of the flow stress, m, which has been shown to correlate well with tensile elongation for different classes of materials (Ref
7, 8). Measurements of flow stress and strain rate sensitivity of flow stress can be conducted in a single test and can be
used to determine the optimum strain rate for superplastic forming (where m is a maximum). Although strain rate
sensitivity is the dominant parameter in superplastic forming, more recent results show that a significant amount of
hardening can occur as a function of superplastic strain even at a constant strain rate (Ref 9, 10). This type of strain
hardening is believed to be related primarily to the grain growth that occurs during superplastic forming. At higher strain
rates, strain hardening is associated with dislocation cell formation in the classical manner.
Forming temperature is just as important a variable in superplastic forming as the strain rate. Temperature variation in a
forming die is a primary source of localized thinning. Characterization of material behavior should therefore include not
only determination of the optimum superplastic temperature but also the sensitivity of flow stress and elongation to
temperature. A large temperature sensitivity of flow stress is not desirable, because local hot spots will lead to severe
strain localization. When strain localization and necking are the dominant modes of failure, it has been shown that tensile
elongation is related to the m value in a predictable manner (Ref 11). However, when fracture intervenes, the m value
does not provide sufficient quantitative characterization, although within the same alloy system it still provides a
qualitative comparison. Fracture is therefore an important consideration in most superplastic materials of engineering
application. An exception is materials with anomalously high diffusivity (for example, Ti-6Al-4V alloys), which do not
show any evidence of internal cavitation or fracture. Superplastic materials that exhibit cavitation at inclusions, triple
points, and second-phase particles generally fail by the interlinking of growing cavities.
Stress-strain rate behavior is usually characterized by a step strain rate test, in which strain rate is increased in
successive steps and an attempt is made to measure the corresponding steady (or saturated) flow stress. A constant flow
stress indicates a negative loading rate, which occurs at a point somewhat beyond the load maximum. However, even if
the load maximum is used as a criterion for calculating these stresses, it can be shown that the error is negligible. Various
arguments have been put forward for the proper selection of flow stress from transient loading response (Ref 12, 13, 14).
However, because of the changing plastic-strain rate during this test, selection of data at the elastic limit from the rapidly
rising portion of the load curve is thought to be inappropriate.
Figure 2 shows a schematic load versus time plot during a step strain rate test of a typical superplastic alloy. The
interesting features are:
• At the low crosshead speeds, the load does not reach a maximum but continues to show a gradual rise
• At some intermediate speed, load reaches a constant plateau
• At higher speeds, it peaks and begins to show a sharp drop
The load increase at the low strain rates, in spite of a decrease in applied strain rate, indicates hardening of the material
with imposed strain. A part of this hardening is due to a rise in plastic-strain rate, which occurs gradually when crosshead
speed is low. However, the extent of hardening observed is considerable and does not saturate even after significant
plastic strain, which suggests other possible sources of hardening. This type of hardening has been observed in other
superplastic materials, such as aluminum-copper eutectic, and is generally attributed to grain growth occurring during
deformation (Ref 15, 16).
The criticism against the use of strain rate jump tests and the selection of maximum load points for obtaining stress values
is that the strain automatically becomes a variable along the - curve. This could be avoided if load relaxation test
results were used to derive - curves. However, more complex transient effects might be associated with load relaxation
tests, and the results might not be meaningful for a forming application in which strain rate generally increases with
accompanying strain. The step strain rate test is therefore believed to be a logical test method for use in superplastic
forming applications, provided the data are obtained with very little strain accumulation.
The - data for Ti-6Al-4V alloy and 7475 aluminum alloy deformed in the superplastic temperature range are presented
in Fig. 3 for a variety of grain sizes. The total accumulated strain is generally less than 0.25 in these tests. At lower strain
rates (<5 × 10
-4
s
-1
), strain hardening does not permit the establishment of a load maximum. To characterize flow stress
free from grain-growth hardening effects, stresses must be selected soon after the elastic portion. If the load rises slowly,
the plastic-strain rate,
p
, can be obtained from: