Try experimental compliance method

Hi Wirat,

The values of the surface energies are already known for many materials including ceramics (obtained experimentally or theoretically).

However, there are techniques to approximate the surface energy theoretically. You can have a look at the book titled

Ceramic Materials: Science and Engineering

by C. Barry Carter, M. Grant Norton

(2007) pages 225-226.

Then, once you have Young's modulus of elasticity and the rupture stress, the flaw size can be obtained by rearranging Griffith's equation.

Regards,

Layal

Hi Arun K V

I am not quite sure what is the experimental compliance method.Could you give me some hint?

Hi Layal Hakim

Thank you so much, I will try and let you know.

You glance the book suggested by Layal Hakim

Ceramics are quasi-brittle materials, i.e. materials in which the fracture process zone is not negligible compared to standard structure size. The correct way to estimate the fracture energy is to run size effect tests. You can find a very comprehensive description in Prof. Bazant's book on fracture:

ZP Bažant, J Planas "Fracture and size effect: in concrete and other quasibrittle materials" CRC press, 1998.

Hi Marco Salviato

Thank you so much, I will try and let you know. Sorry I just get back to my question.

You cannot measure the fracture energy from the results of bend testing alone. This is because there is no information on the size of the flaw that is causing fracture. Griffith's criteria relates the flaw size and the applied stress to the fracture energy. But, you do not know either the flaw size or the fracture energy from a bending test. In order to obtain he fracture energy you must start with a known crack size and measure the critical applied "stress" that results in crack extension.

If you have limited equipment available you could try the indentation toughness method. This requires only a Vicker's microhardness test machine. See papers by B. R. Lawn from the early 1980s. Also note that this will not usually ive an entirely accurate number due to two main issues: 1) the indentation process establishes a residual stress field and 2) many ceramics display R-curve behavior (increase in toughness with increase in crack length) via a number of mechanisms (Marco's answer above alludes to this behavior by invoking a non-negligible process zone).

Note that it is possible to use indentation in initiate a crack of known (measured) size and then perform a bending test to find the critical applied loading that causes material failure. If one assumes this indentation crack is an elliptical crack there are solutions for the KI under uniform far-field tension. Note that the comments on residual stress field around the indent and R-curve behavior are still applicable.

https://www.researchgate.net/publication/301348952_Licensed_Under_Creative_Commons_Attribution_CC_BY_Investigation_on_Mode_-_I_Fracture_Parameters_Using_Steel_Fibers_in_High_Strength_Concrete

Article Licensed Under Creative Commons Attribution CC BY Investigat...