Stress Position
8. Conclusions
This investigation presents a thorough and critical evaluation of major strength-controlling variables for a ceramic material, namely porcelain. Systematic changes made to porcelain composition, ranging from slight (alteration of filler particle size) to major (complete filler substitution) were physically and experimentally evaluated. The effects of firing temperature (over-firing/ under-firing) on mechanical properties were also evaluated. The Griffith flaw criterion served as the basis for examining the relationships between historically debated strength- dictating parameters to try and gain an understanding as to what materials and/or processes (intrinsic or extrinsic) determine the strength of the porcelain, and to what extent, if at all, they are dominant. Based on initial findings, an additional hypothesis was tested regarding the nature of flaws within these materials. It is now believed that there may be a single dominant flaw population in these porcelains, introduced as agglomerates of precursor filler particles that result in large interstitial voids when the body is fired. These critical flaws can only be eliminated through more efficient processing techniques, which involve more thoroughly dispersing particle agglomerates.
A new technique was developed for measuring fracture surface energy using a crazed glaze layer to introduce precise flaws to the surface of a porcelain body. By measuring the glaze thickness using SEM techniques, a precise measure of the flaw length was obtained, since SEM micrographs consistently show that crazing flaws extend straight through the glaze layer and arrest at the body interface. These glaze cracks act as critical flaws, as indicated by the dramatic decrease in measured mechanical strength of bodies in the presence of crazed glazes, versus identical unglazed counterparts. Therefore, the critical flaw size is equivalent to the glaze flaw length. Along with measured values for elastic modulus, Poisson’s ratio, the value of flaw size was input into a derivative of the Griffith equation, modified for geometry (Equation 61), along with the failure stress of an unglazed specimen, resulting in a value for fracture surface energy of the base unglazed porcelain. Fracture surface energies for Silica B and Alumina B compositions were 4.5 J/m2 and 8.4 J/m2, respectively. Silica C porcelain had a fracture surface energy value of 4.7 J/m2, similar to that of Silica B, which was expected due to their similar compositions.
Surface energy estimates using existing KIc values (~1.0 MPa·m1/2) resulted in a γ value of 4 J/m2 for silica porcelain. This showed good agreement with experimental results, lending credibility to the accuracy of the new technique. A linear relationship between elastic modulus and fracture surface energy was observed for the porcelain bodies tested, as well as for other materials which possess similar bonding character (mixed ionic/covalent Si-O, Al-O bonds), including polycrystalline alumina. The relationship resulted in an equation (y = 0.0683x – 0.1691) that was used to predict the fracture surface energy of a series of untested porcelain bodies, knowing only their elastic moduli. Using this surface energy calculation with measured values for elastic modulus, Poisson’s ratio, and failure stress, the calculation of critical flaw size for each porcelain material was made via a revised Griffith equation (Equation 60). The significance of this method is that, due to the recognition of the specific mathematical relationship between elastic modulus and fracture surface energy of porcelain bodies (γ scales with E), measurement techniques for elastic modulus and failure stress which are both relatively commonplace can be used to determine not only the fracture surface energy, a property that is sometimes dubiously quantified, but also the critical flaw size within the porcelain, which is often very difficult to measure without the use of fractography. For an opaque material with a complex microstructure such as porcelain, inspection techniques are particularly difficult to use. It is believed that this relationship is not unique to porcelains. It is quite conceivable that relationships exist between other materials that, between them, share similar bonding character. It would be only a matter of experimentally evaluating a different series of like materials in order to establish its unique relationship, and similar results could be derived. Therefore, through the use of a few routine experimental techniques and the well-established Griffith model, information about a material that previously required several more experiments to acquire can be more readily ascertained. It is believed that results calculated relating the fundamental nature of materials to their properties can often be more accurate than those measured using a standard technique because, as it has been shown, current testing techniques often contain many uncontrollable sources of experimental error.
In order to maximize both physical and mechanical properties, one of the critical parameters is firing temperature. Porcelain bodies possess a relatively wide temperature regime in which
properties are optimal, known as the firing range. Outside of this range, there was shown to be a dramatic decrease in overall performance, due to either under-firing or over-firing. Experimentally evaluating porcelain bodies in a gradient furnace by simultaneously firing many samples over a wide range of temperatures (1019–1325°C) resulted in the designation of the firing range for several porcelain compositions. This was based on the observation of a plateau region of maximum bulk density and linear firing shrinkage. Silica B porcelain showed an effective firing range of 1250–1280°C, alumina B porcelain 1260–1290°C, and stoneware porcelain showed the most versatility, with an effective firing range of 1250–1300°C. Based on these results (and a parabolic fit to the data), a series of trials were carried out in which the three compositions were fired to three different peak temperatures within the designated firing range, as well as one above and one below the ideal temperature region, ideally to obtain over- and under-fired bodies.
