Page 87 - Instrumentation Reference Book 3E

72 Measurement of strain

times the thickness of either of them. Strains of centimeter, or perhaps only a few millimeters
interest are commonly very small; for elastic where very localized strains are to be studied.
behavior, where concern is usually concentrated, Both considerations point to the need for very fine
strains do not exceed about lop3. Many metals wire, and diameters of 15-30 micrometers are used.
break if they are stretched by a few percent and The effective length is increased by having several
changes in length of a few parts in a million are elements side by side as shown in Figure 4.3. Lar-
sometimes of interest, but when these are used to ger tags are attached at the ends of the strain-
produce even small changes in the resistance of R sensitive wire for connecting leads to.
we can take advantage of the precision with
which resistance can be measured in order to get 4.2.2 Foil gauges
a precise figure for strain.
The resistance of a conductor of length 1, cross- An alternative to using wire is to produce the
sectional area A and resistivity p is conductor from a foil-typically 4 micrometers
thick-by etching. Figure 4.4 illustrates a typical
R=- Pl shape. Foil gauges have the advantage that their
A flatness makes adhesion easier and improves heat
dissipation (see below) as well as allowing a wider
When a strain All1 is imparted, it causes a frac- choice of shape and having the tags for the leads
tional change of resistance integral with the strain-sensitive conductor, and
they are in fact more widely used now than wire
gauges.

since there will be a Poisson contraction in A and FOIL STRAIN GAUGE
there may also be a change in resistivity. The ratio TERMINOLOGY
(AR/R)/(Al/l) is called the gauge factor of a
strain gauge. If there were no change in resistiv-
ity, it would be 1 + 2p about 1.6 for most metals,
whereas it is found to be 2 or more, demonstrat- I’
ing that the sensitivity of strain gauges is \ GAUGEALIGNMENT
increased by a change in p.
Nickel alloys are commonly used as the strain- \ TRAhlSVERSE
sensitive conductor, notably Nichrome (nickel-
chromium) and Constantan (copper-nickel). As
well as paper, epoxy resins and polyamide films
are used for the backing insulator.
Strain gauges are available commercially as
precision tools; units supplied in one batch have
closely similar characteristics, notably a quoted
gauge factor. . SOLDER
TABS
Figure 4.4 Shape of foil gauge. Courtesy, Micro-
4.2.1 Wire gauges Measurements Division, Measurements Group Inc.
It is easier to measure resistances accurately when
their values are not too low and this will also help
to avoid complications in allowing for the effect 4.2.3 Semiconductor gauges
of lead resistances in series with the active gauge Another version of strain gauge employs semi-
element. On the other hand, gauges should not be conductor material, commonly silicon. Because
too big, in order to measure strain effectively “at a the resistivity is higher, the sensitive element can
point;” this calls for dimensions of the order of a be shorter, wider, and simpler: Figure 4.5. The
great advantage of semiconductor strain gauges is
that their resistivity can be very sensitive to strain,
allowing them to have gauge factors many times
(typically 50) greater than those of simple metals,
but they tend to have higher temperature
sensitivity and are less linear. They can be
made integral with structural components and
are used in this way for pressure measurement
Figure 4.3 Layoutof wiregauge. (see Chapter 9).