Nanomaterials Mechanical Properties

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1 Nanomaterials Mechanical Properties Observations/predictions : lower elastic moduli than for conventional grain size materials (30-50%) very high hardness and strength values for nanocrystalline pure metals (~ 10 nm grain size) are 2 to 7 times higher than those of larger grained (>1 µ m) metals a negative Hall-Petch slope, i.e., decreasing hardness with decreasing grain size in the nanoscale grain size regime ductility-perhaps superplastic behavior-at low homologous temperatures in brittle ceramics or intermetallics with nanoscale grain sizes, believed due to diffusional deformation mechanisms

2 Hall- Petch Hardness of Cu H - H Nanocrystalline Copper Conventional Copper (nm) Arzt, MPI Stuttgart

3 0 Lattice defects Cracks Surface Crystalline structure Lattice defects Prof.. Raabe, Max-Planck-Institut für Eisenforschung Phase diagramme

4 Classical effect of grain size on yield stress ( τ) Hall- Petch Effect of pores, impurities khp τ = khp = constant, dislocation pile-up Classical Hall Petch I II III?

5 Limits to Hall-Petch behaviour: dislocation curvature vs. grain size d d τ = k HP d < (a) d ~ (b) iameter of islocation loop: A clear limit for the occurrence of dislocation plasticity in a poly-crystal is given by the condition that at least one dislocation loop must fit into average grain Arzt, MPI Stuttgart T T d d 2 Gb 2 : Line tension

6 Limit to Hall Petch: The characteristic length, the loop diameter must now be compared with the grain size as the relevant size parameter d (τ ) = 2 H-P: Td Gb τ = = b lnτ = ln Gb ln 1 lnτ = ln khp ln 2

7 T r 1 0 d 2 Gb = ln 4π r r 1 0 : upper cut-off distance (several µ m) r : lower cut-off distance (2-10 b) For nanomaterials, r 1 = T d = 2 Gb ln 4π r 0 τ = Gb 2π ln r 0 ρ Small grains: dislocation source in the grain boundary dislocation Gb τ ln 2π 1 1 ; Obstacle spacing L ρ r 0

8 Simulation van Swygenhoven, PSI

9 Ni, d = 12 nm van Swygenhoven, PSI

10 Ni, d = 12 nm van Swygenhoven, PSI

11 Ni, d = 12 nm van Swygenhoven, PSI

12 iffusional creep as a size effect iffusional creep is driven by gradients in normal tractions on grain boundaries (a). Fine arrows delineate the paths for transport of matter. This mechanism ceases to operate (b) once a grain boundary dislocation loop no longer fits into a grain facet (d > ). τ = 2 ε kt C1 v Ω τ = 3 ε kt C2δ b b Ω

13 One can note that in very small grains the rate of creep may no longer be controlled by the diffusion step [as is tacitly assumed in equations but by the deposition and removal of atoms at the grain boundaries. Ashby have shown that for such interface-controlled diffusional creep the grain size dependence is much weaker τ = ε ktgbb C4eff Ω 1 2 1/ 2 This result was obtained by modeling the interface reaction as the climb motion of an array of grain-boundary dislocations. Here eff is an effective diffusivity, b b the Burgers vector of a boundary dislocation and C 4 numerical constant.

14 Metals as Nanocomposite Bulk/Grain boundary H = (1 f ) H + fh f = d ( d δ ) 3 / d G GB 3 3 H = H + k d G 0G G 1/ 2 H = H + k d GB 0GB GB 1/ 2 υd ln 3 3 d δ d d δ r0 H = H0 G + k G + d 3 3 d d υdc ( ) 3 ( ) 1/2 ln r 0

15 Metals as Nanocomposite Bulk/Grain boundary

16 Ceramics Nanocomposites Strength and toughness of Al 2 O 3 /SiC and SiAlON/SiC nanocomposites as a function of SiC content 1000 Strength (MPa) Toughness (MPaxm 1/2) SiC content (vol %) C.E. Borsa, S. Jiao, R.I. Todd and R.J. Brook, J. Microscopy 177 (1994) 305 [ii] R. W. avidge, R.J. Brooks, F. Cambier, M. Poorteman, A. Leriche,. O Sullivan, S. Hampshire and T. Kennedy, J. Eur. Ceram. Soc. 16 (1996) 799

17 Mechanism Zener grain boundary pinning mechanism Reduction in processing flaw size Comment Matrix grain sizes are drastically reduced (typical for nanocomposites) Strength increase can be fully explained by observed change in processing flaw type (careful processing is very important) Crack eflection (Kmechanism) Thermal expansion mismatch (grain boundary strengthening) Average internal stresses (grain boundary strengthening) Local stress distribution (grain boundary strengthening) Cracks seem to be reflected at SiC particles (importance for toughening is unclear) Fracture mode is changed to transcrystalline if (eg. For Al 2 O 3 /SiC) Average tensile stresses in matrix if (toughness is reduced) Local compressive stresses in matrix grain boundaries if (can explain change in fracture mode)

18 Critical flaw size reduction (c-mechanism) Zener grain size boundary pinning: R 3 r V 4 f Reduction in processing flaw size: Hot pressing,hip Crack healing (annealing treatment): compressive stress around the nanoparticles in the matrix

19 Thermal expansion mismatch Crack deflection ( ) T T particle matrix dt * plastic α = α α 0 σ = T 1+ v 2E m m * α 1 2v + E p p 3 3 σ T r σ T = σ r T σ r T 2 = x r x

20 Average internal stresses * σ p 2(1 V f ) β α = E (1 V )( β + 2)(1 + v ) + 3 βv (1 v ) m f m f m * σ 2V f β α m = E (1 V )( β + 2)(1 + v ) + 3 βv (1 v ) m f m f m Thermoelastical data for matrix and nanophase E[Mpa] ν α[10-6 K -1 ] Al 2 O Si 3 N MgO TiN ~470 ~ SiC v β = 1 2v Average residu al stress [MP a] m p E. E p m <σm> <σp> Volume fraction Vf SiC particles in Alumina

21 Local stress distribution z 600 nm 300 nm x y Fig. 19. Configuration for the stress distribution model in Fig. 20.