A model of traps for yield in amorphous glassy polymers

Abstract

Constitutive equations are derived for the viscoelastic and viscoplastic behavior of amorphous glassy polymers at isothermal loading with small strains. The model is based on the trapping concept: a disordered medium is treated as an ensemble of plastic¯ow units (with the characteristic size of micrometers), which, in turn, consist of a number of cooperative rearranging regions (with the characteristic length of nanometers). The viscoelastic response is described by rearrangement of relaxing regions, whereas the viscoplastic behavior is modeled as irreversible deformation of plastic units. Adjustable parameters are found by ®tting observations for aromatic polyesters, nylon-66, polycarbonate block copolymers and an epoxy glass. Fair agreement is demonstrated between experimental data and results of numerical simulation. IntroductionThe paper is concerned with the viscoelastoplasticity of amorphous glassy polymers at isothermal loading with small strains. Time-dependent behavior of solid polymers in the vicinity of the yield point has attracted essential attention in the past decade, [12,13,18,27,35,64,66]. However, despite a number of studies dealing with the subject, it is dif®cult to mention constitutive relations that provide an adequate description of viscoelastoplastic phenomena at the molecular level, [6].Yield is conventionally revealed in uniaxial tests with constant rates of strain as a point of maximum on the stress±strain curve, which is followed by a drop of stress, a plateau region and a region of a monotonic growth of stresses. Observations show that the yield point depends on the rate of strain _ , [5,7,10,12,14,35,45,46,50,55,56,62,63,69,71], the program of loading and the strain state, [12,34,42,43,44,48,71,72], temperature T, [5, 7, 9, 15, 19, 20, 35, 55, 56, 71], and pressure p [7, 43, 57], as well as on the molecular weight, [40], orientation of chain molecules, [4,54], degree of crosslinking, [15,50], composition [52,69] and the annealing time, [8,33,39].This study focuses on the effect of the strain rate _ on the stress±strain relations. Our objective is to develop a molecular model which correctly describes an increase in the yield stress r y with _ . We con®ne ourselves to amorphous polymers with a pronounced yield point on the stress±strain curve in a temperature range far below the glass transition temperature T g .A number of phenomenological and molecular models in viscoelasticity and viscoplasticity have been derived in the past decades. Three main phenomenological approaches may be mentioned to the design of constitutive relations for the viscoelastoplastic behavior of glassy polymers.