佘妍妍-Influence ofporosityonmechanicalbehaviourandgaspermeability.pdf
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Influence of porosity on mechanical behaviour and gas permeabilityof Ti compacts prepared by slip castingQian Xua,n, Brian Gabbitasa, Steven MatthewsbaWaikato Centre for Advanced Materials (WaiCAM), School of Engineering, University of Waikato, Private Bag 3105, Hamilton, New ZealandbSchool of Engineering and Advanced Technology, Massey University, Private Bag 102904, North Shore City 0745, Auckland, New Zealanda r t i c l e i n f oArticle history:Received 20 May 2013Received in revised form22 August 2013Accepted 27 August 2013Available online 2 September 2013Keywords:Porous materialsTitaniumSlip castingMechanical characterisationFracturea b s t r a c tPorous titanium compacts with porosity in the range of 12.335.3 vol% were fabricated by slip casting.Slip casting is emerging to be an attractive process for fabrication of porous titanium products. Themechanical properties, fracture morphology, gas permeability, pore size analysis and pore shape factorsfor the porous Ti compacts were determined for different porosity levels. A decreasing porosity levelresulted in less open porosity and gas permeability, reduced pore size, and an increased tensile stress andelongation. The mechanical properties of porous titanium compacts produced by slip casting werecomparable with more conventional press and sintered materials at the same porosity levels. Theoreticalmodels for tensile stress and ductility as a function of porosity were examined and incorporated into theresults and differences between the theoretical models and experimental results are discussed. The poreshape factor analysis showed that tensile loading would stretch the pores in the compacts to producemore irregular pores, which were acting as linkage sites to allow the propagation of cracks. Additionally,a novel interconnected pore characterisation method using ammonium meta-tungstate solution ispresented. By using backscatter scanning electron microscopy, the interconnected pores can be directlyobserved.& 2013 Elsevier B.V. All rights reserved.1. IntroductionPorous titanium (Ti) is an excellent filter material used in thechemical and processing industries, owing to its outstandingcorrosion resistance, high strength-to-weight ratio, large specificsurface area and high gas and liquid permeability 1. A stable andpermanent thin layer of TiO2forms on the surface of titanium atroom temperature, and it is able to regenerate immediately afterdamage. This thin film of TiO2allows Ti to be used in highlycorrosive environments and aggressive media in which stainlesssteel cannot provide sufficient corrosion resistance, such as sea-water, oxidising chlorine, salt acidic solutions containing oxidants,etc. 2,3. For ceramic filters, fragility is a main issue in practice andthermal shock is another potential problem which limits their usewhen there are frequent and rapid changes in process gastemperature 4. Typical uses of porous Ti filters can be found inair and water purification processes 5,6, filtering of titaniumtetrachloride liquid 7 and in pulp and paper plants 2.Ti has a strong chemical affinity to oxygen, especially attemperatures above 400 1C, followed by fast diffusion of oxygeninto the matrix, which results in embrittlement 8. Because of thelarge surface area of porous Ti and therefore a high propensity tooxygen contamination, a low temperature powder metallurgyroute is a promising way to fabricate porous Ti products.In powder metallurgy, the sintered density, porosity andmechanical properties of Ti compacts can be affected by sinteringconditions, powder particle size and shape, alloying elements,interstitial elements, etc. Oh et al. 9 fabricated porous Ti with aporosity ranging from 5.0 to 37.1 vol% by sintering sphericaltitanium powder particles. Their work showed that the initialpowder size and sintering pressure are two dominant factors incontrolling the densification process of porous Ti compacts,whereas sintering temperature has only a small effect. A sinteringstudy examined the effect of sintering atmospheres on the densityand mechanical properties of sintered Ti compacts, revealing thatat similar levels of the sintered density, the Ti compacts sintered inargon had much lower tensile properties than those sinteredunder vacuum 10. Recent research has shown that additions ofalloying