Effects of Grain Size

4 Key excerpts on "Effects of Grain Size"

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  eBook - ePub

  Advances in Multi-Physics and Multi-Scale Couplings in Geo-Environmental Mechanics

  • Francois Nicot, Olivier Millet(Authors)
  • 2017(Publication Date)
  • ISTE Press - Elsevier

    (Publisher)

  g follows:

  f g

  = k ×

  d g ζ

    [4.1]

  Where k and ζ are experimentally identified. In accordance with [JAE 67] , the crushing stress σg inducing grain breakage is calculated as follows:

  σ g

  =

  f g

  d g 2

  = k ×

  d g

  ζ − 2

    [4.2]

  Typical values for ζ are close to 1.5 for a large variety of rocks and, at the grain scale, brittle heterogeneous materials. Assuming that crack propagation in a brittle grain is a volumetric process, the survival probability

  Ps

  of a particle of volume V under a stress σ is assumed to obey a Weibull distribution:

  P s

  V σ

  = exp

  −

  V

  V 0

  ×

  σ

  σ 0

  m

  = exp

  −

  d

  d 0

  n d

  ×

  σ

  σ 0

  m

    [4.3]

  Where m is the Weibull modulus,

  nd

  is the geometric similarity coefficient (usually assumed to be equal to 3 for volumetric similarities) and

  σ0

  ,

  V0

  and

  d0

  are the characteristic strength, volume and size respectively. Equations [4.2] and [4.3] can be connected in order to relate the representative failure parameters ζ and m . For a given survival probability, m is then related to ζ by:

  ζ = 2 −

  n d

  m

    [4.4]

  With a central value of ζ close to 1.5, a typical value for the Weibull modulus m is about 6 if

  nd

  = 3.

  On the other hand, the literature provides many examples in which the friction angle of a soil mass decreases when the maximum grain size is increased. The latter can be seen as the consequence of the former process: particle breakage induces more contractancy due to the rearrangement of the fragments and, consequently, less shear strength resistance of the grain assembly. The challenge has then been to establish the extrapolation rules and their conditions of applicability. Based on an in-depth review of past experimental results, Frossard et al. [FRO 12] proposed such a predictive method and applied it to parabolic failure envelopes representative of crushable materials [DEM 77]

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  eBook - ePub

  Nanomaterials and Nanocomposites

  Synthesis, Properties, Characterization Techniques, and Applications

  • Rajendra Kumar Goyal(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  3   Effect of Particle Sizes on Properties of Nanomaterials  

  As discussed in Chapter 1 , the nanomaterials are materials which have at least one dimension of the order of 1–100 nm. Due to high-surface area to volume ratio, significant fraction of surface atoms, reduced grain size, and their significant volume fraction of grain boundaries and triple junctions, nanomaterials exhibit many unusual thermal, mechanical, electrical, chemical, and electrochemical properties compared to conventional polycrystalline or amorphous materials. In this chapter, the effect of particle or grain size on the thermal, mechanical, electrical, magnetic, optical, and catalytic properties of nanomaterials is discussed.

    3.1Thermal Properties 3.1.1Melting Point

  Melting point is the temperature when atoms, ions, or molecules of a crystalline material change their periodic ordered state to the disordered state. A number of studies reveal that the melting point of metals such as In, Sn, Pb, Bi, Cd, Al, Ag, and Au decreases with decreasing their size particularly below 30 nm. The melting initiates from the surface of the materials and is characterized by the increased mobility of the atoms or molecules in the top surface layers. The diffusion coefficient of these atoms approaches liquid-like values at temperatures much lower than the melting point of the bulk material [1 –6 ]. This is because of the high-surface area to volume ratio of the nanoparticles which in turn have high-surface energies; hence, the activation energy required for the melting of the surface atoms is lower than the bulk. An example of a decrease in melting point of aluminum (Al) as a function of Al clusters is shown in Figure 3.1 . There is a decrease in the melting point as the cluster size decreases. A reduction of 140°C has been reported for the Al clusters with radii of ∼ 2 nm [5 ].

