Size effects in uniaxial deformation of single and polycrystals: a discrete dislocation plasticity analysis

Balint, D.; Deshpande, V.S.; Needleman, A.; Giessen, van der Erik

doi:10.1088/0965-0393/14/3/005

Cited by 103 publications

(96 citation statements)

References 22 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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“…For the larger, 1.0µm and 2.0µm grains, stress-strain recovery shows a linear response until the initial nucleation of dislocations from sources followed by stress relief at approximately 0.1% strain. Similar simulation behavior showing stress relaxation has been presented elsewhere (Deshpande, 2001;Balint, 2006). After relaxation, depending on the specific material properties considered, the grain behavior either exhibits strain hardening with additional applied load or fluctuation about a constant stress state.…”

Section: Discrete Dislocation Plasticity Formulation and Resultssupporting

confidence: 69%

Multiscale Modeling of Structurally-Graded Materials Using Discrete Dislocation Plasticity Models and Continuum Crystal Plasticity Models

Saether

Hochhalter²,

Glaessgen³

2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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A multiscale modeling methodology that combines the predictive capability of discrete dislocation plasticity and the computational efficiency of continuum crystal plasticity is developed. Single crystal configurations of different grain sizes modeled with periodic boundary conditions are analyzed using discrete dislocation plasticity (DD) to obtain grain size-dependent stress-strain predictions. These relationships are mapped into crystal plasticity parameters to develop a multiscale DD/CP model for continuum level simulations. A polycrystal model of a structurally-graded microstructure is developed, analyzed and used as a benchmark for comparison between the multiscale DD/CP model and the DD predictions. The multiscale DD/CP model follows the DD predictions closely up to an initial peak stress and then follows a strain hardening path that is parallel but somewhat offset from the DD predictions. The difference is believed to be from a combination of the strain rate in the DD simulation and the inability of the DD/CP model to represent non-monotonic material response.

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“…Calculations are conducted for three realisations of obstacle and source distributions and the tension/compression curves presented are averages over these three realisations. The absence of a clear specimen size effect on the tension/compression response is in contrast to the results previously reported by Deshpande et al [13] and Balint et al [35]. This difference is rationalised as follows.…”

Section: Uniaxial Tensile/compressive Response Of the Crystalcontrasting
confidence: 66%

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals
Irani
¹
,
Remmers
²
,
Deshpande
³

2017
Acta Mech. Sin.
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Plastic size effects in single crystals are investigated by using finite strain and small strain discrete dislocation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip systems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete dislocation plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. However, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bending stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations. B Vikram S. Deshpande

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Size effects in uniaxial deformation of single and polycrystals: a discrete dislocation plasticity analysis

Cited by 103 publications

References 22 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

Multiscale Modeling of Structurally-Graded Materials Using Discrete Dislocation Plasticity Models and Continuum Crystal Plasticity Models

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

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