elements (Fe and Zr) to Ti powder could enhance thesintering densification of Ti compacts prepared by powder injec-tion moulding, but the mechanical properties were not improved11. Moreover, Qian 12 has summarised the tensile properties ofcold compacted and sintered Ti as a function of oxygen content. Ata similar level of sintered density, an increase in oxygen contentincreases the strength of sintered Ti compacts, whereas theductility reduces.Contents lists available at ScienceDirectjournal homepage: /locate/mseaMaterials Science & Engineering A0921-5093/$-see front matter & 2013 Elsevier B.V. All rights reserved./10.1016/j.msea.2013.08.051nCorresponding author. Tel.: 64 7 8384466x6796; fax: 64 7 8384835.E-mail address: qx17waikato.ac.nz (Q. Xu).Materials Science & Engineering A 587 (2013) 123131The porous Ti compacts in this study were produced by a slipcasting route, which, in a previous study was demonstrated to be afeasible process for manufacturing porous Ti products 13.Ohkawa et al. studied Ti slip casting for dental applications usingsodium alginate as a binder 14. Due to the contamination fromthe decomposition of sodium alginate, a TiC phase was found inthe sintered Ti compact. Thus, a brittle sintered Ti part wasproduced. In another Ti slip casting study, a slurry formed froma mixture of Ti and TiH2powder was used to make a Ti foam witha porosity ranging from 56.1 vol% to 65.2 vol% and compressivestrengths ranging from 120 MPa to 150 MPa 15. To the best of ourknowledge, a comprehensive and quantitative understanding ofthe effect of porosity on the mechanical behaviour of Ti producedby slip casting has not yet been reported. In this study, the effect ofporosity on gas permeability, pore size distribution, pore shape,degree of interconnected pores and mechanical behaviour of slipcast Ti has been examined. Moreover, theoretical models andexperimental work from previous researchers have been com-pared with the current experimental results to enhance ourunderstanding of the slip casting process.2. Background2.1. Tensile strength (TS) versus porosity relationship for sinteredmetalsMany theoretical models for the tensile behaviour of sinteredmetals have been derived by considering the micromechanisms offailure. Griffiths et al. 16 derived an analytical model of the TS ofporous materials based on the ratio of load-bearing area andapparent cross-sectional area, as shown below:stsoAbAa 1?P2=31where stis the TS of the porous material, sois the TS of the bulkmaterial, Aais the apparent cross-sectional area, Abis the load-bearing area, is an empirical constant and P is the level ofporosity in vol%. Griffith et al. suggested that the value of can bevaried from 0.98 to 1.30, depending on the pore distribution andthe interaction effect of the stress concentrations. With regard tothe pore distribution, is equal to 0.98 for regular tetrahedronsand 1.077 for irregular tetrahedrons. However, when a porousmaterial is subjected to a tensile stress, there is a local stressconcentration induced around the pore cavity. To take into accountthe interaction effect of stress concentrations, the value wouldincrease further.In 1981, Fleck and Smith 17 developed a brick model, asshown below:stso 1?P2=322This model simplified the Griffithss model by treating the powderparticles as solid cubes and pores as cubic spaces and assumedthat there is no effect of the stress concentration on the poregeometry.Haynes 18 also proposed a model by assuming no micro-structural defects in the sintered metal, as shown below:stso K1?PM3where K is a constant that depends on the test geometry andprocessing details and M is the exponential dependence on thelevel of porosity, which normally varies from 3 to 6. The value of Mwill be affected by the stress concentration and premature fracturethat is produced by crack propagation from pore to pore. In thisstudy, all the equations (1)(3) have been compared with experi-mental data and the detailed results and discussion are presentedin Section 4.2.2. Ductility to porosity relationship for sintered metalsHaynes 19 proposed an empirical equation that related theporosity level with the ductility of sintered metals, as presentedbelow:reloVPVs 1?P3=21C P2?1=24where Vpis the notional branch volume of a porous material, Vsisthe notional branch volume of a bulk material, ois the ductility ofthe bulk material, relis the relative ductility of the porous