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RSA-G2 Getting Started Guide Page 58
Definition of Compliance and Stiffness
For this discussion, we define
compliance
as displacement, in microns, per kilogram of applied force. Both
transducer and sample exhibit compliance. Stiffness is the reciprocal of compliance.
Transducer compliance is the transducer shaft displacement resulting from force applied to the transducer.
Shaft displacement is measured by a position sensor on the transducer shaft.
Sample compliance is sample displacement resulting from force applied to the sample. Sample stiffness
denotes the force (kg) generated by displacement of the sample during deformation, per micron of sample
displacement.
The RSA-G2 measures sample deformation (strain) by taking the difference between the motor and trans
-
ducer displacement signals. The measurement is sensitive to limits in strain resolution, as well as variations
in motor, and transducer, calibration and linearity. Under “ideal” conditions, the sample deformation is rel -
atively large, and as such, the transducer displacement is much smaller than the motor displacement. The
difference between the two (used to obtain sample displacement) is therefore a large number, and the rela -
tive error associated with the measurement is small. However, this error becomes significant when very
stiff samples (low sample compliance) are tested, and the transducer displacement becomes close to the
motor displacement. In this case, the difference between the two displacements is small, and the relative
error is large, and of similar magnitude as the measurement.
This condition is indicated by the measured strain value being significantly smaller than the commanded
strain value. As a practical guideline, actual strain should be greater than 10 percent of the com -
manded strain. If actual strain is much lower, the sample needs to be made less stiff by lengthening it and
making it narrower and/or thinner. If necessary, change the geometry.
Sample compliance, or stiffness, is related to both the modulus and geometry of the sample. Since the
modulus is, for the most part, fixed, the sample geometry is normally adjusted to obtain the desired sample
compliance. It is critical that the sample compliance be within the operational range of the instrument
otherwise inconsistent or incorrect results will be obtained.
Maximum and Minimum Sample Compliance
The sample geometry must be chosen such that, at the lowest temperatures (where the sample modulus is
the greatest and the force generated the highest), the limitations of the transducer are not exceeded. There -
fore, you should have a cursory knowledge of the range of both the modulus and the sample stiffness over
the temperature range during testing.
The following guidelines offer recommended sample testing limits in terms of sample compliance.
• The minimum sample compliance that provides reasonably accurate data is 10 µm/kg. Below this
value, the measured sample strain is subject to significant errors due to limits in the hardware
transducer compliance correction.
• The recommended minimum sample compliance is 20 µm/kg, above which point the transducer
compliance correction is sufficiently accurate to provide accurate strain measurements.
• The maximum sample compliance that can be accurately tested is (1500 µm) / (0.0001 kg) =
1.5e6 µm/ kg. This is based on the sample generating a force of 0.1 gm (the lower limit of the trans -
ducer measurement range) with a motor displacement of ± 1.5 mm in specs (the maximum dynamic
strain amplitude).
• The recommended maximum sample compliance is 2e5 µm/kg.
• The key to selecting sample size is to ensure that, under all test conditions, sample compliance is
greater than transducer compliance.