# Flow stress

Flow stress is defined as the instantaneous value of stress required to continue plastically deforming the material - to keep the metal flowing. The flow stress for a given material in continuum mechanics is dependent upon the temperature, ${\displaystyle T}$, true strain, ${\displaystyle \epsilon }$, and strain rate, ${\displaystyle {\bar {\epsilon }}}$. Therefore, it can be written a some function of those properties[1]:

${\displaystyle {\bar {\sigma }}=f(\epsilon ,{\bar {\epsilon }},T)}$

The exact equation to represent flow stress is dependent upon the particular material and the plasticity model being used. Other models may also include the effects of strain gradients[2].

Itt is the middle value between yield strength and ultimate strength of the metal as a function of strain, which, for some materials, can be expressed:[3]

Yf = Kεn

Hence, Flow stress can also be defined as the stress required to sustain plastic deformation at a particular strain.

The flow stress is a function of plastic strain.

The following properties have an effect on flow stress: chemical composition, purity, crystal structure, phase constitution, exit microstructure, grain size, and heat treatment[4].

The flow stress is an important parameter in the fatigue failure of ductile materials. Fatigue failure is caused by crack propagation in materials under a varying load, typically a cyclically varying load. The rate of crack propagation is inversely proportional to the flow stress of the material.

## References

1. ^ Saha, P. (Pradip) (2000). Aluminum extrusion technology. Materials Park, OH: ASM International. p. 25. ISBN 9781615032457. OCLC 760887055.
2. ^ Soboyejo, W. O. (2003). Mechanical properties of engineered materials. Marcel Dekker. pp. 222–228. ISBN 9780824789008. OCLC 649666171.
3. ^ Mikell P. Groover, 2007, "Fundamentals of Modern Manufacturing; Materials, Processes, and Systems," Third Edition, John Wiley & Sons Inc.
4. ^ "Metal technical and business papers and mill process modeling". web.archive.org. 2014-08-26. Retrieved 2019-11-20.