materialand C is a constant which measures the sensitivity of the ductilityto porosity content. Haynes 19 defines the notional branchvolume as the volume of pore-free material which will undergothe same total deformation as the porous specimen when strainedto fracture. In his model, he assumed that powder particles arebonded together by necks to form a network in a sintered metalmaterial. When the material is subjected to tensile stress, theindividual necks in the material behave like miniature tensilespecimens, whereas most of the deformation occurs at thenarrower parts of the necks. Haynes suggested that the numberof branches depends on the number of contacts between powderparticles in the green state.3. Experimental methods3.1. Preparation methodsPorous Ti compacts with porosities in a range of 12.335.3 vol%were fabricated by slip casting (Table 1). Fine?325 mesh(r44 m)titaniumpowder(purity:99.95%;XianBaodePowder Metallurgy Co. Ltd., China) produced by the hydride/dehydride (HDH) process were employed in this study, as shownin Fig. 1. Further details of the slip casting process for Ti have beenreportedelsewhere13.Eachslipcastrectangularpart(40 mm?10 mm?20 mm) was sintered under high vacuum(3?10?3Pa). The porosity range was controlled using differentsintering conditions such as sintering temperature (1000 1C,Table 1The total porosity, oxygen content and carbon content of porous Ti compacts prepared by slip casting and sintered under various conditions.Sintering temperature (1C)Sintering time (h)Heating rate (1C/min)Cooling rate (1C/min)Total porosity (%)Oxygen content (wt%)Carbon content (wt%)1000110Furnace cooling35.327Furnace cooling27.7210Furnace cooling30.60.450.0511100210Furnace cooling21.90.440.04312000.510Furnace cooling16.4210Furnace cooling13.70.470.04627512.3Q. Xu et al. / Materials Science & Engineering A 587 (2013) 1231311241100 1C and 1200 1C), sintering time (0.5 h, 1 h and 2 h), heatingrate (5 1C/min, 7 1C/min and 10 1C/min) and cooling rate (5 1C/minand furnace cooling). Oxygen and carbon levels in the titaniumcompacts were analysed by the Leco combustion technique.Oxygen and carbon levels in the as-received titanium powderwere 0.32 wt% and 0.02 wt%, respectively. After sintering, theoxygen and carbon contents in the sintered Ti compacts remainedreasonably consistent for each of the sintering temperatures usedin this work, as shown in Table 1.3.2. Porosity and open porosityThe total porosity and the open porosity in sintered Ti com-pacts were measured by the Archimedes method, in which thesintered compacts were vacuum impregnated overnight withdistilled water.3.3. Permeability and pore size analysisThe permeability and pore size analysis was determined usinga pore size distribution analyser (GaoQ Functional Materials Ltd.,China). The samples were wire electric discharge machined to a2 mm thickness and 20 mm diameter circular shape and prior tothe test, both sides of the samples were ground and fine polishedto remove the blockage effect from the pores after machining. Anultrasonic bath was then used to clean up the samples. The testingmethods were based on ASTM F316-03 20. The samples werefixed in place using a sample holder sealed by silicon washers,which was connected to a gas flow tube. Nitrogen gas was flushedthrough the samples at different flow rates and the correspondingpressure differences were recorded by a pressure sensor. Thepermeability coefficient was determined using Darcys law 21.In the sintered porous material, each pore may have manydiameters. Herein, for each pore, the pore size in the materialwas measured based on the most constricted pore throat diameterin the pore. Information about pore throat diameter is useful inestimating the size of the debris that might pass through a filter21.3.4. Interconnected pore characterisationA characterisation technique for the identification of intercon-nected pores was developed using ammonium meta-tungstate(AMT, (NH4)H2W12O40?nH2O), which is a 99.99% water solublechemical. AMT was dissolved in distilled water with a mass ratio of2:1. The samples were then immersed in the AMT solution andkept under vacuum conditions until no bubbles came out. Thesamples were dried in an oven at 40 1C and then put into a mufflefurnace and heated to 550 1C and held for 3 h. Mooney et al. 22indicated that AMT is completely transformed to tungsten trioxide(WO3) at 450 1C. Thus, tungsten trioxide would