4. Elastic modulus behavior of porous ceramics

The KIC values in Table 2 were the expected ones for highly porous ceramics and they were compatible with data from the literature [24, 54, 55]. However, these results must be interpreted carefully, because of the crack-tip blunting mechanism due to the presence of surrounding pores (see Figure 13). This mechanism may decrease the stress intensity factor at the notch tip. Consequently, the crack propagation should not follow the required linear-elastic

Table 2 Results of fracture energies (γeff and γWOF) and the fracture toughness (KIC) for macroporous foamed Al2O3 [58].

) <sup>γ</sup>WOF (J/m<sup>2</sup>

0.86 0.02 4.68 0.5 15.81 0.8 0.42 0.03 0.87 0.01 3.62 0.3 14.46 0.95 0.35 0.05 0.90 0.02 3.72 0.6 15.39 1.0 0.37 0.02 0.92 0.02 4.15 0.8 12.27 1.1 0.36 0.02 0.94 0.03 3.55 0.35 13.32 0.9 0.34 0.09

) KIC (MPa.m1/2)

Based on that, we would like to raise the following issues: Does it make sense to measure the fracture toughness (KIC) of porous ceramics knowing that the stress intensity factor at the notch tip is decreased by the crack-tip blunting? Or, instead of this, would the total work-of-

The results of total work-of-fracture energy (γWOF) presented in Table 2 agree with the values

Figure 14. Fracture surface of macroporous foamed Al2O3 showing the characteristics of the fracture and notched

conditions for the fracture toughness measurement.

) <sup>γ</sup>eff (J/m<sup>2</sup>

Density, r (g/cm<sup>3</sup>

188 Recent Advances in Porous Ceramics

surfaces [58].

fracture energy be a more realistic measure for these materials?

obtained for Al2O3 produced using intermediate grain sizes (10–50 μm) [56].

As well known, accurate elastic moduli are measured dynamically by measuring the frequency of natural vibrations of a beam, or by measuring the velocity of sound waves in the material. Both depend on ffiffiffiffiffiffiffiffi E=r p , so if density (r) is known, E can be determined. These properties (r, E) reflect the mass of atoms, the way they are packed in material and the stiffness of the bonds that hold them together. For instance, Table 3 presents the literature data of elastic modulus for several synthetic and natural porous brittle materials.

Considering that microscaled damage in ceramics can be caused in processing as well as during their application, a technique that detects the in situ microcracks evolution is important to estimate the life operation of them [65].

The in situ elastic modulus measurement as a function of temperature may identify the causes of microcracks in material, which is very helpful to adjust ceramic processing and design the material microstructure for an extended period of use.


Table 3. Elastic modulus values for porous and brittle materials.

In this context, this section is divided into two parts. In the first part, a review about theoretical models to describe the effect of porosity on the elastic modulus of porous ceramics is presented. Then, the second part presents and discusses the elastic modulus behavior as a function of temperature for the foamed Al2O3 ceramics.

Overall, little research in the literature considers porous ceramics as anisotropic material in the

Mechanical Properties of Porous Ceramics http://dx.doi.org/10.5772/intechopen.71612 191

For instance, Rodrigues et al. [71] compared experimental data of the elastic moduli of Al2O3 foams (P: 60–90%) to several models proposed in the literature, as depicted in Figure 15. These authors considered the Al2O3 foams as isotropic material and, therefore, the experimental data

This analysis, however, needs to be considered carefully because the foamed ceramics of high porosity (P > 60%) are usually anisotropic material and the mentioned models are valid only

Roy et al. [61], Wu et al. [59] and Lichtner [28] clearly showed that the extent of anisotropy, and its effect on the elastic modulus measurements, is strongly dependent on the porosity level, mainly for porosities higher than 40%, which is the case of the most foamed ceramics and

Moving to the elastic modulus behavior at heating, Salvini et al. [48] evaluated the in situ elastic modulus behavior of foamed Al2O3 to identify the changes at the curing, drying and

The tests of elastic modulus were carried out in the range of temperature from 50 to 1400C in air with heating and cooling rates of 2C/min and a holding time of 4 h at 1400C. After that, additional thermal cycles of elastic modulus measurements were carried out up to 1400C.

