Size effects under homogeneous deformation of single crystals: A discrete dislocation analysis☆

Guruprasad, P. J.; Benzerga, A. Amine

doi:10.1016/j.jmps.2007.03.009

Cited by 96 publications

(65 citation statements)

References 33 publications

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“…These findings suggest that fundamentally different dislocation motion mechanisms might be operating in fcc and bcc crystals at nanoscale. The experimental results reported here are consistent with recent computational findings by molecular dynamics and dislocation dynamics simulations [2,8,[15][16][17][18][19][20][21]. Most of these computational works have primarily addressed the deformation of fcc crystals, where dislocations easily split into ribbons separated by stacking faults, preventing them from cross slipping and restricting them to gliding only in f111g-type planes [22].…”

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confidence: 88%

Fundamental Differences in Mechanical Behavior between Two Types of Crystals at the Nanoscale

2008

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We present differences in the mechanical behavior of nanoscale gold and molybdenum single crystals. A significant strength increase is observed as the size is reduced to 100 nm. Both nanocrystals exhibit discrete strain bursts during plastic deformation. We postulate that they arise from significant differences in the dislocation behavior. Dislocation starvation is the predominant mechanism of plasticity in nanoscale fcc crystals, while junction formation and hardening characterize bcc plasticity. A statistical analysis of strain bursts is performed as a function of size and compared with stochastic models. DOI: 10.1103/PhysRevLett.100.155502 PACS numbers: 62.25.ÿg, 61.46.Hk, 81.07.ÿb, 81.16.Rf The mechanical behavior of crystals is dictated by dislocation motion in response to applied force. While it is difficult to observe the motion of individual dislocations, several correlations can be made between the microscopic stress-strain behavior and dislocation activity. In bulk, plasticity in metals occurs by the motion of dislocations, which multiply in the course of plastic deformation causing strain hardening. Although this fundamental concept is often assumed to be applicable to crystals of any dimensions, numerous recent studies have shown that conventional plasticity breaks down at the submicron scale. Recently, many experimental and computational investigations of fcc crystals (Au, Al, Cu, Ni) have demonstrated a pronounced size effect, whose main premise is ''smaller is stronger '' [1-11]. In this work we investigate flow stress as a function of diameter in gold (fcc) and molybdenum (bcc) single crystal nanopillars subjected to uniaxial microcompression. The results that follow suggest that fcc and bcc crystals have fundamentally different plasticity mechanisms when reduced to nanoscale with significant strain hardening present in the latter and virtually none in the former. In a striking deviation from classical mechanics, there is a significant increase in strength as crystal size is reduced to 100 nm; however, in gold crystals (fcc) the highest strength achieved represents 44% of its theoretical strength, while in molybdenum crystals (bcc) it is only 7%. This suggests that plasticity in Au is likely controlled by nucleation of new dislocations rather than by interactions of the preexisting ones. On the contrary, the smallest molybdenum nanopillar achieves only 7% of its theoretical strength, implying that plasticity is likely driven by the intricate motion and interactions of dislocations inside the pillar rather than by nucleation events. These remarkable differences in mechanical response of fcc and bcc crystals to uniaxial microcompression challenge the applicability of conventional strain hardening to nanoscale crystals. Single crystal nanopillars described in this work were fabricated via the focused ion beam system and subsequently uniaxially compressed along the h001i direction in the nanoindenter with a flat punch tip of 30 m diameter. The specifics of fabrication and testing conditions are b...

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confidence: 88%

Fundamental Differences in Mechanical Behavior between Two Types of Crystals at the Nanoscale

2008

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“…These immobile junctions, which act as obstacles to slip and possibly also anchoring points for new 'dynamic' Frank-Read sources, can be destroyed by sufficiently high resolved shear stresses on the participating dislocations. The resulting evolution of the source and obstacle population was shown to predict strain hardening as well as size effects in micron-sized compression specimens (Benzerga et al, 2004;Guruprasad and Benzerga, 2008). An alternative approach adopted by Gómez-Garcia et al (2006) considered a single crystal undergoing nominally homogeneous deformation, a cross-section plane of which was analyzed using periodic boundary conditions to simulate bulk behavior.…”

Section: Introductionmentioning

confidence: 99%

Strain hardening in 2D discrete dislocation dynamics simulations: A new ‘2.5D’ algorithm

Keralavarma

2016

Journal of the Mechanics and Physics of Solids

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The two-dimensional discrete dislocation dynamics (2D DD) method, consisting of parallel straight edge dislocations gliding on independent slip systems in a plane strain model of a crystal, is often used to study complicated boundary value problems in crystal plasticity. However, the absence of truly three dimensional mechanisms such as junction formation means that forest hardening cannot be modeled, unless additional so-called '2.5D' constitutive rules are prescribed for short-range dislocation interactions. Here, results from three dimensional dislocation dynamics (3D DD) simulations in an FCC material are used to define new constitutive rules for short-range interactions and junction formation between dislocations on intersecting slip systems in 2D. The mutual strengthening effect of junctions on preexisting obstacles, such as precipitates or grain boundaries, is also accounted for in the model. The new '2.5D' DD model, with no arbitrary adjustable parameters beyond those obtained from lower scale simulation methods, is shown to predict athermal hardening rates, differences in flow behavior for single and multiple slip, and latent hardening ratios. All these phenomena are well-established in the plasticity of crystals and quantitative results predicted by the model are in good agreement with experimental observations.

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“…Use is made of M-DDP simulations that were previously carried out for planar crystals subjected to plane strain uniaxial compression [6]. The imposed boundary conditions do not preclude specimen rotation.…”

Section: Resultsmentioning

confidence: 99%

“…In [6] the crystal width H was varied between 0.2 and 12.8 µm such that a constant lengthto-width aspect ratio was maintained (= 3). A nominal strain rate of the order of 10 4 s −1 was applied to all crystals irrespective of their size.…”

Section: Resultsmentioning

confidence: 99%

“…The concept has also proven useful in interpretations of discrete dislocation dynamics (DD) simulations in the presence of macroscopic strain gradients [5]. In a recent study [6] the authors have developed a method to compute the GND density in the course of DD simulations directly. In particular, they showed a strong correlation between emerging GND density at sufficient resolution and size effects in the absence of macroscopic strain or stress gradients.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Evolution of geometrically necessary dislocation density from computational dislocation dynamics

Guruprasad¹,

Benzerga²

2009

IOP Conf. Ser.: Mater. Sci. Eng.

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Size effects under homogeneous deformation of single crystals: A discrete dislocation analysis☆

Cited by 96 publications

References 33 publications

Fundamental Differences in Mechanical Behavior between Two Types of Crystals at the Nanoscale

Fundamental Differences in Mechanical Behavior between Two Types of Crystals at the Nanoscale

Strain hardening in 2D discrete dislocation dynamics simulations: A new ‘2.5D’ algorithm

Evolution of geometrically necessary dislocation density from computational dislocation dynamics

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