A continuous threshold model for the visco-elasto-plastic behavior of PET based multi-layer polymeric films

The envelopes of the super-pressure balloons fabricated by the French space agency (CNES) are made of a multi-layer polymeric film that shows substantial viscoelastic and viscoplastic behavior, both depending nonlinearly on stress. A model is presented that takes into account stress depending viscoelastic and viscoplastic strain response functions observed in uniaxial creep experiments. For easy numerical implementation, the strain response functions are represented by a Prony series, whose coefficients form a continuous spectrum on the logarithmic retardation time scale. The observed response functions are generated by an exponential power law distribution of the Prony coefficients with exponent 3. The distribution is fully characterized by three stress dependent parameters: its center, width, and an intensity factor, corresponding to the maximum coefficient. Creep and recovery experiments show that both viscoelastic and viscoplastic strain are highly stress dependent over a limited stress range and are approximately linear at low stresses and around the maximum stress reached during flight. A continuous threshold function is proposed that approximates well the observed stress dependence of the intensities. It is assumed that the other viscoelastic (viscoplastic) parameters change around the same threshold as the viscoelastic (viscoplastic) intensity and are approximately constant elsewhere. The model reproduces very well the strain response observed in creep and recovery experiments with different creep stresses.