A Cooperative Mechanism Limiting the Spectral Width of Stress Relaxation Processes in Solids

Abstract

A recently developed two-level cooperative model of stress relaxation in solids is shown to describe correctly the experimental finding F/a'f; x 0.1, with F denoting the maximum slope of the relaxation curves in a a (stress)-ln t (time) diagram, and u ; the initial effective stress. The basic idea underlying the model is the notion of multiple transitions between the two levels, such transitions being induced by spontaneous events by a similar mechanism as in B-E statistics. The spectrum of relaxation times, t, is determined by the size distribution of the clusters, the r values being inversely proportional to the cluster size. A subdivision of the relaxing system into smaller cooperating regions is one of the consequences of the constancy of the ratio FIG:.Es wird gezeigt, daO ein kiinlich entwickeltes kooperativea Zwei-Niveau-Nodell der Spannungsrelaxation in Festkorpern das experimentelle Egebnie F/uZ =s 0,l korrekt beschreibt, wobei F der maximale Anstieg der Relaxationskurven in einem u (Spannungs)-In t(Zeit)-Diagramm und u: die effektive Anfangsspannung sind. Die dem Modell zugrunde liegende Idee ist dsB Auftreten von Mehrfach-tlibergiingen zwischen den beiden Niveaus, wobei die ubergiinge durch spontane Ereignisse eines Shnlichen Mechanismus wie in der B-E-Statistik induziert werden. Das Spektrum der Relaxationszeiten, t, wird durch die GroOenverteilung der Cluster bestimmt, dabei sind die t-Werte invers proportional zur ClustergroRe. Eine Unterteilung des relaxierenden Systems in kleinere kooperierende Bereiche ist eine der Konsequenzen der Konstanz des Verhaltnisses F]o$.

Stress relaxation, creep, and internal stresses in high density polyethylene filled with calcium carbonate

“…(2). The cooperative model, which provides an explanation for this relation, applies only to the exponential law region [16,17]. When deriving the cooperative model only a very simple type of interaction between the flow units was assumed, and it is likely that in the power-law region the cooperation is more complex.…”

“…One example is the relation given by eq. (2), which however can be accounted for by assuming that flow in solids is governed by cooperation between the flow units responsible for the macroscopic stress relaxation (or creep) behaviour of materials [16,17].…”

A two-level system with induced transitions as a model of stress relaxation

“…The method used in arriving at eq. (2) has been described earlier [4]. It is based on the existence of a maximum cluster size of the multiple a --* b transitions, simple reasoning leading to the conclusion that this cluster size is approximately equal to the distribution parameter /7 in the above equations.…”

“…[3,4] we considered the possibility of developing a model with transitions of both a ~ b and b ~ a type. At low rates of exhaustion of the a-level, such a model could be considered as a quasi-equilibrium system.…”

“…Eq. (2) has been shown to apply equally well to metals, polymers and ionic solids [3][4][5][6]. In the following we will denote the effective stress by cr only.…”