Plastic strain and strain gradients at very small indentation depths

Tymiak, N. I.; Kramer, Donald E.; Bahr, David F.; Wyrobek, Thomas J.; Gerberich, William W

doi:10.1016/s1359-6454(00)00378-5

Cited by 161 publications

(84 citation statements)

References 23 publications

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“…This indentation size effect (ISE) has been explained using the concept of geometrically necessary dislocations (GNDs) and strain gradients. [4][5][6][7][8][9][10][11][12][13][14][15][16][17] According to this picture, the hardness increases with decreasing depth of indentation because the total length of geometrically necessary dislocations forced into the solid by the self-similar indenter scales with the square of the indentation depth, while the volume in which these dislocations are found scales with the cube of the indentation depth. This leads to a geometrically necessary dislocation density that depends inversely on the depth of indentation.…”

Section: Introductionmentioning

confidence: 99%

A search for evidence of strain gradient hardening in Au submicron pillars under uniaxial compression using synchrotron X-ray microdiffraction

et al. 2008

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When crystalline materials are mechanically deformed in small volumes, higher stresses are needed for plastic flow. This has been called the "Smaller is Stronger" phenomenon and has been widely observed. Various size-dependent strengthening mechanisms have been proposed to account for such effects, often involving strain gradients. Here we report on a search for strain gradients as a possible source of strength for single-crystal submicron pillars of gold subjected to uniform compression, using a submicron white-beam (Laue) x-ray diffraction technique. We have found both before and after uniaxial compression, no evidence of either significant lattice curvature or sub-grain structure. This is true even after 35% strain and a high flow stress of 300 MPa were achieved during deformation. These observations suggest that plasticity here is not controlled by strain gradients or sub-structure hardening, but rather by dislocation source starvation, wherein smaller volumes are stronger because fewer sources of dislocations are available. Text only2

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Section: Introductionmentioning

confidence: 99%

A search for evidence of strain gradient hardening in Au submicron pillars under uniaxial compression using synchrotron X-ray microdiffraction

et al. 2008

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“…Various authors who reported about such experiments [5][6][7][8][9][10] observed that for most annealed single-crystals, such as Cu, W, Fe, Al, or NiAl, distinct pile-up patterns occur only in certain directions around the indentation depending on the crystallographic orientation of the single-crystal [5][6][7][8][9][10]. Very detailed atomistic simulations about the incipient stages of nanoindentation in face centered cubic single crystals were recently conducted by Li et al [11] and Van Vliet et al [12].…”

Section: Introductionmentioning

confidence: 99%

Orientation dependence of nanoindentation pile-up patterns and of nanoindentation microtextures in copper single crystals

Wang¹,

Raabe²,

Klüber³

et al. 2004

Acta Materialia

264

149

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“…Unfortunately, in situ identification of the spatial location and character of the first dislocation is not possible, 12,13 which precludes direct comparison with experiment. Although experimental loaddisplacement results are readily available, 14 the current method only yields the characteristics of the initial dislocation in a perfect crystal, rather than predicting the full plastic behavior involving many dislocations. However, our analysis clearly demonstrates that DFT-and EAM-based calculations lead to sharply different dislocation emission results.…”

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confidence: 99%

“…The first dislocations obtained with both the EAM and DFT-LQC lie within the upper bound provided by the elastic-plastic boundary obtained experimentally for Al(100) via atomic force microscopy. 14 In closing, some of the limitations and possible extensions of the method are noteworthy. The Cauchy-Born rule, as used in the present implementation of the method, does not permit the description of lattice defects such as dislocations.…”

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confidence: 99%

Density-functional-theory-based local quasicontinuum method: Prediction of dislocation nucleation

et al. 2004

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We introduce the density functional theory (DFT) local quasicontinuum method: a first principles multiscale material model that embeds DFT unit cells at the subgrid level of a finite element computation. The method can predict the onset of dislocation nucleation in both single crystals and those with inclusions, although extension to lattice defects awaits new methods. We show that the use of DFT versus embedded-atom method empirical potentials results in different predictions of dislocation nucleation in nanoindented face-centered-cubic aluminum. In this paper we establish the feasibility of embedding density functional theory (DFT) into large-scale macroscopic finite-element calculations. The embedding takes place at the subgrid level and exploits the Cauchy-Born hypothesis, 1 whereby the local deformation computed at a quadrature point of the finite-element grid is applied to an infinite crystal lattice, whose energy and state of stress is then evaluated with DFT. We call our method DFT-LQC in reference to the local quasicontinuum (LQC) or Cauchy-Born approach, 2 in anticipation of a future nonlocal extension of the method.The impetus for multiscale descriptions of materials such as DFT-LQC derives from two main sources. From a topdown viewpoint, empirical constitutive models which remain reliable under extreme conditions of pressure, deformation, and deformation rate are often not available for use in largescale engineering simulations. Alternately, it is often desirable to extend the applicability of fundamental theories to engineering spatial and temporal scales. Methods such as DFT-LQC meet these demands by supplying a fundamental description of the material and embedding this description into large-scale engineering simulations.The LQC method, including extensions dealing with complex lattices, has been extensively used by Tadmor et al.,3,4 who used the method to study the nanoindentation of silicon and to analyze the process of polarization switching in PbTiO 3 . Tadmor et al. based their subgrid atomistic calculations on empirical potentials or effective Hamiltonians fitted to first principles calculations.The chief contribution of the present work is to establish the feasibility of using DFT, as opposed to empirical or effective interatomic potentials, as the fundamental description of materials such as aluminum in LQC calculations. Since DFT is a first-principles theory (see Ref. 5, and references therein for background), it may be expected to result in increased fidelity of the calculations, especially when the material is subject to an environment where the empirical potentials were not calibrated. A case in point is provided by nanoindentation, which induces high pressures and deformations under the indenter, even in the elastic range. Indeed, we show that the use of DFT versus embedded-atom method (EAM) empirical potentials results in vastly different predictions of dislocation nucleation in nanoindented facecentered-cubic (fcc) aluminum.The general DFT-LQC method consists of embedding DFT calcul...

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Plastic strain and strain gradients at very small indentation depths

Cited by 161 publications

References 23 publications

A search for evidence of strain gradient hardening in Au submicron pillars under uniaxial compression using synchrotron X-ray microdiffraction

A search for evidence of strain gradient hardening in Au submicron pillars under uniaxial compression using synchrotron X-ray microdiffraction

Orientation dependence of nanoindentation pile-up patterns and of nanoindentation microtextures in copper single crystals

Density-functional-theory-based local quasicontinuum method: Prediction of dislocation nucleation

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