New Line Model for Optimized Dislocation Dynamics Simulations (original) (raw)
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Accelerating force calculation for dislocation dynamics simulations
arXiv (Cornell University), 2023
Discrete dislocation dynamics (DDD) simulations offer valuable insights into the plastic deformation and workhardening behavior of metals by explicitly modeling the evolution of dislocation lines under stress. However, the computational cost associated with calculating forces due to the long-range elastic interactions between dislocation segment pairs is one of the main causes that limit the achievable strain levels in DDD simulations. These elastic interaction forces can be obtained either from the integral of the stress field due to one segment over the other segment, or from the derivatives of the elastic interaction energy. In both cases, the results involve a double-integral over the two interacting segments. Currently, existing DDD simulations employ the stress-based approach with both integrals evaluated either from analytical expressions or from numerical quadrature. In this study, we systematically analyze the accuracy and computational cost of the stress-based and energy-based approaches with different ways of evaluating the integrals. We find that the stress-based approach is more efficient than the energy-based approach. Furthermore, the stress-based approach becomes most cost-effective when one integral is evaluated from analytic expression and the other integral from numerical quadrature. For well-separated segment pairs whose center distances are more than three times their lengths, this one-analytic-integral and one-numerical-integral approach is more than three times faster than the fully analytic approach, while the relative error in the forces is less than 10 −3. Because the vast majority of segment pairs in a typical simulation cell are well-separated, we expect the hybrid analytic/numerical approach to significantly boost the numerical efficiency of DDD simulations of work hardening.
Numerical methods to improve the computing efficiency of discrete dislocation dynamics simulations
Journal of Computational Physics, 2006
Dislocation dynamics (DD) is a method to simulate the collective dynamic behavior of dislocations and the plasticity of metals on a mesoscopic scale. A DD simulation is computationally demanding due to the fact that the stress field of a dislocation segment is long-ranged and it needs to examine a possible intersection between dislocation segments during their motion. The computing efficiency of a serial DD code is enhanced by using the so-called Ôbox methodÕ. The box method employing 21 3 boxes achieves 30-fold speed ups in the case involving 20,000 segments. The modified serial DD code has then been parallelized by using the standard message passing interface (MPI). Both the stress computation and handling segment intersection have been parallelized by using the domain decomposition method. Performance test on IBM p690 architecture shows that the parallel scheme adds up 20-fold speed ups when using 36 processors. Thus the parallel DD code presented here is about 600 times faster than the previous code. We present a parallel algorithm for highly complex dependencies in handling segment intersections and the performance test results in detail.
Defect hardening modeled in 2D discrete dislocation dynamics
Materials Science and Engineering: A, 2009
Two-dimensional discrete dislocation dynamics simulations are used to model the plastic deformation of an fcc metallic material containing large densities of defects. An obstacle model is proposed, based on the line tension concept. Increasing yield strength and hardening are obtained when the obstacle density is increased and destroyable junctions are included. A high dislocation source density is used to obtain a good dissemination of dislocations. Over 30% of the total density is stored as junctions. Slip is shown to be localized within a few intense slip bands, whatever the obstacle density. This localization is quantified as a function of the density of obstacles.
Journal of Engineering Materials and Technology, 2012
In latent interactions of dislocations, junction formation is one of the most important phenomena that contribute to the evolution of strength. In this work, the latent hardening coefficients for pure aluminum are estimated using 3D multiscale dislocation dynamics program (MDDP). Three well-known junction configurations, namely, the Hirth lock, the glissile junction, and the Lomer lock, are studied using 3D discrete dislocation dynamics simulations. The evolution of strength is discussed as a function of the resolved shear stress (RSS) and the number of junctions for the three junctions investigated. Hirth lock and Lomer lock are found to be the weakest and strongest junctions, respectively. Collinear reaction of dislocations does not form a junction but causes a higher strength than a Lomer lock. Quantitative and qualitative results are compared with those found in the literature.
From Dislocation Junctions to Forest Hardening
Physical Review Letters, 2002
The mechanisms of dislocation intersection and strain hardening in fcc crystals are examined with emphasis on the process of junction formation and destruction. Large-scale 3D simulations of dislocation dynamics were performed yielding access for the first time to statistically averaged quantities. These simulations provide a parameter-free estimate of the dislocation microstructure strength and of its scaling law. It is shown that forest hardening is dominated by short-range elastic processes and is insensitive to the detail of the dislocation core structure.