infill the inter-connected pores in the porous Ti compacts. Prior to makingobservations, the samples were wire cut machined and the cuttingsurface ground. WO3and titanium have very different atomicnumber, therefore, the interconnected pores could be observed bybackscattered electrons using a Hitachi S4000 scanning electronmicroscope (SEM).3.5. Tensile testingTensile testing of porous Ti compacts was carried out at roomtemperature using an Instron tensile testing machine at a strainrate of 1?10?4s?1. Dumbell shaped specimens for tensile testing,with a rectangular gauge cross section of 2?2 mm2and a gaugelength of 10 mm, were wire electric discharge machined fromsintered Ti compacts. The fracture surface of the tensile specimenswas examined using a Hitachi S4000 scanning electron micro-scope (SEM). The longitudinal plane of fractured specimens, whichhad been prepared by grinding and polishing, were also examined.3.6. Pore shapeThe pore shape was measured on microstructures obtainedusing optical microscopy using image analysis software (Image-Pro Plus). A pore shape factor, F, was used to qualitativelycharacterise the pore shape using Eq. (5) 23, where A is themeasured area of a pore and P is the measured perimeter of a pore.As the pore shape factor approaches one, it denotes a round pore.As the value approaches zero, it indicates an irregular pore:F 4AP254. Results and discussion4.1. Open pores and permeabilityFig. 2 shows the open porosity level (Popen) and permeability inthe sintered Ti materials as a function of the total porosity (Ptotal)ranging from 12.3 vol% to 35.3 vol%. The gas permeability showed0%5%10%15%20%25%30%35%40%0.11101001000Volume FractionParticle Size (m)Fig. 1. (a) Morphology of HDH Ti powder particles. (b) Particle size distribution ofHDH Ti powder.Q. Xu et al. / Materials Science & Engineering A 587 (2013) 123131125a strong positive linear correlation with the total porosity ofsintered Ti compacts. A linear relationship was indicated betweenthe total porosity and the open porosity for the sintered porous Ticompacts. The empirical relationship can be expressed asPopen 0:99nPtotal?0:06;0rPtotalr50%6It is interesting to note that the open porosity level of sintered porousTi compacts reaches zero when the total porosity is about 6 vol%. Inother words, it is expected that all the pores are closed when theporosity level is below 6 vol%. A similar finding was also concludedby Coleman and Beere 24. They investigated the sintering of openand closed porosity using urania (UO2), which showed that all thepores are closed when the residual porosity is below 8 vol%.The open porosity fraction in titanium compacts as a functionof the total porosity produced by different processing techniques iscompared in Fig. 3. Oh et al. 9 showed the highest open porosityfraction in the porous titanium compacts, which were produced bypowder press and vacuum sintering using spherical titaniumpowders. The porosity level was controlled by the use of differentsintering conditions (sintering temperature and sintering pres-sure) and the powder particle size varied from 65 m to 374 m.The high open porosity fraction was due to the large powderparticle size. Erk et al. 25 employed thermoreversible gel castingof titanium hydride (TiH2, r45 m) with polypropylene space-holders (35 m) to fabricate porous titanium products. The volumeof pores in their work depended on the volume fraction ofspaceholders. After sintering for 10 h at 1000 1C, the pore size intheir material ranged from 30 m to 50 m. A relatively low openporosity fraction at a similar level of total porosity was thereforeproduced. However, at a total porosity level above 35 vol%, thecorresponding open porosity fraction was close to unity, whichwas comparable with the results of Oh et al. 9. By comparing thedata from this study with these two techniques, slip castingshowed an open porosity fraction at intermediate values.4.2. Pore size analysisAs mentioned before, for each pore, the pore size is a measure ofthe most constricted pore throat diameter of the pore. The averagepore size is therefore the average value of the pore throat diameters ofall pores and the maximum pore size is therefore the largest of themost constricted pore throat diameter of all pores. As shown inTable 2, the average pore size in the compacts decreased withdecreasing porosity level. However, the maximum pore size in thecompacts was random. The measurement range of the pore sizeanalyser is from 0. 