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Chapter 4 MICROHARDNESS STUDIES 4.1. Introduction The microhardness of a substance is an important parameter to define the strength of its material. This property is basically related to the crystal structure of the material or in other words, the way in which the atoms are packed and the electronic factors operating to make the structure ~tab1e.l.~ Physically speaking, hardness is the resistance offered by the crystal for the movement of dislocations and practically it is the resistance offered by the crystal for localized plastic deformation. Hardness testing provides useful information about the mechanical properties like elastic constants, yield strength etc of materials. Elastic deformation developed in a material when subjected to indentation is ~ e r n h a r d suggested t~ that a part of directly proportional to the plastic def~rmation.~ the energy absorbed during indentation is used in producing plastic deformation and the rest increases the surface free energy. Hardness value depends on the method of measurement that in turn determines the scale of hardness obtained. In metals, polymers and organic solids, an indenter is pressed in to the surface and the size of the permanent indentation mark formed is measured. In certain materials, the indenter is pressed in to the material and the hardness is determined by the extent to which it had penetrated under load. In the case of minerals and brittle solids, hardness is calculated on the basis of scratch produced in one material by another of specific hardness number. 4.2. Various Testing Methods There are many methods for measuring hardiless of materids but the most commonly used form of measuring hardness ir: che indexation type. ~ a b o r ~ discusses an elaborate description of these methods with f&ir aLvan:-ges and limitations as follows. Static Indentation Tests In these tests, a ball, cone or pyramid is used as an indenter, which is forced in to the surface and the load per unit area of the impression measures the hardness of the surface. The Brinel, Vickers, Rockwell, Monotron and Knoop tests are of this type. , spherical indenter is pressed under a In the Brinell hardness ~ e s t a~hard fixed normal load on to the smooth surface of the material under examination. When equilibrium has been reached the load and the indenter are removed and the diameter of the impression is measured. The Brinell hardness number HBis defined as the maximum applied load per contact area. Another type of indenter, which is most commonly used, is the conical or pyramidal indenter in the ludwick and Vickers Hardness Testers. In the Knoop indenter, the indentation is in the form of an elongated pyramidal impression, its length been seven times its width. This indenter is particularly suitable for the study of anisotropy in hardness. Scratch Tests In this test it is observed whether one material is capable of scratching another. If a material is able to scratch the other it is said to be harder than the other. Plowing Tests In these tests a blunt element (usually diamond) is moved across a surface under controlled conditions of load and geometry and the width of the groove is the measure of hardners. The Bierbaum Test is of this type. Rebound Tests In these tests, an object of standard mass and dimension is bounced from the tests surface and tile height of rebound is taken as the measure of hardness. The Shore Sceloroscop. is an instrument of this type. Damping Tests Ir r'lese te?ts, a change in amplitude of a pendulum having a hard pivot ~estingon the test swface is the measure of hardness. The Herbert pendulum test is ot this type. 93 Microhardness Studies Cutting Tests In these tests, a sharp tool of given geometry is used to remove a chip of standard dimensions. Abrasion Test In this test, hardness is defined as the resistance to mechanical wear, a measure of which is the amount of material removed under specified conditions. For example, a specimen under test is loaded against a rotating disc, and the rate of wear is a measure of hardness. Erosion Tests In these tests, sand or abrasive grain is made to strike the specimen under standard condition and the loss of material in a given time is taken as a measure of hardness. This method is used to measure the hardness of grinding wheels. Recent reports have shown that an ultrasonic hardness tester consisting of the modification of the Brine11 indenter has been developed which enables instantaneous automatic readout using ultrasonics7. Hardness