- Original Paper
- Open Access
Prediction of buckling force in hourglass-shaped specimens
International Journal of Mechanical and Materials Engineering volume 16, Article number: 10 (2021)
It is important to avoid buckling during low-cycle fatigue testing. The buckling load is dependent on the specimen shape, material properties, and the testing machine. In the present investigation of hourglass-shaped specimens the importance of the diameter to radius of curvature is examined. Diameters of 5 and 7 mm are examined with a ratio of radius of curvature to diameter of 4, 6, and 8. The machine used is an Instron 8800 with elongated rods for a climate chamber. This leads to a reduced stiffness of the machine during compression testing. A finite element model (in Abaqus) is developed to identify the critical buckling force. For hourglass-shaped specimens, buckling means onset of sideways movement, without a drop in the applied load which is typical for conventional Euler buckling. The onset of sideways movement is identified experimentally by analysis of the data from extensometer and the load cell. This model is verified by experiments and fits within 0.6 to − 11% depending on the specimen diameter and diameter to radius of curvature ratio. The smallest deviations are obtained for the 7-mm-diameter specimen with deviation varying from 0.6 to − 3.3% between the model and the experiments. The current investigation is done with a commercially available hot rolled structural steel bar of Ø16 mm.
Specimen design due to fatigue testing machine construction limits are not well described in the literature. Therefore, a method to identify the limits for an actual machine is needed. During axial low-cycle fatigue testing, one has to make sure that this buckling is avoided in the compression cycle. Hourglass-shaped specimens are suited to investigate low-cycle fatigue. The hourglass shape is suitable to resist buckling during the compression phase compared to a uniform section specimen. It is time-consuming to determine the onset of buckling by experiments alone and buckling might damage the laboratory equipment. Therefore, one needs to find a method to calculate the critical buckling force, i.e., the onset of sideways movement during the compression cycle. This is different from Euler buckling as this kind of buckling occurs at a force lower than maximum force. During Euler buckling, a sudden drop in force is observed. For an hourglass-shaped specimen, buckling (the onset of sideways movement) is observed without a sudden drop in force. This paper shows a method developed to calculate this critical buckling force and experiments to verify the model.
In the literature, there are limited descriptions of specimen design for low-cycle fatigue specimens by a finite element model and corresponding verification by experiments. The paper of Sandhya et al. (1994) gives a valuable description of experiments with different specimen geometries. Narendra et al. (2019) investigated low-cycle fatigue behaviour and cyclic placiticty of mild steel. Hales et al. (2014) presented a code of practice for the determination of cyclic stress-strain data. Nogami et al. (2010) studied the effect of specimen shape on the low-cycle fatigue life of small specimens. The investigation includes the results of finite element model. Skelton (2013) describes tests with different R/d ratios and a parallel section of the specimen.
The design of low-cycle fatigue specimen is of great importance when it comes to setting up reproducible tests. Therefore, the standard from the American Society of Testing and Materials, ASTM E606/606M (2012), has been used as a guideline for the specimen geometry. In the current investigation, specimens were designed with a R/d ratio from 4 to 8, which is well defined by ASTM E606/606M (2012). A conventional mild low-carbon steel was used. In order to identify the onset of buckling, an examination of the flexibility (the derivative of elongation to force) was analyzed from experimental data, as conventional buckling is associated with a rapid c