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If Pat pays 12485 and 52 cents for a 25000 zero coupon bond that matures in 8 years what is his annual rate of return?
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∙ 13y ago
9.066% annually compounded or 8.87% semi-annually compounded.
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∙ 13y ago
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Where is the Mountain Top Arboretum Inc in Tannersville New York located?
The address of the Mountain Top Arboretum Inc is: Po Box 379, Tannersville, NY 12485-0379
Purchased merchandise on account 12000 fob shipping point seller added 485 of prepaid freight charges to the invoice how to journalize in purchases journal?
[debit] Merchandise account 12000 [Debit] Freight in 485 [Credit Accounts payable / cash 12485
What are the first 2000 multiples of 11?
11 * 1 = 11 (and so on) 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220 231 242 253 264 275 286 297 308 319 330 341 352 363 374 385 396 407 418 429 440 451 462 473 484 495 506 517 528 539 550 561 572 583 594 605 616 627 638 649 660 671 682 693 704 715 726 737 748 759 770 781 792 803 814 825 836 847 858 869 880 891 902 913 924 935 946 957 968 979 990 1001 1012 1023 1034 1045 1056 1067 1078 1089 1100 1111 1122 1133 1144 1155 1166 1177 1188 1199 1210 1221 1232 1243 1254 1265 1276 1287 1298 1309 1320 1331 1342 1353 1364 1375 1386 1397 1408 1419 1430 1441 1452 1463 1474 1485 1496 1507 1518 1529 1540 1551 1562 1573 1584 1595 1606 1617 1628 1639 1650 1661 1672 1683 1694 1705 1716 1727 1738 1749 1760 1771 1782 1793 1804 1815 1826 1837 1848 1859 1870 1881 1892 1903 1914 1925 1936 1947 1958 1969 1980 1991 2002 2013 2024 2035 2046 2057 2068 2079 2090 2101 2112 2123 2134 2145 2156 2167 2178 2189 2200 2211 2222 2233 2244 2255 2266 2277 2288 2299 2310 2321 2332 2343 2354 2365 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10978 10989 11000 11011 11022 11033 11044 11055 11066 11077 11088 11099 11110 11121 11132 11143 11154 11165 11176 11187 11198 11209 11220 11231 11242 11253 11264 11275 11286 11297 11308 11319 11330 11341 11352 11363 11374 11385 11396 11407 11418 11429 11440 11451 11462 11473 11484 11495 11506 11517 11528 11539 11550 11561 11572 11583 11594 11605 11616 11627 11638 11649 11660 11671 11682 11693 11704 11715 11726 11737 11748 11759 11770 11781 11792 11803 11814 11825 11836 11847 11858 11869 11880 11891 11902 11913 11924 11935 11946 11957 11968 11979 11990 12001 12012 12023 12034 12045 12056 12067 12078 12089 12100 12111 12122 12133 12144 12155 12166 12177 12188 12199 12210 12221 12232 12243 12254 12265 12276 12287 12298 12309 12320 12331 12342 12353 12364 12375 12386 12397 12408 12419 12430 12441 12452 12463 12474 12485 12496 12507 12518 12529 12540 12551 12562 12573 12584 12595 12606 12617 12628 12639 12650 12661 12672 12683 12694 12705 12716 12727 12738 12749 12760 12771 12782 12793 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21934 21945 21956 21967 21978 21989 22000
What influence does grain size have on mechanical properties of metal?
Influence of grain size on following properties of meatals:- Hardness Strength Impactness Toughness Creep Fatigue Ductility Malleability Durability Brittleness INTRODUCTION Yttria-stabilized tetragonal zirconia polycrystals (Y-TZP) have proved to be important structural ceramics. High strength and fracture toughness make them attractive candidates for a number of demanding applications. It was established that these advantageous properties are strongly influenced by the ceramic microstructure [1]. The relationships between microstructure and mechanical properties in Y-TZP ceramics have been studied extensively over the past two decades. It is now generally agreed that the transformation toughening effect (stress-induced tetragonal to monoclinic phase transformation) in Y-TZP ceramics is grain size dependent [2 7]. The larger the tetragonal grains the greater propensity to undergo stress-induced transformation to an equilibrium structure, resulting in an enhanced toughness. The maximum toughness lies near the critical grain size, where the tetragonal grains undergo spontaneous tetragonal to monoclinic transformation [7]. It was found that this critical grain size depends on the yttria content [6, 7]. However, the critical grain size, cited for 3Y-TZP (3 mol% Y2O3), which is the most common zirconia ceramic material, varies significantly (from 1 to 6 µm) [3, 8-9]. This could be attributed to different processing procedures that result in different ceramic microstructures. Thus, microstructural parameters like porosity, grain size distribution, yttrium distribution in grains, purity, phase assemblage, etc. need to be taken into account for evaluating the microstructure. In contrast to the fracture toughness the strength of 3Y-TZP reaches its maximum usually at smaller grain size [5, 10]. Increasing size of failure origin coupled with microstructural coarsening was identified as the reason for strength decrease in ceramics with large grains [11]. However, the increase of strength with decreasing grain size cannot be extended to the nanocrystalline range in 3Y-TZP. Eichler et al. [10] determined the strength maximum for 3Y-TZP in the submicron range and noted a clear strength decrease in the nanocrystalline grain size range (~100 nm). In this case, the strength decrease was attributed to the grain size dependence of fracture toughness. A decrease in the fracture toughness was observed as the grain size changed from the submicrometre to the nanometre range [10, 12]. These results validate the assumption that the increase of critical defects during microstructural coarsening is connected with the formation of stress induced transformed regions at the free surface and takes place preferentially in ceramics