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
Temperature-dependent size effects on the strength of Ta and W micropillars
Oscar Torrents Abad,Oscar Torrents Abad,Jeffrey M. Wheeler,Johann Michler,Andreas S. Schneider,Eduard Arzt,Eduard Arzt +6 more
TL;DR: In this paper, the size effect of focused ion beam-milled body-centered cubic (BCC) micropillars was systematically studied by performing high-temperature compression tests on Ta and W single crystal pillars at temperatures up to 400°C.
Journal ArticleDOI
Size effects under homogeneous deformation of single crystals: A discrete dislocation analysis
TL;DR: In this paper, the effect of size on micron scale crystal plasticity under conditions of macroscopically homogeneous deformation was investigated, and the authors showed a strong size-dependent dependence of flow strength and work-hardening rate at the micron-scale.
Journal ArticleDOI
The crack tip fields in strain gradient plasticity: the asymptotic and numerical analyses
TL;DR: In this article, the authors investigated asymptotic crack tip singular fields and their domain of validity for mode I cracks in solids characterized by the phenomenological strain gradient plasticity theory proposed by Fleck NA, Hutchinson JW.
Journal ArticleDOI
Scale dependence of mechanical properties of single crystals under uniform deformation
A. Amine Benzerga,N.F. Shaver +1 more
TL;DR: In this paper, the effect of size on micro-scale crystal plasticity under nominally uniform compression was investigated by using a physical representation of dislocation sources and obstacles in the undeformed samples.
Journal ArticleDOI
Flaw Tolerance in a Thin Strip Under Tension
Huajian Gao,Shaohua Chen +1 more
TL;DR: In this paper, the Griffith model and the Dugdale-Barenblatt model were used to show that flaw tolerance is achieved when the dimensionless number A n =ΓE/(S 2 H) is on the order of 1, where r is the fracture energy, E is the Young s modulus, S is the strength, and H is the characteristic size of the material.
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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