away by the dislocation motion, resulting in defect free dislocation channels, and the width of plastic flow localization occurred in the dislocation channel can be limited by the interaction among opposing dislocation dipole segments. Even though the results of microscopic simulation can corroborate the TEM observations in the sense that irradiation-induced defect clusters can be partially removed by interacting with the dislocation [14,15], leading to defect free channels in the deformed irradiated material [16], they cannot be used to predict the bulk engineering-level deformation behaviors of irradiated materials.

On the macroscopic engineering scale, many experiments have been carried out to investigate the effects of irradiation-induced microstructure changes on flow stress, hardness and ductility of various polycrystalline bcc, fcc and hcp metals [5,[17], [18], [19], [20]]. For bcc metals, Byun et al. [17] found that macroscopic plastic instability occurs even under the irradiation dose of 0.1 dpa, and deformation localization typically exhibits in the form of shear bands. This indicates that plastic deformation is mainly localized within these bands as a result of inhomogeneous deformation through the specimen. Consequently, the highly localized flow leads to very low overall ductility. Grain-level material and microstructure heterogeneity have been established as a source for inhomogeneous deformation and strain localization, which can lead to overall plastic instability and failure of the sample [21]. For irradiated materials, however, the interplays among hardening from irradiation defects, softening from the interaction of mobile dislocations and irradiation defects, and softening due to elevated service temperatures have not been quantitatively elucidated. Dislocation channel that evolves from the deformation dislocations in the localized yielding is one of the possible physical reasons for understanding the strain localization [22]. Strain localization in the form of shear bands is a common deformation mode for nonlinear materials under compression, and plastic instability may further trigger the shear band formation. In general, the topological feature of shear band is a narrow zone that contains intense shearing strain. This kind of localized strain region is usually an origin/precursor of cracking, which may eventually lead to specimen fracture.

Generally speaking, the generation of irradiation-induced defect clusters can greatly increase plastic deformation resistance. The unirradiated tungsten is known to be resistant to shear banding because of its high ductile-to-brittle transition temperature. For ultrafine-grained pristine tungsten, Wei et al. [23] concluded that the thermally activated nucleation of kink-pair and its subsequent propagation, known as dislocation-mediated plastic deformation, can reduce the strain rate sensitivity during uniaxial dynamic compression, leading to severe shear localization and the formation of cracks.

According to aforementioned analyses, there is no doubt that defect clusters as weak/strong obstacles to the dislocation glide require extra force to overcome. Many experimental and theoretical studies focus on irradiation hardening in terms of hardness and macroscopic stress-strain curves, but the underlying deformation mechanisms regarding the competition and accommodation of the multiple softening (temperature) and hardening (irradiation defects) mechanisms on macroscopic deformation pattern remain elusive. To this end, two issues need to be clarified: 1) How the intrinsic features (i.e., size and density) of irradiation-induced defects influence the plastic flow behavior; 2) How the plastic instability triggered by deformation heterogeneity leads to the shear band formation in irradiated tungsten under compression.

This work aims to quantitatively investigate the flow stress, strain hardening and deformation modes of pristine and irradiated tungsten samples using a predictive simulation approach. More specifically, the crystal plasticity finite element model (CPFEM) is employed to simulate the irradiation temperature- and dose-dependent stress-strain curves and the associated deformation field under uniaxial compression loading. A previously developed mechanism-based model [24], considering both thermal softening and irradiation hardening, is utilized to assess the yield stress of irradiated tungsten. Accordingly, the microstructure-property relationship of irradiated tungsten is established to predict the plastic deformation behavior. The CPFEM predicted stress-strain curves are validated by experimental data reported in the literature, and the predicted strain localization pattern is also compared with experimental observations.