Deformation uniaxial

Whereas k = 1.3 is derived from the above-presented NSE data, k = 2.75 is expected for a four-functional PDMS network of Ms = 5500 g/mol on the basis of Eq. (67). Similar discrepancies were observed for a PDMS network under uniaxial deformation [88]. Elowever, in reality this discrepancy may be smaller, since Eq. (67) provides the upper limit for k, calculated under the assumption that the network is not swollen during the cross-linking process due to unreacted, extractable material. Regardless of this uncertainty, the NSE data indicate that the experimentally observed fluctuation range of the cross-links is underestimated by the junction constraint and overestimated by the phantom network model [89],... 

In uniaxial deformation, the energetic contribution to the total elastic force [4,5,16,80-82] is given by the thermodynamically exact relation... 

Uniaxial deformations give prolate (needle-shaped) ellipsoids, and biaxial deformations give oblate (disc-shaped) ellipsoids [220,221], Prolate particles can be thought of as a conceptual bridge between the roughly spherical particles used to reinforce elastomers and the long fibers frequently used for this purpose in thermoplastics and thermosets. Similarly, oblate particles can be considered as analogues of the much-studied clay platelets used to reinforce a variety of materials [70-73], but with dimensions that are controllable. In the case of non-spherical particles, their orientations are also of considerable importance. One interest here is the anisotropic reinforcements such particles provide, and there have been simulations to better understand the mechanical properties of such composites [86,222],... 

The comparison between experimental and predicted intensity (Fig. 10.3) reveals deviations between theory and experimental data already at relatively low uniaxial deformation. A reasonable explanation is an increase of lattice distortions by local tensions which modify the envelope and thus the total intensity. Theoretical computation of mechanical anisotropy in a bcc-lattice supports the explanation [265],... 

R > is the mean square end-to-end distance of the polymer chain. Consider a sample stretched by a factor Ay in the Y direction and Az in the Z direction. A general deformation can be easily treated, but for simplicity only uniaxial stretching or isotropic swelling will be examined. Note that under conditions of uniaxial deformation, the volume of the sample changes very little. This change may be ignored, and it becomes convenient to set Az = A and Ax — Ay. ... 

A theoretical investigation of the use of NMR lineshape second moments in determining elastomer chain configurations has been undertaken. Monte Carlo chains have been generated by computer using a modified rotational isomeric state (RIS) theory in which parameters have been included which simulate bulk uniaxial deformation. The behavior of the model for a hypothetical poly(methylene) system and for a real poly(p-fluorostyrene) system has been examined. Excluded volume effects are described. Initial experimental approaches are discussed. 

Classical molecular theories of rubber elasticity (7, 8) lead to an elastic equation of state which predicts the reduced stress to be constant over the entire range of uniaxial deformation. To explain this deviation between the classical theories and reality. Flory (9) and Ronca and Allegra (10) have separately proposed a new model based on the hypothesis that in a real network, the fluctuations of a junction about its mean position may may be significantly impeded by interactions with chains emanating from spatially, but not topologically, neighboring junctions. Thus, the junctions in a real network are more constrained than those in a phantom network. The elastic force is taken to be the sum of two contributions (9) ... 

Bicakci, E., Zhou, X. and Cakmak, M., Phase and uniaxial deformation behavior of ternary blends of poly(ethylene naphthalate), poly(ether imide) and poly(ether ether ketone), 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. 1593-1599. 

In a sample under small uniaxial deformation, the negative quotient of the lateral strain (flat) and the longitudinal strain (fiong) in the direction of the uniaxial force... 

Note 1 Lateral strain f lat is the strain normal to the uniaxial deformation. 

Note 4 For an anisotropic material, // varies with the direction of the uniaxial deformation. 

Component stress tensor resulting from a tensile uniaxial deformation. 

Note 1 The stress tensor for a uniaxial deformation is given in Definition 3.1. 

Component stress tensor resulting from a compressive uniaxial deformation. Note See notes 1 and 2 of Definition 3.2. 

Force resulting from an applied tensile or compressive uniaxial deformation divided by the initial cross-sectional area of the sample normal to the applied deformation. 

Note 3 Young s modulus may he evaluated using tensile or compressive uniaxial deformation. If determined using tensile deformation it may be termed tensUe modulus. Note 4 For non-Hookean materials the Young s modulus is sometimes evaluated as ... 

Note 3 For elastomers, which are assumed incompressible, the modulus is often evaluated in uniaxial tensile or compressive deformation using X - as the strain function (where X is the uniaxial deformation ratio). In the limit of zero deformation the shear modulus is evaluated as... 

Interpretation of the viscoelastic behaviour of a liquid or solid in simple shear or uniaxial deformation such that... 

Note 1 ymay be in simple shear or uniaxial deformation. 

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