( ) − + π σ =σ =− 1 D 4x 4D Dt 2P 2 2 2 4 2 y (2) 0 xy τ = (3) Where P is the applied load, D is the disk diameter, t is thickness and x is the horizontal position along disk diameter. For crack opening, only σx matters, because σy is a compressive type of stress. σ1 component acting over the x direction and under the load line (x = 0) expression (1) is reduced to: Dt 2P 1 x π σ =σ = (4) Above expression ignores the existence of contact stresses acting near the points where loads are applied. Expression (4) is used in this work to determine Ultimate Compressive Strength (Suc). LOCALIZED FRACTURE In the preliminary tests was observed that due to existence of contact stresses plus the fact that the contact area in this case is very small considered the body shape, localized stresses will fracture contact regions, thus altering stress distribution, crack initiation region and rendering useless expression (4) [11,12]. Controlling Localized Fracture To avoid fracture initiation at the contact areas it was used an elastomeric rubber layer, applied to the contact region, to reduce magnitude of localized acting stresses. In this study latex was used and eliminated the problem. The used layer thickness measured 0.2 mm. New Stress Distribution At Contact Area The presence of that rubber layer is modeled as an elastic foundation and its presence alters stress distribution at contact region by increasing contact surface thus loading distribution area. Johnson shows that the new contact pressure distribution is paraboloidal rather than ellipsoidal as given by Hertz theory. Although localized stress field changes, at the center of the disk, where fracture is supposed to have started, no influence is felt, once contact stresses, regardless its shape, are expected to act at no more than up to 0.15D from the contact surfaces [13]. UNCERTAINTY MEASUREMENT Uncertainty measurements, related to existing errors associated with the measurement system and material properties dispersion, for the proposed tests, are determined as described by ISO standards [14]. For the measurement system, these errors are originated from the load cell (ultimate compressive load) and the caliper (pellets dimensions). Both uncertainty sources combined and expanded to yield a 95% confidence level are called U95 and are represented by error bars on the following figures. RESULTS AND DISCUSSION Waste addition to the clayey ceramic mass clearly influences the ceramic pellets properties. Figure 1 shows the ceramic pellets Ultimate Compressive Strength (Suc) variation as a result of the oil sludge waste addition. As can be noticed from this figure, the addition of oil sludge waste reduced the strength of the ceramic pellets. As shown in Figure 2, the pellets linear shrinkage is decreased with waste addition. Error bars size is
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