1 m to 100 m, therefore, the average pore size inthe porous compact with 12.3 vol% porosity was too small to measure.The powder particle size of the raw Ti materials has asignificant impact on the pore size. Hirschhorn 26 fabricatedporous Ti compacts using powder ranging in size from 88 m to149 m. He noted that at porosity levels of 3540 vol%, the averagepore size in the compacts was from 10 to 15 m. At a porosity levelof about 15 vol%, the average pore size was about 12 m. For theslip casting process in this study, very fine powder (r44 m) wasused, which produced much smaller pores in the Ti compacts. Thisinformation could be a way of controlling the pore size to givedifferent levels of porosity.4.3. Interconnected pore characterisationIn order to characterise the interconnected pores, ammoniummeta-tungstate (AMT) was used as a medium to seep through theporous titanium compacts. At temperatures above 450 1C, AMTformed tungsten trioxide. In Fig. 4, energy-dispersive X-ray spec-troscopy (EDX) mapping shows a typical interconnected pore inthe treated porous Ti compacts and thus demonstrates thattungsten oxide can fill up or at least coat the inside of theinterconnected pores. Pores that showed no evidence of thepresence of WO3were assumed to be isolated pores and notconnected in any way to the surface. In Fig. 5, Ti compacts withdifferentporositylevels(27.7 vol%,21.9 vol%,16.4 vol%and12.3 vol%) were treated with AMT and the backscattered electronimages revealed the interconnected pores, which showed up asthe lighter areas in the micrographs. As the porosity leveldecreased, the percentage of interconnected porosity was reduced.In Fig. 5(c), a few isolated pores were observed, as pointed out bythe arrows. At a porosity of 12.3 vol%, the pore size decreasedfurther and there was less porosity, so the magnification used forSEM imaging was lowered to better illustrate the overall distribu-tion of interconnected pores in the compact. There is also anincrease in the number of isolated pores that can be observed andthe pore shape is more spherical (Fig. 5(d).Dullien 27 mentioned a similar interconnected pore character-isation technique using Woods metal, which is a eutectic alloy witha low melting point of 70 1C. The porous metal is impregnated withmolten Woods metal. When cooling, the interconnected pores areeasy to distinguish using backscattered electrons. However, WoodsFig. 2. Open porosity level and permeability of sintered porous Ti compacts as afunction of total porosity.0 0.2 0.4 0.6 0.8 1 0% 10% 20% 30% 40% 50% Open Porosity FractionTotal Porosity (POpen Porosity FractionTotal Porosity (Ptotaltotal) )Oh, et al. (2003) Erk, Dunand & Shull (2008) Experimental Fig. 3. Open porosity fraction in the porous titanium compacts as a function of totalporosity.Table 2The pore size analysis on the different porosity levels of sintered Ti compacts.Porosity (%)Average pore size (m)Maximum pore size (m)12.31.6Q. Xu et al. / Materials Science & Engineering A 587 (2013) 123131126metal is extremely harmful to human health, especially the vapourfrom molten Woods metal, due to the involvement of lead andcadmium in the composition. The method presented here, usingammonium meta-tungstate, is more effective.4.4. Tensile strength (TS) of sintered porous TiTensile testing results from Ti compacts with different levels ofporosity showed that tensile strength was strongly dependent onthe degree of porosity. Because the amount of oxygen and carbonin the sintered Ti was little affected by sintering temperature, asshown in Table 1, changes in the mechanical behaviour of thesintered Ti due to variations in oxygen or carbon content should beminimal. In Fig. 6, by using regression analysis, the empiricalrelationship between the TS and porosity can be expressed asstso 1:31?2P;0:1rPtotalr0:57where stis the TS (MPa) of the porous material, sois the TSof the bulk material (550 MPa for Grade 4 Ti bulk material ASTMB348-11) and P is the fractional porosity of a sintered compact.From Eq. (7), it is reasonable to predict that st0 MPa whenP50.0 vol%, which is close to the green density of a slip castFig. 