 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 change in strain and/or force. To predict the critical buckling force, finite element models were made using the finite element code (Abaqus Dassault Systèmes®). The material model in the commercially available code (Abaqus) was calibrated based on tensile tests of the material. The model was validated by experimental tests in order to verify the critical buckling force for the actual material.
In this work, the specimens were tested in an Instron servo-hydraulic testing machine (Instron 8800). The specific machine is equipped with a climate chamber for testing temperatures ranging from − 70 to 350 °C and therefore has elongated rods for the allowance of the specimen mounting heads inside the chamber. This gives a wide experimental range. The elongation rods are treaded onto the piston rod of the machine. Thereby, some mechanical flexibility is introduced. However, the experiments must be designed so that buckling is avoided during the compression phase of the cycle.
Methods and experimental design
Material, constitutive model, and parameter identification
The material used for these tests is a commercial quality hot rolled structural steel S355J2-1.0577. The specimens were machined from a Ø = 16-mm bar which were approved according to EN10025-1 (2004). The minimum required yield strength is 355 MPa and the ultimate tensile strength is within 510-680 MPa according to EN10025-1 (2004). A computer numerical controlled (CNC) lathe was used to machine the specimens. A high-quality surface finish is not considered to be critical for the onset of buckling in a one-cycle compression test.
The material model is based on von Mises yield criterion, the associated flow rule, and a modified Voce law. Calibration was based on tensile tests. Design of the tensile specimens was done according to Fig. 1. Diameters were measured on the individual specimens tested. Three specimens in parallel were tested. The deformation of the specimens was measured by a longitudinal extensometer with a gage length of 12.5 mm. The tensile experime