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
A micromechanics-based strain gradient damage model for fracture prediction of brittle materials – Part I: Homogenization methodology and constitutive relations
TL;DR: In this article, a self-consistency with respect to the choice of the RVE has been established for the strain gradient constitutive relation for heterogeneous materials with micro-cracks.
Journal ArticleDOI
High-entropy monoborides: Towards superhard materials
TL;DR: In this paper, single-phase high-entropy monoborides (HEMBs) of the CrB prototype structure have been synthesized for the first time and the load-dependent hardness of (V0.2Cr 0.2Nb 0.5W 0.98 N) was measured to be ~22.
Journal ArticleDOI
A strain gradient-strengthening law for particle reinforced metal matrix composites
Lanhong Dai,Z. Ling,Yilong Bai +2 more
TL;DR: In this article, a strain gradient strengthening law is developed in which the role of Ashby's geometrically-necessary dislocation idea is emphasized, and the essence of the strengthening-particle size effect in two-phase MMCp is clearly revealed.
Journal ArticleDOI
Model and experiments on strain gradient hardening in metallic glass
TL;DR: In this paper, a dislocation-based strain gradient indentation model was proposed and good agreement was obtained, while an alternate strain gradient plasticity indentation was developed based on cluster theory of yield for glassy metal.
Journal ArticleDOI
The origins of electromechanical indentation size effect in ferroelectrics
TL;DR: In this article, the authors argue that flexoelectricity is the coupling of strain gradients to polarization and exists in both ordinary and nonferroelectric dielectrics.
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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