usually implies resistance to deformation, which in turn denotes the ability of one body to resist penetration by another. It depends on the elastic and plastic properties of both the indenter and the indented material. Among the various methods for hardness measurements as described above, the most common method is the microindentation method; and pyramid indenters are found to be best suited for hardness tests due to two reasons; (a) the contact pressure for a pyramid indenter is independent of indent size and (b) pyramid indenters are less affected by elastic release than other indenters. The Vickers pyramid indenter, whose opposite faces contain an angle of 136". is the most widely accepted pyramid indenter. Nanostructered metals and ceramics cm have improved mechanical properties compared to conventional materials as a result of the ultrafine micro~tructure~-~. Many materials. studied the micro lrardness behavior of different nanostructered For example Nieman, Weertman and siegels reported that nanocrystalline palladium samples (20 nm) show a four-fold increase in hardness compared to coarse- grained (100 pm) palladium and a doubling in hardness for nanocrystalline copper samples (25 nm) over coarse-grained (50 pm) copper. Nanocrystalline materials provide a promising way to generate ductile ceramics but, poses new problems to physicists and material scientists on the property-structure relationship. In studying the mechanical behaviour of nanocrystalline metals and alloys, conflicting results have been obtained for the dependence of hardness on grain size. For example the Jang and ~ o c h " , Qin, Wu and zhangll', Ganapathy and ~ i ~ e n c ~found ", an increase in hardness with decrease in grain size. The conventional relationship for this behaviour in coarse-grained materials is described by the Hall-Petch equation8-" where Hv is the hardness, Ho and k are constants, and dl is the average grain size. According to these investigators, the increase in hardness with decreasing grain size is observed to the finest grained material examined, although its variation with grain size may be less than that in the case of conventional grain size materials. Obviously, the equation has limitations because the strength cannot increase indefinitely with decreasing grain size. From a practical viewpoint, for example, the strength value cannot exceed the theoretical strength, i.e., the strength of a perfect whisker. Additionally, any relaxational processes at grain boundaries, associated with an extremely fine grain size, could lead to a decrease in strength and this could result in an inverse d relationship below some critical grain size. In the absence of - such grain boundary relaxation mechanism, a region of constant strength with decreasing grain size may be expected. In the case of the Hall-Petch relation, there is an inherent upper limit on strength, that is, below the theoretical strength. This is because the strengthing mechanism is based on dislocation pile-ups at physical obstacles such as grain boundaries. As the grain size of a polyc~ystallinematerial decreases, a stage will be reached at whjch each individual grain will no longer be able to support more than one dislocation. At this point the Hall-Petch relation will no longer hold". From another point of view, when the grain size approaches zero, the material essentially becomes amorphous. The grain boundary strengthing effect will then disappear. The hardness of an amorphous material is ir~deedlower than its crystalline counterpart. In summary, strength (or hardness) may be expected to Microhardness Studies 95 decrease or at least be constant when the grain size is below the critical value for dislocation pile-ups and at this critical value the Hall-Petch relation would no longer be observed. Depth sensing indenter devices, known as nanoindenters, mainly using Vickers diamond pyrarnid~,'~-~~are now employed for studying mechanical properties of materials. The hardness number Hv is defined as the ratio of applied load, P to contact area A between the indenter and sample, i.e., Hv = P/A (4.2) This area is defined by the pyramid geometry. In the case of a square base Vickers pyramid, the contact area is A = dSZ sin (8/2) (4.3) where 0 = 136" is the angle between opposite faces, and d is the diagonal length of impression. Thus, the Vickers hardness number is given by Hv = 1.8544 P / & ~ ~ / r n r n ' (4.4) In apparent contrast to this behavior, Lu, Wei and wang'', Christman and Jain 14, and Chokshi, Rosen, Karch and ~leiter", reported