Results showed that, for the three porcelain bodies, ideally firing the samples (within their firing range) resulted in the highest strength. Under-firing all bodies resulted in poor strength and low elastic modulus due to the presence of voids and unconsolidated raw materials, an effect of incomplete microstructural sintering, confirmed via SEM analysis. Over-firing the bodies had a similar negative effect on the strength of the Silica B and stoneware compositions; the microstructures were characterized by enlarged pores, indicative of gas evolution and bloating.
Alumina B porcelain displayed only a slight declination in strength when fired at its maximum temperature (1310°C), indicating that the temperature regime selected for testing may have been inadequate to produce an over-fired microstructure. Elastic modulus results were more characteristic, showing a declination for both alumina and stoneware compositions. Silica porcelain B displayed an increase in E at its maximum firing temperature (1290°C), relative to lower temperatures. It is speculated that the silica and alumina porcelain were not fired at high enough temperatures to obtain truly over-fired microstructures; their behavior and microstructure were indicative of only nominal over-firing. The stoneware composition behaved precisely as predicted; it was fired well under (1160°C) and over (1310°C) its normal operating temperature (~1250°C).
Using the experimentally measured elastic modulus, Poisson’s ratio, and mechanical strength, the previously developed characterization model was applied to these three porcelain compositions in order to obtain values for critical flaw size, observing changes with firing temperature. Results, however, indicated that measured critical flaw size was essentially unaffected by changes in firing temperature. Silica B maintained an average flaw size of 79.1 µm, for alumina B it was 70.7 µm. Stoneware porcelain showed a fairly constant average critical flaw size of 107.9 µm at lower temperatures, but flaw size increased dramatically at higher temperatures (>1270 °C). A possible reason for this discrepancy involves the presence of large cracked grog particles located within the microstructure, as shown in SEM micrographs, which confound the calculation. Overall data suggest that, regardless of firing treatment, critical flaws of a constant size exist in the porcelain. Furthermore, critical flaw size showed no strong correlation to bulk density. This is contrary to the popular theory that a less-dense microstructure results in larger critical flaws. Although these parameters do affect the size of pores and microstructural defects within to an extent, in the presence of larger intrinsic flaws, their contribution to affecting critical flaw size is negligible. Data suggest the critical flaws within these porcelains transcend firing temperature and density; therefore, they must be introduced to the microstructure in a way not yet considered.
Very commonly, filler particles are cited as the critical flaws within porcelain bodies. To test this theory, several different species and sizes of filler particles were substituted into very similar porcelain body compositions. This series of experiments was meant to document the effect of different filler particle composition and particle size on measured mechanical properties of porcelain. Fillers were selected based on their relative strengths as well as thermal expansion coefficients relative to that of the glass phase. Quartz and alumina, commonly used fillers, were tested alongside Mullite and Mg-Al Spinel, two materials not commonly used as filler materials.
Combined with quartz and alumina, these four filler species provide a fairly broad range of grain strengths and CTEs to carry out a systematic analysis with respect to mechanical properties.
Using X-ray diffraction techniques, the residual strain generated within the filler grains as a result of the CTE mismatch was quantified for quartz (112), alumina (116), mullite (121), and spinel
(400) over a series of different bodies containing a range of filler particle sizes. The CTE of quartz, alumina and spinel being higher than that of the glass phase resulted in tensile strain between planes of atoms. Mullite, having a CTE lower than that of the glass, was subject to compressive strain, registering a net ‘negative’ strain. Overall results indicated a positive increase in residual strain with particle size for quartz, alumina and spinel bodies. For quartz and alumina bodies, critical particle size levels were reached (87 µm and 180 µm, respectively), above which residual strain was observed to decrease as particle size increased further. In this regime, filler particles spontaneously fail during cooling, causing a relaxation in strain. No inflection point was observed for spinel, but it is likely that one does exist for larger particle sizes outside the scope of the sizes tested. A defined trend for mullite porcelain with respect to particle size was not observed, thought perhaps to be confounded by the additional mullite that exists within the matrix phase that would contribute to the X-ray diffraction pattern. No observation of X- ray peak splitting was made; therefore, separation of nucleated mullite from included mullite strain was not mathematically possible. Based on the fact that different critical strain maxima were achieved in Silica A and Alumina A porcelain compositions, it is proposed that the glass phase is the stronger species. If it were weaker than the filler particles, the strain maxima for both compositions would be the same fixed value. Therefore, it can be said that the filler particles (quartz: 2 GPa, alumina: 5 GPa) are both weaker than the surrounding glass phase. When exposed to atmosphere, the glass becomes quite weak due to stress corrosion of the surface bonds. In a pristine environment, not unlike the interior of a porcelain specimen, glass has shown to have increased tensile strength, on the order of 7 GPa or higher. Overall, mechanical strength was shown to decrease with increasing filler particle size. Furthermore, the flexure strength of Alumina A body > Spinel A body > Mullite A body > Silica A body, in line with the relative strength of each filler material. An interesting effect observed over a regime of very small particle sizes for Silica A porcelain is that the flexure strength actually increased from 48 to 50 MPa as particle size increased from 5 to 25 µm. This is contrary to the typical observation of strength decrease with increasing filler particle size that is observed for bodies containing 25-µm or larger quartz particles. This is proposed to be due to favorable prestressing of the glass phase by filler
particles, which generates overlapping zones of increased glass phase compression.
