Slide 9
For the ductile materials
we can determine the initial yield stress from the torquedisplacement
curve. The material yields when it begins to undergo permanent deformation.
This permanent deformation is accompanied by nonlinearity of the
torquetwist curve. Defining the exact onset of nonlinearity and
hence onset of yielding can be difficult. Thus as a practical approach,
engineers often use the offset method.
The offset method
is usually stated in terms of strain. In this method a line is drawn
parallel to the linear part of a stressstrain curve, but displaced
to the right by 0.1 to 0.2% strain. The stress where this line intersects
the stressstrain curve is then deemed to be the yield stress.
In this lab we do
not measure strain directly – we measure twist. To use the
offset method, an offset twist must be defined consistent with the
offset strain idea. Here we have chosen to reduce the offset to
0.1% shear strain. Using the relation between strain and twist we
can calculate an offset twist. For example, for a gauge length of
50mm and outer radius of 6.35mm, the offset twist that is equivalent
to 0.1% offset strain is .008 radians. The intersection of the offset
line with the torquetwist curve gives the torque at yield, about
40 Nm in the example shown.
Once the yield torque
is known, the yield stress can be computed from tau yield equals
yield torque times outer radius of gauge section divided by polar
moment of inertia, J.
