A constitutive equation for stratospheric balloon materials

Abstract

The selection of a suitable material for use as a reliable stratospheric balloon gas barrier and structural component is based on a variety of properties. Due to a more desirable combination of properties, the low density polyethylene that has been used for the last half century has been replaced during the last decade by linear low density polyethylene (LLDPE). This paper describes the effort to characterize the time dependent properties of a 38 micron coextrusion of LLDPE. The nonlinear viscoelastic constitutive equation presented may be used to accurately describe the creep andor relaxation of this film when subjected to a biaxial state of stress, such as might be required for an extended balloon flight. Recent laboratory data have been used to mod@ an existing model of LLDPE to account for differences caused by the coextrusion process. The new model wiU facilitate structural design optimization and reliability assessment, and may be further utilized as a predictive tool to benefit in-flight operations. Current structural analysis tech&ques based on linear elastic properties have predicted stresses in excess of those which would actually exist.

Maximally stable lobed balloons

“…(2) is a simplified form of the effective stress proposed by Rand and Sterling (2006). Hence, the area minimization problem can be stated as follows:…”

Large Strain Viscoelastic Model for Balloon Film

“…The results from the least square procedure are plotted in Figs. (2) and (3). The creep compliance of the film in the machine direction, D 11 , is expressed as a Prony series of 15 terms at the reference temperature T 0 = 293.16 K. The master curve is plotted in Fig.…”

“…StratoFilm 420, the LLDPE based film currently used for NASA superpressure balloons, is both viscoelastic and anisotropic. 3 A constitutive model that accurately predicts the anisotropic, viscoelastic material response at large strains will avoid over-conservative designs based on incorrect estimates of localized stress concentrations.…”

Modelling of Anisotropic Viscoelastic Behaviour in Super-Pressure Balloons

“…Based on the integration method proposed in reference 13, an algorithm has been developed for anisotropic material behavior that implements the biaxial approach of Rand and co-workers. 6,12 This algorithm was implemented in ABAQUS, but would be equally suitable for any displacement based finite element software, where strain components are used as the independent state variables. The ABAQUS interface for a user-defined material (UMAT) passes the current time increment ∆t and the corresponding strain increment ∆ε, determined using the Jacobian matrix at the end of the The incremental method requires the transient strain function ∆D to be expressed in terms of a sum of exponentials, called a Prony series, and the strain/stress history needs to be stored at the end of each increment for each strain/stress component and each Prony term.…”