Schmid's law

In materials science, Schmid's law (also Schmid factor^[a]) describes the slip plane and the slip direction of a stressed material, which can resolve the most shear stress.

Schmid's Law states that the critically resolved shear stress ( $τ$ ) is equal to the stress applied to the material ( $σ$ ) multiplied by the cosine of the angle with the vector normal to the glide plane ( $φ$ ) and the cosine of the angle with the glide direction ( $λ$ ). Which can be expressed as:^[2]

\tau =m\sigma

where $m$ is known as the Schmid factor

m=\cos(\phi )\cos(\lambda )

Both factors $τ$ and $σ$ are measured in stress units, which is calculated the same way as pressure (force divided by area). $φ$ and $λ$ are angles.

The factor is named after Erich Schmid who coauthored a book with Walter Boas introducing the concept in 1935.^[3]

^ Merkel, Manfred; Karl-Heinz Thomas (2008). Taschenbuch der Werkstoffe (in German) (7th ed.). München: Fachbuchverlag Leipzig im Carl Hanser Verlag. ISBN 9783446411944.
^ Caceres, Pablo G. "Deformation of Single Crystals" (PDF). Retrieved 15 May 2014.
^ Schmid, Erich; Walter Boas (1935). Kristallplastizität: Mit Besonderer Berücksichtigung der Metalle (in German) (1st ed.). Springer. ISBN 978-3662342619.

Cite error: There are <ref group=lower-alpha> tags or {{efn}} templates on this page, but the references will not show without a {{reflist|group=lower-alpha}} template or {{notelist}} template (see the help page).

[merkel-thomas-1] Merkel, Manfred; Karl-Heinz Thomas (2008). Taschenbuch der Werkstoffe (in German) (7th ed.). München: Fachbuchverlag Leipzig im Carl Hanser Verlag. ISBN 9783446411944.

[Caceres-3] Caceres, Pablo G. "Deformation of Single Crystals" (PDF). Retrieved 15 May 2014.

[schmid-boas-1935-4] Schmid, Erich; Walter Boas (1935). Kristallplastizität: Mit Besonderer Berücksichtigung der Metalle (in German) (1st ed.). Springer. ISBN 978-3662342619.

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