Meaning
Viscoelastic simulation of polymers requires a mathematical representation that describes how the material relaxes or creeps over time under a given load. This mathematical model is called a prony series and it consists of a sum of decaying exponential terms that represent different molecular relaxation times. The equation fits stress relaxation or creep data obtained from physical tests.
It does not apply to materials that exhibit purely elastic or plastic behavior.
Mathematical Form
Combining multiple Maxwell elements in parallel represents the relaxation modulus as a function of time. Each term in the prony series contains a weight factor and a characteristic relaxation time that corresponds to a specific molecular movement within the polymer chain. This multi-term approach allows the model to match the complex, time-dependent behavior of polymers across several decades of time.
Simulation Input
Finite element analysis software requires these coefficients to predict the long-term warpage and deformation of parts. Engineers input the parameters into the solver to run time-dependent structural analyses. This ensures that the model can calculate how snap-fits lose their holding force over time.
Moulding Consequence
Relaxation behavior represented by these mathematical terms is strongly influenced by the moulding process itself. Fast cooling rates in the mould can freeze the polymer molecules in a highly strained state, altering the relaxation times from those of an annealed test specimen. When the simulated prony series does not match the actual relaxation behavior of the moulded part, the part may fail or warp prematurely in service, which can lead to costly product recalls or structural failures in critical assemblies that could have been avoided with accurate physical testing.
