Author details

Umaru Ahmadu<sup>1</sup> \*, Alhassan Muazu<sup>2</sup> and Sadiq Umar<sup>3</sup>

\*Address all correspondence to: u.ahmadu@yahoo.com


## References


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dielectric loss decreased. Electrical parameters such as the real part of impedance (Z<sup>0</sup>

studied through impedance spectroscopy. Nyquists plots of Ba(Ti0.96Sn0.02Zr0.02)O3 ceramic show both bulk and grain boundary effects at 400�C which indicates the NTCR behavior of the sample. Therefore, Ba(Ti0.96Sn0.02Zr0.02)O3 ceramic is considered as a promising low-cost material for thermistor applications. The electrical relaxation process occurring in the material

) as a function of both frequency and temperature have been

00

\*, Alhassan Muazu<sup>2</sup> and Sadiq Umar<sup>3</sup>

1 Department of Physics, Federal University of Technology, Minna, Nigeria

3 Department of Physics, Ahmadu Bello University, Zaria, Nigeria

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2 Department of Physics, Federal College of Education (T), Bichi, Kano, Nigeria

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Author details

Umaru Ahmadu<sup>1</sup>

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\*Address all correspondence to: u.ahmadu@yahoo.com

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**Chapter 10**

Provisional chapter

**Mechanical Properties of Porous Ceramics**

It is widely known that increasing interest in porous ceramics is due to their special properties, which comprise high volumetric porosity (up to 90%) with open or closed pores, and a broad range of pore sizes (micropores: d < 2 nm; mesopores: 50 nm > d > 2 nm and macropores: d > 50 nm). These properties have many uses comprehending macroscaled devices, mesoscaled materials and microscaled pieces. During their usage, these materials are usually submitted to thermal and/or mechanical loading stresses. Therefore, it is a premise to understand how these porous structures behave under thermomechanical stresses to design materials that show adequate properties for the required application. In this context, the aim of this chapter is to review the mechanical properties of macroporous

DOI: 10.5772/intechopen.71612

Keywords: porous ceramics, foams, mechanical properties, elastic modulus, fracture

It is widely known that increasing interest in porous ceramics is due to their special properties, which comprise high volumetric porosity (up to 90%) with open and interconnected or closed and isolated pores, and a broad range of pore sizes (micropores: d < 2 nm; mesopores: 50 nm > d > 2 nm and macropores: d > 50 nm). These properties have many uses comprehending macroscaled devices (filters for liquid metals [1, 2], thermal insulating refractories [3, 4], bioceramics for bone regeneration [5–7], filters for water treatment [8], acoustic insulating tiles [9]),

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Mechanical Properties of Porous Ceramics

Vânia Regina Salvini, Victor C. Pandolfelli and

Vânia Regina Salvini, Victor C. Pandolfelli and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71612

Dirceu Spinelli

Abstract

ceramics.

energy

1. Introduction

Dirceu Spinelli


#### **Mechanical Properties of Porous Ceramics** Mechanical Properties of Porous Ceramics

DOI: 10.5772/intechopen.71612

Vânia Regina Salvini, Victor C. Pandolfelli and Dirceu Spinelli Vânia Regina Salvini, Victor C. Pandolfelli and Dirceu Spinelli

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71612

#### Abstract

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[59] Plocharski J, Wieczoreck W. PEO based composite solid electrolyte containing NASICON.

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[61] Sarangi S, Badapanda T, Behera B, Anwar S. Frequency and temperature dependence dielectric behavior of barium zirconate titanate nanocrystalline powder obtained by mechanochemical synthesis. Journal of Materials Science: Materials in Electronics. 2013;

[62] Ranjan R, Kumar N, Behera B, Choudhary RNP. Investigations of Impedance and Electric Modulus Properties of Pb1-xS mx(Zr0.45Ti0.55)1x/4O3ceramics. Advanced Materials Let-

[63] Ganguly P, Jha AK, Deori KL. Complex impedance studies of tungsten–bronze structured Ba5SmTi3Nb7O30 ferroelectric ceramics. Solid State Communications. 2008;146(11-12):472-

[64] Hirose N, West AR. Impedance spectroscopy of undoped BaTiO3 ceramics. Journal of the American Ceramic Society. 1996;79:1633-1641. DOI: 10.1111/j.1151-2916.1996.tb08775.x

[65] Dutta A, Bharti C, Sinha TP. AC conductivity and dielectric relaxation in CaMg1/3Nb2/3O3.

[66] Morrison FD, Sinclair DC, West AR. Characterization of lanthanum doped barium titanate ceramics using impedance spectroscopy. Journal of the American Ceramic Society.

[56] Yadav KL, Sharma P. Indian Journal of Engineering & Materials Sciences. 2008;15:61

tium titanate. Materials Today: Proceedings. 2016;3:2321-2328

[54] Ganguly P, Jha AK. Journal of Alloys and Compound. 2010;495:7-12

ceramics. Journal of Alloys and Compound. 2012;537:197

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477

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10.1111/j.1151-2916.1989.tb07706.x

170 Recent Advances in Porous Ceramics

It is widely known that increasing interest in porous ceramics is due to their special properties, which comprise high volumetric porosity (up to 90%) with open or closed pores, and a broad range of pore sizes (micropores: d < 2 nm; mesopores: 50 nm > d > 2 nm and macropores: d > 50 nm). These properties have many uses comprehending macroscaled devices, mesoscaled materials and microscaled pieces. During their usage, these materials are usually submitted to thermal and/or mechanical loading stresses. Therefore, it is a premise to understand how these porous structures behave under thermomechanical stresses to design materials that show adequate properties for the required application. In this context, the aim of this chapter is to review the mechanical properties of macroporous ceramics.

