Influence of Thermally Induced Chemorheological Changes on the Inflation of Spherical Elastomeric Membranes

Abstract

When an elastomeric material is deformed and subjected to temperatures above some chemorheological value T cr (near 100-C for natural rubber), its macromolecular structure undergoes time and temperature dependent chemical changes. The process continues until the temperature decreases below T cr . Compared to the virgin material, the new material system has modified properties (often a reduced stiffness) and permanent set on removal of the applied load. A recently proposed constitutive theory is used to study the influence of chemorheological changes on the inflation of an initially isotropic spherical rubber membrane. The membrane is inflated while at a temperature below T cr . We then look at the pressure response assuming the sphere's radius is held fixed while the temperature is increased above T cr for a period of time and then returned to its original value. The inflation pressure during this process is expressed in terms of the temperature, representing entropic stiffening of the elastomer, and a time dependent property that represents the kinetics of the chemorheological change in the elastomer. When the membrane has been returned to its original temperature, it is shown to have a permanent set and a modified pressure-inflated radius relation. Their dependence on the initial inflated radius, material properties and kinetics of chemorheological change is studied when the underlying elastomeric networks are neo-Hookean or Mooney-Rivlin. (2000): 74F05, 74F25, 74D10, 74E94. Mathematics Subject Classifications

On a possible methodology for identifying the initiation of damage of a class of polymeric materials

“…It would be appropriate at this juncture to mention that there have been several studies of multi-network polymers wherein one allows for scission and reformation of network junctions (see [1][2][3][4][5][6][7][8]). One could view scission as damage and the formation of new networks as a possible healing process.…”

On the mechanics of elastomers undergoing scission and cross-linking

“…For Mooney-Rivlin networks, expressions were also derived for the post-scission torsional stiffness, as well as the residual stress and twist on release of the torque. The postscission relation between inflating pressure and deformed radius of a spherical membrane was considered in [34]. A well-known phenomenon of elastic spherical membranes is that their pressure-radius plot may have an up-down-up shape, depending on the material properties.…”

Estimation of the Elastic Properties of Polymer Plates Using a Structured Light Technique

“…As an alternative, the bulge test is used for determining the mechanical properties under biaxial tension conditions with small bending component [5]. Among the different test methods for Young's modulus determination, the bulge test has become popular for sheet metal [6][7][8][9], thin films [10][11][12][13], polymers [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], and biological materials [29]. In comparison to uniaxial tests, higher strain values can be achieved by bulge tests [7,16] and the maximum strain obtained in uniaxial tensile test before necking is relatively small [6].…”

“…The bulge test has been successfully applied [6,9,12,[15][16][17][18][19][20][21][22][23][24][26][27][28][29] and differences have been observed in comparison with uniaxial tests. This test is suitable for investigating polymer blends for large biaxial plastic deformation prior to failure [16].…”

“…This test is suitable for investigating polymer blends for large biaxial plastic deformation prior to failure [16]. Currently, it has been applied for determining stress-strain curves [9,16,29], pressure versus out-of-plane displacement curves [20,29], Young's modulus [28], changes of plate thickness [23,29], radius of curvature [29], hyperelastic model parameters [24], strain distribution [22], mechanism of bursting [26], transient surface shapes [19], anisotropy coefficients [6], thermally induced changes [14,25,27] and mechanical properties of biological tissues [30]. The results presented by many researchers show good agreement with theoretical values and with other methods of testing, such as biaxial extension and uniaxial tension.…”