Prony Series Viscoelastic Modeling for Sensor Packaging Stress Relaxation Analysis
Prony series modeling converts polymer relaxation data into actionable sensor zero-drift predictions, isolating packaging strain from true physical signals.
Relaxation Modulus
Stress Decay
Time dependent material responses describe the reduction in internal stress while a constant strain is maintained on a specimen. The value known as relaxation modulus measures the ratio of the remaining stress to the initial strain as a function of time. It characterizes how polymers dissipate energy and shed loads through molecular rearrangement.
This property is required for predicting the long term seal force of gaskets and O-rings.
Viscoelastic Relaxation
Molecular motion within the polymer chain allows the material to reach a new equilibrium state after an initial deformation. Over the course of the test, the relaxation modulus decreases from an initial glassy value toward a lower equilibrium plateau. The rate of this decline depends on the internal friction and the degree of crosslinking in the material.
A fast decay suggests a material that is more fluid in nature.
Thermal Acceleration
Temperature shifts significantly influence the speed of the stress reduction process. Measuring the relaxation modulus at several temperatures allows for the creation of a master curve using the time temperature superposition principle. Superposition technique predicts the behaviour of the material over years by observing it for only a few days at elevated temperatures.
It is a standard practice in the qualification of structural adhesives.
Precision Measurement
Specialized load cells and displacement sensors are necessary to capture the subtle changes in force over long durations. Environmental stability in the lab ensures that thermal expansion of the test rig does not interfere with the relaxation modulus reading. If the temperature fluctuates by even half a degree, the resulting stress changes could be misinterpreted as material relaxation.
Regular calibration of the instrument ensures the accuracy of these long term measurements.