Keywords: porous ceramics, foams, mechanical properties, elastic modulus, fracture energy

#### 1. Introduction

It is widely known that increasing interest in porous ceramics is due to their special properties, which comprise high volumetric porosity (up to 90%) with open and interconnected or closed and isolated pores, and a broad range of pore sizes (micropores: d < 2 nm; mesopores: 50 nm > d > 2 nm and macropores: d > 50 nm). These properties have many uses comprehending macroscaled devices (filters for liquid metals [1, 2], thermal insulating refractories [3, 4], bioceramics for bone regeneration [5–7], filters for water treatment [8], acoustic insulating tiles [9]),

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

mesoscaled materials (membranes for catalysis [10], drug release substrates [11, 12]) and microscaled pieces (e.g., multifunctional materials where gravimetric properties are critical as batteries [13] and electronic sensors [14]).

2. Influence of microstructural parameters on the mechanical strength of

The objective here is not to carry out an extensive revision of the fracture of brittle porous materials, but to present results which serve as a basis to the authors´ proposal in this chapter. First of all, fracture of porous ceramics is better described by the quasi-brittle behavior as their ultimate fracture is triggered by many local events (different from essentially brittle behavior of glass ceramics), yet they are not preceded by highly dissipative processes associated with plastic deformation and strain hardening (as observed in ductile metals) [21]. Quasi-brittle

As mentioned earlier, the real data of the mechanical properties of porous materials indicate

Questions have been raised about the models proposed by Gibson and Ashby (GA) [22, 23], which indicate that the relative strength of a porous material is a function of its relative density

> <sup>¼</sup> <sup>C</sup> <sup>r</sup> rs <sup>m</sup>

where σ and r are, respectively, the fracture strength and the density of porous material; σ<sup>S</sup> and r<sup>S</sup> are the fracture strength and the density of solid material, respectively; C is a dimensionless constant and the exponent m depends on the pore morphology (m = 3/2 for open pores or m = 2 for closed ones). The Gibson and Ashby (GA) models are based on the bending or

Figure 1 shows the relative strength predicted by the Gibson and Ashby models plotted together with experimental data of porous ceramics from different researchers. It can be seen a disagreement between the theoretical curves of GA models and the experimental results.

Colombo et al. [24] attributed microstructural factors for the lack of fitting data to the Gibson and Ashby models, as shown in Figure 1, as they do not consider the distribution of pore sizes,

Seeber et al. [25] also noted that the drop in mechanical properties of foamed ceramics was disproportionately greater than what was to be expected solely from increasing the porosity. These authors suggested this behavior must be an influence of the pore size or the strut

Nevertheless, Salvini et al. [27] suggested that a parameter which expresses the processing method to produce the porous structure should be considered by the mechanical models. For instance, porous ceramics with similar porosity and density ranges can be produced using different ceramic methods such as sacrificial fugitives, replica templates and directing foaming. However, each method provides a different number of struts (ligaments) of distinct solid particle

neither have mixed pores (open and closed) nor flaws in the pore wall (struts).

thickness, as reported by Brezny and Green [26] in a previous paper.

packing, which influences the final mechanical behavior of the material.

(1)

173

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

that their mechanical behavior depends on more than just porosity of the materials.

σ σs

fracture behavior is also observed in rocks, bones and ceramic composites.

porous ceramic materials

as follows:

buckling of cell edges.

During their usage, these materials are usually submitted to thermal and/or mechanical loading stresses. Therefore, it is a premise to understand how these porous structures behave under thermomechanical stresses to design materials that show adequate properties for the required application.

Despite the importance of porosity for application of these materials, there is not a general consensus about the dependence of mechanical properties on porosity parameters. In other words, the real data of the mechanical properties of these materials indicate that their mechanical behavior depends on more than just porosity of the materials.

Since its introduction to the ceramic community in the 1970s, the area of fracture mechanics has made significant contributions to improving ceramics. As an example, the combination of fracture toughness, fracture statistics and fractography has made it possible to identify critical flaws in material and, consequently develop better and reliable advanced ceramics. In addition, the contribution of fracture mechanics was fundamental in understanding the fracture process in brittle materials.

Recognizing that the area behind a crack was responsible for the increase in the R-curve in ceramics was particularly relevant. One issue concerning the uses of brittle ceramics is associated with the statistical and size-dependence of their fracture properties, which can make reliable prediction, a difficult task. Two other problems are the absence of design methodology for brittle ceramics and the high costs of producing the ceramic components [15].

Nowadays, the ceramic community is witnessing a "boom" of nature inspired materials using hierarchical structures that should have the same behavior or qualities as the natural ones. Various papers [16–20] in the literature show beautiful structures of natural materials and their mimicked copies by researchers. The capacity of a human being's observation, also a characteristic controlled by nature, has been the driving force to imitate natural hierarchical structures and their qualities.

In this context, the aim of this chapter is to review the mechanical properties of macroporous ceramics. The following issues are of particular interest to this chapter:


All these questions need to be considered in order to advance not only the processing of porous ceramic materials but also to design their structures for specific applications.
