Aluminium Design and Construction John Dwight

The two terms in this expression are respectively the elastic and plastic
strains. It will be seen (Figure 4.9) that the curve produced automatically
satisfies two necessary requirements, whatever the value of n:
1. There is (effectively) a linear elastic range.
2. The plastic strain correctly equals 0.002 when the stress reaches � o .
The role of the index n is to control the curvature of the knee on the
curve. A high n produces a curve with a relatively abrupt knee, a low n
one with a more rounded knee. One can thus refer to ‘high-n’ and ‘lown’
materials. n typically ranges from 40 down to 5 for aluminium materials.
4.4.2 Stress-strain curve for minimum strength material
For any given alloy the actual properties of the material (as supplied)
will vary considerably from batch to batch, and also along the length
of an extrusion. For analytical purposes, it may be necessary to define
a stress-strain curve that would represent the response of minimum
strength material, i.e. material that just attains the specification values
for f o , f u and el. Referring to Figure 4.10, a curve is needed that goes
through the proof-stress point A and also the fracture point B. This is
achieved by putting � o =f o in equation (4.3), and taking n as follows:
(4.4)
The curvature of the knee, defined by n, is strongly dependent on the
ultimate-proof ratio f u /f o but is insensitive to the elongation el. A material
with a low value of f u /f o will exhibit a relatively abrupt knee (high n),
whereas for material having a high f u /f o the knee will be more rounded
Figure 4.10 Construction for obtaining a stress-strain curve to represent minimum
strength material.
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