Yield stress

The yield stress describes the external ( true ) stress required to achieve and maintain plastic flow in the uniaxial stress state of a material. ${\displaystyle k_{f}}$

The yield stress in a volume usually decreases with increasing temperature. Exceptions are some intermetallic compounds , in which an increase in the yield stress is observed with increasing temperature; this is also known as a yield stress anomaly.

The yield stress is used to determine the deformation resistance and is given in the unit Pascal  (Pa) - that is, N / m ² .

Hypotheses for the determination of the uniaxial yield stress from the stress tensor were formulated by Tresca or von Mises , for example .

Dependencies

The yield stress is a function

• the degree of deformation
• the forming speed
• the forming temperature
• the state of tension, consisting of
  • the hydrostatic pressure (possibly causing an isotropic change in size while maintaining the shape) and
  • the deviatoric stress component (changes the shape while maintaining the volume)
• the microstructure
• of the material .

The parameters influence each other and usually also depend on the material.

Johnson-Cook equation

The Johnson-Cook equation describes the dependence of the yield stress on the strain , the strain rate and the temperature for a certain material: ${\displaystyle \varepsilon }$ ${\displaystyle {\dot {\varepsilon }}}$ ${\displaystyle \vartheta }$

${\displaystyle k_{f}(\varepsilon ,{\dot {\varepsilon }},\vartheta )=(A+B\varepsilon ^{n})\cdot \left(1+C\cdot \ln {\frac {\dot {\varepsilon }}{\dot {\varepsilon _{0}}}}\right)\cdot \left[1-\left({\frac {\vartheta -\vartheta _{0}}{\vartheta _{m}-\vartheta _{0}}}\right)^{m}\right]}$

With

• material-specific experience , , , and ${\displaystyle A}$ ${\displaystyle B}$ ${\displaystyle C}$ ${\displaystyle n}$ ${\displaystyle m}$
• the reference strain rate ${\displaystyle {\dot {\varepsilon _{0}}}=1\,\mathrm {Hz} }$
• the melting temperature of the material ${\displaystyle \vartheta _{m}}$
• the ambient temperature . ${\displaystyle \vartheta _{0}=20^{\circ }\mathrm {C} }$

See also

• Rheology
• Yield point
• Flow curve
• Ductility
• viscosity
• toughness
• Stress-strain diagram
• pressure
• Residual stress

literature

• Hensel, Spittel: Power and labor requirements of sculptural shaping processes. German publishing house for basic industry, Leipzig 1978.
• Hinkfoth: massive forming. Wissenschaftsverlag MAINZ, Aachen 2003, ISBN 3-86130-184-9 .

Individual evidence

1. ↑ Gordon R. Johnson, William H. Cook: A constitutive model and data for metals subjected to large strain rates and high temperatures . In: Proceedings of the seventh international symposium on ballistics. The Hague, Netherlands 1983, p. 541-547 .