Schmid's law of shear stress

The schmidsche shear stress law (according to Erich Schmid ) describes the resolved shear stress in a sliding of a crystalline material defined by a tensile force is claimed: ${\displaystyle \tau }$

${\displaystyle \tau =\sigma \cos(\gamma )\cos(\kappa )}$

With

• the tensile stress ${\displaystyle \sigma }$
• the Schmid factor or Schmid's orientation factor ${\displaystyle \cos(\gamma )\cos(\kappa )}$
  • the angle between tensile stress and slip direction ${\displaystyle \gamma }$
  • the angle between tensile stress and slip planes normal . ${\displaystyle \kappa }$

Dislocations on the slip system with the largest Schmid factor first reach the critical shear stress and begin to slip , i.e. H. the material is plastically deformed . As a result of this plastic deformation, the (uniaxial) tension caused by the tensile force usually leads to a rotation of the crystal and thus to a change in the angles and . ${\displaystyle \gamma }$ ${\displaystyle \kappa }$

If both of the above If the angle is 45 °, the Schmid factor is maximum and thus also the resulting shear stress. If one of the two angles is 90 °, there is and no tension acts on the displacements of the sliding system under consideration. ${\displaystyle \tau =0,}$

literature

• Günter Gottstein: Physical basics of materials science . 2nd Edition. Springer, Berlin et al. 2001, ISBN 3-540-41961-6 , pp. 213 ff . ( limited preview in Google Book search).

Individual evidence

1. ^ Manfred Merkel, Karl-Heinz Thomas: Taschenbuch der Werkstoffe . 7th, improved edition. Fachbuchverlag Leipzig in Carl Hanser Verlag, Munich 2008, ISBN 978-3-446-41194-4 , p. 80 ( limited preview in Google Book search).
2. ↑ Schmid's law of shear stress. Retrieved October 30, 2016 .