Stress strain behavior of ceramics
Stressstrain behavior of ceramics:
Almost the entire ceramic compound consists of ionic bonds.
Ceramic materials:
 Glasses
 Glass ceramics
 Clay product
 Structural products
 White wares
 Abrasive
 Refractories
 Fire clay
 Cement
 Advanced ceramics
The stressstrain behavior of brittle ceramic is not usually obtained by tensile test.
In the testing of ceramic material 3 point loading scheme and four point loading scheme is used.
In 3 point loading scheme:
 First the material is prepares in the required geometry (either rod having circular or rectangular cross section).
 Second, the ceramic materials are difficult to grip without fracturing. So, three point loading scheme is used. tn this scheme, load is applied in middle or the end of the ceramic rod placed over two knives support as shown in figure.
 The strain for brittle fracture in ceramics is too small only about 0.1 % strain. So, specimen is perfectly align to avoid the presence of bending stress.
Stress is computed from the specimen thickness is bending moment, moment of inertia of crosssection (geometrical moment of inertia). The maximum tensile stress exist or the bottom specimen surface directly below the point of load application.
The stress of fracture using flexural strength of modulus of rapture or bend strength. It is denoted by \(\sigma_f\). The stress at fracture using this flexure test is known as the flexural strength, modulus of rupture, fracture strength, or bend strength, an important mechanical parameter for brittle ceramics i.e.
\(\sigma_{fs}\)=flexural strength
=fracture strength
=bend strength
=modulus of rupture
The stress at fracture using this flexure test is known as the flexural strength, modulus of rupture, fracture strength, or bend strength, an important mechanical parameter for brittle ceramics
$$\sigma_{fs}=\frac{3F_fL}{2bd^2}\dotsm(1)$$
For rectangular cross section
\(F_f\)=applied load at fracture
L=effective length of rod
B=breadth
D=thickness
For the rod having circular crosssection, the fracture strength is given by,
$$\sigma_{fs}=\frac{F_fL}{\pi R^3}\dotsm(2)$$where R=radius of specimen
The maximum bending moment for the specimen in this type of loading scheme is given by,
M=effective load\(\times\) load distance from centre
=\(\frac{F}{2}\times \frac{L}{2}\)
=\(\frac{FL}{4}\)
\(I_g\)=I=geometrical moment of intertia
=\(\frac{bd^3}{12}\) (for rectangular)
=\(\frac{\pi R^4}{4}\) (for circular)
The stress on specimen is given y,
$$\sigma=\frac{MC}{I}$$
Where,
C=distance from centre to outermost fiber
=R(radius)
=\(\frac{d}{2}\) (half thickness)
\(\sigma=\frac{FL}{4}.\frac{d}{2}\times \frac{1}{bd^3}\) (for rectangular)
\(\sigma=\frac{FL}{4}\times R\times \frac{4}{\pi R^4}\) (circular)
\(\therefore \sigma_{fs}=\frac{3F_fL}{2bd^2}\) (for rectangular)
\(\sigma_{fs}\)=\(\frac{FL}{\pi R^3}\) (for circular)
Characteristics flexural strength for different material is quite higher than that of modulus of elasticity. So magnitude of flexural strength is always measured flexural test except tensile strength.
Elastic behavior of ceramics:
The stress strain for ceramic using flexural test is similar to tensile as shown in figure.
Properties:
 The stressstrain is almost for ceramic material up to fracture strength.
 For given value of stress is too small in comparison to metals and polymers. This indicates the brittle nature of ceramic material.
 For crystalline material, plastic deformation occurs by the motion of dislocation.
 The rate of deformation in noncrystalline ceramics is due to applied stress and they deform by viscous force.
 In crystalline ceramic, the contribution to modulus of elasticity is due to ionic bond wheras for noncrystalline ceramics it is due to covalent bond.
The elastic stress–strain behavior for ceramic materials using these flexure tests is similar to the tensile test results for metals: a linear relationship exists between stress and strain.
References:
Callister, W.D and D.G Rethwisch. Material Science and Engineering. 2nd. New Delhi: Wiley India, 2014.
Lindsay, S.M. Introduction of Nanoscience . New York : Oxford University Press, 2010.
Patton, W.J. Materials in industry . New Delhi : Prentice hall of India, 1975.
Poole, C.P. and F.J. Owens. Introduction To Nanotechnology. New Delhi: Wiley India , 2006.
Raghavan, V. Material Science and Engineering. 4th . New Delhi: PretenceHall of India, 2003.
Tiley, R.J.D. Understanding solids: The science of Materials. Engalnd : John wiley & Sons , 2004.
1. Process of 3 point loading system
 First the material is prepares in the required geometry (either rod having circular or rectangular cross section).
 Second, the ceramic materials are difficult to grip without fracturing. So, three point loading scheme is used. tn this scheme, load is applied in middle or the end of the ceramic rod placed over two knives support as shown in figure.
 The strain for brittle fracture in ceramics is too small only about 0.1 % strain. So, specimen is perfectly align to avoid the presence of bending stress.
2. Some formulas
$$\sigma=\frac{MC}{I}$$
\(\therefore \sigma_{fs}=\frac{3F_fL}{2bd^2}\) (for rectangular)
\(\sigma_{fs}\)=\(\frac{FL}{\pi R^3}\) (for circular)

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