The Cross Notched Roller Test (X-NRT): Effective Volumes and Effective Surfaces for Weibull Strength Scaling

In order to compare strength testing results of ceramic specimens obtained through different testing methods, the knowledge of the effective surface or effective volume is essential.

In this repository, data to determine the maximum tensile stress, the effective surface and effective volume for the "Cross Notched Roller Test", described in [https://doi.org/10.1016/j.jeurceramsoc.2025.117931], is given. The relevant geometrical and material parameters to determine the effective surface or effective volume are:

-Roller diameter D
-Roller length H
-Notch length l
-Notch width w
-Notch root radius rn
-Poisson's ratio v
-Weibull modulus m

The data is available within:

1 <= H/D <= 5
0.7 <= l/D <= 0.9
0.02 <= w/D <= 0.37
0 <= rn/w <= 0.5
0.1 <= v <= 0.4
1 <= m <=50

Based on the data, the maximum tensile stress can be determined from an interpolation of "finter" and the relevant geometrical properties (see equation 8 in the paper cited above). The normalized effective surface or effective volume can be determined through interpolation of the data of in the same way.
The normalization volume Vnorm and normalization surface Snorm are given through the volume (= Pi*H*(D/2)^2) and cylindrical surface (= Pi*H*D) of the roller, respectively.
To aid evaluation, interpolation files in Python, Excel and Mathematica are also provided in this repository.

Additional information:

-Data-files (.csv,.tsv,.xlsx)

The structure of the data in each row is as follows:

H/D || l/D || w/D || rn/w || v || m || finter || Veff/Vnorm || Seff/Snorm

All files provided follow this convention, and the permutation follows m -> v -> rn/w -> w/D -> l/D -> H/D

-Interpolation files (.xlsx,.py,.nb)

The Interpolation implemented in the Excel-file is linear, while the others are cubic. The difference is quantified in the main manuscript. The results from Python- and Mathematica-files vary slightly.

Excel-file:

Entering the specimen geometry and material parameters will automatically adjust the values for the maximum tensile stress and all effective quantities.

Python-file:

The .csv-files have to be in the same directory as the script. Running the script opens prompts in the command line
to enter the specimen geometry and material parameters. Afterwards, results for the maximum tensile stress and all effective quantities are given.

Mathematica-file:

The .csv-files have to be in the same directory as the script. The rows marked in red represent the input-lines
for the specimen geometry and material parameters. Results for the maximum tensile stress and all effective quantities are given in lines highlighted in green.