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
Effect of thermo-mechanical cycling on the microstructure and strength of lath martensite in the weld CGHAZ of HSLA steel
TL;DR: In this article, the effect of thermo-mechanical cycling on the microstructure and strength of lath martensite in the weld Coarse Grained Heat Affected Zone (CGHAZ) was investigated.
Journal ArticleDOI
The effect of indenter angle on the microindentation hardness
TL;DR: In this article, the Nix-Gao relation between the microindentation hardness and indentation depth also holds for other indenter angles, and the effect of friction is negligible for relatively flat indenters (e.g. Berkovich indenter), but may be significant for sharp indenters.
Journal ArticleDOI
Determination of the matrix in situ flow stress of a continuous fibre reinforced metal matrix composite using instrumented indentation
TL;DR: In this paper, the authors employed nanoindentation to determine the flow stress of a pure aluminium matrix of a composite reinforced with continuous alumina fibres, which depends on the geometry of the indenter and can be deduced using the reverse method established by Bucaille et al.
Journal ArticleDOI
Solute hydrogen and hydride phase implications on the plasticity of zirconium and titanium alloys: a review and some recent advances.
TL;DR: Under tensile loading, it was showed that hydrides enhance the hardening process in relation with internal stress due to strain incompatibilities between the Zr and Ti matrix and hydride phases.
Journal ArticleDOI
Latest Developments in Modeling and Characterization of Joining Metal Based Hybrid Materials
TL;DR: Khoddam et al. as mentioned in this paper reviewed the theoretical and experimental studies of the interface inside several metal-based composites, including interface bonding's critical parameters, characterization techniques of joining processes, potential applications, and their future perspectives.
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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