with grains near the critical size [11]. Nevertheless, special processing of TZP ceramics has been reported, which can partially eliminate the increase of critical defects during coarsening, resulting in almost constant strength, independent of grain size [8, 9]. Original papers Ceramics − Silikáty 52 (3) 165-171 (2008) 165 EFFECT OF GRAIN SIZE ON MECHANICAL PROPERTIES OF 3Y-TZP CERAMICS MARTIN TRUNEC Department of Ceramics and Polymers, Brno University of Technology Technicka 2896/2, 616 69 Brno, Czech Republic E-mail: trunec@fme.vutbr.cz Submitted June 21, accepted September 4, 2008 Keywords: Zirconia, Nanoceramics, Transformation toughening, Microstructure, Mechanical properties The dependence of mechanical properties of 3Y-TZP ceramics on their grain sizes in the range from 0.19 µm to 2.15 µm has been investigated. Vickers indentation tests were used to determine hardness and fracture toughness. The hardness decreased with increasing grain size. The fracture toughness was almost constant for ceramics with the grain size up to 0.40 µm and then grew with increasing grain size up to 7.8 MPam0.5 for ceramics with grain size of 1.8 µm. Above this grain size a spontaneous transformation from tetragonal to monoclinic phase occurred. Ceramic samples with grain sizes of 0.30 µm and 0.78 µm yielded similar bending strength, 1020 and 1011 MPa, respectively. The microstructural coarsening required for achieving larger grain size resulted in a higher scatter of strength values, which was demonstrated by a lower Weibull modulus (13.0 vs. 7.54). The mechanical properties of nanocrystalline 3Y-zirconia ceramics coarsened to the grain size range from 0.085 to 0.70 µm were also investigated and compared. Differences in mechanical behaviour of investigated ceramics were observed and their possible causes discussed. The objective of the present investigation was to describe the dependence of mechanical properties of commercial submicrometre-grained 3Y-TZP ceramics on grain size and to compare their mechanical properties to the mechanical properties of nanocrystalline zirconia ceramics and nanocrystalline ceramics coarsened to the submicrometre range. EXPERIMENTAL Two zirconia powders stabilized by 3 mol% Y2O3 were used for the preparation of test specimens. Commercial zirconia powder TZ-3YB (Tosoh, Japan) was cold isostatically pressed at 300 MPa into disk-shaped bodies (diameter 28 mm; thickness 5 mm). For comparison, a nanocrystalline zirconia powder B261 (BUT, Czech Republic) was used. Details of the preparation of the nanopowder can be found in [13]. Nanocrystalline powder was cold isostatically pressed at 1000 MPa without additives. The pressed bodies were 18 mm in diameter and 5 mm thick. These bodies were ground to a thickness of 1.5 mm prior to sintering. Both types of bodies were densified by pressureless sintering in air at temperatures from 1100 to 1650°C and dwell times ranging from 0 to 50 hours. The density of sintered specimens was determined by the Archimedes method [14] with distilled water as the immersing medium. The relative density of all ceramic bodies was calculated using the value 6.1 g·cm-3 for the theoretical density of 3Y-TZP. The grain size of the sintered ceramics was evaluated by linear intercept method (without correction) on scanning electron microscopy (SEM) micrographs of polished and thermally etched samples, in a similar way as in [15]. At least three micrographs and total of 300 intersects were evaluated to determine the average grain size for each sintering batch. The phase composition of the sintered ceramics was determined by X-ray diffraction (XRD) analysis (X´pert, Philips, the Netherlands). The X-ray spectra of polished and fracture surface were obtained and the phase content was quantified using Rietveld analysis. For hardness and fracture toughness evaluation Vickers indentation tests (LV 700, Leco, USA) were used. Prior to indentation ceramic disks were mounted in a resin and their surfaces ground and polished (finishing with 1 µm diamond polishing fluid). Hardness tests were performed at a load of 9.8 N (1 kg) and a hold of 15 s. For determining the Vickers hardness, HV (MPa), the following expression was used: HV = 1.8544 P/d 2, (1) where P is the applied load and d is the average diagonal line length of the indentation. Ten indentations were made for each sample. Toughness was calculated directly from the crack lengths produced by Vickers indentation at higher loads. Applied loads were 49.05 N (5 kg), 98.1 N (10 kg), 196.2 N (20 kg) and 294.3 N (30 kg) always with a hold of 15 s. The crack lengths were measured immediately after indentation using a calibrated optical microscope. The fracture toughness, KIc (MPam0.5), was calculated using the equation given by Niihara et al. [16] for Palmqvist cracks: KIc = 9.052 × 10-3 H3/5 E2/5 d c-1/2 , (2) where H is the hardness, E the Young modulus (a value of 210 GPa has been assumed for all the samples), d is the average diagonal line length of the indentation and c is the length of the Palmqvist crack. Ten valid measurements were determined for each sample. The valid measurements had to satisfy the requirements of the JIS R 1607 [17] on acceptable indentation cracks. The flexural strength was determined for selected ceramic samples in four-point bending at a crosshead speed of 2 mm/min, using fully articulated fixture with a 10 mm inner and 20 mm outer span (in the "A" arrangement according to the EN 843-1 [18]). Ceramic bars with dimensions ca. 2.5 × 2 × 25 mm3 were cut from the disks, ground and polished (finally with 1-2 µm grained diamond paste). The parameters of the Weibull strength distribution were calculated numerically, in compliance with the ENV 843-5 [19]. RESULTS AND DISCUSSION Microstructure and phase analysis Various sintering schedules were applied to zirconia green bodies to obtain dense sintered ceramics with different grain sizes. Only those sintering schedules that resulted in sintered densities exceeding 99% of theoretical density (% t.d.) were employed. A temperature of 1400°C was the lowest temperature used in sintering the TZ-3YB ceramics; this was necessary to obtain a dense sintered body. Larger grains were obtained by the action of both higher sintering temperatures and longer sintering times. Sintering schedules and resulting densities and grain sizes are shown in Table 1. The density of sintered TZ-3YB bodies was constant up to the sintering temperature of 1650°C. At the sintering temperature of 1650°C the density of TZ-3YB ceramics decreased with increasing sintering time. The structure of ceramics remained dense but the theoretical density of these ceramics decreased due to spontaneous transformation of the tetragonal into the monoclinic phase (see Table 1). The average grain size of TZ-3YB ceramics ranged from 0.19 µm (sintered at 1400°C/2 h) to 2.15 µm (sintered at 1650°C/50 h). The Trunec M. 166 Ceramics − Silikáty 52 (3) 165-171 (2008) critical grain size for spontaneous transformation from tetragonal to monoclinic phase lies between 1.8 and 2.15 µm, where the content of monoclinic phase in TZ 3YB ceramics increased dramatically. The sample sintered at 1650°C for 50 hours consisted of 77 % monoclinic phase and was severely cracked due to volume changes accompanying t→m transformation. Mechanical properties could not be determined for these ceramics. Several authors [8, 9, 11] have found large cubic grains in thermally treated 3Y-TZP samples. In our case no exaggerated grain growth was observed during the microstructural coarsening. The zirconia nanopowder B261 could be sintered to dense bulk ceramics already at the temperature of 1100°C and dwell time of 4 hours. The microstructure remained nanoscaled with an average grain size of 85 nm. Microstructural coarsening occurred at higher sintering temperatures. However, the grain growth kinetics of B261 ceramics was different from that in TZ 3YB ceramics. B261 ceramics sintered at 1550°C/5 h had larger grains than TZ 3YB ceramics sintered under the same conditions (0.70 vs. 0.48 µm). Moreover, the density of B261 ceramics decreased sharply already at small grain sizes where no monoclinic phase was detected. Figure 1 shows the density as a function of grain size for both TZ-3YB and B261 ceramics. The reason for the density change in B261 ceramics is not completely clear. According to the equilibrium phase diagram given by Scott [20] the maximum amount of cubic phase occurring in 3 mol% Y2O3-ZrO2 ceramics sintered at 1550°C can be about 28 %. Matsui et al. [21] showed that in tetragonal zirconia ceramics similar to TZ-3YB the Y3+ ions segregated at grain boundaries over a width of ~10 nm. Consequently, the cubic phase started to form from grain boundaries and a triple junction, at which Y3+ ions were segregated. A mixed tetragonal- cubic structure was confirmed in TZ-3YB ceramics by XRD analysis. In B261 ceramics the nanocrystalline structure probably allowed other mechanisms of phase structure development to take place that resulted in the one-phase tetragonal structure. This fact could explain the faster grain growth found in B261 ceramics. Typical microstructures of TZ-3YB ceramics are shown in Figures 2-4 and microstructures of B261 ceramics are shown in Figures 5 and 6. The holes and voids visible in micrographs on Figures 4 and 6 are believed not to be pores but rather to result from pulling out the grains during grinding and polishing. Effect of grain size on mechanical properties of 3Y-TZP ceramics Ceramics − Silikáty 52 (3) 165-171 (2008) 167 Table 1. Sintering schedules of zirconia ceramics and resulting density, grain size and monoclinic phase content. Sintering schedule Density Relative density Grain size m - ZrO2 Powder/Sample (°C)/(h) (g/cm3) (% t.d.) (µm) (%) TZ - 3YB 1400/2 6.07 99.5 0.19 0 TZ - 3YB 1500/2 6.08 99.7 0.30 0 TZ - 3YB 1550/0 6.09 99.8 0.29 0 TZ - 3YB 1550/2 6.09 99.8 0.40 0 TZ - 3YB 1550/5 6.09 99.8 0.48 0 TZ - 3YB 1550/10 6.09 99.8 0.54 0 TZ - 3YB 1600/2 6.09 99.8 0.53 0 TZ - 3YB 1600/5 6.09 99.8 0.68 0 TZ - 3YB 1600/10 6.08 99.7 0.78 0 TZ - 3YB 1650/10 6.08 99.6 0.99 3 TZ - 3YB 1650/20 6.08 99.6 1.37 6 TZ - 3YB 1650/30 6.04 99.1 1.79 13 TZ - 3YB 1650/50 5.68 93.1 2.15 77 B 261 1100/4 6.07 99.4 0.085 0 B 261 1300/6 6.04 99.0 0.19 0 B 261 1450/2 5.93 97.3 0.33 0 B 261 1550/5 5.71 93.6 0.70 0 Figure 1. Density of TZ-3YB and B261 ceramics as a function of grain size. Grain size (µm) Density (g cm-3) 5.9 5.7 0.0 6.1 0.4 1.6 2.0 6.0 5.8 6.2 1.2 0.8 TZ-3YB B261 Mechanical properties Ten Vickers hardness tests were performed for each ceramic. Average hardness values and their standard deviation are given in Table 2. The hardness of TZ-3YB ceramics clearly decreased with increasing grain size from HV = 12620 MPa at grain size of 0.19 µm to HV = 10971 MPa at grain size of 1.79 µm. The graph in Figure 7 shows the hardness of TZ-3YB ceramics as a function of the inverse square root of grain size. The values in the graph could be reasonably fitted with a line (r2 = 0.94), which means that this dependence followed the Hall-Petch relationship. The hardness of B261 ceramics showed a higher dispersion but the linear fit seems to be also reasonable. Different parameters of the fits (lower hardness of B261 compared with TZ-3YB ceramics) could be attributed to different phase structure (mixed tetragonal-cubic vs. pure tetragonal). Trunec M. 168 Ceramics − Silikáty 52 (3) 165-171 (2008) Figure 2. SEM micrograph showing the microstructure of the TZ-3YB ceramics sintered at 1400°C for 2 h. Figure 3. SEM micrograph showing the microstructure of the TZ-3YB ceramics sintered at 1650°C for 20 h. 1 µm 5 µm Figure 4. SEM micrograph showing the microstructure of the TZ-3YB ceramics sintered at 1650°C for 50 h. Figure 5. SEM micrograph showing the microstructure of the B261 ceramics sintered at 1100°C for 4 h. 5 µm 500 nm Figure 6. SEM micrograph showing the microstructure of the B261 ceramics sintered at 1550°C for 5 h. 2 µm Different loads of Vickers indenter in the range from 49.05 N (5 kg) to 294.3 N (30 kg) were used to generate cracks in ceramic samples. It was verified that in all cases only Palmqvist cracks were produced. Fracture toughness values calculated from crack lengths using Equation (2) at different loads are shown in Table 2. The indenter load of 49.05 N (5 kg) generated unstable cracks that grew further after load release. It was not possible to measure the crack length reliably, therefore the fracture toughness calculated from this load was not included in the Table 2. The graph in Figure 8 shows the dependence of fracture toughness of TZ-3YB ceramics at different loads on grain size. The values of fracture toughness determined at different loads varied significantly. Nevertheless, the dependence of toughness on grain size showed the same trend for all loads. To obtain the most reliable value for the fracture toughness, an average of values determined at different loads was calculated (see Table 2). Figure 9 gives the dependence of the average fracture toughness on grain size for both TZ-3YB and B261 ceramics. This dependence can be divided in two areas. The toughness was almost constant (~ 5.1 MPam0.5) up to a grain size of 0.4 µm. In ceramics with larger grains, the toughness increased linearly up to the grain size of 1.8 µm, where the maximum toughness (7.8 MPam0.5) was found. Above this grain size spontaneous transformation to the monoclinic phase occurred. Figure 9 shows that both ceramics, TZ-3YB and B261, followed the same toughness dependence on grain size. It also follows from this figure that the transformation toughness effect is grain size dependent only above a particular tetragonal grain size (approx. 0.4 µm). Effect of grain size on mechanical properties of 3Y-TZP ceramics Ceramics − Silikáty 52 (3) 165-171 (2008) 169 Table 2. Hardness, HV, fracture toughness, KIc, and their standard deviations, s, of zirconia ceramics. Fracture toughness Sintering Hardness 10 kg 20 kg 30 kg Average schedule HV s KIc s KIc s KIc s KIc Sample (°C)/(h) (MPa) (MPam0.5) TZ - 3YB 1400/2 12620 186 4.94 0.07 5.29 0.06 5.49 0.05 5.24 TZ - 3YB 1500/2 12264 135 4.91 0.06 5.20 0.08 5.41 0.05 5.17 TZ - 3YB 1550/0 12137 224 4.89 0.29 5.10 0.06 5.38 0.05 5.12 TZ - 3YB 1550/2 12007 103 4.89 0.05 5.14 0.03 5.40 0.03 5.14 TZ - 3YB 1550/5 11970 113 5.06 0.07 5.23 0.05 5.45 0.06 5.25 TZ - 3YB 1550/10 11738 127 5.53 0.13 5.41 0.07 5.62 0.07 5.52 TZ - 3YB 1600/2 11858 363 5.15 0.16 5.29 0.07 5.57 0.04 5.34 TZ - 3YB 1600/5 11849 551 5.80 0.21 5.43 0.05 5.62 0.04 5.62 TZ - 3YB 1600/10 11588 176 6.39 0.09 5.53 0.03 5.72 0.03 5.88 TZ - 3YB 1650/10 11361 293 6.75 0.21 5.82 0.12 5.87 0.06 6.15 TZ - 3YB 1650/20 11145 341 7.11 0.12 6.52 0.10 6.09 0.06 6.57 TZ - 3YB 1650/30 10971 293 7.94 0.24 7.50 0.54 7.80 0.15 7.77 B 261 1100/4 12867 789 4.89 0.08 5.35 0.14 - - 5.12 B 261 1300/6 12485 218 4.79 0.07 5.15 0.12 5.38 0.08 5.11 B 261 1450/2 10587 657 4.73 0.09 5.30 0.27 - - 5.02 B 261 1550/5 10080 435 5.98 0.45 5.79 0.21 5.99 0.40 5.92 Figure 7. The dependence of the hardness of TZ-3YB and B261 ceramics on the inverse square root of grain size. d-1/2 (µm-1/2) Hardness (MPa) 11 000 10 000 0.4 12 000 0.8 2.0 2.4 11 500 10 500 12 500 1.6 1.2 13 000 2.8 3.2 3.6 TZ-3YB B261 Figure 8. Fracture toughness of TZ-3YB ceramics as a function of grain size determined at different indentation loads. Grain size (µm) Fracture toughness (MPa m0.5) 6 4 0.0 8 0.4 1.6 2.0 7 5 9 1.2 0.8 10 kg load 20 kg load 30 kg load Recently Vickers indentation fracture toughness tests (VIF) were reviewed in detail [22]. It was concluded that VIF techniques are not suitable for reliable measurement of fracture toughness, KIc, because the crack arrest process occurs in a multiple-crack environment and in highly complex residual stress conditions. To verify our fracture toughness results determined by the indentation method, two standardized methods were applied. Unfortunately, the results obtained by "Chevron V Notch" method (CVN) and "Single Edged V Notch Beam" method (SEVNB) showed extremely high scatter (5-12 MPam0.5), thus it was not possible to find any dependence on grain size. The reason for such high variance is not clear and may be connected with the toughening effect in TZP ceramics. From this point of view the indentation method utilized in the present investigation provided more consistent results compared with the CVN and SEVNB methods. The four-point bending strength of TZ-3YB bars with a grain size of 0.30 µm (sintered at 1500°C/2 h) and 0.78 µm (sintered at 1600°C/10 h) was determined and compared. Figure 10 shows the Weibull plot of both materials. Although the average strength of samples varying in grain size was similar (1020 MPa vs. 1011 MPa), it can be seen in the graph that the scatter of strength values was higher for TZ-3YB ceramics with larger grains. This observation was confirmed by calculation of Weibull moduli. The Weibull modulus was m = 13.0 for ceramics with the grain size of 0.30 µm and m = 7.54 for ceramics with the grain size of 0.78 µm. It was verified statistically that these values are significantly different. According to the linear fracture mechanics the body with higher fracture toughness should possess the higher strength. In our case TZ-3YB ceramics with a grain size of 0.78 µm had higher toughness than ceramics with a grain size of 0.30 µm (5.88 vs. 5.17 MPam0.5). Unfortunately, the