Prestressing caused by quartz grains within this size regime has a net positive effect, hindering the ease of flaw propagation through the glass, resulting in a higher observed strength. In this way, filler grains below a certain size actually may be beneficial to the strength of porcelain.
Stresses generated by larger grains can provide even higher zones of compression; however, the beneficial effect is often negated due to size effects such as spontaneous or premature grain fracture due to the high amount of stored stress within the microstructure.
Data indicate no strong correlation between critical flaw size and filler particle size or species, maintaining a relatively constant value for each composition over the entire size range tested;
typically two to three times the primary filler size. Overall, critical flaw sizes ranged from 90–120 µm, while filler sizes ranged from 10–150 µm. Individually, each composition maintained a critical flaw size that was essentially constant, with standard deviations of ± 4 µm or less. This is contrary to the notion that in the literature primary filler particles are often identified as critical flaws in porcelain bodies. In fact, data from this investigation show no correlation between critical flaw size and primary filler particle size. It is proposed that, although under extenuating circumstances, the presence of a very large included grain may adversely affect the mechanical strength of porcelain by acting as a critical flaw, primary filler particles of sizes typically used in industry (<45 µm) cannot act alone as critical flaws. It is hypothesized that an agglomerate of these particles, however, could.
The mechanical strength of these porcelain materials is to some extent dependent on a number of parameters; elastic modulus, density, firing temperature, filler particles, composition, etc.
Critical flaws have been determined to be the underlying factor that governs the overall strength of the material. Variations of these aforementioned constraints will absolutely affect the grain size or pore size of a material. However, results of this study indicate that this does not affect critical flaws contained within these bodies. Data indicate no strong correlation of critical flaw size to firing temperature, bulk density, filler particle size or type. In most cases critical flaw sizes were several times larger than that of primary filler particles or pores existing within the microstructure,
which in literature are consistently defined as the critical flaws. Based on these findings, this cannot be true. In these bodies, whatever effect firing temperature and filler size have on the body is completely superceded by the presence of larger critical flaws. What was observed was that for a given composition critical flaw size is virtually identical, regardless of treatment. The question remains as to the precise identity of these flaws as well as the mechanism that controls their size.
Results of this investigation have led to the proposal that critical flaws and the size of those critical flaws are intrinsic to the porcelain, introduced to the system as a result of inefficient processing. The body compositions studied resulted in different average critical flaw sizes, but standard deviations were very small considering the broad range of systematic changes made to the overall composition and microstructure. Among those samples prepared using the same process or in the same location, critical flaw size was virtually identical. The reason for this is believed to be associated with mixing efficiency and the presence of agglomerated non-plastic particles within the material. A particle cluster that survives the mixing process into the fired body can result in a large flaw or void several times the size of a primary particle, which corresponds to the estimates of critical flaw size on the order of several particle diameters. Laboratory-prepared samples consistently contained larger flaw sizes than those prepared in an industrial setting, which makes sense in terms of the relative mixing efficiency that can be achieved on a small scale, relative to a large-scale industrial process. Porcelain B bodies were fundamentally different (one containing alumina and one containing silica filler), yet their critical flaw sizes were remarkably similar. The fact that both bodies were processed identically at the same location supports the notion that it is the processing step that is the critical factor in determining the critical flaw size. By increasing the mixing efficiency of a process, it is believed that fewer particle agglomerates will survive into the finished microstructure, and as a result the mechanical strength will increase.
To test the hypothesis that particle clusters could be the critical flaws within the microstructure, and that previous experimental results (mechanical testing, calculation of critical flaw size) could
be indicative of this phenomenon, a series of four-point flexure test simulations were developed, using flaw probability and random number theory. This model relies on the fact that the bending moment within a flexure specimen creates a stress gradient that diminishes toward the specimen neutral axis. Results indicate that in a microstructure containing only one flaw size, if there are sufficiently few flaws per unit volume, a distribution of strengths is generated and average strength increases. This is because in a system containing randomly located flaws under constant flexure load, the probability of a flaw occupying a region where the stress is sufficient to cause it to propagate is less than 1.00. Too many flaws (>100 per cm3) will result in one strength value (weakest), since the probability of a critical flaw occupying the zone where it will extend approaches unity. Based on a cursory evaluation of the relationship between strength standard deviation and flaw population, a typical quartz porcelain body (Silica A) was estimated to have only 17.0 ± 4 large flaws per cm3, a number suitable for a system that satisfies the original hypothesis. Based on these overall results, it was deemed possible that there could be one population of flaws within these porcelain bodies, brought about by filler particle agglomerates inefficiently eliminated during the processing step. Verification of fracture origins as particle agglomerates on broken specimens would be extremely difficult to accomplish; however, filler particle agglomerates on the order of critical flaw size were positively identified in several SEM micrographs.