4. Energy-dispersive X-ray spectroscopy (EDX) mapping analysis of an AMT impregnated porous Ti compact after heat treatment. The bright areas indicate a lowconcentration of the element mapped and dark areas show a high concentration of the element mapped.Fig. 5. Backscatter electrons (BSE) images of interconnected pores in the porous Ti compacts at different porosity levels: (a) 27.7 vol% porosity; (b) 21.9 vol% porosity;(c) 16.4 vol% porosity; and (d) 12.3 vol% porosity. Isolated pores are pointed out by the arrows.0 200 400 600 800 10% 20% 30% 40% Tensile Stress (MPa)PorosityTensile Stress (MPa)Porosity(a) (b) (c) (d) (e) (f) Fig. 6. Plot of tensile strength against the total porosity of sintered Ti compacts:(a) experimental data from slip casting; (b) the trend line of experimental data;(c) Hayness model (st50 MPa; K1.5; M3); (d) Griffithss model (st550 MPa;0.981); (e) modified Griffithss model (st730 MPa; 1.3); and (f) thebrick model.Q. Xu et al. / Materials Science & Engineering A 587 (2013) 123131127compact. However, Eq. (7) also shows that st730 MPa whenP0 vol%, which is above the TS of the bulk commercially pureGrade 4 Ti material (550 MPa). Thus, this equation may only befeasible to use at porosity levels above 10 vol%.In Fig. 6, by fitting Griffithss model, Fleck and Smiths brickmodel and Hayness model to the experimental data, Haynessmodel shows the best fit, which is almost identical to the trend-line. For the Hayness model, the K and M values were found to be1.5 and 3, respectively. The K value can be an indicator of effectivestress concentration factor. The M value implies a moderate effectand takes account of both pore geometry and the interaction effectof stress concentrations around the pores. Both the Griffithssmodel and Fleck and Smiths brick model show a lower bound tothe experimental data. In this case, Fleck and Smiths brick modelwas the least successful in predicting the strength to porosityrelationship and this indicates that the interaction of stressconcentrations is an important factor that must be considered inthe model. In the Griffithss model, the value is found to be 0.981when using 550 MPa as the tensile strength of the bulk Ti. It isnoteworthy that by increasing the tensile strength of the bulk Ti to730 MPa in the Griffithss model, and altering the value to 1.3, asshown in Fig. 6(e), the modified Griffithss model displays areasonable fit with the experimental data. However, 730 MPa isnot a realistic value for the tensile strength of Grade 4 Ti materials;therefore, it implies that the Griffithss model has limitations inpredicting the tensile strength variation as a function of theporosity in a material, whereas Hayness model is a more feasibleapproach for predicting the tensile strength of porous Ti compactsproduced by slip casting.4.5. Ductility of sintered porous TiThe relative ductility (the ductility of porous Ti divided by theductility of bulk Ti) of sintered porous Ti compacts, prepared by slipcasting, varied linearly with the porosity level in the compacts(Fig. 7). The elongation of the bulk Ti was 15%, which was obtainedby extrapolating the trend line. At a porosity of 12.2 vol%, the averagerelative ductility of a porous Ti compact was 0.71, which is equivalentto an elongation of 10.7%. As the porosity increased to 35.5 vol%, therelative ductility decreased to only 0.07, which is equivalent to anelongation of 1%. The C value in Hayness equation (Eq. (4) isadjustable, which is defined as a measure of the sensitivity of theductility to the porosity content in the material. By fitting Haynessequation with the data, the value obtained for C was 80 (Fig. 7d). Theductility data from Hirschhorn et al.s work 26, which investigatedthe ductility of porous Ti in a porosity range from 4 vol% to 34 vol% isalso presented in Fig. 7b. Hirschhorn et al. produced Ti compactswith different porosity levels by varying the compaction pressurefrom 0.3 MPa to 965 MPa and then sintering. The elongation of bulkTi materials used in the model was about 20%, which was estimatedfrom their elongation graph. Comparing data from Hirschhorn et al.swork with the modified Hayness model, the C value was also foundto be 80. Furthermore, the data from Bourcier et al. 28 has beenincluded in Fig. 7c. They fabricated porous Ti compacts with aporosity range from 0.3 vol% to 8.7 vol%, by a press and sinterapproach, using a similar level of powder particle size as Hirschhornet al.s work. The elongation of bulk Ti used in this model was about38%, which was also estimated from their data. By fitting theHayness model to Bourcier et al.s data, the C value obtained wasincreased to 1600 (Fig. 