effect of higher toughness was suppressed by an effect of bigger critical defects due to microstructural coarsening [10]. The competition of these two effects resulted in ceramics with strengths apparently independent of grain size. However, the size and distribution of defects during coarsening cannot be efficiently controlled, which resulted in the lower Weibull modulus for ceramics sintered at higher temperature. CONCLUSION The effect of grain size on mechanical properties of commercial submicrometre-grained 3Y-TZP ceramics (TZ-3YB) and nanocrystalline 3Y-zirconia ceramics (B261) was investigated. The following conclusions could be drawn: 1.The hardness of both TZ-3YB and B261 ceramics decreased with increasing grain size. However, the hardness was lower in coarsened nanoceramics. This could be attributed to different mechanisms of the development of phase structure in nanoceramics compared with submicrometre-grained ceramics. 2.The fracture toughness was almost constant (5.1 MPam0.5) up to the grain size of 0.4 µm. Above this grain size, the fracture toughness started to grow and reached the maximum of 7.8 MPam0.5 at the grain size of 1.8 µm. Further grain growth resulted in spontaneous transformation from tetragonal to monoclinic phase and damage of the samples due to cracking. Both ceramics followed the same grain size depen-dence of fracture toughness. 3.The four-point bending strength of TZ-3YB ceramics with grain size of 0.30 and 0.78 µm was similar, 1020 MPa and 1011 MPa, respectively. The higher Trunec M. 170 Ceramics − Silikáty 52 (3) 165-171 (2008) Figure 9. Average fracture toughness of TZ-3YB and B261 ceramics as a function of grain size. Grain size (µm) Fracture toughness (MPa m0.5) 6 4 0.0 8 0.4 1.6 2.0 7 5 9 1.2 0.8 TZ-3YB B261 Figure 10. Weibull plot of the bending strength data for TZ-3YB ceramics sintered at 1500°C for 2 h and at 1600°C for 10 h. ln (bending strength, MPa) ln{ln[1/(1-P)]} -3 -5 6.6 -1 6.7 7.0 7.1 -2 -4 0 6.9 6.8 TZ-3YB - 1500°C/2 h TZ-3YB - 1600°C/10 h 1 2 7.2 fracture toughness inherent to ceramics with larger grain size was counterbalanced with an increase of critical defects due to microstructural coarsening. Moreover, the Weibull modulus declined from m = 13 at a grain size of 0.30 µm to m = 7.54 at a grain size of 0.78 µm. Acknowledgement The author gratefully acknowledges the funding provided by the Czech Ministry of Education under grant MSM 0021630508. Dr. A. Buchal and Mrs. D. Janova are kindly acknowledged for providing XRD analyses and SEM images, respectively. The author wishes to thank Mrs. Z. Skalova for her help with the experimental work. References 1. Hannink R. H. J., Kelly P. M., Muddle B. C.: J.Am.Ceram. Soc. 83, 461 (2000). 2. Lange F. F.: J. Mater.Sci. 17, 225 (1982). 3. Lange F. F.: J.Mater.Sci. 17, 240 (1982). 4. Becher P. F., Swain M. V.: J.Am.Ceram.Soc. 75, 493 (1992). 5. Wang J, Rainforth M., Stevens R.: Br.Ceram.Trans.J. 88, 1 (1989). 6. Suresh A., Mayo M. J., Porter W. D., Rawn C. J.: J.Am. Ceram.Soc. 86, 360 (2003). 7. Bravo-Leon A., Morikawa Y., Kawahara M., Mayo M. J.: Acta Mater. 50, 4555 (2002). 8. Ruiz L., Readey M. J.: J.Am.Ceram.Soc. 79, 2331 (1996). 9. Casellas D., Feder A., Llanes L., Anglada M.: Scr.Mater. 45, 213 (2001). 10. Eichler J., Rödel J., Eisele U., Hoffman M.: J.Am.Ceram. Soc. 90, 2830 (2007). 11. Casellas D., Alcala J., Llanes L., Anglada M.: J.Mater.Sci. 36, 3011 (2001). 12. Cottom B. A., Mayo M. J.: Scr.Mater. 34, 809 (1996). 13. Trunec M., Maca K.: J.Am.Ceram.Soc. 90, 2735 (2007). 14. EN 623-2: Advanced Technical Ceramics - Monolithic Ceramics. General and Texture Properties. Part 2: Determination of Density and Porosity, CEN, Brussels 1993. 15. Maca K., Trunec M., Chmelik R.: Ceramics-Silikaty 51, 94 (2007). 16. Niihara K., Morena R., Hasselman D. P. H.: J.Mater.Sci. Lett. 1, 13 (1982). 17. JIS R 1607: Testing Methods for Fracture Toughness of High Performance Ceramics, Japanese Standards Association, Tokyo 1990. 18. EN 843-1: Advanced Technical Ceramics - Monolithic Ceramics. Mechanical Properties at Room Temperature. Part 1: Determination of Flexural Strength, CEN, Brussels 1995. 19. ENV 843-5: Advanced Technical Ceramics - Monolithic Ceramics. Mechanical Properties at Room Temperature. Part 5: Statistical Analysis, CEN, Brussels 1996. 20. Scott H. G.: J.Mater.Sci. 10, 1527 (1975). 21. Matsui K., Horikoshi H., Ohmichi N., Ohgai M.: J.Am. Ceram.Soc. 86, 1401 (2003). 22. Quinn G. D., Bradt R. C.: J.Am.Ceram.Soc. 90, 673 (2007). Effect of grain size on mechanical properties of 3Y-TZP ceramics Ceramics − Silikáty 52 (3) 165-171 (2008) 171 VLIV VELIKOSTI ZRN NA MECHANICKÉ VLASTNOSTI 3Y-TZP KERAMIKY MARTIN TRUNEC Odbor keramiky a polymerù, Vysoké uèení technické v Brnì, Technická 2896/2, 616 69 Brno Mechanické vlastnosti 3Y-TZP keramiky byly zkoumány v závislosti na velikosti zrn v rozsahu od 0,19 µm do 2,15 µm. Vickersovy indentaèní testy byly použity pro stanovení tvrdosti a lomové houževnatosti. Tvrdost klesala s rostoucí velikostí zrn. Lomová houževnatost byla témìø konstantní pro keramiky se zrny do 0,4 µm a poté rostla se zvyšující se velikosti zrn až na 7,8 MPam0,5 u keramiky se zrny o velikosti 1,8 µm. U vìtších zrn došlo ke spontánní transformaci tetragonální fáze na monoklinickou. Keramické vzorky s velikostí zrn 0,30 µm a 0,78 µm mìli podobnou pevnost v ohybu, 1020 a 1011 MPa. Mikrostrukturní zhrubnutí, které bylo nezbytné pro dosažení vìtších zrn, vedlo k vyššímu rozptylu pevností, což se projevilo snížením Weibullova modulu (13,0 vs. 7,54). Pro srovnání byly také zkoumány mechanické vlastnosti nanokrystalické 3Y-ZrO2 keramiky, jejíž zrna byla zhrublá na velikost od 0,085 do 0,70 µm. Byly zjištìny rozdíly v mechanických vlastnostech zkoumaných keramik. Možné pøíèiny tìchto rozdílù byly diskutovány.
