Crystal Elasticity

2Macroscopic Elasticity: Dimensionless Representation and Simplification

Crystal elasticity covers a wide range of stiffnesses. For example, for pure metals at ambient temperature, Young’s modulus of a polycrystal varies by about 20 GPa for lead and over 400 GPa for tungsten.

Therefore, comparing the elasticity of all these types of crystals may seem impossible, but if it is likely to bring a certain consistency, this can be used to classify all the crystals having the same symmetry.

The starting point of this comparison is obviously a dimensionless representation of elasticity. This phenomenological approach can be found in the literature, based on a representation of ratios of elastic constants. A first study (Ledbetter 2007) is cited here, grouping metals with face-centered cubic symmetry, as well as transition metals (actinides and lanthanides) of hexagonal symmetry in a Blackman diagram: C₁₂/C₁₁ versus C₄₄/C₁₁. The various types of crystals are classified on curves parameterized by Zener anisotropy. These studies were then resumed (Paszkiewicz and Wolski 2007) with another type of representation, Every diagrams (Every and Stoddart 1985), using other ratios of constants.

This chapter proposes a similar study which optimizes the type of dimensionless representation that can be used to describe orthotropic symmetries in the simplest possible manner.

2.1. Cubic symmetry: cc and fcc metals

As already noted, due to their high symmetry, cubic monocrystals have only three independent ...