A concurrent irradiation-mechanics multiscale coupling model

Highlights

• A novel concurrent irradiation-mechanical multiscale coupling model is developed.

• Models of irradiation defect kinetics and irradiation hardening are established.

• The difference between post irradiation and concurrent irradiation-deformation tests are disclosed.

• Dislocation channel formation is not always correlated with yield drop.

Abstract

The vast majority of our current knowledge regarding the basic mechanisms controlling irradiation effect on mechanical properties is based almost entirely on the results of post-irradiation experiments or theoretical models. However, the concurrent effects of irradiation, mechanical stress, and thermal damage on the failure phenomena of materials and components remain largely unexplored due to its internal multiscale-multiphysics coupling nature. We present here a concurrent irradiation-mechanics multiscale coupling model. The concurrent evolutions of nanoscale irradiation defect clusters, microscale dislocation configurations, and mechanical responses are well captured based on coupling cluster dynamics, discrete dislocation dynamics, and the finite element methods using an effective time marching scheme. Model predictions of defect densities and size are in general agreement with experimental observations. Irradiation hardening is shown to take place also in samples undergoing concurrent irradiation-mechanical loading, similar to samples tested post-irradiation. However, the occurrence of plastic flow localization and dislocation channel formation is not accompanied with apparent yield drop (softening) under concurrent irradiation-mechanical loading conditions, which is different from the post-irradiation case.

Introduction

Understanding the performance degradation of irradiation material is of great importance for the safety and reliability of nuclear fission or fusion power plants (Hill 2008; Zinkle and Busby 2009; Zinkle and Was 2013; Alawadi and Abdolvand 2020; Reali et al., 2021; Tondro and Abdolvand 2021). Numerous efforts have been made with the aim of describing the evolution of irradiation-induced defects and establishing a link between defect densities and sizes and the degradation in mechanical performance (Victoria et al., 2000; Chen et al., 2016; Cui et al., 2017; Rovelli et al., 2017; Chen et al., 2020; Shang et al., 2021). Several degradation phenomena in irradiated materials have been observed, such as irradiation hardening, embrittlement, creep, and volumetric swelling (Byun et al., 2008; McMurtrey et al., 2015; Garud 2016; Xia et al., 2019; Xiao 2019; Khiara et al., 2021; Lin et al., 2021). However, the current understanding regarding the irradiation effects on these properties, in particular irradiation hardening and embrittlement, is based almost entirely on the results of post-irradiation experiments or theoretical models. In contrast, materials employed as structural components in fission or fusion reactors are exposed simultaneously to neutron irradiation, external stress, and high-temperature (Singh et al., 2003; Singh et al., 2004; Pakarinen et al., 2013; Terentyev et al., 2015). Several fundamental questions then arise: (1) what is the concurrent effects of neutron irradiation and mechanical loading on the deformation and failure process, and (2) are post-irradiation tests able to effectively determine the performance of in-reactor structures?

Previous efforts have led to a relatively clear physical picture of the generation and evolution of irradiation-induced defects (Fan et al., 2011; Dunn et al., 2013; Cui et al., 2017; Gu et al., 2017; C. Sobie, Capolungo et al. 2017; Zhu et al., 2017; Nordlund et al., 2018; Kohnert and Capolungo 2019; Fan et al., 2020). Irradiation firstly causes collision cascades of displacement atoms, generating numerous Frenkel pairs as vacancies and self-interstitial atoms. These points defects diffuse, recombine, aggregate and dissociate in the material, leading to the production of high densities of nanoscale defect clusters. They are mainly characterized as stacking fault tetrahedra (SFT) and interstitial loops in face centered cubic (FCC) metals, and interstitial loops and nano-voids in body centered cubic (BCC) metals. These irradiation defects interact with other features of the microstructure, like dislocations and precipitates, resulting in the collective mechanical response of the material. On the one hand, these defects obstruct dislocation motion, leading to irradiation hardening. On the other hand, they may be swept away, absorbed, or destroyed by moving dislocations, causing the formation of defect-free channels (so-called dislocation channels or cleared channels) and the appearance of deformation localization (i.e. micro shear bands). Such deformation localization is widely observed in irradiated materials (Lee et al., 2001; Byun and Hashimoto 2006; Xiao 2019), and is believed to be one main origin of irradiation embrittlement (Byun and Hashimoto 2006; Xiao 2019), and significantly increases the susceptibility to stress corrosion cracking initiation (Was et al., 2012; McMurtrey et al., 2015; Patra and McDowell 2015).

