Constitutive analysis of the nonlinear viscoelasticity of polymer fluids in various types of flow

The theoretical background, the applicability and the limitations are discussed of the factorable single integral constitutive equation which expresses the stress as: p(t) = {dollar}-rm psb{lcub}o{rcub}{dollar}1 + {dollar}intsbsp{lcub}-infty{rcub}{lcub}rm t{rcub}{dollar}m(t {dollar}-{dollar} t{dollar}spprime{dollar}) {dollar}Slbrackxisb{lcub}rm t{rcub}{dollar}(t{dollar}spprime{dollar})) dt{dollar}spprime{dollar}.; The value of the memory function m(t {dollar}-{dollar} t{dollar}spprime{dollar}) is uniquely determined by the time difference t {dollar}-{dollar} t{dollar}spprime{dollar}; the nonlinear strain tensor {dollar}Ssb{lcub}rm t{rcub}{dollar}(t{dollar}spprime{dollar}) is a function of the relative strain {dollar}xisb{lcub}rm t{rcub}{dollar}(t{dollar}spprime{dollar}) between times t and t{dollar}spprime{dollar} only. Assuming {dollar}Ssb{lcub}rm t{rcub}{dollar}(t{dollar}spprime{dollar}) and m(t {dollar}-{dollar} t{dollar}spprime{dollar}) as material specific, their shape has to be obtained from experimental data.; The factorable single integral constitutive equation is derived from the simple fluid theory. The relationship between this equation and the equations derived from molecular-kinetic models as the Lodge model, the Wagner model and the Doi-Edwards model is discussed.; Four polymer melts have been thoroughly characterized in simple shear flow and in simple extensional flow to determine the applicability range of the investigated constitutive equation and to test the methods to obtain m(t {dollar}-{dollar} t{dollar}spprime{dollar}) and {dollar}Slbrackxisb{lcub}rm t{rcub}{dollar}(t{dollar}spprime{dollar})). The most accurate way is described of determining the memory function. The methods are discussed to obtain from various types of experiment, the simple shear strain measure, S{dollar}sb{lcub}12{rcub}{dollar} ({dollar}gammasb{lcub}rm t{rcub}{dollar}(t{dollar}spprime{dollar})), i.e. the 12-component of {dollar}Ssb{lcub}rm t{rcub}{dollar}(t{dollar}spprime{dollar}), expressed as a function of the relative shear {dollar}gammasb{lcub}rm t{rcub}{dollar}(t{dollar}spprime{dollar}), and the simple extension strain measure, S{dollar}sb{lcub}rm E{rcub}lbrackvarepsilonsb{lcub}rm t{rcub}{dollar}(t{dollar}spprime{dollar})), i.e. the difference between the 11- and 22-component of {dollar}Ssb{lcub}rm t{rcub}{dollar}(t{dollar}spprime{dollar}), expressed as a function of the relative Hencky strain {dollar}varepsilonsb{lcub}rm t{rcub}{dollar}(t{dollar}spprime{dollar}).; A number of empirical relations between dynamic or time-dependent rheological functions and steady-state functions, such as the Cox-Merz rules and the mirror relations of Gleissle are incorporated into the constitutive equation. The results are confronted with experimental data. The experimental strain measures S{dollar}sb{lcub}12{rcub}(gamma{dollar}) and S{dollar}sb{lcub}rm E{rcub}(varepsilon{dollar}) have been used to test some empirical relations between the nonlinearity in the two flow geometries.; The functions S{dollar}sb{lcub}12{rcub}(gamma{dollar}) and S{dollar}sb{lcub}rm E{rcub}(varepsilon{dollar}) determined in this work and by others for a large number of materials are compared with the theoretical functions predicted by the Doi-Edwards theory and by a modification of this theory. The nonlinear strain measures for various crosslinked rubbers are presented as well.; Some examples are discussed where the separability of time and deformation effects is not possible.