7e), which is almost 200 times more than theC values obtained from the current work and Hirschhorn et al.swork. In Hayness model, the C value is defined as a parameter whichmeasures the sensitivity of the ductility to the porosity content in thematerial. As Haynes mentioned in his paper, the C value may be anindicator of the ability of the material to strain harden. A low C valueindicates the material strain hardens strongly. The interstitial ele-ment oxygen may play a key role in affecting the C values and alsothe ability of Ti to strain harden. The increased amount of theinterstitial oxygen could strain harden Ti by increasing dislocationdensity 29. In other words, those Ti products with a high oxygencontent strain harden more strongly than those with lower oxygencontent. The oxygen content level in Bourciers work was below0.15 wt%, which satisfied the requirements of Grade 1 commerciallypure Ti (ASTM B348-11). Although Hirschhorn et al. did not mentionthe oxygen level in their as-sintered Ti compacts, the tensile strengthof bulk Ti from their work was about 400450 MPa and theelongation of bulk Ti was about 20%. To some extent, they wereconsistent with the standards of Grade 3 commercially pure Ti (ASTMB348-11). Grade 3 commercially pure Ti normally has a slightlyhigher oxygen content (0.35%) than Grade 1 commercially pure Ti.Furthermore, the average oxygen content in the current work wasabout 0.46%. Therefore, the differences in the C values should indicatethe degree to which the Ti strain hardens and which is caused by thedifferent amounts of interstitial oxygen in the matrix.4.6. FractographyFig. 8 shows the fracture surfaces and a view of the longitudinalplane for porous Ti specimens with different porosity levels aftertensile testing. At 29.7 vol% porosity, the fracture zone was con-centrated in the sintered necks (Fig. 8(a). The necked region waslimited to the points between particles, as pointed out by thearrows. A significant number of sharp tips formed by discreteparticles can be seen in the vicinity of the fracture in Fig. 8(b). Thiscan be explained by the inefficient bonding strength betweenparticles at this stage, causing some particles to be pulled out bythe tension force. The pores were interconnected and irregular inshape, created by the initial packing structure of the sinteredpowder particles. At 21.2 vol% porosity, there is a more densifiedmicrostructure in which some of the pores had become round andthe necking area slightly larger due to the neck growth duringdensification, as pointed out by the arrows (Fig. 8(c). In the crackregion, fewer sharp tips can be seen (Fig. 8(d). At 16.4 vol%porosity, there was evidence of slip planes in the fracture surfaceidentified by the rectangular box in Fig. 8(e). This indicates thatthe material had undergone some degree of ductile deformationunder tension. The arrows in Fig. 8(e) point to fracture necks. InFig. 8(f), the fracture surface in the crack region is smoother thanthose seen in the previous two samples due to the lower porosityin the material. At 12.3 vol% porosity, a few ductile dimples can beobserved at some locations in the fracture surface, as pointed outby the arrows in Fig. 8(g) but the relatively small area indicatesthat densification of the Ti compact was not high enough. Anincreased number of slip planes can also be found in the material,0 0.2 0.4 0.6 0.8 1 0% 10% 20% 30% 40% 50% Relative DuctilityTotal PorosityRelative DuctilityTotal Porosity(a) (b) (c) (d) (e) Fig. 7. Plot of elongation against the total porosity of sintered Ti compacts:(a) experimental data from current work; (b) data from Hirschhorns work;(c) data from Bourciers work; (d) modified Hayness model with C80; and(e) modified Hayness model with C1600.Q. Xu et al. / Materials Science & Engineering A 587 (2013) 123131128as outlined by the rectangular boxes in Fig. 8(g). The fractureprofile in Fig. 8(h) shows a flatter surface, because of the lowerporosity and smaller pore size in the material. Overall, the SEMmicrographs of the fracture surfaces from the porous Ti samplesshow that cracks were propagated through the pores in thematerial. A high porosity level in sintered Ti leads to a brittlefracture surface and low porosity produces some areas of ductilityin the fracture surface. Therefore, the porosity level and the poresize in the sintered Ti material have a significant effect on thetensile behaviour.4.7. Pore shape analysisPore shape analysis was performed at different locations on thefractured tensile samples from the porous Ti as outlined in Fig. 9.Point 1 is at the fractured tip of the tensile specimen, point 2 is atthe end of the shoulder of the tensile specimen, and point 3 is atthe end of the grip section. Two porosity levels were selected,29.7 vol% and 12.3 vol%, respectively. In addition, an analysis wasalso done for comparison on as-sintered samples that had notbeen tensile tested. In Fig. 10(a), at point 1 and point 2, the poreFig. 