Compressor Instability with Integral Methods Episode 1 Part 3 ppsx

Chapter 2 Abrasive Materials 2.1 Classification and Properties of Abrasive Materials A large number of different types of abrasive materials is available for blast clean- ing applications. Most frequently applied abrasive materials are listed in Table 2.1. Table 2.2 lists numerous physical, chemical and technical properties of commercial abrasive materials. Basically, there can be distinguished between metallic abrasive materials and non-metallic abrasive materials. The evaluation of an abrasive material for blast cleaning applications includes the following important parameters: r material structure; r material hardness; r material density; r mechanical behaviour; r particle shape; r particle size distribution; r average grain size. 2.2 Abrasive Material Structure and Hardness 2.2.1 Structural Aspects of Abrasive Materials Structural aspects of abrasive materials include the following features: r lattice parameters; r crystallographical group and symmetry; r chemical composition; r crystallochemical formula; r cleavage; r inclusions (water–gas inclusion and mineral inclusion). A. Momber, Blast Cleaning Technology 7 C  Springer 2008 8 2 Abrasive Materials Table 2.1 Annual abrasive consumption in the USA for blast cleaning processes (Hansink, 2000) Abrasive type Consumption in Mio. of tonnes Coal boiler slag 0.65 Copper slag 0.1–0.12 Garnet 0.06 Hematite 0.03 Iron slag 0.005 Nickel slag 0.05 Olivine 0.03 Silica sand 1.6 Staurolite/zirconium 0.08–0.09 Steel grit and steel shot 0.35 Table 2.3 lists typical values for some abrasive materials. Table 2.4 displays a commercial technical data and physical characteristics sheet for a typical blast cleaning abrasive material. Abrasive particles contain structural defects, such as microcracks, interfaces, inclusions or voids. Very often, these defects are the result of the manufacturing process. Strength and fracture parameters of materials can be characterised through certain distribution types. A widely applied distribution is the Weibull distribution, and it was shown by Huang et al. (1995) that this distribution type can be applied to abrasive materials. The authors derived the following relationship between fracture probability, particle strength and particle volume: F(σ F ) = 1 − exp  −V P ·  σ F σ ∗  m W  (2.1) The strength parameter σ* is a constant, which is related to the defects distri- bution. The power exponent m W is the so-called Weibull modulus; it can be read from a graphical representation of (2.1). Low values for m indicate a large intrinsic variability in particle strength. A Weibull plot for aluminium oxide abrasive par- ticles, based on the results of compressive crushing tests, is displayed in Fig. 2.1. Values for the Weibull modulus estimated for different abrasive materials are listed in Table 2.5. There is a notable trend in the values that both fracture strength and Weibull modulus drop with increasing particle size. Therefore, scatter in strength of abrasive particles can be assumed to be wider for larger particles. The relation- ship between abrasive particle size and fracture strength of the particles is shown in Fig. 2.2. This phenomenon can be explained through the higher absolute number of defects in larger particles. The probability that a defect with a critical dimension (for example, a critical crack length in a fracture mechanics approach) exists increases with an increasing number of defects. This effect was also observed by Larssen-Basse (1993). This author found also that the Weibull modulus of abrasive particles depended on the atmospheric humid- ity. Larssen-Basse (1993) performed crushing tests with SiC-particles, and he found that, if humidity increased, the Weibull modulus and the number of fragments both 2.2 Abrasive Material Structure and Hardness 9 Table 2.2 Selected abrasive properties (References: manufacturer data) Brand name Bulk density a in t/m 3 Apparent density in t/m 3 Hardness b–e Melting point in ◦ C Grain size min–max in mm Major