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, $T$, true strain, $\epsilon$, and strain rate, ${\bar {\epsilon }}$. Generally, above 0.5 T_m (the absolute melting temperature of an alloy) the plastic deformation mechanisms favour strain rate sensitivity whereas at room temperature metals are generally strain-dependent. Therefore, it can be written as some function of those properties:

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

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.

It 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:

Y_f = Kεⁿ

• Y_f = Flow stress, MPa
• ε = True strain
• K = Strength Coefficient, MPa
• n = Strain hardening exponent

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.

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.