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.为对比不同测试方法得到的陶瓷试样强度测试结果，掌握有效表面积或有效体积的相关知识至关重要。 本仓库提供了参考文献[https://doi.org/10.1016/j.jeurceramsoc.2025.117931]中所述的十字缺口滚轮测试（Cross Notched Roller Test）的最大拉应力、有效表面积及有效体积计算所需数据。用于计算有效表面积或有效体积的相关几何与材料参数包括： - 滚轮直径D - 滚轮长度H - 缺口长度l - 缺口宽度w - 缺口根部半径rn - 泊松比（Poisson's ratio）v - 威布尔模量（Weibull modulus）m 数据的适用范围满足以下约束条件： 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 基于上述数据，可通过对finter参数及相关几何特性进行插值计算得到最大拉应力（详见上述引用论文中的公式8）。归一化有效表面积或有效体积也可通过相同方式对数据进行插值得到。 归一化体积Vnorm与归一化表面积Snorm分别对应滚轮的体积（= π*H*(D/2)²）与圆柱表面积（= π*H*D）。 为便于评估，本仓库同时提供了Python、Excel及Mathematica格式的插值文件。 附加信息： - 数据文件（.csv、.tsv、.xlsx） 每行数据的结构如下： H/D || l/D || w/D || rn/w || v || m || finter || Veff/Vnorm || Seff/Snorm 所有提供的文件均遵循此格式，参数排列顺序为：m → v → rn/w → w/D → l/D → H/D - 插值文件（.xlsx、.py、.nb） Excel文件中的插值方式为线性插值，其余格式文件采用三次插值，二者差异已在主稿件中量化说明。Python与Mathematica文件的计算结果存在细微差异。 Excel文件： 输入试样几何与材料参数后，将自动更新最大拉应力及所有有效参量的计算结果。 Python文件： 需将.csv数据文件与脚本置于同一目录下。运行脚本后，将在命令行中弹出参数输入提示，随后输出最大拉应力及所有有效参量的计算结果。 Mathematica文件： 需将.csv数据文件与脚本置于同一目录下。红色标注行代表试样几何与材料参数的输入位置，绿色标注行将输出最大拉应力及所有有效参量的计算结果。