Polymers viscoelastic deformation

Micro-mechanical processes that control the adhesion and fracture of elastomeric polymers occur at two different size scales. On the size scale of the chain the failure is by breakage of Van der Waals attraction, chain pull-out or by chain scission. The viscoelastic deformation in which most of the energy is dissipated occurs at a larger size scale but is controlled by the processes that occur on the scale of a chain. The situation is, in principle, very similar to that of glassy polymers except that crack growth rate and temperature dependence of the micromechanical processes are very important. 

The effect of gas compression on the uniaxial compression stress-strain curve of closed-cell polymer foams was analysed. The elastic contribution of cell faces to the compressive stress-strain curve is predicted quantitatively, and the effect on the initial Young s modulus is said to be large. The polymer contribution was analysed using a tetrakaidecahedral cell model. It is demonstrated that the cell faces contribute linearly to the Young s modulus, but compressive yielding involves non-linear viscoelastic deformation. 3 refs. 

Dynamic mechanical tests measure the response of a material to a periodic force or its deformation by such a force. One obtains simultaneously an elastic modulus (shear, Young s, or bulk) and a mechanical damping. Polymeric materials are viscoelastic-i.e., they have some of the characteristics of both perfectly elastic solids and viscous liquids. When a polymer is deformed, some of the energy is stored as potential energy, and some is dissipated as heat. It is the latter which corresponds to mechanical damping. 

Linear amorphous polymers can behave as either Hookian elastic (glassy) materials, or highly elastic (rubbery) substances or as viscous melts according to prevailing temperature and time scale of experiments. The different transitions as shown schematically in Figure 5.1 are manifestations of viscoelastic deformations, which are time dependent [1]. 

When all these variables are fixed for a particular specimen, it will still be observed that the properties of the material will depend strongly on the temperature and time of testing compared, say. to metals. This dependence is a consequence of the viscoelastic nature of polymers. Viscoelasticity implies that the material has the characteristics both of a viscous liquid which cannot support a stress without flowing and an elastic solid in which removal of the imposed stress results in complete recovery of the imposed deformation. 

In order to have enough data to characterise the viscoelastic behaviour of an amorphous polymer fully, it is necessary to collect data on relaxations over about ten to fifteen decades of time. In practice, this is extremely tedious, and may not even be possible. To overcome the problem, use is made of the fact that, for most amorphous polymers, a deformation for a short period of time at one temperature is equivalent to a longer period at a lower... 

To cause a polymer to deform or flow requires the application of a force. If a force is applied and then withdrawn quickly, the polymer molecules tend to revert to their previous undeformed configuration, a process called relaxation. In other words, the polymer melt exhibits a certain elastic quality. This elasticity comes about because the molecules were disturbed from what was a thermodynamically favorable arrangement. If, however, the force is applied gradually and consistently, the molecules begin to flow irreversibly. (Silly putty, a siloxane polymer, is ideal for demonstrating this effect. If dropped, it bounces but it can be shaped by the slow application of pressure.) Because of entanglement of the polymer chains and frictional effects, the flowing liquid will be very viscous. This combination of properties, namely elasticity and viscous flow, is why polymers are referred to as viscoelastic materials. 

In the last chapter we discussed the relation between stress and strain (or instead rate-of-strain) in one dimension by treating the viscoelastic quantities as scalars. When the applied strain or rate-of-strain is large, the nonlinear response of the polymeric liquid involves more than one dimension. In addition, a rheological process always involves a three-dimensional deformation. In this chapter, we discuss how to express stress and strain in three-dimensional space. This is not only important in the study of polymer rheological properties in terms of continuum mechanics " but is also essential in the polymer viscoelastic theories and simulations studied in the later chapters, into which the chain dynamic models are incorporated. 

Under static loading conditions where either the stress or strain is keeping constant polymer materials (especially thermoplastics) show non-linear viscoelastic deformation behaviour to appear as retardation (creep) or relaxation. Long-term investigations to analyse creep or relaxation can be accomplished at flexural, indentation, or uniaxial tensile or compression loading as a function of time and loading level as well as environmental conditions such as temperature, media etc. (see [13Gre], p. 171 - 183). 

