Microstructure-Properties - Materials Science and Engineering

More documents

Recommendations

Info

4 Objective Linear Ferromagnets Non-linear properties Electric. Conduct. Tensors Elasticity Symmetry Elasticity • Elasticity: example of a property that requires tensors to describe it fully. • Even in cubic metals, a crystal is quite anisotropic. The [111] in many cubic metals is stiffer than the [100] direction. • Even in cubic materials, 3 numbers/coefficients/moduli are required to describe elastic properties; isotropic materials only require 2. • Familiarity with Miller indices is assumed.
5 Objective Linear Ferromagnets Non-linear properties Electric. Conduct. Tensors Elasticity Symmetry Elastic Anisotropy: 1 • First we restate the linear elastic relations for the properties Compliance, written S, <strong>and</strong> Stiffness, written C (!), which connect stress, σ , <strong>and</strong> strain, ε. We write it first in vector-tensor notation with “:” signifying inner product (i.e. add up terms that have a common suffix or index in them): σ = C:ε ε = S:σ • In component form (with suffixes), σ ij = C ijkl ε kl ε ij = S ijkl σ kl
Page 1 and 2: 1 Objective Linear Ferromagnets Non
Page 3: 3 Objective Linear Ferromagnets Non
Page 11 and 12: 11 Objective Linear Ferromagnets No
Page 17 and 18: 17 Effect of symmetry on stiffness
Page 41: 41 Objective Linear Ferromagnets No

Microstructure-Properties - Materials Science and Engineering

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?