% between average of experiments and model. The model shows a significant better correlation for the larger diameter specimen. One can see from Table 3 that a larger diameter (d) gives a higher measured buckling force as expected. It is also clear that the smaller ratio R/d between the specimen diameter (d) and the radius of curvature (R) gives a higher buckling force.
A large diameter gives a smaller deviation between the experiment and the model. The model allows the whole bottom grip of the specimen to move freely in the X-Z plane. This is a simplification that does not include the stiffness with respect to sideways movement of the lower elongation rod of the test machine as can be seen from the photo in Fig. 4. This simplification is expected to give lower buckling force values in the model than in the experiments. In general, it is observed that the calculated values from the model are smaller than the measured values from the experiments.
This investigation was adopting a 3D model perfectly straight with the resultant of the force applied coinciding with the model’s axis. The onset of buckling is normally caused by a perturbation for a perfectly straight model. In the current investigation, the perturbation is expected to be caused by a numerical effect in the calculations. Other factors influencing the onset of buckling could be tilting of the specimen or geometric imperfections in the shape of the specimen. By adapting a 0.1 and a 1° tilting of the specimen to the compression axis, the used model gave a lower buckling force than was found in the experiments. The determination of the degree of tilting will therefore cause a substantial uncertainty in the model. The same goes for the determination of the value of machine stiffness for predicting the onset of sideways movement of the specimen. Both these factors will influence the predicted buckling force.
The observed phenomenon named buckling in this work is principally different from a classic buckling. In those cases, the onset of sideways movement will 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 