[Image above] Examples of tensile stress field variations for samples with different relative thicknesses (t/RS): a) t/RS = 0.05, b) t/RS = 0.25, and c) t/RS = 0.5. Each contour gives a 10%-percentile of the maximum stress from 0 (blue) to the maximum stress (red). Gray represents compressive stresses. Credit: Staudacher et al., Journal of the European Ceramic Society (CC BY 4.0)
Before products are shipped out to customers, they must undergo quality assurance testing to ensure the product is safe to use in its intended application. But designing tests that accurately mimic real-world operating conditions can be surprisingly challenging, even for common use cases.
For example, consider methods for testing a material’s strength. Three-point and four-point bending tests are widely used due to the straightforward nature of these tests, which only place a load on the sample in one direction (uniaxial force). However, in service, ceramic components are often biaxially loaded, meaning they experience stress along two axes at the same time.
Biaxial strength testing methods do exist and have some advantages over uniaxial bending methods, such as simpler sample preparation. However, due to the sample experiencing load along multiple axes, analyzing the stress profile is more difficult.
The ball-on-three-balls (B3B) biaxial testing method is especially challenging to analyze. In this method, a disk-shaped sample is supported by three balls and then axially loaded from the opposite side via a fourth ball.
Unlike some testing methods, for which an analytical description of the stress field is available, a simple analytical expression for the stress field in the B3B test is not available. As such, the effective volume and effective surface for a B3B test sample—which is used in Weibull strength scaling to compare the respective strength results from different methods—must be determined and investigated through finite element analysis.
Until now, values for the effective volume and effective surface of B3B test samples were only available for a small range of geometries and materials. But a new open-access paper, courtesy of researchers from the University of Leoben in Austria, provides tabulated data for a wide range of B3B sample geometries and materials.
The researchers used two finite element analysis models to determine the effective volume and effective surface for both disk- and square-shaped samples. They provide these values as tabulated data in various formats—along with the tools to use them for specific samples—in the paper’s supplementary material section.
The researchers demonstrated the use of this data through an example of pooled Weibull evaluation. However, they also discussed the limitation of their data and tools, which is only valid for combinations of testing and material parameters as given in Table 2.
“If the tested specimens surpass these limits significantly, the authors recommend individual FEA [finite element analysis] to determine the most accurate results for the effective volume and surface,” they write.
The open-access paper, published in Journal of the European Ceramic Society, is “The ball-on-three-balls strength test: Effective volumes and surfaces for Weibull strength scaling” (DOI: 10.1016/j.jeurceramsoc.2023.09.018).