What are all the numbers 1-1000000?
Numbers 1 to 30,000!1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 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618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 1180, 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28143, 28144, 28145, 28146, 28147, 28148, 28149, 28150, 28151, 28152, 28153, 28154, 28155, 28156, 28157, 28158, 28159, 28160, 28161, 28162, 28163, 28164, 28165, 28166, 28167, 28168, 28169, 28170, 28171, 28172, 28173, 28174, 28175, 28176, 28177, 28178, 28179, 28180, 28181, 28182, 28183, 28184, 28185, 28186, 28187, 28188, 28189, 28190, 28191, 28192, 28193, 28194, 28195, 28196, 28197, 28198, 28199, 28200, 28201, 28202, 28203, 28204, 28205, 28206, 28207, 28208, 28209, 28210, 28211, 28212, 28213, 28214, 28215, 28216, 28217, 28218, 28219, 28220, 28221, 28222, 28223, 28224, 28225, 28226, 28227, 28228, 28229, 28230, 28231, 28232, 28233, 28234, 28235, 28236, 28237, 28238, 28239, 28240, 28241, 28242, 28243, 28244, 28245, 28246, 28247, 28248, 28249, 28250, 28251, 28252, 28253, 28254, 28255, 28256, 28257, 28258, 28259, 28260, 28261, 28262, 28263, 28264, 28265, 28266, 28267, 28268, 28269, 28270, 28271, 28272, 28273, 28274, 28275, 28276, 28277, 28278, 28279, 28280, 28281, 28282, 28283, 28284, 28285, 28286, 28287, 28288, 28289, 28290, 28291, 28292, 28293, 28294, 28295, 28296, 28297, 28298, 28299, 28300, 28301, 28302, 28303, 28304, 28305, 28306, 28307, 28308, 28309, 28310, 28311, 28312, 28313, 28314, 28315, 28316, 28317, 28318, 28319, 28320, 28321, 28322, 28323, 28324, 28325, 28326, 28327, 28328, 28329, 28330, 28331, 28332, 28333, 28334, 28335, 28336, 28337, 28338, 28339, 28340, 28341, 28342, 28343, 28344, 28345, 28346, 28347, 28348, 28349, 28350, 28351, 28352, 28353, 28354, 28355, 28356, 28357, 28358, 28359, 28360, 28361, 28362, 28363, 28364, 28365, 28366, 28367, 28368, 28369, 28370, 28371, 28372, 28373, 28374, 28375, 28376, 28377, 28378, 28379, 28380, 28381, 28382, 28383, 28384, 28385, 28386, 28387, 28388, 28389, 28390, 28391, 28392, 28393, 28394, 28395, 28396, 28397, 28398, 28399, 28400, 28401, 28402, 28403, 28404, 28405, 28406, 28407, 28408, 28409, 28410, 28411, 28412, 28413, 28414, 28415, 28416, 28417, 28418, 28419, 28420, 28421, 28422, 28423, 28424, 28425, 28426, 28427, 28428, 28429, 28430, 28431, 28432, 28433, 28434, 28435, 28436, 28437, 28438, 28439, 28440, 28441, 28442, 28443, 28444, 28445, 28446, 28447, 28448, 28449, 28450, 28451, 28452, 28453, 28454, 28455, 28456, 28457, 28458, 28459, 28460, 28461, 28462, 28463, 28464, 28465, 28466, 28467, 28468, 28469, 28470, 28471, 28472, 28473, 28474, 28475, 28476, 28477, 28478, 28479, 28480, 28481, 28482, 28483, 28484, 28485, 28486, 28487, 28488, 28489, 28490, 28491, 28492, 28493, 28494, 28495, 28496, 28497, 28498, 28499, 28500, 28501, 28502, 28503, 28504, 28505, 28506, 28507, 28508, 28509, 28510, 28511, 28512, 28513, 28514, 28515, 28516, 28517, 28518, 28519, 28520, 28521, 28522, 28523, 28524, 28525, 28526, 28527, 28528, 28529, 28530, 28531, 28532, 28533, 28534, 28535, 28536, 28537, 28538, 28539, 28540, 28541, 28542, 28543, 28544, 28545, 28546, 28547, 28548, 28549, 28550, 28551, 28552, 28553, 28554, 28555, 28556, 28557, 28558, 28559, 28560, 28561, 28562, 28563, 28564, 28565, 28566, 28567, 28568, 28569, 28570, 28571, 28572, 28573, 28574, 28575, 28576, 28577, 28578, 28579, 28580, 28581, 28582, 28583, 28584, 28585, 28586, 28587, 28588, 28589, 28590, 28591, 28592, 28593, 28594, 28595, 28596, 28597, 28598, 28599, 28600, 28601, 28602, 28603, 28604, 28605, 28606, 28607, 28608, 28609, 28610, 28611, 28612, 28613, 28614, 28615, 28616, 28617, 28618, 28619, 28620, 28621, 28622, 28623, 28624, 28625, 28626, 28627, 28628, 28629, 28630, 28631, 28632, 28633, 28634, 28635, 28636, 28637, 28638, 28639, 28640, 28641, 28642, 28643, 28644, 28645, 28646, 28647, 28648, 28649, 28650, 28651, 28652, 28653, 28654, 28655, 28656, 28657, 28658, 28659, 28660, 28661, 28662, 28663, 28664, 28665, 28666, 28667, 28668, 28669, 28670, 28671, 28672, 28673, 28674, 28675, 28676, 28677, 28678, 28679, 28680, 28681, 28682, 28683, 28684, 28685, 28686, 28687, 28688, 28689, 28690, 