<FLOW> sellars_tegart

Description

This is a flow rule given by C M Sellars and W J Tegart in 1969 as a proposed rate equation for hot forming conditions. The use of a hyperbolic sine function allows for increasing overstress at low strain rates, which is followed by essentially a saturation level of overstress. Another way of describing the model is viscous at low overstress levels followed by essentially rate independent behavior for high stresses. Normally this behavior would be combined with hardening (viscoplasticity) and not taken as a pure viscous creep law.

The rule is given as:

(402)\[\dot{\lambda} = \epsilon_0\left[ \sinh\left<\frac{f}{\sigma_0}\right>\right]^m\]

Note that the Z-mat formulation utilizes a ratio of the overstress by a normalizing flow stress \(\sigma_0\). Once the overstress becomes of the order of the flow stress this law will make the transition to rate independence.

Many uses of this equation include explicitly the activation energy term to scale the flow viscosity according to thermally activated mechanisms. In Z-mat the activation term should be entered in using the coefficient mechanism (either as tables or functions) for the value of de0.

Syntax

The flow law accepts coefficients de0, m, sigma0

Example

An example input using the coefficient mechanism to add thermal activation is given below:

*flow sellars_tegart
  de0    function  0.202e-2*exp(-401.0/(8.3144e-3*(temperature+273.0)));
  sigma0 120.0
  m      1.44