Microstructure 3 Poisson

The elastic properties of PS depend on its microstructure and porosity. The Young s modulus for meso PS, as measured by X-ray diffraction (XRD) [Ba8], acoustic wave propagation [Da5], nanoindentation [Bel3] and Brillouin spectroscopy [An2], shows a roughly (1-p)2 dependence. For the same values of porosity (70%), micro PS shows a significantly lower Young s modulus (2.4 GPa) than meso PS (12 GPa). The Poisson ratio for meso PS (0.09 for p=54%) is found to be much smaller than the value for bulk silicon (0.26) [Ba8]. 

The material properties used in the simulations pertain to a new X70/X80 steel with an acicular ferrite microstructure and a uniaxial stress-strain curve described by er, =tr0(l + / )", where ep is the plastic strain, tr0 = 595 MPa is the yield stress, e0=ff0l E the yield strain, and n = 0.059 the work hardening coefficient. The Poisson s ratio is 0.3 and Young s modulus 201.88 OPa. The system s temperature is 0 = 300 K. We assume the hydrogen lattice diffusion coefficient at this temperature to be D = 1.271x10 m2/s. The partial molar volume of hydrogen in solid solution is... 

The relationship between the structure of the disordered heterogeneous material (e.g., composite and porous media) and the effective physical properties (e.g., elastic moduli, thermal expansion coefficient, and failure characteristics) can also be addressed by the concept of the reconstructed porous/multiphase media (Torquato, 2000). For example, it is of great practical interest to understand how spatial variability in the microstructure of composites affects the failure characteristics of heterogeneous materials. The determination of the deformation under the stress of the porous material is important in porous packing of beds, mechanical properties of membranes (where the pressure applied in membrane separations is often large), mechanical properties of foams and gels, etc. Let us restrict our discussion to equilibrium mechanical properties in static deformations, e.g., effective Young s modulus and Poisson s ratio. The calculation of the impact resistance and other dynamic mechanical properties can be addressed by discrete element models (Thornton et al., 1999, 2004). 

Figure 1-2 show the relationship between Young s modulus, Poisson s ratio and the thermal expansion coefficient of TiC-NiyAl composites and the volume fraction of NiyAl, respectively. For the discussion of the relationship between the properties and the material microstructures, figure 1-2 also give the numerical results of Young s modulus, Poisson s ratio and the thermal expansion coefficient of TiC-NiyAl composites calculated by a two-... 

Evans and collaborators [59] have shown how an anisotropic microstructure consisting of nodules and fibrils can be produced in polytetrafluoroethylene (PTFE) that gives rise to a very large negative Poisson s ratio. Figure 7.22 is a schematic representation of the deformation of microporous PTFE. 

In a further study, Evans and Alderson [61-63] showed that in both PTFE and ultrahigh molecular weight polyethylene (UHMPE) an isotropic microstructure of nodules and fibrils, shown schematically in Figure 7.24 can give rise to a negative Poisson s ratio. Essentially this arises because when the materials are stretched the extension of the fibrils causes the nodules to move apart. 

Table 1. Microstructural parameters for mica glass ceramic materials. For aU materials, the volume fraction is Vf 70%, the elastic modulus E ps 70 GPa and Poisson s ratio v ps 0.26. Platelet dimensions measured from sectioned and etched samples. Yield stress was determined according to a procedure given in reference 12.

Figure 8.35 A schematic representation of the structural changes observed in microporous polytetrafluoroethylene undergoing tensile loading in the x direction (a) initial dense microstructure, (b) tension in fibrils causing transverse displacement of anisotropic nodal particles with lateral expansion, (c) rotation of nodes producing further lateral expansion and (d) fully expanded structure prior to further, plastic deformation due to node break-up. (Reproduced from Evans, K.E. and Caddock, B.D. (1989) Microporous materials with negative Poisson s ratios. II. Mechanisms and interpretation. J. Phys. D. Appl. Phys., 22, 1883. Copyright (1989).)...

Figure 8.37 Schematic diagram of an isotropic microstructure consisting of nodules and fibrils that causes a negative Poisson s ratio when pulled In any direction. (Reproduced from Evans, K.E. and Alderson, K.L (1992) The static and dynamic moduli of auxetic microporous polyethylene. ]. Mater. Sci. Lett, 11, 1721. Copyright (1992) Springer Science and Business Media.)...

Xu, T. and Li, G.Q. (2011) A shape memory polymer based syntactic foam with negative Poisson s ratio. Mater. Sci. Eng. A-Struct. Mater Properties,Microstructure and Processing, 528, 6804-6811. 

Caddock, BD. and Evans, K.E. (1989) Microporous materials with negative Poisson s ratios. I. Microstructure and mechanical properties. J. Phys. D. Appl. Phys., 22,1877. 

Mills and Zhu [73] used the same microstructural model assuming 60% of the polymer in the cell faces and compression in the (001) direction. Cell edges were bent and compressed axially, while cell faces acted as membranes. The predicted Young s moduli were slightly low (Fig. 10) because compressive face stresses were ignored, but the Poisson ratio was correctly predicted. The predicted value of collapse stress for polyethylene foams was close to the experimental value. 

It is now known that auxeticity and NTE are phenomena that may be observed in a variety of materials. The way these properties arise in a particular material may be dependent on the way that particular features in the material s micro- or nanostructure deform when subjected to a thermal or mechanical load (the deformation mechanism). In other words, the geometry of the microstructure/nanostructure plays an important role in defining the Poisson s ratio (Alderson 1999) or the thermal expansion coefficient. In this respect, it should be noted that some of the geometry/ deformation mechanisms that lead to particular values of the Poisson s ratios or thermal expansion coefficients are independent from the scale of structure. Moreover, in the past decade, it became common practice to use macroscaled models to ease examination and explanation of the interplaying mechanisms that lead to the deformation of the geometry at the micro- and nanoscales. 

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