composite in % Technical name Abrablast – 4.3 9 b 1,900 – Al 2 O 3 (71.9) Zirconium corundum Abramax 1.0–2.0 3.95 2,200 c 2,000 – Al 2 O 3 (99.6) Corundum Abrasit 1.1–2.3 3.96 2,100 c 2,000 – Al 2 O 3 (96.4) Corundum Afesikos 1.4 2.6 8 b – 0.04–1.4 SiO 2 (53) Aluminium silica Afesikos HS 2.83 4.1 8 b – 0.04–1.4 SiO 2 (36) Garnet Afesikos SK 1.8 3.96 9 b – 0.06–2.8 Al 2 O 3 (99.3) Corundum Asilikos 1.3 2.5–2.6 7–8 b – 0.06–2.8 SiO 2 (51) Aluminium silica Cast steel – – 60 d – 0.12–3.36 – – Garnet – 3.9–4.1 8–9 b 1,315 – SiO 2 (41.3) Garnet Glass beads 1.5 2.45 6 b – 0.07–0.4 SiO 2 (73) – GSR 3.7–4.3 7.4 44–58 d – 0.1–2.24 – Cast steel Cast iron 2.7–4.3 7.4 56–64 d –upto3.15–– Ceramic spheres 2.3 3.8 60–65 d – 0.07–0.25 ZrO 2 (67) Ceramics MKE 1.75 3.92 1,800–2,200 e – 0.001–2.8 Al 2 O 3 (99.6) Corundum Olivine 1.7–1.9 5.3 6.5–7 b 1,760 0.09–1.0 MgO (50) – Scorex 1.35 – – – 0.5–2.8 SiO 2 (40) Refinery slag Steel grit – 7.5 48–66 d – 0.2–1.7 – – Steel shot – 7.3 46–51 d – 0.2–2.0 – – Testra 1.2–1.4 2.5–2.7 7 b – 0.09–2.0 SiO 2 (54) Melting chamber slag a Depends on grain size Hardness parameter: b Mohs; c Vickers; d Rockwell; e Knoop 10 2 Abrasive Materials Table 2.3 Structural properties of abrasive materials (Vasek et al., 1993) Material Damaged grains (%) Lattice constant ( ˚ A) Cell volume ( ˚ A 3 ) Almandine 5–60 11.522 (0.006) 1,529.62 Spessartine – 11.613 (0.005) 1,566.15 Pyrope – 11.457 (0.005) 1,503.88 Grossular 30 11.867 (0.005) 1,671.18 Andradite 80–90 12.091 (0.009) 1,767.61 increased. This feature can be attributed to moisture-assisted sharpening of the tips of surface defects present in the particles. The presence of defects, such as cracks and voids, affects the cleaning and degradation performance of abrasive materials. Number and size of defects are, Table 2.4 Data sheet for a garnet blast cleaning abrasive material (Reference: GMA Garnet) Parameter Value Average chemical composition SiO a 2 36% Al 2 O 3 20% FeO 30% Fe 2 O 3 2% TiO 2 1% MnO 1% CaO 2% MgO 6% Physical characteristics Bulk density 2,300 kg/m 3 Specific gravity 4.1 Hardness (Mohs) 7.5–8 Melting point 1,250 ◦ C Grain shape Sub-angular Other characteristics Conductivity 10–15 mS/m Moisture absorption Non-hydroscopic Total chlorides 10–15 ppm Ferrite (free iron) <0.01% Lead <0.002% Copper <0.005% Other heavy metals <0.01% Sulphur <0.01% Mineral composition Garnet (Almandine) 97–98% Ilmenite 1–2% Zircon 0.2% Quartz (free silica) <0.5% Others 0.25% a Refers to SiO 2 bound within the lattice of the homo- geneous garnet crystal (no free silica) 2.2 Abrasive Material Structure and Hardness 11 Fig. 2.1 Weibull plot for the strength of aluminium oxide particles (Verspui et al., 1997). Abrasive particle size: 10–500 μm therefore, important assessment criteria. Cast steel shot, for example, should not contain cracked particles, as illustrated in Fig. 2.3, in excess of 15%. Cast steel grit should not contain cracked particles, as shown in Fig. 2.4, in excess of 40% (SFSA, 1980). Requirements for the defects of particles of metallic abrasive mate- rials are listed in Table 2.6. Table 2.5 Strength parameters for abrasive materials (Yashima et al., 1987; Huang et al., 1995) Abrasive material Grain size in mm Fracture strength in MPa Weibull modulus ∗ a in MPa/mm 3 Brown corundum 2.58 67.5 1.98 228.8 1.85 78.6 2.47 142.8 1.29 115.4 2.88 135.1 0.78 200.5 3.47 149.0 Rounded corundum 1.85 96.1 3.41 160.8 White corundum 1.29 79.5 2.57 127.3 Sintered corundum 1.85 110.8 3.85 174.9 Green silicon carbide 1.85 62.2 1.92 155.5 Quartz 0.1–2.0 – 21.0 – Glass beads – – 5.90 – a Defect distribution parameter 12 2 Abrasive Materials Fig. 2.2 Relationship between abrasive particle size and particle fracture strength (values from Huang et al., 1995) Fig. 2.3 Cracks in cast steel shot particles; magnification: 10× (SFSA, 1980) 2.2 Abrasive Material Structure and Hardness 13 Fig. 2.4 Cracks in cast steel grit particles; magnification: 10× (SFSA, 1980) 2.2.2 Hardness of Abrasive Materials The hardness of abrasive materials is usually estimated by two