Materials and Processes in Manufacturing

E. Paul DeGarmo, J T. Black, Ronald A. Kohser

Chapter 17 Fundamentals of Metal Forming

Process and Material Deformation Behavior Models

Process models are useful for predicting process behavior and so can be used for process design, process control, process operation and demonstrating understanding of details of the process. The intent of this exercise is to show that process models can become complex quickly as the number of process variables increases. As process and material behavior models become more complicated process analysis becomes increasingly complex and the use of analytic and numerical techniques is necessary to describe the process.

A simple deformation process is considered in the exercise - uniaxial deformation at constant strain rate. The exercise is to predict material flow stress during the deformation process. Change in material temperature during the process is specified, much as the workpiece material temperature changes in manufacturing processes due to either cooling of an initially heated workpiece, or heating of the workpiece during processing to make processing easier.

The concept emphasized in this exercise is outlined in more detail below.

The effect of strain hardening on the flow stress and deformation behavior of ductile materials was the topic of the Chapter 2 exercises. In general terms, the flow stress, s, during deformation over time, t, varies with strain, e, and is

s(t) = s(e)
with e(t)
and a widely used model of flow stress is s = K en

With this material behavior model and a material deformation process model, say uniaxial tensile deformation, it is not difficult to estimate useful quantities. For example, an estimate of the the change in flow stress when deformation is doubled can be estimated fairly easily, even though the flow stress is a nonlinear function of strain.

It is expected that material flow stress will depend on temperature, T, and strain rate, de/dt = q, in addition to the amount of deformation.

s(t) = s( e(t), T(t), q(t) )
The functional relationship will not be simple. While the flow stress model is not real, to make a point the model could be
s(t) = ( K1 en ) ( K2 Tm ) ( K3 qp )
The point being that, now the same question of what is the flow stress if strain is doubled is not so easy to answer.

Predicting process behavior may require significant insight and thought even with models that appear to be simple. For example the linear material behavior model

s = so + n e + p q
with so the initial flow stress
is used in the exercise. An important manufacturing process parameter is temperature since material strength, strain hardening behavior, and strain rate sensitivity depend on it.

The exercise problem is,
- for a constant strain rate, uniaxial tensile deformation process,
- in which temperature varies over time,
- and flow stress, strain hardening behavior and strain rate sensitivity depend on temperature,
estimate the flow stress over time.
That is the flow stress behavior model is

s(t) = so(T) + n(T) e(t) + p(T) q
with T(t)

In summary, formal, mathematical, techniques are usually needed to use realistic manufacturing process models.

© 2002 by B. E. Klamecki. All rights reserved.