Dislocation-Based Deformation Mechanisms in Metallic Nanolaminates
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cles in a crystal is in the micron ränge, the continuum Hall-Petch strengthening may be worked out in order of magnitude by considering the simplest possible case, as outlined in Figure la, with straightedge dislocations piled up against an interface which resists the leading dislo cation with a "barrier stress" of r*. Dislo cations are assumed to glide on the slip plane, provided that a resolved shear stress T0 is reached on the plane. The TU has many c o m p o n e n t s , i n c l u d i n g a lattice resistance (Peierls stress), solid Solution effects, and precipitation hard ening. The n u m b e r of dislocations at one end of the pileup is approximated by N = TTh'(T — r0)/C'b,x where T is the re solved shear stress across the slip plane, b is the unit slip distance (or Burgers vector magnitude) provided by a Single dis location, and G' = G/(l — v), where G is the elastic shear modulus, and v is Poisson's ratio. At the point when the leading dislocation is just able to cross the inter face, N(T — T0) = T*. If N is eliminated be tween these expressions, the Hall-Petch equation,
Introduction The appeal of nanolayered materials from a mechanical viewpoint is that, in principle, plastic deformation can be confined to small volumes of material by Controlling both the frequency and magnitude of obstacles to dislocation motion. As we shall see, the spacing of obstacles can be used to impart large plastic anisotropy and work hardening. However, how strong can such materials be made as layer thickness (and therefore obstacle spacing) is decreased to the nanoscale level? In perspective, large, micron-scale, polycrystalline materials generally display improved yield strength (and fracture toughness) as grain size is decreased. This behavior at the micron scale can be explained via modeis that are built on two assumptions: (1) the strength of ob stacles to crystal slip is sufficiently large to require pileups of numerous dislocations in order to slip past them; and (2) the strength of such obstacles does not change, even if their spacing is decreased. The modeling presented here shows that these assumptions may break down at the nanometer scale. The result is that there is a critical layer thickness in the nanometer ränge, below which improvement in strength does not occur. Our discussion to follow briefly outlines a more macroscopic, micron-scale approach to determine yield strength, and then contrasts that with a sequence of events leading up to yield in nanolay ered materials. We also address whether
MRS BULLETIN/FEBRUARY 1999
nanoscale materials are expected to exhibit more uniform or coarse slip than micron-scale materials. Finally, a semi quantitative model of yield strength is developed which requires, as input, the strength of an interface to crystal slip transmission across it. We discuss several contributions to the interfacial strength and apply the theory to demonstrate a peak in strength for a 50 vol% Cu-50 vol% Ni multilayered sample.
The Continuum Approach at the Micron Scale When the distance /;'
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