Constitutive relations for strain and failure of filled polymer materials in dominant axial tension processes under various barothermal conditions

Abstract

The earlier proposed relation between true stress and logarithmic strain deviators, which has the form of a generalized Maxwell viscoelastic model and contains functionals of internal time and aging, is specified in the class of axial tension processes. It is suggested to characterize the local deficiency of a filled polymer material by two scalar quantities having the meaning of the relative internal separation area (the damage parameter) and the rated strain capacity exhaustion (the criterion parameter determining the destruction point). These parameters are described by kinetic equations and do not decrease in the loading process but increase only as the process activity parameter (the current-to-maximum-attained strain intensity ratio) is equal to unity. The right-hand sides of the kinetic equations for the internal time and the failure parameter depend on the strain rate intensity. The variation in the material instantaneous stiffness (aging) is described by a product of functions of the current values of the process damage and activity parameters. It is assumed that the bulk strain is quasi-elastic; it is proportional to the reduced stress intensity (with aging taken into account) and the difference between the damage and its threshold value below which there is no dilatation. The hydrostatic pressure and temperature are taken into account by two factors depending, respectively, on the stress state form parameter (the first-to-second stress tensor invariant ratio) and on the temperature, which are introduced into the right-hand sides of the model equations. We propose a generalization of the model to the case of variation in the phase state of the binder (embrittlement at low temperatures). We present the incremental form of the constitutive relations, which is used to integrate them numerically. We give a detailed description of the model identification procedure (after the relaxation kernel is determined in the standard way) from the results of the following base experiments: for constant values of the hydrostatic pressure, temperature, and tension strain rate (two-three levels of these parameters in their ranges used in application, each loading until failure) as well as for complete unloading (a single experiment). The experimental data (for three highly filled vulcanizates) published by Ozupik, Schapery, and Jung (more than 50 loading programs, including those of cyclic and nonisothermal type), are used to perform identifications and verifications of the proposed constitutive relations. We show that, in the class of processes under study, the engineered values (such as variations in the axial stress and bulk strain and the destruction point) lie within the limits typical of the corresponding experimental spread in mechanical properties of the material under study.