The Notched Roller Test (NRT): Effective Volumes and Effective Surfaces for Weibull Strength Scaling
Description
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 "Notched Roller Test", described in [https://doi.org/10.1016/j.jeurceramsoc.2014.02.009], is given. The relevant geometrical and material parameters to determine the effective surface or effective volume are: -Roller diameter D -Roller length H -Roller chamfering radius rf -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 <= 3 0 <= rf/D <= 0.05 0.74 <= l/D <= 0.9 0.05 <= w/D <= 0.2 0 <= rn/w <= 0.5 0.1 <= v <= 0.4 1 <= m <=50 Based on the data for stress interpolation, the maximum tensile stress can be determined from an interpolation of "finter" and the relevant geometrical properties (see equation 1 in the paper cited above). The normalized effective surface or effective volume can be determined through interpolation of the Seff and Veff data of this repository in the same way. The normalization volume Vnorm and normalization surface Snorm are given through the volume (= Pi*H*(D/2)^2) and surface (= Pi*H*D + 2*Pi*(D/2)^2) 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 file for stress evaluation is as follows: H/D || rf/D || l/D || w/D || rn/w || v || finter All files provided follow this convention, and the permutation follows v -> rn/w -> w/D -> l/D -> rf/D -> H/D The structure of the data in each file for the evaluation of Veff and Seff is as follows: H/D || rf/D || l/D || w/D || rn/w || v || m || Veff/Vnorm || Seff/Snorm All files provided follow this convention, and the permutation follows m -> v -> rn/w -> w/D -> l/D -> rf/D -> H/D -Interpolation files (.xlsx,.py,.nb) The Interpolation implemented in the Excel-file is linear, while the others are cubic. 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. 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. Afterwards, results for the maximum tensile stress and all effective quantities are given in lines highlighted in green.
Files
Steps to reproduce
These results were obtained through Finite Element Analysis (ANSYS 13) for a quarter-model of the NRT using SOLID186 elements. A sufficient number of elements within the ligament was ensured, with a minimum of 16 elements in radial direction (for the longest notches) and a maximum of 24 elements in radial direction (for the shortest notches). To ensure that only the relevant stresses and no numerical artifacts are taken into account for the evaluation of the effective quantities, only selected elements were considered (see Figure 1 in Description.pdf). The selection is defined by a cylindrical coordinate system through the roller axis, where elements which are closer to the load introduction than 30° are excluded, and where elements closer to the center of rotation than “D/2-(D/2-l)/2” are excluded. This holds true for both the effective volume and the effective surface, but the latter one was restricted to only surface elements. The data was parametrically determined for a wide range of relevant geometries and materials, resulting in a total of 11520 datapoints for the stress evaluation and a total of 345600 datapoints each for the evaluation of effective surface and volume. For the latter, the multiaxial stress state was considered through the First-Principal-Stress criterion. More information on the utilized model is found in [https://doi.org/10.1016/j.jeurceramsoc.2014.02.009], and more information on the post-processing to obtain effective surface and volume from Finite Element Analysis results is found in [https://doi.org/10.1016/j.jeurceramsoc.2023.09.018]. The data for the closely related "Notched Ball Test" (NBT), "Notched Roller Test" (NRT) and "Cross Notched Roller Test" (X-NRT) are all available on Mendeley Data: NBT: [https://doi.org/10.17632/fc5rgbj3b4.1] NRT: [https://doi.org/10.17632/pdxy669fvk.1] X-NRT: [https://doi.org/10.17632/9ctpg2p6bj.1]