8. Fracture surface examined by SEM: (a, b) 29.7 vol%; (c, d) 21.2 vol%; (e, f) 16.4 vol% and (g, h) 12.3 vol%. The fracture necks are pointed out by the arrows and the slipplanes are outlined by the rectangular boxes.Q. Xu et al. / Materials Science & Engineering A 587 (2013) 123131129shape factor distributions were comparable; the pore shape factordistribution at point 3 and in the as-sintered sample was similar.Points 1 and 2 have more irregular pores compared with point3 and pores found in the as-sintered samples. This is becausepoints 1 and 2 have been subjected to more severe tensile loadingand point 3 to the least tensile loading. As the porosity wasdecreased to 12.3 vol% (Fig. 10(b) and although there were fourdifferent pore shape factor distributions, points 1 and 2 stillshowed more irregular pores than point 3 and those in the as-sintered sample. By comparing the pore shape factor of as-sinteredsamples in Fig. 10(a) and (b), as expected, the higher porosity levelof porous Ti compacts had more irregular pores than the lowerporosity ones. Under tension, the pores in the lower porositycompacts are opened up to form irregular pores. To some extent,the lower value of pore shape factor also indicates an elongatedpore, since a long rectangular shape would give a low value for theshape factor parameters according to Eq. (5). In other words,spherical pores are being stretched in tension to an elongatedshape and cracks are propagated through the pores, which areacting as linkage sites.4.8. Tensile fracture model of porous materialsBased on the results shown above, a fracture model for sinteredporous metal materials under tensile loading is proposed in Fig. 11assuming spherical powder particles. The mechanical behaviour ofporous materials at two different porosity levels has been illu-strated. At high porosity levels, the strength and ductility of thematerial relies on the necking between particles, due to the smallamount of densification. At this stage, the pore shape is irregular.As the densification process develops further, the pores becomerounder and the porosity level decreases significantly so thatthe strength and ductility of a material is increased. In thiscase, the loading stretches the spherical pores first to producemore irregular pores. Tiny pores are then generated to form adimple fracture surface in the materials under the tension force. Asa result, the pores grow and the cracks propagate through thepores causing the failure.5. ConclusionsThis study has systematically investigated the effect of the porevolumefractionontheporeinterconnectivity,mechanicalFig. 9. Locations in a fractured tensile specimen used for image analysis.0%5%10%15%20%25%00.81Frequency3Original120%5%10%15%20%25%00.81Frequency12Original3Pore Shape FactorIrregular SphericalPore Shape FactorIrregular SphericalFig. 10. Pore shape factor distributions for two porous Ti compacts: (a) 29.7 vol%porosity and (b) 12.3 vol% porosity.Fig. 11. Tensile fracture models of porous materials.Q. Xu et al. / Materials Science & Engineering A 587 (2013) 123131130behaviour and pore size and shape of Ti compacts prepared by slipcasting. The following conclusions can be made: Decreasing porosity resulted in a linear reduction in theamount of open porosity and a linear reduction in perme-ability. A slip casting process for making porous Ti showed amoderate fraction of open pores compared with a press andsintering route and a gel-casting route. A novel way of observing the degree of interconnectedporosity using ammonium meta-tungstate solution was pre-sented, which proved to be an effective approach. A linear relationship existed between tensile strength and thedegree of porosity in compacts. The Hayness model gave agood data fit; the pore geometry and interaction of stressconcentrations should be consider
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