Experimental lower bounds on geometrically necessary dislocation density

Kysar, Jeffrey W.; Saito, Yuki; Oztop, M.S.; Lee, Dong−Yun; Huh, Woonghee Tim

doi:10.1016/j.ijplas.2010.03.009

Cited by 179 publications

(115 citation statements)

References 79 publications

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“…wedge indentation (Kysar et al, 2010;Öztop, 2011;Dahlberg et al, 2014). The single slip simple shear problem, described in Section 3 and It is possible to achieve increasingly non-uniform GND density distributions, when decreasing the influence of L, however, decreasing L until a satisfactory micro-structure is achieved clearly does not guarantee the proper size-dependence in the hardening behavior.…”

Section: Back Stress Formulations and Resultsmentioning

confidence: 99%

“…These measurements show highly nonuniform and discontinuous lattice rotations, which are linked directly to the existence of geometrically necessary dislocations (GNDs), revealing distinct dislocation wall and cell pattern formation. Details on the experimental methods employed bÿ Oztop (2011) can also be found in Kysar et al (2010) and Dahlberg et al (2014), also showing highly localized GND structures.…”

Section: Introductionmentioning

confidence: 99%

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On modeling micro-structural evolution using a higher order strain gradient continuum theory

El-Naaman

Nielsen

Niordson

2016

International Journal of Plasticity

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Published experimental measurements on deformed metal crystals show distinct pattern formation, in which dislocations are arranged in wall and cell structures. The distribution of dislocations is highly non-uniform, which produces discontinuities in the lattice rotations. Modeling the experimentally observed micro-structural behavior, within a framework based on continuous field quantities, poses obvious challenges, since the evolution of dislocation structures is inherently a discrete and discontinuous process. This challenge, in particular, motivates the present study, and the aim is to improve the micro-structural response predicted using strain gradient crystal plasticity within a continuum mechanics framework. One approach to modeling the dislocation structures observed is through a back stress formulation, which can be related directly to the strain gradient energy. The present work offers an investigation of constitutive equations for the back stress based on both considerations of the gradient energy, but also includes results obtained from a purely phenomenological starting point. The influence of model parameters is brought out in a parametric study, and it is demonstrated how a proper treatment of the back stress enables dislocation wall and cell structure * Tel: +45 4525-4020, Fax: +45 4593-1475 URL: saeln@mek.dtu.dk (S.A. El-Naaman)

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Section: Back Stress Formulations and Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On modeling micro-structural evolution using a higher order strain gradient continuum theory

El-Naaman

Nielsen

Niordson

2016

International Journal of Plasticity

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“…Arsenlis & Parks (1999) argue that the differences between this approach and the linear programming scheme are likely to be small. Kysar et al (2010), however, show that differences can become significant under conditions of plane strain.…”

Section: (A) Geometrically Necessary Dislocations In Hcp and Fcc Crysmentioning

confidence: 93%

Crystal plasticity analysis of micro-deformation, lattice rotation and geometrically necessary dislocation density

2012

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A gradient-enhanced crystal plasticity model is presented that explicitly accounts for the evolution of the densities of geometrically necessary dislocations (GNDs) on individual slip systems of deforming crystals. The GND densities are fully coupled with the crystal slip rule. Application of the model to two distinct and technologically important crystal types, namely hcp Ti and ccp Ni, is given. For the hcp crystals, slip is permitted with a-type slip directions on basal, prismatic and pyramidal planes and c + a-type slip directions on pyramidal planes. First, a single crystal under four-point bending is simulated as the uniform strain gradient expected in the central span provides a good validation of the code. Then, uniaxial deformation of a model near-a Ti polycrystal has been analysed. The resulting distributions of GND densities that develop on the various slip system types have been compared with independent experimental observations. The model predicts that GND density on the c + a systems is approximately an order of magnitude lower than that for a-type systems in agreement with experiment. For the ccp case, slip is considered to take place on the <110>{111} slip systems. Thermal loading of a single-crystal nickel alloy sample containing carbide particles of size approximately 30 mm has been analysed. Detailed comparisons are presented between model predictions and results of high-resolution electron backscatter diffraction (EBSD) measurements of the micro-deformations, lattice rotations, curvatures and GND densities local to the nickel-carbide interface. Qualitatively, good agreement is achieved between the coupled and decoupled model elastic strains with the EBSD measurements, but lattice rotations and GND densities are quantitatively well predicted by the coupled crystal model but are less well captured by the decoupled model. The GND coupling is found to lead to reduced lattice rotations and plastic strains in the region of highest heterogeneity close to the Ni matrix/particle interface, which is in agreement with the experimental measurements. The results presented provide objective evidence of the effectiveness of gradient-enhanced crystal plasticity finite element analysis and demonstrate that GND coupling is required in order to capture strains and lattice rotations in regions of high heterogeneity.

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“…This therefore provides an underdetermined problem, with fewer constraints than potential dislocation types for which we want to determine densities. There are many routes discussed in the literature to treat this problem (Britton et al, 2009;Gardner et al, 2010;Kysar et al, 2010;Kysar et al, 2007;Sun et al, 2000) (Arsenlis and Parks, 1999;Field et al, 2010;Hardin et al, 2011;Hardin et al, 2013;Ruggles and Fullwood, 2013) (Demir et al, 2009), with varying degrees of success and merit. We choose to select a solution that physically supports the curvature measured and also minimises the total line energy, accounting for differences between screw and edges using isotropic elastic energies, of the dislocations used (this a L 1 minimisation scheme).…”

Section: Hr-ebsd and Gnd Densitymentioning

confidence: 99%

The orientation and strain dependence of dislocation structure evolution in monotonically deformed polycrystalline copper

Jiang

Britton

Wilkinson

2015

International Journal of Plasticity

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Experimental lower bounds on geometrically necessary dislocation density

Cited by 179 publications

References 79 publications

On modeling micro-structural evolution using a higher order strain gradient continuum theory

On modeling micro-structural evolution using a higher order strain gradient continuum theory

Crystal plasticity analysis of micro-deformation, lattice rotation and geometrically necessary dislocation density

The orientation and strain dependence of dislocation structure evolution in monotonically deformed polycrystalline copper

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