Compression Crystal strain model

Properties.—Studies of the mechanical properties of (SN) crystals using compression stress-strain techniques under ambient conditions, show plastic behaviour resembling that of a highly anisotropic metal, and Young s modulii, parallel and perpendicular to the chain axis, were found to be 21 and 1.4 GPa, respectively. Crystals of (SN) , mechanically deformed and examined using transmission electron microscopy, show the formation of a number of kink bands perpendicular to the chain axis, and a model has been formulated to enable prediction to be made of kink angles. ... 

The first theoretical considerations concerning n (p) and G (p) of concentrated 3-D emulsions and foams were based on perfectly ordered crystals of droplets [4,5,15-18]. In such models, at a given volume fraction and applied shear strain, all droplets are assumed to be equally compressed, that is, to deform affinely under the applied shear thus all of them should have the same shape. Princen [15,16] initially analyzed an ordered monodisperse 2-D array of deformable cylinders and concluded that G = Qiox(p < (/), and that G jumps to nearly the 2-D Laplace pressure of the cylinders at the approach of ( > = 100%, following a ( — dependence. 

Figure 2 shows the basic physical idea of the microstructure of the continuum rheologicS model we proposed earlier (2). The layers can be idealized as separated by porous slabs, which are connected by elastic springs. Liquid crystals may flow parallel to the planes in the usual Newtonian manner, as if the slabs were not there. In the direction normal to the layers, liquid crystals encounter resistance through the porous medium, proportional to the normal pressure gradient, which is known as permeation. The permeation is characterized by a body force which in turn causes elastic compression and splay of the layers. Applied strain from the compression causes dislocations to move into the sample from the side in order to relax the net force on the layers. When the compression stops and the applied stress is relaxed the permeation characteristic has no influence on stress strain field. 

H6 and BCT4 both have a bulk modulus which, within the tight-binding model is comparable in magnitude to that of diamond. In accord with an empirical TB scheme [24] H6 seems to be even harder than diamond while SCF plane wave calculations [25,26] predict that the almost equal bulk moduli of BCT4 and H6 are 17% below the diamond value. The bulk moduli of the models have been determined by calculating the elastic compliances after applying suitable strains to the crystals and inversion of the volume compressibility [68]. 

The idealization of the two coupled crystalline and amorphous components of HDPE as joined sandwich elements and their interactive plastic deformation by crystal plasticity and amorphous flow comes close to the assumptions of the Sachs model of interaction. Thus, the composite model employing a Sachs-type interaction law does indeed result in quite satisfactory predictions both for the stress-strain curve and for the texture development in plane-strain compression flow and even in other modes of deformation (Lee et al. 1993b). In the following sections we discuss the application of the composite model to plane-strain compression flow and compare the findings of the model with results from corresponding experiments. 

Figure 1. The remanent strain saturation curve dividing remanent strain space into regions that are attainable and unattainable by a polycrystal assembled from randomly oriented tetragonal single crystals. Only remanent strain states below the curve are attainable by such a material. The dots are numerical results from Landis (2003a) obtained using a micromechanical self consistent model, and the line is one divided by the function/given in Eqs. (2.7) and (2.8). The remanent strain invariants 4 and are defined in Eq. (2.5) and the results are normalized by the saturation strain in axisymmetric compression s. ...

---