Le Journal de Physique IV, 2001
The elastic field of complex 3-D dislocation ensembles is described by differential geometric representations, which allow computer simulations of mesoscopic plastic deformation without additional ad hoc approximations for short-range dislocation reactions. The simple vector forms of differential geometry are independent of the coordinate system, and facilitate studies of dislocation generation, pileup formation, grainboundary interaction, finite-length dipole nucleation and break-up, junction nucleation and destruction, interaction with defect clusters, and self-consistent boundary conditions. It is shown that the elastic field can be described in terms of simple combinations of three basic vectors and their dyadics in real and reciprocal space. These vectors are the unit tangent, Burgers vector, and unit radial vector between a source point on the dislocation and a field point. With the only limitation being dislocation cores interpenetrating up to one Burgers vectors, a review of recent progress and examples of the aforementioned short-and long-range dislocation reactions are given, with particular emphasis on computational issues of space and time resolution.
Mesoscopic scale simulation of dislocation dynamics in fcc metals: Principles and applications
This paper reviews the methods and techniques developed to simulate dislocation dynamics on a mesoscopic scale. Attention is given to techniques of acceleration and to the implementation of special boundary conditions. Typical results concerning the deformation of a bulk crystal, the effect of image forces and the combination with a finite-element code to simulate the indentation test are presented. The limits and future development of each application are discussed. 755 756 M Verdier et al modelling the behaviour of bulk crystal, and for situations where a complex boundary is required, such as surfaces taking into account image forces or indentation of a crystal. In the last part, typical results concerning each case are presented and the limit of the various methods are discussed.
Discrete dislocation simulations and size dependent hardening in single slip
Le Journal de Physique IV, 1998
Plastic deformation in two-dimensionalmonophase and composite materials is studied using a discrete dislocation dynamics method. In this method, dislocations are represented by line defects in a linear elastic medium, and their interactions with boundaries or second-phase elastic particles are incorporated through a complementary finite element solution. The formulation includes a set of simple constitutive rules to model the lattice resistance to dislocation glide, as well as the generation, annihilation and pinning of dislocations at point obstacles. The focus is on the predicted strain hardening of these materials when only a single slip system is active. When the particle morphology is such as to require geometrically necessary dislocations, hardening in the composite materials exhibits a distinct size effect. This size effect is weaker than that predicted by simple analytical estimates based on geometrically necessary dislocations.
Model validation of a 3D simulation of dislocation dynamics: Discretization and line tension effects
Acta Metallurgica et Materialia, 1992
Some fundamental aspects of 3D computer modelling of plastic flow are presented together with the results of a detailed study of related approximations, such as the discretization of space and of dislocation line curvature. More specifically, the stress field generated by different discretizations of dislocation loops and the critical stress for dislocation multiplication through the Frank-Read mechanism, are compared to the predictions of the elastic theory of dislocations in the isotropic approximation. Although crude in appearance, the approximation adopted in these simulations to describe the curvature does not drastically affect the behaviour. Moreover, it leads to critical stress values for a pinned dislocation segment in excellent agreement with previous computations. R6sura6-Afin de valider certaines des approximations fondamentales d'une simulation num6rique fi 3D de la plasticit6, nous avons &udi6 l'influence du mode de discr6tisation de l'espace et de la courbure des dislocations. Plus particuli6rement, le champ de contrainte engendr6 par diff6rentes discr&isations des boucles de dislocation, ainsi que laa contrainte seuil de multiplication par le m6canisme de Frank Read, ont 6t6 compar6es aux r6sultats pr6dits par la thdorie 61astique en milieu isotrope. On v6rifie, que le mode de discr6tisation, adopt6 pour la courbure des lignes de dislocations, n'affecte pas de faqon significative le comportement du mod61e num&ique. De plus, les r6sultats obtenus pour la contrainte critique d'instabilit6 d'un segment de dislocation ancr6 fi ses extr6mit4s, sont en trds bon accord avec les r6sultats num6rique d6jfi publi6s. Zusammenfassung-Einige Approximationen bezfiglich auf eine 3 D numerische Simulation des plastischen Fliessens sind nachgepr/ift worden zur Untersuchung des Einflusses der Diskretisierung des Raums und der Versetzungskui:mmungslinie. Vor allen sind das durch verschiedene Diskretisierungen der Versetzungsschleifen erzeugte Spannungsfeld und die durch den Frank Read Mechanimus hervorgerufene kritische Druckspannung der Versetzungsvervielfachung mit den sich aus der Theorie der isotropen Elastizit/it ergebenden Werte verglichen worden. Es wird gezeigt, dass die angewandte Diskretisierung f/Jr die Versetzungskr/immunglsinie das Verhalten des Simulationsmodells nicht stark beeinflusst. Dar/ider hinaus stimmen die fiir kritische Druckspannung eines an seinen Endpunkten verankerten Versetzungssegments erhaltenen Knickwerte mit den schon ver6ffentlichten Ergebnissen sehr gut Oberhein.