Irradiation hardening and deformation localization have been investigated extensively based on post-irradiated experimental tests (Byun and Hashimoto 2006; Byun et al., 2008; Jiao and Was 2010) or theoretical analysis (Barton et al., 2013; Cui, Po et al. 2018; Xiao et al., 2019; Cui et al., 2021). It is generally believed that the occurrence of deformation localization is accompanied by the yield drop phenomena, and is mainly observed in irradiated materials at high irradiation doses (Zinkle and Singh 2006; Barton et al., 2013). However, experiments show that these observations in the post-irradiated state are fundamentally different from those exposed to a dynamic irradiation environment in a fission or fusion reactor (Singh et al., 2004). During in-reactor mechanical tests, the transition from the elastic to plastic regime occurs smoothly and without any sharp transient in the form of a yield drop. Instead, strain hardening and deformation localization may occur at the same time. The underlying mechanism of these discrepancies is still largely unexplored.

At present, there are very few experiments (Singh et al., 2003; Singh et al., 2004; Pakarinen et al., 2013) focusing on concurrent irradiation and mechanical deformation. Neutron irradiation experiments at high temperatures and under external loading are expensive and time-consuming, and it's not easy to determine the deformation and irradiation coupling mechanism because of the limitations of experimental conditions. From the theoretical perspective, to the best of our knowledge, no model has ever been developed, which can disclose the underlying physical mechanism and at the same time explain the different experimental observations on deformation localization during post-irradiation tests and in-reactor tests.

During the past decades, modeling efforts have separately focused on either the evolution of irradiation-induced defects, or irradiation effects on the mechanical response (Cui et al., 2021). For example, the method of cluster dynamics (CD) was developed to capture the nucleation and growth of defect clusters produced by irradiation(Kohnert et al., 2018). On the other hand, the method of discrete dislocation dynamics (DDD) was capable of simulating the collective evolution of dislocations(Hussein and El-Awady 2016; Fan et al., 2021), and modeling the interaction mechanisms between dislocations and irradiation defects (Sobie, Capolungo et al. 2017; Li et al., 2019). Furthermore, continuum mechanics methods, like crystal plasticity and the finite element methods were advanced for relatively large-scale problems(Barton et al., 2013; Jiao et al., 2021; Li et al., 2021). Each of these methods alone cannot answer the fundamental questions regarding why the hardening behavior and the degree of plastic deformation localization of irradiated materials are different under post-irradiation and in-reactor experiments.

Mechanism-based theory and models of material response under simultaneous loading and irradiation are therefore urgently needed. The key problem here is that the generation and evolution of nanoscale irradiation-induced defects and microscale dislocations are strongly coupled. Irradiation defect kinetics is strongly influenced by the external loading condition, as well as the existence of dislocations. For example, atomistic simulations show that external stress influences the collision cascade process (Kirsanov et al., 1991; Beeler et al., 2015). Recently, Li et al. (Li et al., 2020) found that increasing the dislocation density inhibits the nucleation of interstitial loops. By coupling crystal plasticity and stochastic cluster dynamics method, it is found that in-situ tests, dislocation multiplication acts as a potent defect accumulation inhibitor, leading to a weak crystal orientation dependence and modest levels of defect hardening (Yu et al., 2021). Therefore, in order to map the space of understanding the concurrent irradiation-mechanical deformation problem, the coupled dynamics of defect clusters and dislocations must be effectively described in the same framework. This leads to several challenges: (1) A time scale mismatch exists between defect cluster dynamics and discrete dislocation dynamics. (2) A spatial scale mismatch exists between point defects, nanoscale irradiation defect clusters, and the microscale complex dislocation network. In particular, different types of irradiation defect clusters coexist and evolve in irradiated materials. (3) With the increase of the irradiation dose, a high density of irradiation defects poses significant computational challenges.

This work aims at overcoming the challenges associated with coupling the dynamics of irradiation defects and dislocation assembles at different spatial and temporal scales. The main objective is to develop an integrated model that couples defect microstructure evolution with the concurrent evolution of the dislocation network under the influence of irradiation, temperature, and external loading. Details of the coupled models are presented in Section 2, where we develop a necessary set of controlling equations for defect clusters, build effective sub-models of dislocation interaction with irradiation-induced defects, and present the coupling strategy. In Section 3, verification cases are given to illustrate the effectiveness of the model by applying it to α-iron. Section 4 is dedicated to discussing the differences between post-irradiation and in-reactor response, while conclusions are given in Section 5.