28691, 28692, 28693, 28694, 28695, 28696, 28697, 28698, 28699, 28700, 28701, 28702, 28703, 28704, 28705, 28706, 28707, 28708, 28709, 28710, 28711, 28712, 28713, 28714, 28715, 28716, 28717, 28718, 28719, 28720, 28721, 28722, 28723, 28724, 28725, 28726, 28727, 28728, 28729, 28730, 28731, 28732, 28733, 28734, 28735, 28736, 28737, 28738, 28739, 28740, 28741, 28742, 28743, 28744, 28745, 28746, 28747, 28748, 28749, 28750, 28751, 28752, 28753, 28754, 28755, 28756, 28757, 28758, 28759, 28760, 28761, 28762, 28763, 28764, 28765, 28766, 28767, 28768, 28769, 28770, 28771, 28772, 28773, 28774, 28775, 28776, 28777, 28778, 28779, 28780, 28781, 28782, 28783, 28784, 28785, 28786, 28787, 28788, 28789, 28790, 28791, 28792, 28793, 28794, 28795, 28796, 28797, 28798, 28799, 28800, 28801, 28802, 28803, 28804, 28805, 28806, 28807, 28808, 28809, 28810, 28811, 28812, 28813, 28814, 28815, 28816, 28817, 28818, 28819, 28820, 28821, 28822, 28823, 28824, 28825, 28826, 28827, 28828, 28829, 28830, 28831, 28832, 28833, 28834, 28835, 28836, 28837, 28838, 28839, 28840, 28841, 28842, 28843, 28844, 28845, 28846, 28847, 28848, 28849, 28850, 28851, 28852, 28853, 28854, 28855, 28856, 28857, 28858, 28859, 28860, 28861, 28862, 28863, 28864, 28865, 28866, 28867, 28868, 28869, 28870, 28871, 28872, 28873, 28874, 28875, 28876, 28877, 28878, 28879, 28880, 28881, 28882, 28883, 28884, 28885, 28886, 28887, 28888, 28889, 28890, 28891, 28892, 28893, 28894, 28895, 28896, 28897, 28898, 28899, 28900, 28901, 28902, 28903, 28904, 28905, 28906, 28907, 28908, 28909, 28910, 28911, 28912, 28913, 28914, 28915, 28916, 28917, 28918, 28919, 28920, 28921, 28922, 28923, 28924, 28925, 28926, 28927, 28928, 28929, 28930, 28931, 28932, 28933, 28934, 28935, 28936, 28937, 28938, 28939, 28940, 28941, 28942, 28943, 28944, 28945, 28946, 28947, 28948, 28949, 28950, 28951, 28952, 28953, 28954, 28955, 28956, 28957, 28958, 28959, 28960, 28961, 28962, 28963, 28964, 28965, 28966, 28967, 28968, 28969, 28970, 28971, 28972, 28973, 28974, 28975, 28976, 28977, 28978, 28979, 28980, 28981, 28982, 28983, 28984, 28985, 28986, 28987, 28988, 28989, 28990, 28991, 28992, 28993, 28994, 28995, 28996, 28997, 28998, 28999, 29000, 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29144, 29145, 29146, 29147, 29148, 29149, 29150, 29151, 29152, 29153, 29154, 29155, 29156, 29157, 29158, 29159, 29160, 29161, 29162, 29163, 29164, 29165, 29166, 29167, 29168, 29169, 29170, 29171, 29172, 29173, 29174, 29175, 29176, 29177, 29178, 29179, 29180, 29181, 29182, 29183, 29184, 29185, 29186, 29187, 29188, 29189, 29190, 29191, 29192, 29193, 29194, 29195, 29196, 29197, 29198, 29199, 29200, 29201, 29202, 29203, 29204, 29205, 29206, 29207, 29208, 29209, 29210, 29211, 29212, 29213, 29214, 29215, 29216, 29217, 29218, 29219, 29220, 29221, 29222, 29223, 29224, 29225, 29226, 29227, 29228, 29229, 29230, 29231, 29232, 29233, 29234, 29235, 29236, 29237, 29238, 29239, 29240, 29241, 29242, 29243, 29244, 29245, 29246, 29247, 29248, 29249, 29250, 29251, 29252, 29253, 29254, 29255, 29256, 29257, 29258, 29259, 29260, 29261, 29262, 29263, 29264, 29265, 29266, 29267, 29268, 29269, 29270, 29271, 29272, 29273, 29274, 29275, 29276, 29277, 29278, 29279, 29280, 29281, 29282, 29283, 29284, 29285, 29286, 29287, 29288, 29289, 29290, 29291, 29292, 29293, 29294, 29295, 29296, 29297, 29298, 29299, 29300, 29301, 29302, 29303, 29304, 29305, 29306, 29307, 29308, 29309, 29310, 29311, 29312, 29313, 29314, 29315, 29316, 29317, 29318, 29319, 29320, 29321, 29322, 29323, 29324, 29325, 29326, 29327, 29328, 29329, 29330, 29331, 29332, 29333, 29334, 29335, 29336, 29337, 29338, 29339, 29340, 29341, 29342, 29343, 29344, 29345, 29346, 29347, 29348, 29349, 29350, 29351, 29352, 29353, 29354, 29355, 29356, 29357, 29358, 29359, 29360, 29361, 29362, 29363, 29364, 29365, 29366, 29367, 29368, 29369, 29370, 29371, 29372, 29373, 29374, 29375, 29376, 29377, 29378, 29379, 29380, 29381, 29382, 29383, 29384, 29385, 29386, 29387, 29388, 29389, 29390, 29391, 29392, 29393, 29394, 29395, 29396, 29397, 29398, 29399, 29400, 29401, 29402, 29403, 29404, 29405, 29406, 29407, 29408, 29409, 29410, 29411, 29412, 29413, 29414, 