Almost the entire ceramic compound consists of ionic bonds.
The stress-strain 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.
Stress is computed from the specimen thickness is bending moment, moment of inertia of cross-section (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 cross-section, 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.
The stress strain for ceramic using flexural test is similar to tensile as shown in figure.
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.
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: Pretence-Hall 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
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)
.
No discussion on this note yet. Be first to comment on this note