PSI - Issue 14

Ashish Mishra et al. / Procedia Structural Integrity 14 (2019) 544–548

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A.Mishra, A. Alankar / Structural Integrity Procedia 00 (2018) 000–000

be tracked. The groundwork for dislocation dynamics (DD) begun back in mid 1960s by Brown (1964), Bacon (1967) and Foreman (1967). Brown (1964) proposed the definition of line tension, i.e., self-stress of a dislocation. Bacon (1967) put forth the methodology to determine the shape of a dislocation under the influence of internal and external stress fields. Foreman (1967) discussed bowing of a dislocation segment pinned at its ends due to the stress field using line tension model proposed by Brown (1964). Later, the concept of three dimensional discrete dislocation dynamics (3D-DDD) framework was given in 1990s by Kubin and Canova (1992) and Devincre et al. (1992). In the early 1990s, Canova and Kubin (1991) and Amadeo and Ghoniem (1990) proposed the first DD tool based on linear elasticity. In 1992, Kubin et al. (1992) presented the first 3D-DDD tool exhibiting the deformation behavior of copper and aluminum single crystals. Currently, there are numerous DD codes (Zbib et al. (1998), Schwarz (1999), Ghoniem and Sun (1999), Cai et al. (2004)) available worldwide which are dedicated to different approaches of line discretization. Dislocations in DD are portrayed by discrete line segments gliding under the influence of driving forces such as externally applied forces, dislocation line tension and interaction forces between dislocations. Matrix is defined as isotropic elastic medium (see Zbib et al. (1998)). DD simulations have been used in the past for analyzing plastic deformation behavior in FCC single crystals such as nickel by Zhou et al. (2010) and copper by Saada (1960). Saada and Veyssiere (2002) pointed out that the presence of short range interactions between dislocations is the primary cause of the flow stress. Subsequently, researchers focused on estimation of the strength of various dislocation reactions using DD programs. In FCC crystals, four independent dislocation reactions occur namely, the Hirth lock, the Lomer lock, the collinear reactions and the glissile junctions (see Saada and Veyssiere (2002)). Akasheh et al. (2007) concluded that the dominant interaction contributing to hardening mechanism is the collinear reaction occurring between interacting dislocations. Later, Alankar et al. (2012) made an attempt to estimate latent hardening coefficients for aluminum crystal which can be used further in crystal plasticity finite element modeling (CPFEM) simulations. It was also concluded that resolved shear stress (RSS) evolves with the formation of new junctions and the stress decreases with the unzipping of junctions. Akarapu et al. (2010) found that hardening observed in DD simulations is attributed to the fact that pinning of dislocation segments occurs because of formation of junction and tangled dislocation structures. DD simulations have been considerably used for analyzing interactions between dislocations, interaction between dislocation and interface, for estimating the materials parameters for larger length scale models i.e. CPFEM, and also for coupling with the finite element simulations. For instance, Akasheh et al. (2007) used Multiscale Dislocation Dynamics Plasticity (MDDP) package to quantify the material parameters for a multiscale model coupled with DD. We use the 3D-DDD simulation package (MDDP) developed by Zbib et al. (1998) for our study on copper single crystals. In this work, we have incorporated an algorithm using which formation of various types of junctions and count can be determined on-the-fly during simulation. Note that usually such data is available as post-processed data. By determining dislocation reactions on-the-fly it is ensured that the conditions of dislocation reactions are precisely captured without needing to store large amount of data over simulation steps. Nomenclature pred  predicted value of stress DD  value of stress obtained from DD simulation error  error between the predicted value of stress and value of stress obtained from DD simulation 2. Simulation details We present DD simulations for investigating dislocation reactions in a copper single crystal specimen subjected to uniaxial tensile loading. The size of simulation cell used was 5000 b ×5000 b ×5000 b , where b is the magnitude of Burgers vector of copper. Periodic boundary conditions (PBC) were used in the X, Y and Z directions for avoiding surface effects. The cell was populated with randomly distributed Frank-Read (F-R) source arms. The minimum segment length of 200 b was taken for numerical integration. Cross-slip activity was allowed to occur. The specimen