Stress relaxation: Experiment, theory, and computer simulation

Abstract

Experimental evidence on stress relaxation is analyzed first for a wide variety of classes of materials: metals and their alloys, synthetic and natural polymers, glasses and frozen non-polymeric organic liquids. Common features of curves σ(t) of relaxation of stress a as a function of time t are discussed, and the importance of the internal stress σ_i(∞) noted. Theoretical approaches are then reviewed, with particular attention to the cooperative model and its modifications; that model corresponds well to the experimental results. Some 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 σ(log t) curves exhibit three regions: initial, nearly horizontal, starting atσ ₀; central, descending approximately linearly; and final, corresponding toσ _i. In agreement with the theory, the slope of the simulated central part is proportional to the initial effective stressσ ₀*=σ ₀−σ _i. 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 ɛ destroys largely the resistance of a material to deformation, resulting in low values of the internal stressσ _i. On the joint basis of experimental, theoretical, and numerical results, we explain the mechanism of stress relaxation in terms of deformations occuring in the immediate environment of the defects. Simulations show several common features in the behavior of metals and polymers. Apart from the defect concentration, the amount of free volumev _f is also important.