Computer Simulation of Stress-Strain Behavior in Polymeric Materials
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COMPUTER SIMULATION OF STRESS-STRAIN BEHAVIOR IN POLYMERIC MATERIALS ROBERT COOK Lawrence Livermore National Laboratory,
Livermore,
CA
94550
ABSTRACT We have developed a model of polymeric materials which includes many of the features of condensed-phase polymer chain dynamics, central among them chain relaxation by conformational motion. The model consists of a number of chains of particles which are connected by bonds with double-welled potentials to approximate the energetics of conformational motion. Interactions between particles on adjacent chains are modeled by shortrange repulsive potentials. We have examined the stress-strain behavior of the model using molecular dynamics simulations and find qualitative agreement with the observed experimental behavior of polymeric materials. INTRODUCTION Below the glass transition temperature, polymeric materials generally exhibit three distinct regions in their stress-strain behavior[l] as qualitatively displayed in Figure 1. The origins of these regions can be traced to the molecular response of individual polymer chains to the applied stress or strain. At low applied stress the material behaves as a linear elastic medium. In this region the removal of the applied stress results in an elastic response of the material without hysteresis. On a molecular level we interpret this region as one where the individual backbone rotational angles and bond angles, and to a lesser degree bond lengths, open and stretch without any significant local translational chain motion. In a microscopic sense the deformation is affine since the deformation is distributed uniformly throughout the sample.
Material failure
Plateau region
SPost-yield region Elastic region
Strain Figure 1. A typical stress-strain curve for a polymer below its glass-transition temperature. Mat. Res. Soc. Symp. Proc. Vol. 79. 1987 Materials Research Society
410
level of stress the modulus is often At some critical abruptly reduced to near zero and the material yields without On a molecular any significant increase in the applied stress. level we interpret this yielding and the associated plateau region in terms of a chain motion in the form of local conformaThese local chain tional changes and associated chain slippage. transitions are from one conformational minimum to another, for example from the more compact gauche state to the more extended In this respect we might term the deformation trans state. microscopically non-affine, since on the scale of the individual chains some sections are moving relative to others. After yielding, the modulus of the material increases abruptly, generally to a level in significant excess of the original modulus. The curve then ends abruptly with material failure. Microscopically this increase in modulus occurs when most of the conformational softness has been "stretched out" and we are once again in a mode of stretching backbone bond angles and bond lengths. Although we have made this analysis in terms of individual chain motions, it is important to note that the observed
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