A Nonlinear Plasto-Viscoelastic Constitutive Equation for Balloon Films

This paper is intended to describe a method to extend the current nonlinear viscoelastic constitutive equation of the current balloon film commonly used in the manufacturing of stratospheric balloons to include plastic deformations that are characterized by large strains. By using the compliance formulation, the nonrecoverable strains caused by plastic deformation may be reliably computed. This is an important property of the pumpkin shaped superpressure balloon now being developed by the National Aeronautical and Space Administration. This new design requires the minimization of excess material which will promote the desired deployment and long term stability of the system. However, the resulting stresses and strains must be within the capability of the material to survive for at least one hundred days. Nomenclature Ar = coefficient of Prony series aT = temperature shift factor for reduced time aσ = stress shift factor for reduced time Dp(σ,t) = plastic creep compliance D0 = elastic portion of creep compliance ∆D(ψ) = transient portion of creep compliance g2(σ) = nonlinear shift factor for master curve P(σ,t) = plastic strain function t = real time ε1 = strain in the machine direction εp = irrecoverable strain εve = nonlinear viscoelastic strain ∆εip = incremental change in plastic strain due to change in stress at ti λr = coefficient used in Prony series σ1 = stress in the machine direction τ = variable time used in integration period ψ = reduced time used with master curve { } = symbol denoting the convolution integral