Dear Colleague,

It seems that the mentioned problem is considered for NiCrMo steel (thickness of specimen from 3 to 25 in mm) in paper of Munz and Keller (http://www.gruppofrattura.it/ocs/index.php/esis/ECF3/paper/viewFile/1361/1034). 

Please check the mentioned link.

With best regards,

Grzegorz

Hello, dear Hossein

   The measured bending strength of ceramics is influenced by the thickness of the specimen. And the thickness effect is caused by a variation in stress gradient. With the smaller thickness, the stress gradient is greater and the measured strength is higher.

Hope this is useful to you.

Best regards,

Nie

Hi, just wanted to add a very recent paper by Horn et. al in which they comment on the notch and out-of-plane effect (related to the thickness of the specimen) on cleavage fracture toughness. It is a vey interesting paper and clearly addresses both effects

http://www.sciencedirect.com/science/article/pii/S0308016117301151?via%3Dihub

Hossein:

There are two prime issues with respect to the effect of specimen thickness on the fracture load or fracture toughness of materials.  The first issue is meeting the plane strain requirement, which means that the plastic-zone size at the crack tip, which scales with (K/sigma-y)2 (where K is the stress intensity and sigma-y is the the yield strength), must be at least an order of magnitude smaller than the out-of-plane thickness dimension B. Once this condition is met, in principle you will measure the lower-bound toughness, KIc. You will find plenty of data on this effect in almost all fracture text books, such as by Knott, Hertzberg, Anderson, Broek, etc.

However, you mention your interest of the thickness effect in brittle and quasi-brittle materials.  Since these are likely to be low toughness and/or high strength materials, you will often easily meet plane-strain conditions with most typical test-piece sizes, which bring up the second issue associated with thickness, which is the question of the statistical sampling volume - this incidentally is a specimen size effect rather than one of just specimen thickness.  In brittle and quasi-brittle materials, their fracture load or strength can be markedly a function of the specimen size - the larger the specimen size, the lower the fracture stress as you are more likely to find a larger, worse-case, defect in a larger sample.  (Leonardi da Vinci found this effect in the 15-16th Century when he discovered that short brittle wires were stronger than long ones!).  Accordingly, the fracture stress will invariably be smaller in larger-sized samples when testing a brittle/quasi-brittle material, such as silicon, graphite and most ceramics - but, as noted above, this is a specimen size effect rather than one of just specimen thickness.  Most ceramics textbooks, such as by Brian Lawn, will have such data to illustrate this effect.  However, you will probably not see this effect in fracture toughness measurements of these materials as you have already put in a worse-case defect with the pre-crack in your fracture toughness specimen.  Once you meet the plane-strain requirement, any further increase in thickness should, in principle, give you the same lower-bound toughness, as is generally found with ductile materials.

ROR

Intrinsic impact toughness of relatively high strength alloys

Dear Hossein, hope the attached paper is useful for what you are looking for.

Regards.