Multiaxial nonlinear viscoelasticity of solid polymers

Abstract

AbstractA scheme is presented for characterizing multiaxial nonlinear viscoelasticity of solid polymers in a manner suitable for application to the prediction of deformation of polymeric parts. The basis of the scheme is the systematic exploitation of simplifications resulting from: (1) restrictions on the class of stress histories considered, (2) material symmetry (e.g., isotropy), and (3) the nature of viscoelastic nonlinearity in any given material. Several classes of stress history are considered. In the special case of inplane response of an isotropic material to a two‐dimensional proportional loading history, it is shown that the nonlinearity can be expressed through the dependences of compressibility B and shear compliance J on two invariants of the stress history: I1 and I2′, which separately characterize the magnitudes of hydrostatic and deviatoric components of the stress tensor. When this approach is applied to the description of biaxial creep and recovery of isotropic polypropylene, it is found that for strains up to 0.012, B is independent of I1 and I2′, while J is linearly related to I1 and I2′. These results are used to predict axial strain and hoop strain in the wall of a pressurized pipe, and the predictions compared with those obtained with three approximate procedures.