Polymers stress-strain

For glassy and crystalline polymers there are few data on the variation of stress relaxation with amplitude of deformation. However, the data do verily what one would expect on the basis of the response of elastomers. Although the stress-relaxation modulus at a given time may be independent of strain at small strains, at higher initial fixed strains the stress or the stress-relaxation modulus decreases faster than expected, and the lloltz-nuinn superposition principle no longer holds. 

The application of finite strains and stresses leads to a very wide range of responses. We have seen in Chapters 4 and 5 well-developed linear viscoelastic models, which were particularly important in the area of colloids and polymers, where unifying features are readily achievable in a manner not available to atomic fluids or solids. In Chapter 1 we introduced the Peclet number ... 

Einaga.Y., Osaki.K., Kurata,M., Kimura,S.,Tamura,M. Stress relaxation of polymers of polymers under large strain. Polymer J. (Japan) 2,550-552 (1971). See also Polymer J. (Japan) 5,91-96 (1973). 

Date,M., Fukada,E. An apparatus for measuring piezoelectric strain and stress constants in polymers. Rep. Progr. Polymer Phys. Japan 13, 375 (1970). 

Hooke s law relates stress (or strain) at a point to strain (or stress) at the same point and the structure of classical elasticity (see e.g. Love, Sokolnikoff) is built upon this linear relation. There are other relationships possible. One, as outlined above (see e.g. Green and Adkins) involves the large strain tensor Cjj which does not bear a simple relationship to the stress tensor, another involves the newer concepts of micropolar and micromorphic elasticity in which not only the stress but also the couple at a point must be related to the local variations of displacement and rotation. A third, which may prove to be very relevant to polymers, derives from non-local field theories in which not only the strain (or displacement) at a point but also that in the neighbourhood of the point needs to be taken into account. In polymers, where the chain is so much stiffer along its axis than any interchain stiffness (consequent upon the vastly different forces along and between chains) the displacement at any point is quite likely to be influenced by forces on chains some distance away. 

The fracture behaviour of polymers, usually under conditions of mode I opening, considered the severest test of a material s resistance to crack initiation and propagation, is widely characterised using linear elastic fracture mechanics (LEFM) parameters, such as the plane strain critical stress intensity factor, Kic, or the critical strain energy release rate, Gic, for crack initiation (determined using standard geometries such as those in Fig. 1). LEFM... 

The model represents a liquid (able to have irreversible deformations) with some additional reversible (elastic) deformations. If put under a constant strain, the stresses gradually relax. When a material is put under a constant stress, the strain has two components as per the Maxwell Model. First, an elastic component occurs instantaneously, corresponding to the spring, and relaxes immediately upon release of the stress. The second is a viscous component that grows with time as long as the stress is applied. The Maxwell model predicts that stress decays exponentially with time, which is accurate for most polymers. It is important to note limitations of such a model, as it is unable to predict creep in materials based on a simple dashpot and spring connected in series. The Maxwell model for creep or constant-stress conditions postulates that strain will increase linearly with time. However, polymers for the most part show the strain rate to be decreasing with time [23-26],... 

In our preliminary report (2), we have chosen poly (methyl methacrylate) or PMMA as a host polymer and methyl acrylate as the guest monomer. They were both crosslinked by a divinyl acrylic monomer. However, because of the similarity in the constitutions of these two components, it was not possible to establish the gradient profile through chemical analysis. In this work, we have selected a halogenated acrylic monomer as the second component to be diffused into PMMA. By analyzing the halogen content, it was possible to determine the profiles of the gradient polymers. Stress-strain measurements of the samples were then carried out on these unique materials. 

Al-Saidi LF, Mortensen K, Almdal K (2003) Environmental stress cracking resistance behaviour of polycarbonate in different chemicals by determination of the time-dependence of stress at constant strains. Polym Degradat Stabil 82(3) 451—461... 

A few rheometers are available for measurement of equi-biaxial and planar extensional properties polymer melts [62,65,66]. The additional experimental challenges associated with these more complicated flows often preclude their use. In practice, these melt rheological properties are often first estimated from decomposing a shear flow curve into a relaxation spectrum and predicting the properties with a constitutive model appropriate for the extensional flow [54-57]. Predictions may be improved at higher strains with damping factors estimated from either a simple shear or uniaxial extensional flow. The limiting tensile strain or stress at the melt break point are not well predicted by this simple approach. 

Y.Einaga, K.Osaki, M.Kurata, Stress relaxation of pol3nmer solutions under large strain, Polym. J. 2 (1971), 550-552. 

An increase in M is also reported to increase the temperature at which a shear to craze transition occurs in both PC and poly(ether sulfone) (PES) and, above the transition temperature, the craze strain, or stress, is greater for the higher molecular weight samples These changes are a result of a greater resistance to disentanglement in the higher M polymers. 

Colomban, R, Analysis of strain and stress in ceramic, polymer and metal matrix composites by Raman spectroscopy, Adv. Eng. Mater., 4, 535, 2002. 

Rate Theory for Unfolding and Refolding of a Helix-like Polymer Exposed to Strain or Stress Pili Elongated in Region II... 

Rate Theory for Elongation and Contraction of a Linear Polymer Exposed to Strain or Stress -Pili Elongated in Region III... 

When a dimensional change in a polymer coating does not match that of its constraint (such as the substrate to which it adheres), the resulting strain generates stress in both the polymer and the substrate. Strain arises in polymers by thermal expansion and contraction ( ), from solvent and by-product evaporation (2), from moisture absorption (2), from cure (2), and from physical aging (12). ... 

For small strains the stress-relaxation rate of vulcanized rubbers at long times is proportional to tan 8 (178). This will also be true at large strains if strain-time factorization applies. The implication of this for the results of Cotten and Boonstra (150) is that tan 8 in unswollen vulcanizates is only little affected by carbon black-polymer interactions at strain levels between 75 and 250% elongation (and at very low frequencies) and suggests that the substantial increases in tan 8 observed in filled rubbers at small strains are due primarily to the effects of secondary filler aggregation. 

Linear elastic solutions from stress analysis handbooks Relatively quick with validated results. Does not account for polymer nonlinearity. May underestimate strains and stresses and underestimate deformations. Standard geometries only. 

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