Stress Relaxation in Metals and Polymers: Theory, Experiment and Computer Simulations
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to the internal
stress ai = a(oo).
We discuss briefly the
experimental evidence as well as the main features of the cooperative theory which does not involve specific features of different classes of materials. The bulk of the paper deals with computer simulations. Simulation results obtained with the method of molecular dynamics are reported for ideal metal lattices, metal lattices with defects, and for polymeric systems. In agreement with both experiments and the cooperative theory, the simulated a (log t) curves exhibit the same three re gions. In agreement with the theory, the slope of the simulated central part is proportional to the initial effective stress u00 =
o- a .
The time
range taken by the central part is strongly dependent on the defect concentration: the lower the defect concentration, the shorter the range. Imposition in the beginning of a high strain e destroys largely the resistance of a material to deformation, resulting in low values of the internal stress o . Since the cooperative theory assumes for particles (atoms, polymer chain segments) the existence of two states, unrelaxed and relaxed, and has a formal connection to the Bose-Einstein (B-E) distribution, we first simulate B-E systems, recording the formation of relaxed clusters of particles of different sizes. Differences in cluster sizes predicted from a B-E model and those obtained from the simulations are recorded and analyzed. Onthe joint basis of experimental, theoretical 99
Mat. Res. Soc. Symp. Proc. Vol. 321. ©1994 Materials Research Society
and simulation results, we explain the mechanism of stress relaxation in terms of deformations occurring in the immediate environment of the defects. These deformations, visible in simulations of both metals and polymers, correspond to cluster relaxations in the cooperative theory, and thus confirm a posteriori the assumptions made in developing the theory. 1.
INTRODUCTION
Mechanical behavior of viscoelastic materials is most often characterized by peforming so-called transient experiments as a function of time: either the deformation under a constant load, that is creep, or the time decay of stress, a= a(t) at a constant strain c, that is stress relaxation 1, 2* Large amounts of information on stress relaxation in polymers and
The information is mostly but polymer-based composites are available. consider experimental and paper we shall In this not only experimental. theoretical information available, and add to it our own results of computer simulations. In distinction to more limited comprehension resulting from the use of a particular technique, we expect to acquire this way a better understanding of the phenomenon itself. 2.
EXPERIMENTAL EVIDENCE
The experimental stress relaxation curves are plotted traditionally in the a =a (log t) coordinates. Better comparison between curves for different materials can be achieved when ao is taken into account as a reducing variable. Already in 1965 one of us 3 used ao*/ o* as the ordinate (o*= a - 0i; ao* and a, are defined above in the abst
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