Anisotropy shrinking

Shrinkage can influence product performances such as mechanical properties. Anisotropy directional property can be used when referring to the way a material shrinks during processing, such as in injection molding (Fig. 2-62) and extrusion. Shrinkage is an important consideration when fabricating... 

In the discussion that follows, the volumetric shrinking and swelling of the gross wood will be treated first, followed by discussion of anisotropy, and finally the effect of stress. 

Although not explicitly stated, the discussion so far is only strictly true for isotropic, e.g., cubic, polycrystalline materials. Crystals that are noncubic and consequently are anisotropic in their thermal expansion coefficients behave quite differently. In some cases, a crystal can actually shrink in one direction as it expands in another. When a polycrystal is made up of such crystals, the average thermal expansion can be very small, indeed. Cordierite and lithium-aluminosilicate (LAS) (see Fig. 4.4) are good examples of this class of materials. As discussed in greater detail in Chap. 13, this anisotropy in thermal expansion, which has been exploited to fabricate very low-a materials, can result in the buildup of large thermal residual stresses that can be quite detrimental to the strength and integrity of ceramic parts. 

According to the Doi-Edwards theory, after time t = Teq following a step deformation at t = 0, the stress relaxation is described by Eqs. (8.52)-(8.56). In obtaining these equations, it is assumed that the primitive-chain contour length is fixed at its equilibrium value at all times. And the curvilinear diffusion of the primitive chain relaxes momentarily the orientational anisotropy (as expressed in terms of the unit vector u(s,t) = 5R(s,t)/9s), or the stress anisotropy, on the portion of the tube that is reached by either of the two chain ends. The theory based on these assumptions, namely, the Doi-Edwards theory, is called the pure reptational chain model. In reality, the primitive-chain contour length should not be fixed, but rather fluctuates (stretches and shrinks) because of thermal (Brownian) motions of the segments. 

Comparing the results of the simulations corresponding to the several values of A with the results of the monomeric shoulder-dumbbell simulations, we see an unexpected non-monotonic behavior. The effect of the introduction of a rather small anisotropy due to the dimeric nature of the particle (small values of the interparticle separation A) leads to the increase of the size of the regions of anomalies (de Oliveira et al., 2010). Nevertheless, the increase of A shrinks those regions. 

Figure 8 shows the degree of shrinkage against tensile load. The direction of stretching and transverse direction shows the expected anisotropy. As the load increases, the shrinking strain shows more hysteresis. 

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