Green bar samples (25 mm 25 mm 150 mm) of foamed Al2O3 containing 5 wt% of high alumina cement were considered for the in situ elastic modulus evaluation. The measurements

Figure 15. Theoretical models predicting the effect of porosity on the relative Young's modulus (continuous lines) and

fitted well with the MacKenzie [68] and Gibson and Ashby (GA) [22, 23] models.

evaluation of their elastic modulus behavior.

for homogeneous and isotropic ones.

natural porous materials.

sintering stages of material.

experimental data of gelcasting Al2O3 foams [71].

Much research over the last decades was dedicated to understanding the influence of the porosity on the elastic modulus of ceramics. Table 4 shows the most common theoretical models concerning the elastic modulus (E) and the porosity (P) correlations.

The Knudsen [66] and Rice [28] models fit well with real data of materials with porosity lower than 50%, as reported by Boccaccini et al. [67] and Ohji et al. [62, 63].

The model proposed by MacKenzie [68] and Kingery [69] is also defined for a lower level of closed pores.

Gibson and Ashby (GA) models [22, 23] indicated that the elastic modulus of a porous material depends only on its relative density and pore morphology.

Boccaccini model [67] introduced the s parameter to indicate the porosity geometry effect on the elastic modulus, that is, the pore shape and its orientation. However, it is valid only for low porosity level (P < 0.4) of closed pores.

In another work Boccaccini et al. [70] also included the topological parameters of highly porous microstructure to the model, besides the geometrical ones. Topological characterization comprehends the separation, the separated volume and the degree of contact and separation in two-phase microstructures. However, an issue that was addressed by the authors in this model is the necessity of a well-characterized porous structure of material, besides its porosity, to achieve rigorous verification of the model.


Table 4 Summary of the elastic modulus (E) and porosity (P) models, where E0 refers to the elastic modulus of solid material.

Overall, little research in the literature considers porous ceramics as anisotropic material in the evaluation of their elastic modulus behavior.

In this context, this section is divided into two parts. In the first part, a review about theoretical models to describe the effect of porosity on the elastic modulus of porous ceramics is presented. Then, the second part presents and discusses the elastic modulus behavior as a

Much research over the last decades was dedicated to understanding the influence of the porosity on the elastic modulus of ceramics. Table 4 shows the most common theoretical

The Knudsen [66] and Rice [28] models fit well with real data of materials with porosity lower

The model proposed by MacKenzie [68] and Kingery [69] is also defined for a lower level of

Gibson and Ashby (GA) models [22, 23] indicated that the elastic modulus of a porous material

Boccaccini model [67] introduced the s parameter to indicate the porosity geometry effect on the elastic modulus, that is, the pore shape and its orientation. However, it is valid only for low

In another work Boccaccini et al. [70] also included the topological parameters of highly porous microstructure to the model, besides the geometrical ones. Topological characterization comprehends the separation, the separated volume and the degree of contact and separation in two-phase microstructures. However, an issue that was addressed by the authors in this model is the necessity of a well-characterized porous structure of material, besides its porosity, to

Dependent on P and on extent of contact

Dependent on relative density and pore

Dependent on P and on porosity geometry

Dependent on P, on geometry and on

Table 4 Summary of the elastic modulus (E) and porosity (P) models, where E0 refers to the elastic modulus of solid

Dependent on the closed pores'

Valid for P < 0:5 and isotropic

Valid for P < 0:5 and isotropic

Valid for P < 0:4 and anisotropic

Valid for R < 1 and anisotropic

Valid for open porous and isotropic material

material

material

material

material

models concerning the elastic modulus (E) and the porosity (P) correlations.

than 50%, as reported by Boccaccini et al. [67] and Ohji et al. [62, 63].

Model Characteristics

type

cos <sup>2</sup>θ

between solids

concentration

of closed pores

topology of porosity

depends only on its relative density and pore morphology.

porosity level (P < 0.4) of closed pores.

achieve rigorous verification of the model.

function of temperature for the foamed Al2O3 ceramics.

closed pores.

