Reproducibility and Cross-Section Definition
The Gaussian error calculation shows that the correct determination of the cross-sectional area has the strongest influence on stress calculation when small specimens are used. Decreasing cross-sectional areas intensify this effect further.
A basic requirement for an error calculation is a precise mathematical description of the cross-sectional area as a function of a measured variable. In the case of a round cross-section, this variable is the diameter. In the case of a rectangular cross-section, dimensional measurement is more complex because the orthogonality of the four-sided cross-section must be verified before the simplified rectangular area formula can be used.
If the geometry is not perfectly rectangular, the real cross-sectional area has to be calculated as a four-sided polygon using the xy-coordinates of each vertex. In addition, the experimental verification that the edges are perfectly sharp, not rounded, and free of cracks or notches becomes critical.
For specimens with rectangular cross-sections and dimensions below 1 mm, the edges are expected to be rounded rather than perfectly sharp, and experimental verification of orthogonality in finite time is practically not feasible. For reliable and reproducible micro tensile testing, the use of a round cross-section is therefore strongly recommended.
Round Geometry and Loading Conditions
At very small dimensions, specimen geometry also affects loading conditions. The JTE publication notes that pulling shoulders should be perpendicular to the tension axis and without offset to each other. If this is not fulfilled, bending can occur during the tensile test.
Circular grinding has an important geometric advantage: when the grinding disc is correctly positioned, the angle between pulling shoulders and tension axis is 90°. Even if side faces of the grinding disc are not perfect, the pulling shoulders remain rotationally symmetric, which avoids the occurrence of a bending moment.