that decreasing the grain size produces softening in nanocrystalline materials. Softening with decreasing grain size has been attributed to the increasing contribution of diffusional accommodation to deformation processes at the finest grains. Hardness of a material is closely related to its plastic deformation and the fracture properties. Significantly increased strength and ductilities have been predicted for nanophase microstructures. The strengtk. of nanophase microstructures is estimated from the Hall-Petch strengthing theory to be up to 30 times that of the coarse grai~r standard.14 The increased ductility (from Coble creep mechanism) is proposed to occur due to the large volume fraction of atoms occupying grain boundary sites and increased diffusion rates along these boundaries " Experimental evidence remains contradictory regarding b?ti~of these theoretical suggestions. ~ l e i t e r 'reported ~ deformation studies of :.acccrystalline Ti02 where he describes significantly enhanced plasticity and formability in this nanophase ceramic during compressive 96 Chapter 4 loading. Nieman, Weertman and Siege1 have reported tensile test results only for nanophase materials. Their work on nanophase Pd and Cu suggests increased strength and decreased ductility as a result of the drastic decrease in grain size. 4.3. Microhardness of Nanocrystaliine Metal Phosphates Nano-sized metallic phosphates, aluminium phosphate (AlP04), copper pyrophosphate (Cu2P207)and magnesium pyrophosphate (MgzP207) are prepared from the thermolysis of new polymer matrix based precursor solutions. The resulting powders are nano-sized, and are of high purity. The details of preparation24are given in the synthesis part in section 2.2. In the present study stoichiometric amounts of the reactants were taken such that the concentration of the reactants were 1.0 OIL-', 0.5 mol~.' and 0.1 mol~.' to produce nanosized Alp04 samples of average grain sizes16.34nm. 13.59 nm and 12.04 nm (samples Al, A2 & A3). Nano-sized powders of Cu~P20,with average grain sizes 33.34 nm, 30.16 nm and 25.5 nm (samples C1, C2 & C3) and Mg2P207 with average grain sizes 25.7 nm, 22.3 nm and 20.8 nm (samples M1, M2 & M3) were also prepared by changing the concentration of the reactants, as described in section 2.2. The microhardness studies of the samples were carried out, using Leitz hardness tester type P 1191 fitted with a Vickers pyramidal diamond intender.25The load P was varied from 0.1 N to 5 N, and the time of indentation was the same (30 sec.) for all trials and samples. For each sample, several trials of indentation with each load were made and the average values of the diagonal lengths of indentation marks were obtained. The Vickers microhardness number Hv at each load was calculated using the relation Hv = 1.8544 p/d2 (GPa) (4.5) where P is the applied load in N and d is the diagonal length of the indentation in m. In this study, the nanopowders of the samples obtained by chemical method as described earlier, were collected and compacted9 for 2 minutes under pressures of 0.3 GPa, 0.34 GPa, 0.38 GPa and 0.41 GPa. The specimens were disc shaped, 13 mm in diameter and 1 to 2 mm in thickness. The densi~ymeasurements of each specimen were made based on Archimedes principle. Microhardness Studies 97 4.4. Results and Discussion Fig 4.1 presents the variation of Vickers microhardness number Hv with indentation loads of the n-A1PO4 sample A1 compacted under different pressures. The hardness shows an increase up to a load of about 2N, and then becomes practically independent of load. The nature of variation of hardness is similar at higher compacting pressures but when the compacting pressure is gradually increased, the hardness also is seen to increase. It is found that the hardness for 0.45 GPa is about two orders greater than that for the same sample compacted under 0.3 GPa. This result indicates that the hardness of Alp04 is strongly related to compacting pressure. Fig.4.2 gives the variation of Hv with indentation loads for different compacting pressures for sample A3. Here also the nature of variation of Hv is similar to sample Al, but Hv has a five-fold increase when compacting pressure is increased from 0.3 GPa to 0.45 GPa. Fig.4.3 and Fig.4.4 give the variation of microhardness with compacting pressures for the Cu2P207samples C1 and C3. In this case, for both samples, the hardness increases up to a load of about 2 N and thereafter remains steady. But Hv increases h m about 500 GPa to 800 GPa when compacting pressure is