Deformation of particles

The major directions of changing porosity in DRP are schematically shown in Figure 9.22 [3,61], As a starting point, one can use the porosity of DRP of monospheres s0 = 0.36-0.42. Values of >s0 increase with particles anisotropy, roughness, and internal porosity, and also with the influence of wall effects at K> 0.1, and DIH > 0.05. Values of < (J are characteristic for polydis-perse particles when denser zones with ordered or unidirectional packings are formed, and also under forced densification and deformation of particles, correspondingly. 

In Chapter 6 we gave a brief account of the normal manner of filling voids. By such a procedure we may reduce the void space to very small amounts. In powder metallurgy the void space is reduced partly by a deformation of particles and partly by a diffusion through slippage of the finer particles to the void spaces. This may be termed particle-pressure diffusion. 

Hersey, J. A., and Rees, J. E. (1970), Deformation of particles during briquetting, paper presented at Proc. 2nd Particle Size Analysis Conference of the Society of Analytical Chemistry, Bradford, 33. 

At the second and third stages, the processes involving plastic deformation of particles are developed. The smaller is particle size, the more efficient are these processes. Dispersion process is overlapped by the formation of secondary particles, while the rate of the latter process is comparable with dispersing rate thus, the surface area remains constant. Chemical reactions take place inside secondary aggregates at the contacts between particles. At the third stage, the crystallization of the products from the solid phase may occur, as well as its repeated amorphization, till some stationary state between these two is achieved. 

Hersey, J.A. Rees, J.E. Deformation of particles during briqueting. Nature 1971, 230, 96. 

Let s establish an increment of deformation and, hence, stress da = dzE. For the moment of time dt, the superfluous stress will decrease due to its distribution over a greater number of particles. It is obvious that the average value of an increment of viscous highly elastic deformations of particles coincides with the average value of elastic deformation. Further, we shall designate superfluous force aj, and notice that for an interval of time dt, stress is constant. In this case, Eq. (2.44) will become ... 

Fig. 11.3. Diagram of possible deformation of contact zone (a) deformation of particle (b) deformation of substrate (c) mutual deformation of particle and substrate (d) deformation of adherent particle with allowance for gap between contiguous bodies x - (dl2) //i + H is the radius of the contact area.

Rzepiela AA, van Opheusden JHJ, van Vliet T (2002) Large shear deformation of particle gels smdied by Brownian Dynamics simulations. Comp Phys Comm 147 303-306. 

By means of PFC ° simulation, we observed the large deformation of particles, obtained several microcosmic parameters such as particle trajectory, porosity, and flow rate in fluid cells. The quantitative change process of these parameters reflects the distribution of degree of erosion and erosion intensity of water flow in slope. The degree of erosion intensity was the highest at toe of the slope it was higher at the top of the slope than that at the middle of the slope surface. 

Since the van der Waals forces depend strongly on the distance a between the particles and on the interparticle contact area, they can be increased by decreasing the former and/or increasing the latter (Eq. 7.4). This can be achieved by plastic or viscoelastic deformation of particle surfaces which depends on the mechanical material properties. 

Although it is a slight reduction, for smaller particles there seems to exist some possibilities of reducing computation load a little. Suppose At is maintained constant for different particle sizes, kn cam be modified in proportion to dp since At = tc /5 x dp / kn /. The relative deformation of particles in collision AXmsxldp, which is proportional to vdp / kn- / )/dp, and accordingly, to dp5/2fc -i/2 (because vx Umfx d ), is reduced in proportion to particle size dp. On the other hamd if the relative deformation Axmax./ dp is kept constant, kn can be modified in proportion to dpS. With this the total CPU time for 150 000 particles (oc At x dp- / k / x dp) could be reduced even more for smaller particles, i.e. from 6 days for dp =lmm particles to 0.6 day for 0.1mm particles. By numerical simulation the authors have recently confirmed this possibility, but anyway, a more novel method to overcome the above difficulty has to be invented. 

Since the conduction of ACAs is based on mechanical particle-electrode contacts, pressure is a requisite to form qualified joints. A typical ACA assembly is shown in Fig. 2. After alignment, pressure is applied on the backside of the chip. The adhesive resin is squeezed out and conductive particles are trapped and deformed between opposing electrodes. Once electrical continuity is generated, the adhesive resin is cured with heat or UV. The intimate particle-electrode contacts are maintained by the cured matrix, and the elastic deformation of particles and electrodes exerts a continuous contact pressure. 

In compression molding, an appropriate weight of resin powder is placed in the cavity of a robust mold, where it is heated above its melting point and compressed by a hydraulically actuated piston. Pressure and heat are maintained for sufficient time that molecular relaxation relieves local internal stresses caused by the deformation of particles. To prevent warpage, pressure is maintained while the molding is cooled. Products of compression molding are typically billets or blanks from which finished articles are subsequently machined. 

However, coUisions are very fast compared to other process in gas-fluidized flow. Therefore, only the net effect of a coUision is of importance. These can be characterized by normal and tangential restitution coefficients. If (hard) particles are packed, also the detailed deformation of particles is not of importance. The force balances are determined by constraints and friction coefficients. 

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