Schmid's Law

Schmid's Law (also Schmid factor, m) describes the slip plane and the slip direction of a stressed material, which can resolve the most amount of 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 glide plane (Φ) and the cosine of the angle with the glide direction (λ). Which can be expressed as:^[1]

${\displaystyle \tau =\sigma *m}$

where m is known as the Schmid factor

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

Both factors τ and σ are measured in stress, which is calculated the same as pressure by dividing force by area. Φ and λ are angles usually measured in degrees.

The factor is named after Erich Schmid who coauthored a book with Walter Boas introducing the concept in 1935.^[2] In German the law is called the "Schmid'sches Schubspannungsgesetz" (Schmid's shear-stress-law), while the factor is either called "Schmid-Faktor" or "Schmid'scher Orientierungsfaktor" (Schmid's orientation factor).^[3]

See also

• Critical resolved shear stress

References

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

Further Reading

• Translation into English: Schmid, Erich; Walter Boas (1950). Plasticity of crystals with special reference to metals. London: F.A. Hughes.