Determination of the critical value of damage in a channel-die rotational compression test
This article describes the problems involved in modelling material cracking in skew rolling processes. The use of the popular damage criteria is impossible because of the lack of a calibration test that would make it possible to determine the critical value of material damage under conditions similar to those found in skew rolling. To fill this gap, a test called channel-die rotational compression was proposed. It consisted of rolling a disk-shaped specimen in a cavity created by two channels of cooperating tools (flat dies), which had heights smaller than the diameter of the specimen. When the rolling path was sufficiently long, a crack formed in the axial zone of the specimen. In this test, modelling using the finite element method made it possible to determine the critical values of material damage. As an illustration, the test was used to determine the critical damage value when conducting a rotational compression process on 50HS steel (1.5026) specimens formed in the temperature range of 950–1200 °C. The analysis was conducted using the Cockcroft–Latham damage criterion.
KeywordsDamage Rotational compression FEM Experiment
Material cracking is a frequent occurrence in skew rolling. In some processes of this type, such as the Mannesmann piercing process, cracking is desirable. In others, it is unacceptable because it induces irreparable damage to the product being formed. Therefore, it is important to monitor cracking beginning at the design stage of a given manufacturing process. High hopes are being pinned on the possibilities offered by computer modelling, which is increasingly used in the analysis of skew rolling processes.
The first reports on the modelling of the Mannesmann effect, which leads to the formation of a crack in the axial zone of a rolled product, were published at the beginning of the twenty-first century. Ceretti et al.  used Deform 2D software to model cracking (under the plane-strain assumption) in the axial zone of a part skew-rolled between flat tools. In their analysis, they adopted the theory of the maximum principal stress σ1, assuming that the critical value of this stress was 30 MPa. When the principal stress in a given element was σ1 > 30 MPa, the element was deleted to model crack formation. This model of cracking was used by Capoferri et al.  in their analysis of the formation of AISI1020 steel pipes (in this case, the limit value of principal stress σ1 was assumed to be 36.5 MPa).
The first attempt to model the Mannesmann piercing process under 3D deformation was made by Ceretti et al. . Their analysis was carried out using the Deform 3D software and introducing several simplifications such as ignoring the piercing plug and thermal phenomena that occur in a workpiece. The calculations were used to analyse the stress state of a product rolled with two rollers. A full 3D model of the rotary piercing process, which took into account the thermal behaviour of the material during forming, was developed by Pater et al. ; however, this model was not used to analyse material cracking. A breakthrough study in this area was conducted by Fanini et al. . In their study, the Forge software and Lemaitre damage law were used to model the cracking in the axial zone of a cylindrical billet. This included the requirement of introducing the initial distribution of the damage in the billet into the model, which was a consequence of the continuous casting process used to form the billet. The modelling results were in good agreement with the experimental results. This method of modelling crack formation was later used in the analyses carried out by Chastel et al.  and Ghiotti et al. . Other damage criteria have also been used in the analysis of the piercing process. For example, Pater and Tofil  used the Cockcroft–Latham criterion to identify the regions that were most susceptible to cracking. Using the same criterion, Skripalenko et al.  determined the effect of rollers on the plasticity of billets. The material cracking was not modelled in either study because the critical damage value was unknown.
It is also necessary to model the effective separation (or failure) of the material in the analysis of helical-groove rolling processes, in which parts rolled in roll passes (formed by the helically cut grooves of two cooperating rollers) are cut off from the billet . Earlier versions of specialised software did not make it possible to model the material separation, which is why it was a common practice in simulation studies to leave small connectors (bridges) between workpieces such as balls or stepped shafts [11, 12, 13, 14]. Recently, however, theoretical models of rolling processes for the production of balls [15, 16] and ball pins  have been developed in which the separation of the material has effectively been simulated. In these models, the Cockcroft –Latham damage criterion was used, with the critical damage value arbitrarily chosen to be in the range of 2–3. It should be emphasised that this value range was selected intuitively and was not based on scientific data. Therefore, we found it necessary to develop a test to determine the critical damage value, which could be applied to skew rolling processes. This type of test, which is called channel-die rotational compression, was developed at the Lublin University of Technology and was the focus of this study. The test is discussed using the example of forming 50HS steel (1.5026) specimens, which can be used in processes such as the helical rolling of grinding mill balls.
Concept of rotational compression between channel-dies
To determine the critical damage value, it is first necessary to experimentally establish the forming length s at which cracking occurs. Next, the test must be simulated using numerical modelling methods to determine the value of the damage function in the axial zone at the moment of crack formation. This value will be equal to the critical damage value sought.
Experimental tests of rotational compression between channel-dies
FEM analysis of rotational compression between channel-dies
The presented 50HS grade steel model was taken from the data library of the Forge® software used in the research.
Friction was modelled using the Tresca model, assuming that the friction factor at the material/tool interface was 0.8 . In addition, it was assumed that during the compression the tools had a constant temperature of 50 °C and the coefficient of heat transfer between the specimen and tools was 10,000 W/m2K.
Results and discussion
This section presents the results of experiments aimed at establishing a critical damage value (CCL) for the 50HS grade steel (1.5026).
In the test of rotational compression between channel-dies, cracking occurred in the axial zone of the specimen.
As the specimen was rotated, radial stresses along the axis of the specimen changed cyclically from compressive to tensile and back again, which, after the specimen had made a critical number of revolutions, led to the formation of a crack.
Despite the relatively long duration of the test under hot forming conditions, the temperature of the material in the axial zone of the specimen did not decrease, but, on the contrary, increased slightly as a result of the conversion of plastic work into heat.
To determine the critical value of damage at a given temperature using the rotational compression test, it was necessary to determine the critical forming length at which cracking occurred.
The critical value of material damage determined in the channel-die rotational compression test depended on the temperature of the test material, with an increase in temperature causing an increase in the critical value of damage.
Rotational compression in a channel is recommended to determine the critical values of material fatigue used in analyses of cross- and skew-rolling processes. In the case of hot rolling 50HS (1.5026) grade steel, the application of the equations shown in (4) is recommended.
The research was conducted under project No. 2017/25/B/ST8/00294 financed by the National Science Centre, Poland.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- 1.Ceretti E, Giardini C, Attanasio A (2001) Analysis of rotary tube piercing process: simulation and experimental results. In: Proceedings of AITEM 01, September 2001, Bari, ItalyGoogle Scholar
- 2.Capoferri G, Ceretti E, Giardini C, Attanasio A (2002) FEM analysis of rotary tube piercing process. Tube Pipe Technology, May/June 55–58Google Scholar
- 3.Ceretti E, Giardini C, Attanasio A, Brisotto F, Capoferri G (2004) Rotary tube piercing study by FEM analysis: 3D simulations and experimental results. Tube & Pipe Technology, March/April 155–159Google Scholar
- 5.Fanini S, Bruschi S, Ghiotti A (2008) Modelling of Mannesmann fracture initiation during cross-roll piercing. In: Proceedings of the 12th metal forming international conference, Krakow, Poland, 357–363Google Scholar
- 10.Yang H, Zhang L, Hu Z (2012) The analysis of the stress and strain in skew rolling. Adv Mater Res 538–541:1650–1653. https://doi.org/10.4028/www.scientific.net/AMR.538-541.1650 CrossRefGoogle Scholar
- 22.Cockcroft MG, Latham DJ (1968) Ductility and the workability of metals. J I Met 96:33–39Google Scholar
- 23.Sebek F (2016) Ductile fracture criteria in multiaxial loading – theory, experiments and application. Doctoral Thesis. Brno University of Technology, Czech RepublicGoogle Scholar
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.