  Figure 3.1

  Melting point as a function of Al cluster size, where T m is the melting point and R is the radii of Al cluster. (Reproduced from Lai S. L., Carlsson R. A., Allen L. H. 1998. Appl. Phys. Lett.

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  eBook - PDF

  Aluminium Alloys and Composites

  • Kavian Omar Cooke(Author)
  • 2020(Publication Date)
  • IntechOpen

    (Publisher)

  95 Section 2 Processing, Characterisation and Testing 97 Chapter 6 Effect of Grain Size on Superplastic Deformation of Metallic Materials Allavikutty Raja, Rengaswamy Jayaganthan, Abhishek Tiwari and Ch. Srinivasa Rakesh Abstract The superplastic deformation exhibited by metals with different grain sizes and their corresponding deformation mechanism influences the industrial metal-forming processes. The coarse-grained materials, which contain grain size greater than 20 μ m, exhibited superplastic deformation at high homologous temperature and low strain rate of the order of 10 − 4 s − 1 . Fine grain materials (1–20 μ m) are generally considered as favorable for superplastic deformation. They possess high-strain-rate sensitivity “m” value, approximately, equal to 0.5 at the temperature of 0.5 times the melting point and at a strain rate of 10 − 3 to 10 − 4 s − 1 . Ultrafine grains (100 nm to less than 1 μ m) exhibit superplasticity at high strain rate as well as at low temperature when compared to fine grain materials. It is attributed to the fact that both temperature and strain rates are inversely proportional to the grain size in Arrhenius-type superplastic constitute equation. The superplastic phenomenon with nano-sized grains (10 nm to less than 100 nm) is quite different from their higher-scale counterparts. It exhibits high ductility with high strength. Materials with mixed grain size distribution (bimodal or layered) are found to exhibit supe-rior superplasticity when compared to the homogeneous grain-sized material. The deformation mechanisms governing these superplastic deformations with different scale grain size microstructures are discussed in this chapter. Keywords: grain size, superplasticity, deformation mechanism, coarse-grained superplasticity, fine-grained superplasticity, ultrafine-grained superplasticity, nano-grained superplasticity, superplasticity of mixed grain sizes 1.

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  eBook - ePub

  Defect Structure and Properties of Nanomaterials

  Second and Extended Edition

  • J Gubicza(Author)
  • 2017(Publication Date)
  • Woodhead Publishing

    (Publisher)

  Chapter 7 Correlation Between Defect Structure and Mechanical Properties of Nanocrystalline Materials Abstract The defect-related mechanical properties of nanomaterials are overviewed. The influence of small grain size on plastic deformation mechanisms, strength, and ductility is discussed. The smaller the grain size in face-centered cubic metals, the higher the activity of twinning at the expense of dislocation glide, while hexagonal close-packed (hcp) materials behave contrarily. The relationship between the dislocation structure and the yield strength is studied in details. Above the grain size of ∼20 nm, the decrease of grain size is accompanied by an increase of yield strength and a decrease of ductility. The loss of ductility can be moderated by the incorporation of coarse grains into the nanocrystalline matrix. A combination of large strength with good ductility can be achieved with nanograins containing high density of twin boundaries. Below the grain size of ∼20 nm, the yield strength is found to decrease with the reduction of grain size, referred to as inverse Hall–Petch effect. The possible explanations of this phenomenon are discussed in details. Contrary to coarse-grained materials, viscous dislocation drag cannot be observed during high strain rate deformation of nanomaterials, since the acceleration of dislocations to very high velocities is hindered by the relatively large dislocation density and the small grain size. Keywords Dislocation density; Ductility; Grain size; Inverse Hall–Petch behavior; Partial dislocation; Strain rate; Twinning; Yield strength 7.1. Effect of Grain Size on Deformation Mechanisms in fcc and hcp Nanomaterials In conventional coarse-grained (CG) metallic materials, the deformation is mainly controlled by the motion of full lattice dislocations in the grain interiors

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