The exercise asks that work material flow stress be predicted. For this introduction a simple deformation situation and simple linear material behavior changes are used. Specifically,
- deformation is uniaxial tensile deformation at constant strain rate, q,
- the material is linearly strain hardening with the strain hardening coefficient dependent on temperature, n(T),
- the strain rate effect is linear with the strain rate coefficient dependent on temperature, p(T),
- the temperature variation during deformation is given as a fraction of melting temperture.
Choose the material behavior parameters to include,
- flow stress a function of only strain, s(e) only,
- flow stress a function of strain and temperature, so(T),
- s(e,T) with strain hardening coefficient, n, dependent on temperature, so(T), n(T).
- s(e,T) with n, and strain rate coefficient, p, dependent on temperature, n(T), p(T),
The change in temperature over time and the dependence of material parameters on temperature are shown
The flow stress at time to is shown,
Select the change in flow stress in the next strain increment,
Estimated and actual flow stress are plotted.
The more general case of nonlinear strain hardening and nonlinear strain rate dependence is probably expected. The situation becomes more complicated very quickly as more realistic material behavior is modeled.