lead to a reduction in measured force which will be at peak at the onset of buckling. In this case, the force is temporarily halting and continues to increase afterwards. The plateau in the force is less than a 1/10 of a second. Classic buckling is based on uniform diameter specimens and is thus not directly valid for hourglass-shaped specimens.
The method to determine the critical buckling force from the experiments used in this work is relatively simple compared to more expensive instrumentation like optical measurement methods with laser Hirose et al. (2000). The accuracy of the presented method is assumed to be high although it requires analysis of the data after the experiment is done.
The ability to predict the critical buckling load is essential for low-cycle fatigue testing in uniaxial mode. This requires availability of a model to predict the onset of buckling as this must be avoided during low-cycle fatigue testing in uniaxial mode.
During low-cycle fatigue testing, the material behavior will change. Before testing of an unknown material, it is uncertain to predict if the critical buckling load will increase or decrease compared to the first compression cycle as the model in this paper presents. In this case, an optical instrument might enable an in situ detection of a possible sideways movement. Independent of the material behavior, a low-cycle uniaxial fatigue test must start with a compression force below the buckling force.
A model for predicting buckling of hourglass-shaped specimen is presented. The model is calibrated based on tensile tests. A finite element software (Abaqus) is used to build the model. Compression tests of hourglassed specimen with diameters of 5 and 7 mm is done. The geometry of the specimens is based on the ASTM 606M standard. The ratio of the radius of curvature (R) in the hourglass section to the diameter (d) in the thinnest section (R/d) was tested at values 4, 6, and 8. A commercial cold-drawn low-carbon steel was used for the tests.
The model showed smaller deviation for the larger diameter (d) specimen. The smallest R/d-ratio gave the largest deviations between the model and the experiments. Specific knowledge about specimen geometry and the maximum planned compression force is necessary to avoid buckling during compression in axial low-cycle fatigue tests. The presented work is limited to the first compression cycle, but is crucial for a successful low-cycle fatigue test.
Availability of data and materials
All the data used in this investigation are available on request from the corresponding author.
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