Mechanical properties of nanocrystalline materials

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].

Indentation size effects in crystalline materials: A law for strain gradient plasticity

Many two-phase alloys work-harden much faster than do pure single crystals. This is because the two phases are not equally easy to deform. One component (often dispersed as small particles) deforms less than the other, or not at all, so that gradients of deformation form with a wavelength equal to the spacing between the phases or particles. Such alloys are ‘plastically non-homogeneous’, because gradients of plastic deformation are imposed by the microstructure. Dislocations are stored in them to accommodate the deformation gradients, and so allow compatible deformation of the two phases. We call these ‘geometrically-necessary’ dislocations to distinguish them from the ‘statistically-stored’ dislocations which accumulate in pure crystals during straining and are responsible for the normal 3-stage hardening. Polycrystals of pure metals are also plastically non-homogeneous. The density and arrangement of the geometrically-necessary dislocations can be calculated fairly exactly and checked by electr...

The deformation of plastically non-homogeneous materials

Dislocation theory is used to invoke a strain gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocation. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening. The theory is a non-linear generalization of Cosserat couple stress theory. Tension and torsion experiments on thin copper wires confirm the presence of strain gradient hardening. The experiments are interpreted in the light of the new theory.

Strain gradient plasticity: Theory and experiment

https://www.tcd.ie/Physics/people/Graham.Cross/SF%20Poster%202011/Schuh-ActaMater07-Mechanical%20behaviour%20of%20amorphous%20alloys.pdf

Mechanical behavior of amorphous alloys

Diffusion-accommodated flow and superplasticity

The problem of sliding at a nonplanar grain boundary is considered in detail. The stress field, and sliding displacement and velocity can be calculated at a boundary with a shape which is periodic in the sliding direction (a wavy or stepped grain boundary): a) when deformation within the crystals which meet at the boundary is purely elastic, b) when diffusional flow of matter from point to point on the boundary is permitted. The results give solutions to the following problems. 1) How much sliding occurs in a polycrystal when neither diffusive flow nor dislocation motion is possible? 2) What is the sliding rate at a wavy or stepped grain boundary when diffusional flow of matter occurs? 3) What is the rate of diffusional creep in a polycrystal in which grain boundaries slide? 4) How is this creep rate affected by grain shape, and grain boundary migration? 5) How does an array of discrete particles influence the sliding rate at a grain boundary and the diffusional creep rate of a polycrystal? The results are compared with published solutions to some of these problems.

M.F. Ashby

Papers

The deformation of plastically non-homogeneous materials

Diffusion-accommodated flow and superplasticity

On grain boundary sliding and diffusional creep

A first report on deformation-mechanism maps

Intergranular fracture at elevated temperature