types of tests: a scratching test for non-metallic abrasive materials, which delivers the Mohs hardness, and indentation tests for metallic materials, which deliver either the Knoop hardness or the Vickers hardness. Respective values for commercial abrasive materials are listed in Table 2.2. Mohs hardness is based on a scale of ten minerals, which is provided in Table 2.7. The hardness of a material is measured against the scale by finding the hardest Table 2.6 Particle defect requirements for metallic abrasive materials (ISO 11124/2-4) Property Chilled iron grit High-carbon cast steel shot High-carbon cast steel grit Low-carbon cast steel shot Particle shape Max. 10% shot or more than half-round Max. 5% non-round Max. 10% shot or more than half-round for grit up to 700 HV; max. 5% for grit above 700 HV Max. 5% non-round Voids Max. 10% Max. 10% Max. 10% Max. 15% Shrinkage defects Max. 10% Max. 10% Max. 10% Max. 5% Cracks Max. 40% Max. 15% Max. 40% None Total defects Max. 40% Max. 20% Max. 40% Max. 20% 14 2 Abrasive Materials Table 2.7 Mohs scale (Tabor, 1951) Material Mohs hardness Talc 1 Gypsum 2 Calcite 3 Fluorite 4 Apatite 5 Orthoclase (Feldspar) 6 Quartz 7 Topaz 8 Corundum 9 Diamond 10 material that the given material can scratch, and/or the softest material that can scratch the given material. For example, if some material is scratched by quartz but not by feldspar, its hardness on Mohs scale is 6.5. In abrasive standardisation, abrasive particles are being rubbed against a glass plate having a Mohs hardness corresponding to 7. If the particles can scratch the plate, their hardness is >Mohs 7. If they do not scratch the plate, their hardness is <Mohs 7. It is because of this pro- cedure that data sheets for mineral abrasive materials often list the Mohs hardness as >7 only. The principles of two frequently applied indentation hardness tests are illus- trated in Table 2.8. In laboratory practice, an abrasive particle is embedded in a special resin matrix, and it is then being polished in order to obtain an even Table 2.8 Indentation hardness measurement methods (Images: TWI, Cambridge, UK) Method Brinell Vickers Principle Measurement Calculation a H B = F π 2 · D ·  D −(D 2 − d 2 ) 1/2  H V = 2 ·F · sin (136 ◦ /2) d 2 a F= indentation load d = indentation size = d 1 + d 2 2 D = indenter size 2.2 Abrasive Material Structure and Hardness 15 (a) (b) Fig. 2.5 Vickers hardness distributions of two cut wire samples (Gesell, 1979). (a) Laboratory sample; (b) Work sample 16 2 Abrasive Materials smooth cross-section where the actual indentation test is being performed. In- dentation hardness values are always dependent on indentation load, and care should be taken to provide the certain applied indentation load in data sheets. Values from indentation hardness tests and from Mohs hardness tests can be re- lated to each other; exceptions are diamond and corundum (Bowden and Ta- bor, 1964). The hardness of metallic abrasive particles is a probabilistic parameter, and the hardness values mentioned in data sheets are mainly mean values only. Two typ- ical abrasive hardness distribution diagrams of cut wire samples are provided in Fig. 2.5. Figure 2.5a shows the distribution of a laboratory sample, whereas Fig. 2.5b illustrates the distribution of a working sample. Although both materials had equal hardness designations of 420 HV, the distributions differed widely. The laboratory sample had a unimodal distribution with a maximum at a Vickers hardness of about 430 HV, whereas the working sample featured a multimodal distribution. The hard- ness distribution of the laboratory sample can be expressed through a Normal dis- tribution – this is shown in Fig. 2.6. This result points to a rather homogeneous response of the wire material to the indentation with the Vickers pyramid, which is not always the case (Lange and Schimm¨oller, 1967). Such a distribution was also reported by Flavenot and Lu (1990) for steel wire shot. Fig. 2.6 Normal distribution function for the laboratory cut wire sample plotted in Fig. 2.5a [...]