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
More filters
Journal ArticleDOI
New insights into the indentation size effect in silicate glasses
TL;DR: In this paper, the authors performed microindentation on silica and soda lime silicate glasses over a wide range of maximum forces and extracted the Vickers hardness by the Oliver and Pharr method.
Journal ArticleDOI
Microstructure-based fatigue modelling with residual stresses: Prediction of the microcrack initiation around inclusions
TL;DR: In this article, a microstructure-based modeling approach is proposed to account for the effects of residual stresses induced by the rapid cooling process on the fatigue crack initiation behavior of a martensitic steel, for which the majority of the fatigue cracks are formed around the calcium aluminate inclusions in experiments.
Journal ArticleDOI
Atomic-scale yield and dislocation nucleation in KBr
TL;DR: In this paper, the authors used atomic force microscopy (AFM) in ultrahigh vacuum to study the deformation of a KBr(100) surface and found that dislocation nucleation is associated with the formation of monatomic terraces.
Book ChapterDOI
Chapter 60 Long-Range internal stresses in deformed single-phase materials: The composite model and its consequences
H. Mughrabi,T. Ungár +1 more
TL;DR: In this paper, the authors present the experimental observations that proved the existence of deformation-induced long-range internal stresses in deformed metals and that lead to the formulation of the so-called composite model of crystal plasticity, and the consequences.
Journal ArticleDOI
Incipient plasticity and surface damage in LiTaO3 and LiNbO3 single crystals
TL;DR: LiTaO3 and LiNbO3 anisotropic single crystal samples were investigated using nanoindentation techniques and focused ion beam-based sub-surface analyses as mentioned in this paper.
References
More filters
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.
Related Papers (5)
An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments
Warren C. Oliver,George M. Pharr +1 more