Deformation Mechanisms in Elastomers – Rubbers

The loading and unloading stress–strain graph for rubber in Figure(1.9) shows that the behaviour as a load is removed is not the same as that when the load is being increased. This is called hysteresis and the curves are said to make a hysteresis loop.On a graph of stress against strain: the area between the curve and the strain axis represents the energy per unit
volume. This is the energy absorbed when a material is being stretched and the energy that is released when the force is removed. Rubber absorbs more energy during loading than it releases in unloading. The difference is represented by the area of the hysteresis loop, shown shaded in the stress–strain graph. The effect of hysteresis in rubber is to transfer energy to its molecules, resulting in heating. Goodrich Flexometer Heat Buildup ASTM
D 623 is an empirical method for comparing cured rubber compounds in terms of their hysteretic behavior.

Mullin’s and Payne’s Effect
Similar to the Payne effect under small deformations is the Mullins effect that is observed under large deformations. The Payne effect is a particular feature of the stress-strain behaviour of rubber, especially rubber compounds containing fillers such as carbon black. It is named after the
British rubber scientist A. R. Payne, who made extensive studies of the effect (e.g. Payne 1962). The effect is sometimes also known as the Fletcher-Gent effect, after the authors of the first study of the phenomenon (Fletcher & Gent 1953). The effect is observed under cyclic loading conditions with small strain amplitudes, and is manifest as a dependence of the viscoelastic storage modulus on the amplitude of the applied strain. Above approximately 0.1 % strain amplitude, the storage modulus decreases rapidly with increasing amplitude. At sufficiently large strain amplitudes (roughly 20%), the storage modulus approaches a lower bound. In that region where the storage modulus decreases the loss modulus shows a maximum. The Payne effect depends on the filler content of the material and vanishes for unfilled elastomers. Physically, the Payne effect can be attributed to deformation-induced changes in the material’s microstructure, i.e. to breakage and recovery of weak physical bonds linking adjacent filler clusters. Since the Payne effect is essential for the frequency and amplitude-dependent dynamic stiffness and damping behaviour of rubber bushings, automotive tyres and other products, constitutive models to represent it have been developed in the past (e.g. Lion et al. 2003).
The Mullins effect is a particular aspect of the mechanical response in filled rubbers in which the stress-strain curve depends on the maximum loading previously encountered. The phenomenon, named for rubber scientist Leonard Mullins, working at the Tun Abdul Razak Research Centre in Hertford, U.K., can be idealized for many purposes as an instantaneous
and irreversible softening of the stress-strain curve that occurs whenever the load increases beyond its prior all-time maximum value. At times, when the load is less than a prior maximum, nonlinear elastic behavior prevails. Although the term ”Mullins effect” is commonly applied to stress softening in filled rubbers.

Permanent Set:
Permanent set is the amount of deformation in a rubber after the distorting load has been removed. It can be defined as a permanent deformation that takes place in the material lower than at the yield point of the material. Permanent set is a complex phenomenon. Parameters that affect permanent set can be broadly described into two categories; 1) Service performance related factors 2) Material compound parameters. Service performance parameters include variables like mode of deformation, strain rates, temperature of application etc. While material compound parameters include variables like type of elastomer, its recipe ingredients, degree and amount of cross-linking etc. An O-ring or a Seal under energized conditions must maintain good contact force throughout the functional life of the products. Contact force is generated between the mating surfaces when one of the mating surfaces deflects and compresses the seal surface. In order for the sealing to remain effective the contact surfaces must return to the undeformed original position when the contacting force is removed. Under these conditions the deflection of the sealing element must be fully recoverable and so hyperelastic by nature. If there is any unrecoverable strain in the material the performance of the seal is diminished and leak would occur from between the surfaces. The key to designing a good sealing element is that the good contact force is as high as possible while at the same time ensuring that the deflection remains
hyperelastic in nature. This requires the use of a material with a good combination of force at a desired deformation characteristic. The relationship between strain and stress is described by the material’s stress-strain curve.

Figure 1: Uniaxial Tension Test Results

Figure 1 shows typical stress-strain curves from a polymer thermoplastic material and thermoset rubber material. Both the materials
have plastic strain properties where when the material is stretched beyond the elastic limit there is some permanent deformation and the material does not fully return to its original undeformed condition. The plastic strain, is the area between the loading and unloading line in both the graphs. In automotive application this permanent plastic strain is observed
more easily in under the hood components located near the engine compartments because of the presence of high temperature conditions. If a polymer part such as intake manifold is stressed to a certain and held for a period of time then some of the elastic strain converts to plastic strain resulting in observations of permanent deformation in the component. There are two physical mechanisms by which the amount of plastic strain increases over time, 1) Stress relaxation and 2) Creep. Creep is an increase in plastic strain under constant force, while in the case of Stress relaxation, it is a steady decrease in force under constant applied deformation or strain. Creep is a serious issue in plastic housings or snap fit components.
In Most Finite Element Analysis softwares stress relaxation and creep can both be modeled with the help of experimental test data