190 Recent Advances in Porous Ceramics

<sup>E</sup> <sup>¼</sup> <sup>E</sup>0e�bP Refs. [28, 66]

Refs. [67, 68]

<sup>E</sup> <sup>¼</sup> C E<sup>0</sup> <sup>r</sup> rs � �<sup>n</sup>

Refs. [22, 23]

<sup>s</sup> <sup>¼</sup> <sup>1</sup>:<sup>21</sup> <sup>z</sup> x � �<sup>1</sup>=<sup>3</sup> <sup>1</sup> <sup>þ</sup> <sup>z</sup>

Ref. [67]

<sup>R</sup> <sup>¼</sup> <sup>d</sup><sup>β</sup> dα , size ratio

Ref. [69]

material.

<sup>E</sup> <sup>¼</sup> <sup>E</sup><sup>0</sup> ð Þ <sup>1</sup>�<sup>P</sup> <sup>2</sup>

R Pþð Þ 1�P R

<sup>E</sup> <sup>¼</sup> <sup>E</sup><sup>0</sup> <sup>1</sup> � <sup>P</sup><sup>2</sup>=<sup>3</sup> � �<sup>s</sup>

<sup>E</sup> <sup>¼</sup> <sup>E</sup><sup>0</sup> <sup>1</sup> � <sup>1</sup>:9<sup>P</sup> <sup>þ</sup> <sup>0</sup>:9P<sup>2</sup> � �, P <sup>≤</sup> <sup>0</sup>:<sup>5</sup>

, C ≈ 1 and 1 < n < 2

x � ��<sup>2</sup> � <sup>1</sup> n o h i <sup>1</sup>=<sup>2</sup> For instance, Rodrigues et al. [71] compared experimental data of the elastic moduli of Al2O3 foams (P: 60–90%) to several models proposed in the literature, as depicted in Figure 15. These authors considered the Al2O3 foams as isotropic material and, therefore, the experimental data fitted well with the MacKenzie [68] and Gibson and Ashby (GA) [22, 23] models.

This analysis, however, needs to be considered carefully because the foamed ceramics of high porosity (P > 60%) are usually anisotropic material and the mentioned models are valid only for homogeneous and isotropic ones.

Roy et al. [61], Wu et al. [59] and Lichtner [28] clearly showed that the extent of anisotropy, and its effect on the elastic modulus measurements, is strongly dependent on the porosity level, mainly for porosities higher than 40%, which is the case of the most foamed ceramics and natural porous materials.

Moving to the elastic modulus behavior at heating, Salvini et al. [48] evaluated the in situ elastic modulus behavior of foamed Al2O3 to identify the changes at the curing, drying and sintering stages of material.

The tests of elastic modulus were carried out in the range of temperature from 50 to 1400C in air with heating and cooling rates of 2C/min and a holding time of 4 h at 1400C. After that, additional thermal cycles of elastic modulus measurements were carried out up to 1400C.

Green bar samples (25 mm 25 mm 150 mm) of foamed Al2O3 containing 5 wt% of high alumina cement were considered for the in situ elastic modulus evaluation. The measurements

Figure 15. Theoretical models predicting the effect of porosity on the relative Young's modulus (continuous lines) and experimental data of gelcasting Al2O3 foams [71].

were carried out according to ASTM C1198–91 using the resonance bar technique (Scanelastic equipment, ATCP, Brazil).

modulus curve observed in the initial stage of heating of the first cycle was caused by the

Mechanical Properties of Porous Ceramics http://dx.doi.org/10.5772/intechopen.71612 193

At higher temperatures, the discontinuities in the temperature range of 200–400C were probably due to dehydration of the phases AH3 (Al2O3.3H2O) and C3AH6 (CaO.Al2O3.6H2O),

After dehydration, the elastic modulus remains stable at a low value until sintering starts at ~900C. After 1100C, the modulus increases rapidly due to sintering involving phase changes and formation of strong atomic bonds, which are characteristics of ceramic compositions.

At ~900C, the CA (CaO.Al2O3) is the first crystalline phase formed, then it reacts with Al2O3 giving CA2 (CaO.2Al2O3) at around 1100C. The formation of CA2 from CA and Al2O3 is

At higher temperatures, the following two competitive phenomena occur: (1) expansion due to

In the second cycle of measurement, no significant difference in the modulus curve was found

In contrast, in case of sintering at 1500C/4 h, the calcium hexa-aluminate CA6 (CaO.6Al2O3) phase is additionally formed due to a reaction of CA2 with Al2O3, which starts at ~1450C. The

Finally, when cooling the modulus curves remained stable without discontinuities, indicating

