Relaxation plastics mechanical behavior

Object in this section is to review how rheological knowledge combined with laboratory data can be used to predict stresses developed in plastics undergoing strains at different rates and at different temperatures. The procedure of using laboratory experimental data for the prediction of mechanical behavior under a prescribed use condition involves two principles that are familiar to rheologists one is Boltzmann s superposition principle which enables one to utilize basic experimental data such as a stress relaxation modulus in predicting stresses under any strain history the other is the principle of reduced variables which by a temperature-log time shift allows the time scale of such a prediction to be extended substantially beyond the limits of the time scale of the original experiment. 

Viscoelastic and rate theory To aid the designer the viscoelastic and rate theories can be used to predict long-term mechanical behavior from short-term creep and relaxation data. Plastic properties are generally affected by relatively small temperature changes or changes in the rate of loading application. 

Takayanagi and co-workers transformed the spring and dashpot relaxation models (Section 1.5.6) to plastic and rubber elements in an effort to better explain the mechanical behavior of poly blends (Takayanagi et ai, 1963). Some simple combinations of the Takayanagi models are shown in Figure 2.11. The plastic phase is denoted by P and the rubber phase by R, while the quantities X and (p are functions of the volume fractions of parallel and series elements, respectively. 

Other polymers are amorphous, often because their chains are too irregular to permit regular packing. The onset of chain molecular motion heralds the glass transition and softening of the polymer from the glassy (plastic) state to the rubbery state. Mechanical behavior includes such basic aspects as modulus, stress relaxation, and elongation to break. Each of these is relatable to the polymer s basic molecular structure and history. 

The preceding sections describe the mechanical behavior of a polymeric sample in terms of creep and stress relaxation. Both elastomeric and plastic materials can be modeled by combinations of springs and dashpots. However, these are only models. Ultimately stress relaxation and creep derive from molecular origins, and it is in this area that more recent studies have been concentrated (11-15). 

In the preparation and processing of ionomers, plasticizers may be added to reduce viscosity at elevated temperatures and to permit easier processing. These plasticizers have an effect, as well, on the mechanical properties, both in the rubbery state and in the glassy state these effects depend on the composition of the ionomer, the polar or nonpolar nature of the plasticizer and on the concentration. Many studies have been carried out on plasticized ionomers and on the influence of plasticizer on viscoelastic and relaxation behavior and a review of this subject has been given 119]. However, there is still relatively little information on effects of plasticizer type and concentration on specific mechanical properties of ionomers in the glassy state or solid state. 

Aside from ion content, a wide range of properties is available in ionomers by control of various processing variables, such as degree of conversion (neutralization), type of counterion, plasticizer content and thermal treatment. Various examples illustrating possible effects of these variables on mechanical relaxation behavior and on such mechanical properties as stiffness, strength, and time- or energy-to-fracture have been given. 

The basic viscoelastic theory assumes a timewise linear relationship between stress and strain. Based on this assumption and using mechanical models thought to represent the behavior of a plastic material, it can be shown that the stress, at any time t, in a plastic held at a constant strain (relaxation test), is given by ... 

Sadanobu, J. and Tsukioka, M., Mechanical relaxation behaviors for homolog poly(alkylenenaphthalate)s, in Proceedings of the 55th SPE ANTEC 97 Conference, May 5-8, 1997, Toronto, ON, Canada, Society of Plastics Engineers, Brookfield, CT, 1997, Vol. 2, pp. 1567-1571. 

In a subsequent communication, Elliott and coworkers found that uniaxially oriented membranes swollen with ethanol/water mixtures could relax back to an almost isotropic state. In contrast, morphological relaxation was not observed for membranes swollen in water alone. While this relaxation behavior was attributed to the plasticization effect of ethanol on the fluorocarbon matrix of Nafion, no evidence of interaction between ethanol and the fluorocarbon backbone is presented. In light of the previous thermal relaxation studies of Moore and co-workers, an alternative explanation for this solvent induced relaxation may be that ethanol is more effective than water in weakening the electrostatic interactions and mobilizing the side chain elements. Clearly, a more detailed analysis of this phenomenon involving a dynamic mechanical and/ or spectroscopic analysis is needed to gain a detailed molecular level understanding of this relaxation process. 

Studies on the mechanical properties of glassy polymer-solvent or, more generally, polymer-diluent mixtures have been primarily concerned with the deformation behavior at small strains which is governed by the viscoelastic properties of the material. From these studies it is well known that diluents significantly affect relaxation processes in glassy polymers, as clearly evidenced by phenomena such as plasticization and antiplasticization... 

Crack Stability. At low test speeds, stable crack growth with an extended stress-whitened plastic zone and crack blunting occur by the same mechanisms as those involved in the kinetics of the plastic zone, namely, rubber cavitation followed by shear deformation of the matrix. The ability of the matrix to shear is controlled by its relaxation behavior, which therefore determines its plasticity and the deformation imposed on rubbery particles distant from the notch. 

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