Model abrasion

Indentation-fracture mechanics approach, which models abrasive-workpiece interactions by the idealized flaw system and deformation produced by an indenter. 

An important appHcation of MMCs in the automotive area is in diesel piston crowns (53). This appHcation involves incorporation of short fibers of alumina or alumina—siHca in the crown of the piston. The conventional diesel engine piston has an Al—Si casting alloy with a crown made of a nickel cast iron. The replacement of the nickel cast iron by aluminum matrix composite results in a lighter, more abrasion resistant, and cheaper product. Another appHcation in the automotive sector involves the use of carbon fiber and alumina particles in an aluminum matrix for use as cylinder liners in the Prelude model of Honda Motor Co. 

Nienow and Conti (1978) developed a model of partiele abrasion at high solids eoneentration based on Rittinger s law of eomminution. When tested experimentally using eopper sulphate and niekel ammonium sulphate erystals in two non-solvent liquids, measured abrasion rates were eonsistent with a seeond-order dependenee of eoneentration as predieted (Figure 5.12). 

The hrst mechanism specihcally for tungsten CMP was proposed by Kaufman et al. [67]. They thought, first, chemical action dissolves W and forms a very thin passivating him which stops growth as soon as it reaches a thickness of one or a few moleculars later. Second, the him is removed locally by the mechanical action of abrasive particles, which contact with the protrude parts of the wafer surface, and then cause material loss. In recent years, most of the analysis and models for metal CMP are built based on the Kaufman model [68,69]. However, the model is not involved in microscopic structure analysis for the polished surface, but focuses on interpreting macroscopic phenomena happening during CMP [18]. 

The CMP process is regarded as a combination of chemical effect, mechanical effect, and hydrodynamic effect [110-116]. Based on contact mechanics, hydrodynamics theories and abrasive wear mechanisms, a great deal of models on material removal mechanisms in CMP have been proposed [110,111,117-121]. Although there is still a lack of a model that is able to describe the entire available CMP process, during which erosion and abrasive wear are agreed to be two basic effects. 

Luo and Domfeld [110] introduced a fitting parameter H , a d5mamical" hardness value of the wafer surface to show the chemical effect and mechanical effect on the interface in their model. It reflects the influences of chemicals on the mechanical material removal. It is found that the nonlinear down pressure dependence of material removal rate is related to a probability density function of the abrasive size and the elastic deformation of the pad. 

Ahmadi, G. and Xia, X., "A Model for Mechanical Wear and Abrasive Particle Adhesion During the Chemical Mechanical Polishing Process," Journal of the Electrochemical Society, Vol. 148, No. 3,2001, pp. G99-G109. 

Even in a homogeneous solid elastic wheel the distortion is complex and requires sophisticated methods to arrive at a precise relation between force and slip. For tires this is even more difficult because of its complex internal structure. Nevertheless, even the simplest possible model produces answers which are reasonably close to reality in describing the force-slip relation in measurable quantities. This model, called the brush model—or often also the Schallamach model [32] when it is associated with tire wear and abrasion—is based on the assumption that the wheel consists of a large, equally spaced number of identical, deformable elements (the fibers of a brush), following the linear deformation law... 

Figure 26.61 shows the abrasion of an OESBR tread compound as function of load for different slip angles on a sharp Alumina 60 surface. Because of the wide range of abrasion rates for different slip angles the abrasion data were plotted on a log scale. It is seen that at the small slip angle the dependence on load is small and becomes more pronounced as the slip angle is increased. This is expected from the bmsh model. At small slip angle the side force is independent of the load and hence it is expected that the abrasion behave in a similar way. 

Having calculated the force for a particular event the slip is calculated using the bush model and hence the energy dissipation is obtained. Using the factors of the abrasion equation, determined with the LAT 100 on an alumina surface the abrasion loss for each event is calculated. The forces are different for a driven and a nondriven axle and accordingly different abrasion rates will result. 

Arena et al. (1983) investigated the coal attrition in a mixture with sand under hot but inert conditions. As they increased the sand particle size while keeping its mass in the bed constant, they observed an increase in the coal attrition rate. They interpreted their results by assuming that the abrasion energy is shared out on the entire material surface. On the same basis Ray et al. (1987a) developed their attrition rate distribution model for abrasion in a fluidized bed. 

Modeling ofBubble-Induced Attrition. Merrick and Highley (1974) have modeled bubble-induced attrition as a comminution process. According to Rittinger s law of size reduction by abrasion (cfi, Perry, 1973), the rate of creation of new surface area AS Al is proportional to the rate of energy input Ah. At... 

Despite the little experimental data, there are two models available in the literature. Adams etal. (1992) considered dense phase conveying. They tried to predict the amount of attrition as a function of conveying distance by coupling a Monte Carlo simulation of the pneumatic conveying process with data from single-particle abrasion tests. Salman et al. (1992) focused on dilute phase conveying. They coupled a theoretical model that predicts the particle trajectory with single particle impact tests (cf. Mills, 1992). 

Results of the Vickers hardness of 15 inorganic and organic salts will be presented. The hardness-force dependency, and the effects of direction dependency were examined. The measured values of the Vickers hardnesses were taken for an attempt to prove a model to calculate the hardness. This model describes the hardness purely by physical properties of the substances. The use of such a model may be an approach for the description of the abrasion resistance of salts. Data describing the abrasion resistance could help in the understanding and interpretation of secondary nucleation phenomena. 

The comparison of the measured and calculated Vickers hardnesses is of acceptable quality. With this physical model of the hardness it should also be possible to compute the Vickers hardnesses of salts with a more complicated lattice structure than the NaCl-structure. This may be an approach for a description of the abrasion resistance of salts. Such a description of the abrasion resistance could be useful in calculating the secondary nucleation rates. 

Figure 10.32 Abrasion-ablation model of relativistic nuclear collisions.

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