The Role of Indentation Depth on the Measured Hardness of Materials

Guzman, M.; Neubauer, G.; Flinn, P. A.; Nix, William D.

doi:10.1557/proc-308-613

Cited by 212 publications

(79 citation statements)

References 6 publications

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“…The strong size-dependence evident at the micron scale in Fig. 1 and in data on other metals (Atkinson, 1995, Ma andClarke, 1995;De Guzman et al, 1993;McElhaney et al, 1998;Poole et al, 1996) constitutes one of the compelling pieces of experimental evidence for the need of an extension of plasticity theory to the micron scale. Here and throughout this paper, the term`micron scale' will be used to refer to the range which extends roughly from a fraction of a micron to tens of microns.…”

mentioning

confidence: 88%

Plasticity at the micron scale

Hutchinson

2000

International Journal of Solids and Structures

352

138

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Over a scale which extends from about a fraction of a micron to tens of microns, metals display a strong sizedependence when deformed non uniformly into the plastic range: smaller is stronger. This eect has important implications for an increasing number of applications in electronics, structural materials and MEMS. Plastic behavior at this scale cannot be characterized by conventional plasticity theories because they incorporate no material length scale and predict no size eect. While micron sized solid objects are too small to be characterized by conventional theory, they are usually too large to be amenable to analysis using approaches presently available based on discrete dislocation mechanics. The relatively large numbers of dislocations governing plastic deformation at the micron scale motivate the development of a continuum theory of plasticity incorporating size-dependence. Strain gradient theories of plasticity have been developed for this purpose. The motivation and potential for such theories will be discussed. Important open issues surrounding the foundations of strain gradient plasticity will also be addressed and a few critical experiments identi®ed. #

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mentioning

confidence: 88%

Plasticity at the micron scale

Hutchinson

2000

International Journal of Solids and Structures

352

138

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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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“…The measured indentation hardness of metallic materials typically increases by a factor of two or three as the indentation depth decreases to submicrons, that is, smaller is harder. [1][2][3][4][5][6][7][8][9][10] Based on the Taylor dislocation model 11,12 and a model of geometrically necessary dislocations (GND) underneath a sharp indenter tip shown in the inset of Fig. 1, Nix and Gao 13 established the following relation between the microindentation hardness H and the indentation depth h for a sharp, conical indenter…”

Section: Introductionmentioning

confidence: 99%

Indenter tip radius effect on the Nix–Gao relation in micro- and nanoindentation hardness experiments

et al. 2004

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Nix and Gao established an important relation between microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments (indentation depths in the micrometer range), but it does not always hold in nanoindentation experiments (indentation depths approaching the nanometer range). We have developed a unified computational model for both micro-and nanoindentation in an effort to understand the breakdown of the Nix-Gao relation at indentation depths approaching the nanometer scale. The unified computational model for indentation accounts for various indenter shapes, including a sharp, conical indenter, a spherical indenter, and a conical indenter with a spherical tip. It is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The unified computational model for indentation indeed shows that the Nix-Gao relation holds in microindentation with a sharp indenter, but it does not hold in nanoindentation due to the indenter tip radius effect.

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The Role of Indentation Depth on the Measured Hardness of Materials

Cited by 212 publications

References 6 publications

Plasticity at the micron scale

Plasticity at the micron scale

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

Indenter tip radius effect on the Nix–Gao relation in micro- and nanoindentation hardness experiments

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