29415, 29416, 29417, 29418, 29419, 29420, 29421, 29422, 29423, 29424, 29425, 29426, 29427, 29428, 29429, 29430, 29431, 29432, 29433, 29434, 29435, 29436, 29437, 29438, 29439, 29440, 29441, 29442, 29443, 29444, 29445, 29446, 29447, 29448, 29449, 29450, 29451, 29452, 29453, 29454, 29455, 29456, 29457, 29458, 29459, 29460, 29461, 29462, 29463, 29464, 29465, 29466, 29467, 29468, 29469, 29470, 29471, 29472, 29473, 29474, 29475, 29476, 29477, 29478, 29479, 29480, 29481, 29482, 29483, 29484, 29485, 29486, 29487, 29488, 29489, 29490, 29491, 29492, 29493, 29494, 29495, 29496, 29497, 29498, 29499, 29500, 29501, 29502, 29503, 29504, 29505, 29506, 29507, 29508, 29509, 29510, 29511, 29512, 29513, 29514, 29515, 29516, 29517, 29518, 29519, 29520, 29521, 29522, 29523, 29524, 29525, 29526, 29527, 29528, 29529, 29530, 29531, 29532, 29533, 29534, 29535, 29536, 29537, 29538, 29539, 29540, 29541, 29542, 29543, 29544, 29545, 29546, 29547, 29548, 29549, 29550, 29551, 29552, 29553, 29554, 29555, 29556, 29557, 29558, 29559, 29560, 29561, 29562, 29563, 29564, 29565, 29566, 29567, 29568, 29569, 29570, 29571, 29572, 29573, 29574, 29575, 29576, 29577, 29578, 29579, 29580, 29581, 29582, 29583, 29584, 29585, 29586, 29587, 29588, 29589, 29590, 29591, 29592, 29593, 29594, 29595, 29596, 29597, 29598, 29599, 29600, 29601, 29602, 29603, 29604, 29605, 29606, 29607, 29608, 29609, 29610, 29611, 29612, 29613, 29614, 29615, 29616, 29617, 29618, 29619, 29620, 29621, 29622, 29623, 29624, 29625, 29626, 29627, 29628, 29629, 29630, 29631, 29632, 29633, 29634, 29635, 29636, 29637, 29638, 29639, 29640, 29641, 29642, 29643, 29644, 29645, 29646, 29647, 29648, 29649, 29650, 29651, 29652, 29653, 29654, 29655, 29656, 29657, 29658, 29659, 29660, 29661, 29662, 29663, 29664, 29665, 29666, 29667, 29668, 29669, 29670, 29671, 29672, 29673, 29674, 29675, 29676, 29677, 29678, 29679, 29680, 29681, 29682, 29683, 29684, 29685, 29686, 29687, 29688, 29689, 29690, 29691, 29692, 29693, 29694, 29695, 29696, 29697, 29698, 29699, 29700, 29701, 29702, 29703, 29704, 29705, 29706, 29707, 29708, 29709, 29710, 29711, 29712, 29713, 29714, 29715, 29716, 29717, 29718, 29719, 29720, 29721, 29722, 29723, 29724, 29725, 29726, 29727, 29728, 29729, 29730, 29731, 29732, 29733, 29734, 29735, 29736, 29737, 29738, 29739, 29740, 29741, 29742, 29743, 29744, 29745, 29746, 29747, 29748, 29749, 29750, 29751, 29752, 29753, 29754, 29755, 29756, 29757, 29758, 29759, 29760, 29761, 29762, 29763, 29764, 29765, 29766, 29767, 29768, 29769, 29770, 29771, 29772, 29773, 29774, 29775, 29776, 29777, 29778, 29779, 29780, 29781, 29782, 29783, 29784, 29785, 29786, 29787, 29788, 29789, 29790, 29791, 29792, 29793, 29794, 29795, 29796, 29797, 29798, 29799, 29800, 29801, 29802, 29803, 29804, 29805, 29806, 29807, 29808, 29809, 29810, 29811, 29812, 29813, 29814, 29815, 29816, 29817, 29818, 29819, 29820, 29821, 29822, 29823, 29824, 29825, 29826, 29827, 29828, 29829, 29830, 29831, 29832, 29833, 29834, 29835, 29836, 29837, 29838, 29839, 29840, 29841, 29842, 29843, 29844, 29845, 29846, 29847, 29848, 29849, 29850, 29851, 29852, 29853, 29854, 29855, 29856, 29857, 29858, 29859, 29860, 29861, 29862, 29863, 29864, 29865, 29866, 29867, 29868, 29869, 29870, 29871, 29872, 29873, 29874, 29875, 29876, 29877, 29878, 29879, 29880, 29881, 29882, 29883, 29884, 29885, 29886, 29887, 29888, 29889, 29890, 29891, 29892, 29893, 29894, 29895, 29896, 29897, 29898, 29899, 29900, 29901, 29902, 29903, 29904, 29905, 29906, 29907, 29908, 29909, 29910, 29911, 29912, 29913, 29914, 29915, 29916, 29917, 29918, 29919, 29920, 29921, 29922, 29923, 29924, 29925, 29926, 29927, 29928, 29929, 29930, 29931, 29932, 29933, 29934, 29935, 29936, 29937, 29938, 29939, 29940, 29941, 29942, 29943, 29944, 29945, 29946, 29947, 29948, 29949, 29950, 29951, 29952, 29953, 29954, 29955, 29956, 29957, 29958, 29959, 29960, 29961, 29962, 29963, 29964, 29965, 29966, 29967, 29968, 29969, 29970, 29971, 29972, 29973, 29974, 29975, 29976, 29977, 29978, 29979, 29980, 29981, 29982, 29983, 29984, 29985, 29986, 29987, 29988, 29989, 29990, 29991, 29992, 29993, 29994, 29995, 29996, 29997, 29998, 29999, 30000 and beyond!