... Sect 3. 6 .3 The power delivered to the cleaning site by 32 2 Abrasive Materials 10 0 1 2 3 10 1 kinetic energy in J Ep = 0.022 J 10 –2 4 glass bead dp = 1. 5 mm 5 6 10 3 10 –4 Vp = 10 0 m/s 10 –5 10 50 10 0 particle velocity in m/s 250 Fig 2 .16 Kinetic energies of abrasive particles; calculated with (2 .14 ) 1 to 3: particle diameter dP = 1. 5 mm; 4 to 6: particle diameter dP = 0.5 mm; 1+ 4: steel ball (ρP = 7 ,30 0... Particles 33 Fig 2 .17 Relationship between loading intensity (particle kinetic energy) and loading frequency ˙ (particle frequency) for three power values 1: m P = 10 kg/min, vP = 10 0 m/s; 2: m P = 10 kg/min, ˙ ˙ ˙ vP = 10 0 m/s; 3: m P = 10 kg/min, vP = 10 0 m/s; 4: m P = 10 kg/min, vP = 10 0 m/s; 5: ˙ ˙ m P = 15 kg/min, vP = 10 0 m/s; 6: m P = 15 kg/min, vP = 10 0 m/s; 7: m P = 15 kg/min, ˙ ˙ ˙ vP = 10 0... Schubert, 19 88) Function Formula M0 (dP ) Logarithmic probability erf Rosin–Rammler–Sperling– Bennett (RRSB) Gates–Gaudin–Schumann (GGS) Gaudin–Meloy 1 − exp dP n M d∗ Significance of d* Equation Medium particle diameter d ln P d∗ σ 2.3a Particle diameter at M0 = 63. 2% 2.3b dP n M d∗ 1 1 2.3c dP 2 d∗ Maximum particle diameter 2.3d – dP d∗ 1 exp( 1) 2.3e 1 exp − Broadbent–Callcott 2.4.2 Particle Diameter... and dPG = 36 2 μm (MG 65), respectively A third approach is the definition of a statistical diameter, dPSt , which follows the equation: dPSt = n i =1 (mi · dPi ) 10 0 (2.5) For the examples in Table 2 . 13 and Fig 2 . 13 , the statistical diameter is dPSt = 6 13 μm (Alumina 700) and dPSt = 34 5 μm (MG 65), respectively 2.4 .3 Alternative Abrasive Particle Size Assessment Methods Particle sizes, but also particle... 577 0.894 0.8 93 0.8 93 0.000 83 0.029 0.000 83 0.02 0.0 011 0.0 0 13 17 , 402 0.000057 24 2 Abrasive Materials Table 2 .12 Shape factors and shape characteristics of garnet abrasive materials (Vasek et al., 19 93) Mineral Subtype Shape parameter F0 Fshape Almandine B M K G – V–A V–B V–C 0.66 0.69 0.68 0.66 0. 71 0.67 0.68 0.65 0.65 0.67 0.66 0.64 0.70 0.65 0.68 0.68 Grossular Andradite 2.4 Abrasive Particle Size... Target material Vickers hardness in GPa Threshold velocity in m/s Aluminium alloy Brass Copper Glass Mild steel Zirconia Silicone carbide Titanium alloy 1. 75 1. 22 0.89 6 .14 1. 98 14 .0 30 .5 3. 25 216 –240 216 –289 250–288 17 5–200 2 01 218 41 48 47–82 17 4–2 03 ... particle, size analysis is carried out by dividing the particles into a number of suitably narrow size ranges Table 2 . 13 presents results of sieve analyses for abrasive particle samples used in 2.4 Abrasive Particle Size Distribution and Abrasive Particle Diameter 25 Table 2 . 13 Sieve analyses results for two abrasive mixtures (Metabrasive Ltd.) Sieve size in μm Weight in % Alumina 700 12 5 15 0 212 30 0... /ϕ: 1 – 0. 01/ 90◦ ; 2 – 0. 03/ 45◦ ; 3 – 0. 01/ 60◦ ; 4 – 0.0 01/ 90◦ ; 5 – 0. 01/ 45◦ ; 6 – 0.0 01/ 15◦ ; 7 – 0.0 01/ 45◦ ; 8 – 0.00 01/ 45◦ regardless of the impact angle A more detailed discussion of these effects is provided by Ciampini et al (2003b) The authors found, among others, that power availability decreased at higher impact angles and with larger relative distances between individual abrasive particles... elevated Table 2 .17 Contamination of recycled abrasive field work mixes (Boocock, 19 94) Sample No Lead in ppma Electric conductivity in μS/cmb 1 2 3 4 5 6 a b 8,200 220 8,400 . 5–60 11 .522 (0.006) 1, 529.62 Spessartine – 11 . 6 13 (0.005) 1, 566 .15 Pyrope – 11 .457 (0.005) 1, 5 03. 88 Grossular 30 11 .867 (0.005) 1, 6 71. 18 Andradite 80–90 12 .0 91 (0.009) 1, 767. 61 increased. This. MPa Weibull modulus ∗ a in MPa/mm 3 Brown corundum 2.58 67.5 1. 98 228.8 1. 85 78.6 2.47 14 2.8 1. 29 11 5.4 2.88 13 5 .1 0.78 200.5 3. 47 14 9.0 Rounded corundum 1. 85 96 .1 3. 41 160.8 White corundum 1. 29 79.5 2.57 12 7 .3 Sintered. 60 d – 0 .12 3. 36 – – Garnet – 3. 9–4 .1 8–9 b 1, 31 5 – SiO 2 ( 41. 3) Garnet Glass beads 1. 5 2.45 6 b – 0.07–0.4 SiO 2 ( 73) – GSR 3. 7–4 .3 7.4 44–58 d – 0 .1 2.24 – Cast steel Cast iron 2.7–4 .3 7.4 56–64 d –upto3 .15 –– Ceramic