Ball-on-3-Balls Test (B3B) – Strength Testing


The Ball on three Balls (B3B) test is a biaxial strength test for brittle materials, which can be applied on specimens having a wide variety of shapes (discs, plates) and sizes (diameter larger then a few millimetres). Since in service, biaxial stress states are very common (e.g. in thermal shock loading), biaxial testing is more realistic in many cases compared to conventional bending testing (were a uniaxial stress state is used). The method has several advantages compared to the common bending tests (e. g. the results are very stable against small geometric inaccuracies of the specimen or test assembly, edge defects are not relevant and there exists a very low influence of friction). 

To calculate the maximum tensile stress in the specimen it is necessary to know the dimensionless factor f and for a comparison of B3B-test results with the results of bending tests it is required to calculate the effective volumes and surfaces of the specimens. The link below takes you to an applet which allows the calculation of all these data for a wide range of geometries (circular discs only). For the evaluation of tests on rectangular plates, please contact us isfk(at)

webMathematica  (Java required)

Terms of Use

This tool is provided by ISFK to promote the use of the B3B-test. The practical use of the test is simple, but its evaluation requires FEM-calculations which we make available here. The use of the tool is free of charge.

If you use data generated with the applet (strength, pre-factor or effective regions) for your work, please cite:

More information, references and application examples

A. Börger, P. Supancic, R. Danzer: "The Ball on three Balls Test for Strength Testing of Brittle Discs - Stress Distribution in the Disc", Journal of the European Ceramic Society 22 [8] (2002), 1425-1436, doi:10.1016/S0955-2219(01)00458-7

A. Börger, P. Supancic, R. Danzer: "The Ball on three Balls Test for Strength Testing of Brittle Discs - Part II: Analysis of Possible Errors in the Strength Determination", Journal of the European Ceramic Society 24 [10-11] (2004), 2917-2928, doi:10.1016/j.jeurceramsoc.2003.10.035

R. Danzer, W. Harrer, P. Supancic, T. Lube, Z. Wang, A. Börger: "The Ball on Three Balls Test - Strength and Failure Analysis of Different Materials", Journal of the European Ceramic Society 27 [2-3] (2007), 1481-1485, doi:10.1016/j.jeurceramsoc.2006.05.034

R. Bermejo, P. Supancic, I. Kraleva, R. Morrell, R. Danzer: "Strength reliability of 3D low temperature co-fired multilayer ceramics under biaxial loading", Journal of the European Ceramic Society 31 (2011), 745-753, doi:10.1016/j.jeurceramsoc.2010.11.031