increased from 0.3 GPa to 0.45 GPa for sample C1. For sample C3 it is from about 600 GPa to 900 GPa when the compacting pressure is increased from 0.3 GPa to 0.45 GPa. These variations are plotted in Fig.4.3 and Fig.4.4. The variation of microhardness with compacting pressures for the Mg2P207 samples MI and M3 are plotted in Fig. 4.5 and Fig.4.6. Both the samples in this case also show an increase of hardness up to a load of'about 2 N and thereafter remain almost steady. Here Hv increases from about 900 GPa to 1100 GPa when the compacting pressure is increased from 0.3 GPa to 0.45 GPa for sample M 1. For sample M3, it is from about 900 GPa to 1200 GPa when the compacting pressure is increased from 0.3 GPa to 0.45 GPa. An important challenge faced in the fabrication of nanoshuctured materials is how to achieve full densification of the powder while simultaneously retaining the nanoscale microstruct~re~~. High densities can be achieved, but are accompanied by significant grain growth. To reduce grain growth at high densities, 98 Chapter 4 Fig.4.1. Variation of microhardness with indentation loads for various compacting pressures of the n-AIR34 sample Al Fig.4.2. Variation of microhardness with indentation loads for various compacting pressures of the n-Alp04 sample A3 99 Microhardness Studies Load (N) Fig.4.3. Variation of microhardness with indentation loads for various compacting pressures of the n- Cu~P207sample C1 Laad (N) Fig.4.4. Variation of microhardness with indentation loads for various compacting pressures of the n- CuzPz07 sample C3 100 Chapter 4 +I I 0 1 2 1 3 4 5 Load (N) Fig.4.5. Variation of microhardness with indentation loads for various compacting pressures of the n- MgzPz07 sample M1 j r 0 7' I 1 2 I I I 3 4 5 Load (N) Fig.4.6.Variatxon of microhardness with indentation loads for various compacting pressures of the n- MgzP207 sample M3 Microhordness Studies random close packing of the nanosize particles in the material is to be achieved prior to sintering. One way to achieve this condition is by compaction of the powder at high pressures. A high-strength piston-cylinder die was used to compact the powder samples and thus high density is achieved in the material. The increase of compacting pressure inevitably leads to further densification of the specimen.27-29 To prove this result, the densities of all the specimens compacted under different pressures were measured. The density increases almost linearly with pressure. In order to show the influence of density on microhardness of the Alp04 sample, the hardness is plotted as a function of density for sample A1 (Fig.4.7). It can be seen that the hardness of n-Alp04 increased from 0.38 GPa to 0.79 GPa as the density changes from 1.48~10"kg/m to 1 . 5 5 ~ 1 0kg/m3. ~ This increase of microhardness with increasing compact pressure actually reflects the effect of density on hardness. This result indicates that the density of n - Alp04 specimen is an important factor affecting its hardness. The variation of microhardness with compacting pressure and density is further intensified as the grain size of the sample is reduced. Fig.4.8 shows that the hardness of n-A1PO4 sample A3 (grain size 12 nm), increased from 0.38 GPa to 1.7 GPa for a variation of density from 1 . 5 1 ~ 1 0kg/m ~ ' to 1 . 6 2 ~ 1 0 ~ kg/m3. Fig.4.9 and Fig 4.10 show the variation of microhardness with densities for Cu2P207 samples C1 and C3. It can be seen from Fig.4.9 that the hardness of sample C1 increases from about 0.4 GPa to 0.75 GPa as the density changes from 1 . 6 2 5 ~ 1 0kg/m ~ to 1 . 7 2 ~ 1 0kg/m3. ~ The corresponding variation for sample C3 (Fig.4.10) is from 0.4 (;Pa to 0.9 GPa for a change of density from 1.685~10'kglm to 1 . 8 ~ 1 0kg/m3. ~ A similar variation of microhardness with density is observed for M g 2 P ~ qsamples M1 and M3 as shown in Fig. 4.1 1 and Fig.4.12. For sample MI, the hardness increases from 0.6 GPa to 1.0 GPa for an increase in density from 1 . 6 7 5 ~ 1 0kg/m3 ~ to 1 . 7 5 ~ 1 0kg/m3 ~ (Fig.4.11). For sample M2 (Fig.4.12) the corresponding variation is from 0.675 GPa to 1.175 GPa when density changes 0~ to 1 . 7 6 5 ~ 1 kg/m3. 0~ from 1 . 6 8 5 ~ 1kg/m Indentation hardness testing is probably the most widespread of all the testing techniques, to assess the mechanical properties of materials. Applications of Chapter 4 102 Fig.4.7. Variation of ~nicrohardnesswith density for various compacting pressures of n-Alp04 sample A l . Fig.4.8. Variation of microhardness with density for various compacting pressures of n-Alp04 sample A3. 