Comer deformation

Ammar A, Leo V, Regnier G (2003) Comer deformation of injected thermoplastic parts. Int J Forming Processes 6 53-70... 

The crystal structure of NiAl is the CsCl, or (B2) structure. This is bcc cubic with Ni, or A1 in the center of the unit cell and Al, or Ni at the eight comers. The lattice parameter is 2.88 A, and this is also the Burgers displacement. The unit cell volume is 23.9 A3 and the heat of formation is AHf = -71.6kJ/mole. When a kink on a dislocation line moves forward one-half burgers displacement, = b/2 = 1.44 A, the compound must dissociate locally, so AHf might be the barrier to motion. To overcome this barrier, the applied stress must do an amount of work equal to the barrier energy. If x is the applied stress, the work it does is approximately xb3 so x = 8.2 GPa. Then, if the conventional ratio of hardness to yield stress is used (i.e., 2x3 = 6) the hardness should be about 50 GPa. But according to Weaver, Stevenson and Bradt (2003) it is 2.2 GPa. Therefore, it is concluded that the hardness of NiAl is not intrinsic. Rather it is determined by an extrinsic factor namely, deformation hardening. 

One could also construct a network involving elements which allow some adjustment in the location of their coupling points in response to deformation. Consider a tetrahedral network element (3) in which two gaussian strands of equal contour length are attached to the comers and joined together at their midpoints by a crosslink ... 

If the network is given a tensile deformation in the 2 direction and the comers move affinely, the four chains in the tetrahedron contribute independently to the modulus, with the well known result obtained from the rubber elasticity theory ... 

Stress calculations are carried out by the finite element method. Here, the commercial finite method code ABAQUS (Hibbit, Karlsson, and Sorensen, Inc.) is used. Other codes such as MARC, ANSYS are also available. To calculate the stresses precisely, appropriate meshes and elements have to be used. 2D and shell meshes are not enough to figure out stress states of SOFC cells precisely, and thus 3D meshes is suitable for the stress calculation. Since the division of a model into individual tetrahedral sometimes faces difficulties of visualization and could easily lead to errors in numbering, eight-comered brick elements are convenient for the use. The element type used for the stress simulation here is three-dimensional solid elements of an 8-node linear brick. In the coupled calculation between the thermo-fluid calculation and the stress calculation a same mesh model have to be used. Consequently same discrete 3D meshes used for the thermo-fluid analysis are employed for the stress calculation. Using ABAQUS, the deformations and stresses in a material under a load are calculated. Besides this treatment, the initial and final conditions of models can be set as the boundary conditions and the structural change can thus be treated. 

In the C09S8 structure [Ojj—Fm3m Co in 32(f) and4(b), S in 24(e) and 8(c)] the anions form a slightly distorted cubic close-packed sublattice. The cations occupy half the tetrahedral and 1/8 of the octahedral sites (Fig. 57). The tetrahedral holes are deformed while the [CoS ] octahedra are regular (228). The tetrahedrally-coordinated cobalt atoms (f) lie at the comers of cubes with edge length 2.50 A (see Fig. 57). Thus, in addition to the four bonds with sulfur these cobalt atoms form half bonds... 

Nieminen et al. [152] observed a different mechanism of plastic deformation in essentially the same geometry, but at higher velocities (100 m/s versus 5 m/s) and with a different model for the potential between Cu atoms. Sliding took place between (100) layers inside the tip. This led to a reduction of the tip by two layers that was described as the climb of two successive edge dislocations under the action of the compressive load. Although wear covered more of the surface with material from the tip, the friction remained constant at constant normal load. The reason was that the portion of the surface where the tip advanced had a constant area. As in Sprensen et al. s work [63], dislocations nucleated at the comers of the contact and then propagated through it. 

The microplatform (sketched in Fig. 7g-i) also works by way of the assistance of microvalves, integrated into the four comers of the chip [77]. The programmed push-and-pull of each microvalve will deform the diaphragms (Fig. 7h) of each valve sequentially, thereby realizing the desired platform function, as shown in Fig. 7i. 

When Pd is deposited on MgO, the activation of C2H2 is much more efficient than for an isolated Pd atom. The structural distortion of adsorbed C2H2 follows the trend comer > edge > terrace > free atom. The contribution of the electron charge transfer from acetylene to Pd or Pdi/MgO, the a donation in the Dewar-Chatt-Duncanson model [231,232], is similar in the four cases, and is much smaller than the charge transfer in the other direction, i.e. from Pd or Pdi/MgO to acetylene. This corroborates the finding that the interaction with the MgO substrate increases the basic character of the Pd atom. The donor capability of Pd increases as a function of the adsorption site on MgO in the order terrace < edge < comer, the same order foimd for the deformation of the acety-... 

Figure 3. Thermally averaged deformation maps. Section (a) at z = 0.75 in the basal plane, (b) at z = 0.625 (containing the tetrahedral position) and (c) at z = 0.5 (containing the octahedral position). The origin is at the top left comer and the a and b axes increase across and down the page respectively. Contours are at intervals of 0.015 a.u. and dotted lines are negative, solid lines are positive.

A similar approach was used by Wijesekera et al. who were attempting to strap a porphyrin with very short alkyl chains - short enough to cause deformation of the porphyrin. Obviously in this case, linking opposite comers of a preformed porphyrin would, at best, give very poor yields. Instead the two halves of the porphyrin were assembled at each end of the strap, and only at the last step was the porphyrin 192 formed by acid-catalyzed intramolecular cyclization under high dilution conditions (Scheme 56). 

In general the antiferrodistortive pattern is more stable than the ferrodistortive order in a 3-dimensional frame-work of comer-connected octahedra (jperov tes, lead nitrocomplexes). As discussed just before the antiferrodistortive order leads to appreciable deformations of those octahedral sites which are occupied by non-Jahn-Teller ions in elpasolite-type stmctuies. Thus the ferrodistortive order may be stabilized also (oxidic elpasolites, alkaline earth nitrocomplexes). The lower transition temperatures of the lead compared to the alkaline earth compounds indicate weaker cooperative-elastic interactions and are possibly caused by the less distinct distortion of the CuNg polyhedra (Table 3). Finally it should be mentioned that the g tensor in the (001) planes of the 7-modifications has an orientation [K 15° ... 

Flat Stayed Plate Unilonn p Staybolts spaced at comers of square of side S 022ep 0.0284(1) - If plate as a whole deforms, superimpose the stresses and deflections on those for flat plate when loaded... 

Observations demonstrated that bonding of concrete slabs with polymer PM reduces vertical and horizontal deformations of them of about 50%, allowing for safe work of airfield pavements. It should be noticed that contractions joints deform horizontally of about 5 mm between winter and summer and similar value was measured in cases of vertical deformation. An example of 24 hours measurements of vertical displacements of airfield slab is presented in Fig. 16 (for original slab with bituminous filling and slab bonded with polymer PM). Comparison of vertical displacement shows that the use of polymer joints in contradiction to bituminous mass reduces warping deformations of the comers about two times, what is very advantageous in aspect of airfield exploitation. 

Figure 10. Pressure-induced structural transformation obtained by MD simulations at room temperature, (a) A framework of comer-shared Si04 tetrahedra in a low-pressure phase (low-oristobalite), where silicon atoms are shown with circles. Oxygen atoms related with the structural transformation are numbered, (b) The framework structure deformed under pressure, (c) The framework structure after released pressure.

---