These findings enhance the understanding not only about the role of specific additives (surfactants and inorganic binders) but also about the crystalline phase transformations and corresponding dimensional changes at sintering of macroporous ceramics. These results have important implica-

This chapter reviews the mechanical properties of porous ceramics with special interest on the

One of the more significant findings to emerge from analysis of mechanical strength section is that, in addition to the porosity of porous ceramics, the number of connecting struts between the cells/pores in the microstructure plays a fundamental role in their mechanical strength behavior. Data from the literature support that once the connecting struts are lost in the porous structure, it is impossible to recover the original mechanical strength of it by merely increasing

Regarding to fracture toughness of porous ceramics, two factors appear to control this property: the presence of surrounding pores at the crack front and the interaction of cracks with the

mechanical strength, fracture toughness and elastic modulus of these materials.

formation of CA6 is also expansive, leading to a superior elastic modulus of material.

tions for developing porous ceramics with superior mechanical properties.

the formation of CA2 phase and (2) shrinkage due to sintering of Al2O3 particles.

besides the decomposition of the organic additives (surfactants).

expansive as a result of anisotropic growth of crystals [72].

conversion of CAH10.

in comparison with the first one.

5. Summary

the struts thickness.

pores in the microstructure.

an absence of microcracking of material.

Figure 16 depicts the in situ elastic modulus evolution (first and second cycles) up to 1400C, in addition to results of the as-sintered foamed Al2O3 at 1500C/4 h. Table 5 presents the crystalline phase changes obtained by X-ray diffraction as a function of temperature for ceramic composition.

The foaming and casting processes of Al2O3 suspension were carried out at room temperature (~25C). As reported by the literature [72], the main cement hydrate phase formed at room temperature is CAH10 (CaO.Al2O3.10H2O). When the temperature increases, this phase partially dehydrates ~110C into a mixture of gibbsite, AH3 (Al2O3.3H2O) and tricalcium aluminate hydrate, C3AH6 (CaO.Al2O3.6H2O). This suggests that the drop of

Figure 16. In situ elastic modulus of macroporous Al2O3: blue curve corresponds to the first cycle up to 1400C of the green sample; the red curve is the measurement after the first cycle, and the green curve corresponds to the measurement after sintering up to 1500C/4 h. The arrows indicate the discontinuities in the curve caused by decomposition or formation reactions of specific ceramic phases [48].


Table 5 Phase changes obtained by X-ray diffraction in alumina composition containing 5 wt% of high alumina cement. The concentration of phases is qualitatively defined by the number of asterisks (\*) displayed [48].

modulus curve observed in the initial stage of heating of the first cycle was caused by the conversion of CAH10.

At higher temperatures, the discontinuities in the temperature range of 200–400C were probably due to dehydration of the phases AH3 (Al2O3.3H2O) and C3AH6 (CaO.Al2O3.6H2O), besides the decomposition of the organic additives (surfactants).

After dehydration, the elastic modulus remains stable at a low value until sintering starts at ~900C. After 1100C, the modulus increases rapidly due to sintering involving phase changes and formation of strong atomic bonds, which are characteristics of ceramic compositions.

At ~900C, the CA (CaO.Al2O3) is the first crystalline phase formed, then it reacts with Al2O3 giving CA2 (CaO.2Al2O3) at around 1100C. The formation of CA2 from CA and Al2O3 is expansive as a result of anisotropic growth of crystals [72].

At higher temperatures, the following two competitive phenomena occur: (1) expansion due to the formation of CA2 phase and (2) shrinkage due to sintering of Al2O3 particles.

In the second cycle of measurement, no significant difference in the modulus curve was found in comparison with the first one.

In contrast, in case of sintering at 1500C/4 h, the calcium hexa-aluminate CA6 (CaO.6Al2O3) phase is additionally formed due to a reaction of CA2 with Al2O3, which starts at ~1450C. The formation of CA6 is also expansive, leading to a superior elastic modulus of material.

Finally, when cooling the modulus curves remained stable without discontinuities, indicating an absence of microcracking of material.

These findings enhance the understanding not only about the role of specific additives (surfactants and inorganic binders) but also about the crystalline phase transformations and corresponding dimensional changes at sintering of macroporous ceramics. These results have important implications for developing porous ceramics with superior mechanical properties.