103 Microhardness Studies Fig.4.9. Variation of microhardness with density for various conipacting pressures of n- CuzPz07 sample C1. -v- 0.41GPa 800 > I / 1680 1700 I I I I I 1720 1740 1760 1780 1800 Density (Kg m") Fig.4.10. Variation of microhardness with density for various co~npactingpressures of n- Cu2P207sample C3. Chapter 4 104 - microhardness indentation techniques, however, experience the load/size effect at low levels of the testing load and have been traditionally described by the power law, P=Adn (4.6) where P is the indentation test load and d is the resulting indentation size3'. A and n are descriptive parameters derived from the curve fitting of experimental results. Equation (4.6) is r e f e d to as Mayer's law. For virtually all materials, the power law exponent, n, is experimentally observed to be between 1 and 2, which indicates that lower indentation test loads result in higher apparent microhardness. This load dependence of hardness has been frequently reported. The indentation loadlsize effect (ISE) on the microhardness has been considered on the basis of a variety of phenomena, including work hardening during indentation, the load to initiate plastic deformation, indentation plastic recovery, the activation energy for dislocation nucleation, surface dislocation pinning, and plastic deformation band spacing. Application of equation 1 yields an n value that is less than 2, indicative of an increasing apparent microhardness at lower indentation test loads. To examine the ISE critically, it is necessary to evaluate an extensive set of experimental microhardness measurements on the material to be studied. A plot of log P versus log d provides a straight tine, the slope of which gives the work hardening coefficient n. These graphs, for the different samples studied, are plotted in Fig.4.13 to Fig. 4.18. Kick proposed a constant value for n =2 for all the indenters and for all 0 2 in the geometrically similar impressions. However, according to ~rodzinski~', region where Hv decreases with increase in load. In the present study, work hardening coefficient n is obtained using least square fit method and is found to be less than 2 for all the samples as given in table 4.1. According tn the Onstrich concept, 32 the lattice is soft if n>2 and the lattice is hard if n <2. h i the high load region, classical Mayer's law is insufficient to explain the variations as the microhardness tends to be load independent. Microhardness Studies 105 Density (Kg m") Fig.4.1 1. Variation of microhardness with density for Various compacting pressures of n- Mg2P207 sample MI. Fig.4.12. Variation of microhardness with density for various compacting pressures of n- Mg2P26sample M3. Chapter 4 106 - log d Fig.4.13.log d vs log P graph for various compacting pressures of n-A1PO4sample A l . log d Fig.4.14.log d vs log P graph for various compacting pressures of n-AlP04 sample A3. Microhardness Studies 107 - log d Fig.4.15.log d vs log P graph for various compacting pressures of n- CuzPz07 sample C1. Fig.4.16.1og d vs log P graph for various compat%ng pressures of n- Cu2P~&saniple C3. Chapter 4 108 1 log d Fig.4.17.log d vs log P graph for various compacting pressures of n- Mg2P207 sample MI. Fig.4.18.log d vs log .? glaph for various compacting pressures of n - hfg2P207 sample M3. 109 Microhardness Studies l Sample I a i n size (nm) I Val: of I Table 4.1. Work hardening coeficient determined for different samples. In this region the indentation test load P related to indentation size d as, Where a1 is the proportionality constant in the load dependent region, a2 that in the load dependent region, PC is the critical applied test load above that the microhardness becomes load independent and do is the corresponding diagonal length. The first term in the equation represents the surface energy contribution while the second term represents the volume energy contribution. Eqn. (4.7) can be rearranged to give P/d = a1 + (PC/'&') d (4.8) Hence a plot of P/d versus d is a straight line and the slope of which gives the value of load dependent microhardness, which when multiplied by the Vicker's conversion factor 1.854 gives the load independent microhardness H,. To investigate the effect of grain size on the the values of the micro hardness number (Hv)are plotted with grain size (dlR)for all the samples as a function of indentation loads (Fig.4.19, Fig.4.20 and Fig.4.21). It can be seen 110 Chapter 4 from the figures that the plots are more or less straight lines with positive slopes, showing that microhardness of each sample increases with decrease of grain size in accordance with the normal Hall-Petch relationship, Fig.4.19 shows the variation of microhardness of n-A1P04 when the grain size changes for various compacting pressures. The value of Hv changes from 545 GPa to 718 GPa when the grain size changes from 16.34 nm to 12.04 nm for the compacting pressure 0.98 N. 