Forming a Titanium Rod by Bending
Due to their high strength and light weight, titanium alloys are widely used in industrial applications where these attributes are crucial factors, such as in sporting goods, biomedical implants, aircraft and aerospace applications.
Bending is a widely adopted cold forming technique used for components made of titanium. One of the major design considerations in forming such components is to account for the elastic recovery after unloading — the so-called spring-back effect. Also, the residual stresses caused in the specimen due to the inelastic deformations during forming have an important effect on the load-carrying capacity of the formed component.
In this News, we present a case study of the bending of a titanium rod. The experimental set up is depicted in the figure below.
Figure The experimental set up for bending a titanium rod
The experimental device consists of 2 rollers and an arm. The stationary roller guides the titanium rod while the moving roller bends it.
The animation above shows the 3D finite element model used in this study and the deformation of the titanium rod due to 90 degree bending . The rod and both rollers are modeled using 20-node brick elements. As can be seen, a higher mesh density is used in the rod where it is being bent while for the rest of the rod a coarser mesh is used for computational efficiency. Due to symmetry of the model and loading, only half of the rod and rollers are modeled. The rollers are assumed to remain elastic during the process while the rod experiences large strain elasto-plasticity. A large strain von Mises plasticity model with isotropic multilinear hardening is used to model the material behavior of the titanium rod.
The animation below shows the contour plots of the accumulative effective plastic strain in the rod and the contact tractions between the rod and the rollers during the forming process. As can be seen, due to bending, large plastic regions develop at the top and bottom of the cross-section of the rod while a significant center region of the rod remains elastic. The size of this core elastic region is the dominant factor in the magnitude of the spring-back after unloading; the larger the volume of the elastic region, the higher the magnitude of the spring-back.
In the reference, results for different sizes of diameters of the rod and rollers are presented and compared with experimental results. These models are all generated using the parametric model generation feature available in ADINA.
This case study presents one of the applications of ADINA in the simulation of forming problems. For some other interesting applications, see Applications of ADINA in Forming Problems.
- J. Adamus, P. Lacki, "Forming of the titanium elements by bending", Computational Material Science, 50:1305–1309, 2011.
Forming, bending, large strain elasto-plasticity, contact, parametric model, titanium, biomedical implants, aircrafts, sporting goods, spring-back
Courtesy of J. Adamus and P. Lacki, Faculty of the Mechanical Engineering and Computer Sciences, Institute of Metal Working, Quality Engineering and Bioengineering, Czestochowa University of Technology, Poland