Strength analysis of structures made of high-filled polymer materials: constitutive equations, methods of boundary value problems solving, account of strain concentration

摘要

We investigate strength, damage accumulation and failure of composite polymer materials with a high degree of dispersion filling (a few tens percent by volume). We consider the class of quasistatic loading processes with axial tension predominance, namely only one of the principal strains is positive (tensile) and its direction remains almost unchanged in the course of loading; hydrostatic pressure and temperature can be changed within certain limits. On basis of the published experimental data derived under uniaxial uniform tension in various barothermal conditions (more than 50 non-stationary loading programmes) we suggest the equation system for modelling the mechanical behaviour of specified materials, namely: the deviatoric relation of gero-endochronic viscoelasticity, the quasielastic equation for volumetric deformation, the kinetic equations for damage and failure parameters, as well as the criterion of failure. The model has a hierarchical structure: first, the material functions are determined for active straining in the normal barothermal conditions; then, if necessary and if relevant experimental data are available, the material functions are determined for unloading and repeated loading, different values of hydrostatic pressure and temperature. The model identification procedure is relatively simple: the material functions are determined sequentially and each of them contains 1-3 constants. The tensorial generalization of this equation system is proposed and the algorithm for numerical solving of initial-boundary value problems is described. This algorithm is implemented in ABAQUS software complex through the UMAT subroutine. We carried out the finite-element analysis of short wide strips with and without holes or cuts in constant rate elongation processes. By comparison of simulation results with published experimental data it was established the need for taking into account the effect of stress-strain state concentration. For this purpose we propose the following generalization of the model: into the equations for damage and failure parameters we introduce the material function of the concentration parameter, which is the ratio of the definite state variable (namely, the failure parameter in the model without taking into account the concentration effect) at a current material point to the mean value of this variable in the point neighborhood of the definite radius. We specify the method for approximate reduction of initial-boundary value problem for the proposed nonlocal theory to the problem for piecewise homogeneous body, composed of a set of material layers, described by local constitutive equations. The method was successfully tested in the strength analysis of strips with holes and cuts (concentrators of middle and high level, respectively). The obtained results show sufficient accuracy of the developed mathematical model - including adequate prediction of the moment and the location of a failure initiation.