'l'he corresponding change in Hv is from 657 GPa to 1260 GPa for the compacting pressure 2.4 N. Fig.4.20 shows the variation of microhardness of nanocrystalline copper phosphate for different grain sizes and compacting pressures. In this case the value of Hv changes from 257 GPa to 298 GPa when the grain size changes from 33.34 nm to 25.5 nm for the compacting pressure 0.98 N. For the compacting pressure 2.4 N, the change in Hv is from 395 GPa to 470 GPa. Fig.4.19. Variation of microhardness with grain size for various compacting pressures of n-AlP84 sample Microhardness Studies Fig.4.20. Variation of microhardness with grain size for various compacting pressures of n- CuzP~07sample Fig.4.21. Variation of microhardness with grain size for various compacting pressures of n- MgzPz07 sample 111 The variation of microhardness of nanocrystalline magnesium phosphate for different grain sizes and compacting pressures is given in fig.3.21. Here the value of Hv changes from 514 GPa to 553 GPa when the grain size changes from 25.7 nm to 20.8 nm for the compacting pressure 0.98 N. The change in Hv is from 621 GPa to 680 GPa, for the compacting pressure 2.4 N. From the experiment.al results obtained above, it can be seen that the microhardness of all the samples studied, is mainly affected by compacting pressure and change in grain size of the material. When the grain size is constant, the hardness behavior is dominated by density due to compacting pressure. On the contrary, when the density of the material is constant, the hardness behavior is controlled by grain size. It is evident that densification and reduction of grain size would increase the hardness of all the nano-sized samples studied. 4.5. Conclusion Indentation hardness testing is the most important testing techniques, to assess the mechanical properties of materials. Among the various indentation hardness testing methods, the Vickers hardness testing method is employed in the present investigation. The microhardness behaviour of all the nanocrystalline samples are studied in terms of various parameters. The hardness number depends on the elastic and plastic properties of both the indenter and the indented material. The variation of Vickers micro hardness numbers (Hv) with indentation loads of all the studied specimens, show an increase of hardness up to a load of about 2 N, and then remains practically constant, independent of load. The hardness shows an increase of two orders when the compacting pressure is increased from 0.3GPa to 0.45GPa for AlP04 sample A1. The corresponding increase is five fold in the case of sample A3. Similar variations are observed for n-CuzP207 samples and for nMg2P207. These variations are explained with the help of the Hall-Petch equation, in which the strengthing mechanism is derived in terms of dislocation pile-ups at grain boundaries. In order to show the influence of density on microhardness, all the specimens are compacted with varying pressures to obtain samples with different densities. The strength of nanophase microstructures having different densities is estimated Microhardness Studies 113 using the Hall-Petch strengthing theory. For sample A l , it is found that the hardness increases from 0.38 GPa to 0.79 GPa as the density is increased from 1 . 4 8 ~ 1 0 ~ kg/m3 to 1 . 5 5 ~ 1 0kg/m3. ~ Similar variations of microhardness with densities are observed for n-CuzP207 and for n-Mg2P207 samples. The variation of microhardness with compacting pressure and density is further enhanced as the grain size of the sample is reduced. A plot of log P ve:rsus log d provides a straight line, the slope of which gives the work hardening coefficient n. Work hardening during indentation is explained on the basis of the theo~yof indentation loadlsize effect (ISE). In the present study, work hardening coefficient n is found to be less than 2 for all the samples, indicating that the lattices are hard. To study the effect of grain size on hardness, the values of the micro hardness number (Hv) are plotted with grain size (dln)for all the samples as a function of indentation loads. 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