Issue 50

K. Singh et alii, Frattura ed Integrità Strutturale, 50 (2019) 319-330; DOI: 10.3221/IGF-ESIS.50.27 320 I NTRODUCTION efect clusters (interstitial & vacancies) produced during irradiation strongly affects the mechanical properties of the structural materials. In irradiated BCC materials, it has been observed that dislocation-loops (interstitial type) are primary defects produced [1]. The interaction of these defects with dislocations controls the material hardening and embrittlement behavior. For the given material, chemical composition and irradiation flux, the number of dislocation- loops ( irr N ) formed, and their diameter ( irr d ) is majorly dependent upon the irradiation dose and temperature respectively [2, 3]. Furthermore, in BCC materials, plasticity is strongly temperature dependent and could be defined according to low and high temperature regimes named as a thermal and athermal regime, respectively [4, 5]. In thermal regime, the plasticity in BCC materials is temperature dependent (kink pair formation) whereas in athermal regime it is mostly independent of temperature. To study such behavior, crystal plasticity models within the finite element methods have become an important tool for material development and continuum mechanics based evaluation of materials [6]. Development of suitable model based on the available experimental data could facilitate in simulating irradiation effects, which otherwise involve considerable time and cost to conduct an experiment in a controlled environment. Dislocation based crystal plasticity can be used at the continuum scale to model the evolution of various crystallographic variables on each slip system to account for heterogeneous plastic strain development in crystal. This will allow to include the physical definition of different plasticity mechanisms depending upon the wide range of temperature and strain rates along with dislocations and dislocation-loops interaction. Crystal plasticity models are developed with dislocation density as internal state variable to investigate the plasticity in BCC materials by Zerilli et al. [7], Armstrong et al. [8], Kubin et al. [9], Stainier et al. [10], Ma et al. [11], Alankar et al. [12], Monnet at al. [13] and Cereceda et al. [14]. Also, attempts have been made to account for irradiation effects on the plasticity of BCC materials. Dispersed barrier hardening model has been used to describe the irradiation dose and temperature effect on the yield stress of the materials [15]. Dislocation multiplication due to their pinning with irradiation-induced defects [16] and assuming the irradiation defects as shearable obstacles for FCC materials [17] is used to study the irradiation defects. In the current work, dislocation density based crystal plasticity material model for BCC material is used to account for temperature dependent plasticity in non-irradiated and irradiated materials. The radiation induced defects are considered by incorporating strength based defect interaction with dislocations and also their impact on the mobile dislocation density in addition to total dislocation density. The developed dislocation based material model takes into account the irradiation defects along with temperature dependent plasticity behavior of BCC materials [7-9]. Constitutive equations adapted (discussed in subsequent sections) to define thermal and as well as athermal regime assist in determining the plasticity behavior for a wide range of temperature and strain rates. The radiation induced defects are accounted by incorporating strength based defect interaction with dislocations and also their impact on the mobile dislocation density in addition to total dislocation density. The model can be used to analyze the effect of irradiation-induced dislocation-loop size and number density on the BCC material, which indirectly simulates the various irradiation conditions on single-crystal. In the present work, the different irradiation conditions are investigated, and results are post-processed to estimate the relative change in the sub-crystalline stress distribution in the form of the Weibull parameters. These parameters will serve as valuable input for the Microstructure Informed Brittle Fracture (MIBF) model to study the effect of various irradiation condition on the fracture response of the BCC materials. The MIBF model is based on a local approach and accounts for microstructural aspects of material along with behavioral law and fracture mechanics [10]. It relies on crystal plasticity results in terms of heterogeneity of the stress field at the microstructure scale to study the compact tension (CT) specimen behavior under applied loading. An elementary volume (zone near the crack tip) consists of cleavage triggering sites like carbides having specific size distribution depending upon materials composition. Each carbide is a potential site for the cleavage and taken as the point of nucleation. The rupture (propagation) will be triggered at such sites according to the Griffith criterion (local stress and critical stress). Finally, the MIBF model provides the failure/rupture probability based on the carbide size distribution and local stress distribution obtained from crystal plasticity. These results are transformed to estimate the variation in toughness as the function of temperature. The dislocation based material model, simulation results, and the effect of various irradiation conditions on the Weibull parameters to be subsequently used in the MIBF model are highlighted and discussed in the following sections. D