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
Discrete dislocation simulation of nanoindentation: the effect of moving conditions and indenter shape
H.G.M. Kreuzer,R. Pippan +1 more
TL;DR: In this paper, the nominal hardness of the material in the model is mainly influenced by the critical shear stress necessary to activate the dislocation sources, whereas the level of decrease of the hardness at small indentation depth is dependent on the lattice friction stress for dislocation movement.
Journal ArticleDOI
Microindentation study of Ti–6Al–4V alloy
TL;DR: In this paper, a microindentation constitutive equation that described the stress as a function of the strain was proposed through dimensional analysis, and the finite element simulation results showed that the predicted computational indentation data from developed constitutive equations can track the microinventation experimental data of Ti-6Al-4V alloy.
Journal ArticleDOI
Nanoindentation initiated dislocations in barium titanate (BaTiO3)
T. Scholz,K. K. McLaughlin,F. Giuliani,William Clegg,F.J. Espinoza-Beltrán,Michael V. Swain,Gerold A. Schneider +6 more
TL;DR: In this paper, a spheroconical shaped indenter together with observations using atomic force microscopy and focussed ion beam cross sections for transmission electron microscopy (TEM) of the contact areas was used to show that dislocation induced deformation also occurs during nanoindentation of BaTiO3.
Journal ArticleDOI
A computational study of a model of single-crystal strain-gradient viscoplasticity with an interactive hardening relation
TL;DR: In this paper, the behavior of a model of single-crystal strain-gradient viscoplasticity is investigated, which is an extension of a rate-independent version, and includes a new hardening relation that has recently been proposed in the small-deformation context (Gurtin and Reddy, 2014).
Journal ArticleDOI
Deformation-induced thermally activated grain growth in nanocrystalline nickel
M.J.N.V. Prasad,Atul H. Chokshi +1 more
TL;DR: Grain growth during indentation at low temperatures has been taken to imply that grain growth is largely stress induced and athermal in nanometals as mentioned in this paper, however, experiments on electrodeposited nano-Ni indicate clearly that the load required for grain growth decreases with an increase in temperature.
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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