Journal ArticleDOI
Indentation size effects in crystalline materials: A law for strain gradient plasticity
William D. Nix,Huajian Gao +1 more
TLDR
In this article, the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations, which leads to the following characteristic form for the depth dependence of the hardness: H H 0 1+ h ∗ h where H is the hardness for a given depth of indentation, h, H 0 is a characteristic length that depends on the shape of the indenter, the shear modulus and H 0.Abstract:
We show that the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations. The model leads to the following characteristic form for the depth dependence of the hardness: H H 0 1+ h ∗ h where H is the hardness for a given depth of indentation, h, H0 is the hardness in the limit of infinite depth and h ∗ is a characteristic length that depends on the shape of the indenter, the shear modulus and H0. Indentation experiments on annealed (111) copper single crystals and cold worked polycrystalline copper show that this relation is well-obeyed. We also show that this relation describes the indentation size effect observed for single crystals of silver. We use this model to derive the following law for strain gradient plasticity: ( σ σ 0 ) 2 = 1 + l χ , where σ is the effective flow stress in the presence of a gradient, σ0 is the flow stress in the absence of a gradient, χ is the effective strain gradient and l a characteristic material length scale, which is, in turn, related to the flow stress of the material in the absence of a strain gradient, l ≈ b( μ σ 0 ) 2 . For materials characterized by the power law σ 0 = σ ref e 1 n , the above law can be recast in a form with a strain-independent material length scale l. ( builtσ σ ref ) 2 = e 2 n + l χ l = b( μ σ ref ) 2 = l ( σ 0 σ ref ) 2 . This law resembles the phenomenological law developed by Fleck and Hutchinson, with their phenomenological length scale interpreted in terms of measurable material parametersbl].read more
Citations
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Journal ArticleDOI
The capillary force in micro- and nano-indentation with different indenter shapes
Shaohua Chen,Ai Kah Soh +1 more
TL;DR: In this paper, the influence of the indenter shapes and various parameters on the magnitude of the capillary force is studied on the basis of models describing the wet adhesion of indenters and substrates joined by liquid bridges.
Journal ArticleDOI
Study of microindentation hardness of different planes of gadolinium calcium oxyborate single crystals
K. Sangwal,A. Kłos +1 more
TL;DR: In this article, the microhardness HV of gadolinium calcium oxyborate single crystals has been investigated on the planes of different orientations as a function of applied load and indenter orientation.
Journal ArticleDOI
A Discontinuous Elastic Interface Transfer Model of Thin Film Nanoindentation
B. Zhou,Barton C. Prorok +1 more
TL;DR: In this paper, a model of thin film indentation that accounts for an apparent discontinuity in elastic strain transfer at the film/substrate interface was developed, whereby, separate weighting factors were applied to account for the influence of the substrate in strain developed in the film and vice-versa.
Irradiation hardening of ODS ferritic steels under helium implantation
TL;DR: In this article, the authors investigated the nano-indentation of ODS ferritic steels after multi-energy Heion implantation, or after irradiation with energetic heavy ions including Xe and Bi-ions.
Journal ArticleDOI
Nano-scale elastic-plastic properties and indentation-induced deformation of single crystal 4H-SiC.
TL;DR: The nanoscale elastic-plastic response of single crystal 4H-SiC has been investigated by nanoindentation with a Berkovich tip, revealing that slippage occurred in the (0001) plane after indentation.
References
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Journal ArticleDOI
The deformation of plastically non-homogeneous materials
TL;DR: The geometrically necessary dislocations as discussed by the authors were introduced to distinguish them from the statistically storages in pure crystals during straining and are responsible for the normal 3-stage hardening.
Journal ArticleDOI
Strain gradient plasticity: Theory and experiment
TL;DR: In this paper, a deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening, which is a non-linear generalization of Cosserat couple stress theory.
Journal ArticleDOI
A phenomenological theory for strain gradient effects in plasticity
TL;DR: In this paper, a strain gradient theory of plasticity is introduced, based on the notion of statistically stored and geometrically necessary dislocations, which fits within the general framework of couple stress theory and involves a single material length scale l.
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An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments
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