Elastic hard polymers stress

Chou, G.J., Hiltner, A. and Baer, E., The role of surfaces stresses in the deformation of hard elastic polypropylene. Polymer, 1986, 27 369 ... 

Nanoindentation is nowadays one of the most used methods to measure the mechanical properties of polymers, attracting great attention as a technique to mechanically characterize polymer nanocomposites [137-142]. This technique uses the same principle as microindentation, but with much smaller probe areas and very low loads (on the order of nanonewtons), so as to produce indentations from less than a hundred nanometers to a few micrometers in size and depth [143]. Although it has been vastly used to characterize the mechanical properties, particularly hardness, elastic modulus, yield stress, and fracture toughness, of several polymers [144—152] and shown to be mainly influenced by the testing procedure, penetration depths, and holding time, limited work has been dedicated to the characterization of the mechanical behavior of polymer nanocomposites using this technique. 

It is somewhat difficult conceptually to explain the recoverable high elasticity of these materials in terms of flexible polymer chains cross-linked into an open network structure as commonly envisaged for conventionally vulcanised rubbers. It is probably better to consider the deformation behaviour on a macro, rather than molecular, scale. One such model would envisage a three-dimensional mesh of polypropylene with elastomeric domains embedded within. On application of a stress both the open network of the hard phase and the elastomeric domains will be capable of deformation. On release of the stress, the cross-linked rubbery domains will try to recover their original shape and hence result in recovery from deformation of the blended object. 

The peculiarities of dynamic properties of filled polymers were described above in connection with the discussion of the method of determining a yield stress according to frequency dependence of elastic modulus (Fig. 5). Measurements of dynamic properties of highly filled polymer melts hardly have a great independent importance at present, first of all due to a strong amplitude dependence of the modulus, which was observed by everybody who carried out such measurements [3, 5]. 

The hardness of a polymer can also be estimated from the modulus of elasticity E (high E modulus indicates high hardness). The advantage here is that every region of elasticity and every degree of hardness can be detected with a single kind of measurement (determination of stress-strain-behavior or torsional oscillation). 

Table 5.2 lists polymers and their tendency toward crystallinity. Yield stress and strength, and hardness increase with an increase in crystallinity as does elastic modulus and stiffness. Physical factors that increase crystallinity, such as slower cooling and annealing, also tend to increase the stiffness, hardness, and modulus of a polymeric material. Thus polymers with at least some degree of crystallinity are denser, stiffer, and stronger than amorphous polymers. However, the amorphous region contributes to the toughness and flexibility of polymers. 

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

A third observation obtained from Figure 27 is the disappearance of these fissures as soon as the film is locally separated (Fig. 27 a, arrow B). It must be assumed, therefore, that the deformation lines close upon stress relieve just as in hard-elastic materials. A characteristic feature of some of those highly crystalline, highly oriented polymers is the fact that they can be extended by 50-100%, this extension being practically completely and inmiediately reversible... 

Contact during and after CMP is between a wafer and a polymer as a pad or brush thus the nature of the contact is predominantly elastic. As we saw in Section 2.1, the ratio of the elastic modulus E and the hardness H determines the extent of the plasticity in the contact region as well as the surface topography. For metals, E/H is typically 100 or greater, whereas for many of the softer polymers (low P s), E/H is only about 10. Thus the contact between metals and polymers is almost completely elastic except against very rough surfaces. Another factor that affects the friction of polymers is the strong time dependence of their mechanical properties most polymers are viscoelastic and also show a marked increase of flow stress with strain rate. 

Neither the uniform strain model nor the uniform stress model is appropriate for this microstructure. Consequently, the elastic moduli of polyurethanes lie between the limits set by Eqs (4.11) and (4.12). For a network chain of Me = 6000, the rubber elasticity theory of Eq. (3.20) predicts a shear modulus of about 0.4 MPa. The hard blocks will have the typical 3GPa Young s modulus of glassy polymers. Increases in the hard block content cause the Young s modulus to increase from 30 to 500 MPa (Fig. 7.13). For automobile panel applications it is usual to have a high per cent of hard blocks so that the room temperature flexural modulus is 500 MPa. 

Still further differences are observed for stress/strain diagrams of what are known as hard elastic or springy polymers. These polymeric states should exhibit a large energy-elastic component which is attributed to a special network structure (see Figure 38-10). However, electron microscopic studies do not provide any evidence for the proposed network structure. 

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