The experiment we introduced at the beginning of the previous subsection is also called the creep experiment. A small stress of Gq is imposed on a solid sample for a time period of to at a constant temperature after the stop of stress, the strain of changing with the time period of t monitors the relaxatirMi curve. There are four typical responses separately corresponding to viscous, elastic, anelastic and viscoelastic responses, as illustrated in Fig. 6.8. The creep curve of polymer viscoelasticity exhibits both instant and retarded elastic responses upon imposing and removal of the stress, and eventually reaches the permanent deformation. 

Polymers undergo deformation under an applied stress over their lifetime some deformations which are irrecoverable once the source of stress is removed are referred to as creep. An understanding of the mechanical response of a polymer can be obtained by investigating the viscoelastic properties using creep experiments, where the behaviour is monitored under small deformational stress. Creep behaviour is an important consideration if the properties and dimensions are to be maintained. Experimental creep behaviour can be quantified using the four-element model with some limitations evident in the viscoelastic transitional region. ... 

Pre-treatment of aluminium). These surfaces all had whiskers of oxide on the outermost parts and in some cases, depending upon the details of the treatment, there were also pores similar to those already described. These whiskers were 100-400 A long and 50-100 A in diameter and the pores were about 400 A in diameter. Their work quite clearly implies that there is a double interlocking, with the whiskers being embedded in adhesive and with the adhesive penetrating the pores. Thus, the region between metal and adhesive has the character of a composite. The mechanism of failure depends upon a viscoelastic deformation of the polymer-adhesive together with a rupture of the other adhesive bonds that have been formed. 

In some previous papers we have shown that the volume behavior of polymers under any thermal history can be described well using a multiparameter model [4,6] based on free volume [7]. It should be pointed out that the multiparameter model, developed by Hutchinson and Kovacs [5,8], was used here in its early version, where the partition parameter x equals zero, i.e., a full structural dependence of the retardation times was assumed. But the whole formalism is easily applied to values of x not equal to zero. Even in this simple version the model will demonstrate its power in predicting viscoelastic deformation properties. 

Kietzmann C, Van der Walt JP, Morsi YS (1998) A free-front tracking algorithm for a control-volume-based Hele-Shaw method. Int J Numer Methods Eng 41 253-269 Kim SH, Kim CH, Oh H, Choi CH, Kim BY, Youn JR (2007) Residual stresses and viscoelastic deformation of an injection molded automotive part. Korea-Australia Rheol J 19 183-190 Klein DH, Leal LG, Garcfa-Cervera CJ, Ceniceros HD (2008) Three-dimensional shear-driven dynamics of polydomain textures and disclination loops in liquid crystalline polymers. J Rheol 52 837-863... 

And although thermoforming is basically a rubbery solid deformation process, the viscoelastic character of the polymer may need to be understood, particularly for the plug-assisted forming process. Computer-aided design programs also may need polymer viscoelastic properties. This may be particularly true for crystalline polymers such as polyethylene and polypropylene when formed above their melt temperatures. This is discussed below. 

The study of polymer viscoelasticity treats the interrelationships among elasticity, flow, and molecular motion. In reality, no liquid exhibits pure Newtonian viscosity, and no solid exhibits pure elastic behavior, although it is convenient to assume so for some simple problems. Rather, all deformation of real bodies includes some elements of both flow and elasticity. Because of the long-chain nature of polymeric materials, their visco-elastic characteristics come to the forefront. This is especially true when the times for molecular relaxation are of the same order of magnitude as an imposed mechanical stress. 

At aU technically relevant temperatures, polymers deform by creep. To describe the time-dependence of plastic deformation, we again exploit equation (8.3). In contrast to the viscoelastic deformation, there is no restoring force in viscoplasticity. Equation (8.3) is thus used to describe the dashpot element connected in series in the four-parameter model from figure 8.7(b). 

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