Time dependent Properties: Creep and Stress Relaxation

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1 The viscoelastic behavior Linear Viscoelastic Behavior The linear viscoelastic behavior is the ratio between stress and strain as a function of time only and does not a function of the magnitudes of stress and strain, in linear viscoelasticity it matters at which instant an effect is created. Stress-strain curves for all viscoelastic solids (time dependent materials) are linear for sufficiently small deformations and strains, to ensure that the specimen cross section does not change appreciably. Generally polymers exhibit the properties of linear viscoelastic behavior at low stresses where strain below ( )%. The end of the region of linear viscoelasticity corresponds to ε = 0.005, so above this limit the material exhibits nonlinear viscoelastic behavior. Time dependent Properties: Creep and Stress Relaxation If a polymeric material is subjected to a constant stress, the strain will not be constant but will increase slowly and continuously with time. This effect is due to a molecular rearrangement induced by the stress. On the release of the stress, the molecules slowly recover their former spatial arrangement and the strain simultaneously returns to zero. This effect is termed creep and is a manifestation of a general property of polymeric solids known as viscoelasticity. For metals, creep effects are negligible at ordinary temperatures except that the very soft metals like lead. For polymers, creep is often occur significantly at ordinary temperatures and even more noticeable at higher temperatures. All plastics will creep to a certain extent. The degree of creep depends on several factors, such as the type of plastic, temperature, and stress level.

2 If the applied load is released before creep rupture occurs, an immediate elastic recovery will happen, equal to the elastic deformation, followed by a period of slow recovery as shown in Fig. (1), where a constant load is applied at t o and removed at t 1. On removing the load from a polymer, the material can recover most, or even all, of the strain through giving it sufficient time. The material in most cases does not recover to the original shape and a permanent deformation remains. This is different from metals where the strain produced by creep is not recoverable. The time taken to recover depends on the initial strain and the time for which the material was creeping under the load. The creep data for polymers can be represented in three ways 1. Creep curve: strain-time curve at constant stress. 2. Isochronous curve: strain-stress curve at constant time. 3. Isometric (stress relaxation) curve: stress-time curve at constant strain. Fig. (1): Creep curve with recovery. The counterpart of creep is stress relaxation, which is defined as a gradual decrease in stress with time under a constant deformation or strain as shown in Fig. (2). This behavior of a polymer is studied by stabilizing a constant deformation to the specimen and measuring the time dependent stress required for maintaining that strain.

3 Fig. (2): Stress relaxation of plastics. Relaxation in polymers is of great practical significance when the polymers are used in applications involving seals and gaskets, The rates of relaxation and creep depend on the particular material. Fig. (2.5) Linear-nonlinear transition of strain-stress relationship with respect to different time levels (isochronous curve).

4 Where the viscous flow occurs, the stress can decay to zero at sufficiently long times, but if there is no viscous flow the stress decays to a finite value, and we obtain an equilibrium modulus or compliance at infinite time. Changing temperature is equivalent to changing the time scale. Time temperature equivalence is applicable to all linear viscoelastic behaviors in polymer. If the data from several relaxation experiments done at different constant strains give the same relaxation modulus G (t), the material is linearly viscoelastic. The stress relaxation modulus at time t is another manifestation of linear viscoelasticity; it is observed in all polymers at strains below The material is linear when J (t) is independent of stress, G (t) is independent of strain, and otherwise it is nonlinear [13]. Relaxation and creep modulus can be plotted against log time to reveal their strong time dependence.

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