Towards Frank-Read Sources in the Continuum Dislocation Dynamics Theory

ABSTRACTIn the current paper we modify the evolution equations of the simplified continuum dislocation dynamics theory presented in [T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, Continuum dislocation dynamics: Towards a physical theory of crystal plasticity. J. Mech. Phys. Solids. (in print)] to account for the nature of the so-called curvature density as a conserved quantity. The derived evolution equations define a dislocation flux based crystal plasticity law, which we present in a fully three-dimensional form. Because the total curvature is a conserved quantity in the theory the time integration of the equations benefit from using conservative numerical schemes. We present a discontinuous Galerkin implementation for integrating the time evolution of the dislocation state and show that this allows simulating the evolution of a single dislocation loop as well as of a distributed loop density on different slip systems.

Download Full-text

Predicting plastic flow and irradiation hardening of iron single crystal with mechanism-based continuum dislocation dynamics

International Journal of Plasticity ◽

10.1016/j.ijplas.2013.01.015 ◽

2014 ◽

Vol 52 ◽

pp. 3-17 ◽

Cited By ~ 69

Author(s):

Dongsheng Li ◽

Hussein Zbib ◽

Xin Sun ◽

Mohammad Khaleel

Keyword(s):

Single Crystal ◽

Plastic Flow ◽

Dislocation Dynamics ◽

Irradiation Hardening ◽

Iron Single Crystal ◽

Continuum Dislocation Dynamics

Download Full-text

Equivalent plastic strain gradient plasticity with grain boundary hardening and comparison to discrete dislocation dynamics

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2015.0388 ◽

2015 ◽

Vol 471 (2184) ◽

pp. 20150388 ◽

Cited By ~ 22

Author(s):

E. Bayerschen ◽

M. Stricker ◽

S. Wulfinghoff ◽

D. Weygand ◽

T. Böhlke

Keyword(s):

Plastic Strain ◽

Yield Strength ◽

Grain Boundary ◽

Continuum Model ◽

Equivalent Plastic Strain ◽

Elastic Interaction ◽

Dislocation Dynamics ◽

Discrete Dislocation Dynamics ◽

Discrete Dislocation ◽

The Continuum

The gradient crystal plasticity framework of Wulfinghoff et al. (Wulfinghoff et al. 2013 Int. J. Plasticity 51, 33–46. ( doi:10.1016/j.ijplas.2013.07.001 )), incorporating an equivalent plastic strain γ eq and grain boundary (GB) yielding, is extended with GB hardening. By comparison to averaged results from many discrete dislocation dynamics (DDD) simulations of an aluminium-type tricrystal under tensile loading, the new hardening parameter of the continuum model is calibrated. Although the GBs in the discrete simulations are impenetrable, an infinite GB yield strength, corresponding to microhard GB conditions, is not applicable in the continuum model. A combination of a finite GB yield strength with an isotropic bulk Voce hardening relation alone also fails to model the plastic strain profiles obtained by DDD. Instead, a finite GB yield strength in combination with GB hardening depending on the equivalent plastic strain at the GBs is shown to give a better agreement to DDD results. The differences in the plastic strain profiles obtained in DDD simulations by using different orientations of the central grain could not be captured. This indicates that the misorientation-dependent elastic interaction of dislocations reaching over the GBs should also be included in the continuum model.

Download Full-text

Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam

MRS Advances ◽

10.1557/adv.2016.75 ◽

2016 ◽

Vol 1 (24) ◽

pp. 1791-1796 ◽

Cited By ~ 4

Author(s):

Alireza Ebrahimi ◽

Thomas Hochrainer

Keyword(s):

Dislocation Density ◽

Slip System ◽

Evolution Equations ◽

Three Dimensional ◽

Dislocation Dynamics ◽

Structure Evolution ◽

Internal Variables ◽

Plastic Shear ◽

Continuum Dislocation Dynamics ◽

Dynamics Simulations

ABSTRACTA persistent challenge in multi-scale modeling of materials is the prediction of plastic materials behavior based on the evolution of the dislocation state. An important step towards a dislocation based continuum description was recently achieved with the so called continuum dislocation dynamics (CDD). CDD captures the kinematics of moving curved dislocations in flux-type evolution equations for dislocation density variables, coupled to the stress field via average dislocation velocity-laws based on the Peach-Koehler force. The lowest order closure of CDD employs three internal variables per slip system, namely the total dislocation density, the classical dislocation density tensor and a so called curvature density.In the current work we present a three-dimensional implementation of the lowest order CDD theory as a materials sub-routine for Abaqus®in conjunction with the crystal plasticity framework DAMASK. We simulate bending of a micro-beam and qualitatively compare the plastic shear and the dislocation distribution on a given slip system to results from the literature. The CDD simulations reproduce a zone of reduced plastic shear close to the surfaces and dislocation pile-ups towards the center of the beam, which have been similarly observed in discrete dislocation simulations.

Download Full-text

Crysal Plasticity Finite Element Simulations based on Continuum Dislocation Dynamics

PAMM ◽

10.1002/pamm.201610151 ◽

2016 ◽

Vol 16 (1) ◽

pp. 325-326

Author(s):

Alireza Ebrahimi ◽

Thomas Hochrainer

Keyword(s):

Finite Element ◽

Finite Element Simulations ◽

Dislocation Dynamics ◽

Continuum Dislocation Dynamics

Download Full-text

Simulation of Dislocation Dynamics in the Continuum Limit

MRS Proceedings ◽

10.1557/proc-538-27 ◽

1998 ◽

Vol 538 ◽

Cited By ~ 1

Author(s):

K. W. Schwarz

Keyword(s):

Slip System ◽

Strong Interaction ◽

Continuum Limit ◽

Dislocation Dynamics ◽

The Self ◽

Burgers Vector ◽

Strained Layer ◽

The Continuum

AbstractPeach-Koehler theory is implemented to simulate the motion of three-dimensionally interacting dislocations, located on various glide planes and having any allowed Burgers vector. The self-interaction is regularized by a modified Brown procedure, which remains stable and loses accuracy in a well-controlled manner as atomic dimensions are approached. The method is illustrated by applying it to several problems involving interacting dislocations in an fcc slip system. The strong interaction of two dislocations on intersecting glide planes is investigated with a view towards developing a set of rules to describe the outcome of such interactions. The effect of Frank-Read sources in relaxing a strained layer are illustrated, both for sources on parallel and on intersecting glide planes.

Download Full-text