The stress field of an array of parallel dislocation pile-ups: Implications for grain boundary hardening and excess dislocation distributions

Schouwenaars, Rafael; Seefeldt, Marc; Houtte, Paul Van

doi:10.1016/j.actamat.2010.04.026

Cited by 39 publications

(14 citation statements)

References 30 publications

(58 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This leads to a lower resultant stress state for dislocation slip [9]. Such a model has been widely used as an explanation for the empirical Hall-Petch relationship [9][10][11] which relates yield strength to grain size of a polycrystalline material by the equation:…”

Section: Introductionmentioning

confidence: 99%

Slip band–grain boundary interactions in commercial-purity titanium

2014

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

Slip band–grain boundary interactions in commercial-purity titanium

2014

View full text Add to dashboard Cite

“…A class of representative two-dimensional dislocation configurations widely studied in the literature are distributions (pile-ups) of dislocation walls consisting of straight and mutually parallel dislocations (e.g. [27,29,32,13,8,40,30,28]). In this scenario, dislocation-dislocation interactions take place in both directions that are in and normal to the dislocation slip planes.…”

Section: Introductionmentioning

confidence: 99%

A continuum model for distributions of dislocations incorporating short-range interactions

Niu

Zhu

Dai

et al. 2018

Communications in Mathematical Sciences

View full text Add to dashboard Cite

Dislocations are the main carriers of the permanent deformation of crystals. For simulations of engineering applications, continuum models where material microstructures are represented by continuous density distributions of dislocations are preferred. It is challenging to capture in the continuum model the short-range dislocation interactions, which vanish after the standard averaging procedure from discrete dislocation models. In this study, we consider systems of parallel straight dislocation walls and develop continuum descriptions for the short-range interactions of dislocations by using asymptotic analysis. The obtained continuum short-range interaction formulas are incorporated in the continuum model for dislocation dynamics based on a pair of dislocation density potential functions that represent continuous distributions of dislocations. This derived continuum model is able to describe the anisotropic dislocation interaction and motion. Mathematically, these short-range interaction terms ensure strong stability property of the continuum model that is possessed by the discrete dislocation dynamics model. The derived continuum model is validated by comparisons with the discrete dislocation dynamical simulation results.

show abstract

“…Low-angle GBs are more readily modeled, due to the greater spacing between GBDs and subsequently greater ease for classifying the distinct atomistic dislocation cores [Lim et al, 2012;Schouwenaars et al, 2010]. Three pure-tilt GBs were simulated in full-atomistic from, using bi-crystals obtained with LAMMPs molecular dynamics simulations [Plimpton, 1995].…”

Section: Utilizing a Dislocation Array Based On Atomistic Calculationmentioning

confidence: 99%

“…It is unlikely that such models will ever be capable of effectively capturing the complexity of cross-slip, multi-junction formation or more complex long-range dislocation force-field effects. Previous studies have evaluated the stress-fields in 'bi-crystals' containing a lowangle GB comprised of an array of dislocations [Schouwenaars et al, 2010;Khan et al, 2004]. However, these did not account for changing crystallography at the interface, and no algorithms were provided to enable dislocation intersection with the GB interface.…”

Section: Introductionmentioning

confidence: 99%

“…However, DD has yet to be implemented in a way that can accommodate dynamic GB interactions in 3D, which is necessary to understand effects of dislocation pileups and re-oriented slip transmission [Mcdowell, 2010]. Previous attempts to model polycrystal DD with mesoscale simulations are mostly limited to two dimensions and generally assume that interfaces are impenetrable to dislocations [Schouwenaars et al, 2010;Kubin et al, 2010;Balint et al, 2008;Nicola et al, 2006]. Only recently, more complex models have been developed in order to enable processes of slip transmission through GBs [Li et al, 2009].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dislocation dynamics in polycrystals with atomistic-informed mechanisms of dislocation - grain boundary interactions

Burbery

Das

et al. 2017

J. Micromech. Mol. Phys.

View full text Add to dashboard Cite

In polycrystalline materials, dislocations can interact with grain boundaries (GBS) through a number of mechanisms including dislocation absorption, pile-up formation, dissociation reactions within the GB plane and (possibly) dislocation nucleation from the interface itself. The effects of dislocation pile-ups contribute significantly to the mechanical behavior of polycrystalline materials by creating back-stresses that inactivate the primary slip systems in the vicinity of the interface, corresponding with the celebrated Hall-Petch relationship between size and strength. However, dislocation pile-ups cannot be contained within the small grain sizes that can be accommodated by molecular dynamics simulations, which to-date remain the primary computational method used to study the discrete structure of GBs.Dislocation dynamics (DD) simulations are a promising framework for computational modeling that are used to provide insights about phenomena that can only be explained from the intermediate scale between atomistic and macro scales. However, a robust framework for modeling dislocation interactions with internal microstructure such as grain boundaries (GBs) has yet to be achieved for 3D models of DD. Furthermore, this is the first implementation which explicitly includes the dislocation content of the interface. The framework described in this paper is effective for studying GBdislocation interactions (including inter-granular effects) and the approach for partitioning the DD simulation domain. To achieve a robust method to differentiate between crystal regions, the present framework utilizes a mesh-based partitioning system. Within each grain, slip systems are determined by the grain orientation. The versatile construction described, allows modeling of an arbitrary crystallography, size and grain geometry. Extrinsic dislocations that intersect the interface are constrained to glide on the line of intersection between the glide plane and GB plane. Atomistically informed criteria for § Corresponding author. N. B. Burbery et al.slip transmission are implemented, based on the geometrically optimal outgoing glide plane which shares a common line of intersection on the GB plane. Slip transmission is only initiated when the resolved shear stress in one of the compatible outgoing slip directions exceeds an approximate threshold resolved shear stress, which is based on observations made with molecular dynamics studies. The primary aim of the present study was to establish a sufficiently 'generic' framework to enable the modelling of various GB structures, polycrystal geometries and crystallographic orientations. The framework described in the present work provides a means to study multi-grain deformation processes governed by dislocations pile-ups at GBs, in detail beyond feasible limits of experiments or atomistic simulation approaches.

show abstract

The stress field of an array of parallel dislocation pile-ups: Implications for grain boundary hardening and excess dislocation distributions

Cited by 39 publications

References 30 publications

Slip band–grain boundary interactions in commercial-purity titanium

Slip band–grain boundary interactions in commercial-purity titanium

A continuum model for distributions of dislocations incorporating short-range interactions

Dislocation dynamics in polycrystals with atomistic-informed mechanisms of dislocation - grain boundary interactions

Contact Info

Product

Resources

About