Journal of Mechanical Science and Technology 27 (3) (2013) 783~792 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-013-0124-9 The effect of anisotropy on wrinkling of tube under rotary draw bending † Kourosh Hasanpour 1,* , Mahmoud Barati 2 , Behnaz Amini 3 and Mehrdad Poursina 1 1 Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, P.O.Box 81746-73441, Isfahan, Iran 2 Department of Applied Mechanics, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran 3 Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch, Iran (Manuscript Received February 9, 2012; Revised August 4, 2012; Accepted October 3, 2012) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract Rotary draw tube bending is one of the most complex tube forming processes subject to different process parameters such as material properties and geometry. This process is being practiced in more and more applications in industry due to its high efficiency, high form- ing precision and quality. However, improper process parameters can lead to wrinkling which restrict the thin walled tube bending. Therefore, the prediction and prevention of wrinkling is very important. Despite its importance, the effect of anisotropy on the occurrence of wrinkling was not considered in the literature up to now. In this investigation, a quantitative study on the wrinkling of thin walled tube bending is carried out through a finite element model of the process using velocity integral parameter, which is used for the detection of wrinkles. The other methods usually warn the wrinkling initiation with no precise location prediction. In addition, the effects of some process parameters, specially normal and planar anisotropy on the tube wrinkling are investigated. It is shown that increasing normal and planar anisotropy (increasing r 0 and r 90 values) result in a decrease in tube wrinkling. Keywords: Normal anisotropy; Planar anisotropy; Rotary draw bending; Velocity integral parameter; Wrinkling ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Thin-walled tubes have been widely used in different indus- tries such as aerospace, automobile and air conditioning indus- tries. The rotary draw bending of the thin walled tubes is broadly applied due to its high forming quality and meeting the requirement of increasing needs for high strength per weight ratio products. However, the inner side of thin walled tubes may experience wrinkling if inappropriate process pa- rameters are employed, especially for tubes with large diame- ter and thin wall thickness. Rapid and accurate prediction of wrinkling phenomenon is one of the key problems that have to be urgently solved for the development of this process. Many researchers have simulated the rotary draw tube bending proc- ess to study the effect of different parameters on the tube wrinkling. Li et al. developed a complete 3D elastic-plastic finite element (FE) model of the process using ABAQUS/explicit code. They analyzed the forming character- istics by analytical and experimental methods. In their paper, the plastic deformation characteristics with small bending radius and interactive effects of push assistant loading condi- tions on wall thinning were investigated [1-6]. Kumar simu- lated rotary draw tube bending to find the optimum process parameters that prevent wrinkle effects, and then studied vari- ous process parameters such as different dies position and tube/different dies interactions [7]. Zhang et al. proposed a modification on the adaptive dynamic relaxation method which improves the efficiency in solving non-linear problems. Then, they analyzed the elastic-plastic bending of circular plates in large deflections and their subsequent wrinkling. Their study led to satisfactory results compared with corre- sponding experimental ones [8]. Yang et al. established a 3D elastic-plastic finite element model and a wrinkling energy prediction model under multi-die constraints considering the characteristics of the bending processes of thin-walled tubes of aluminum with large diameters [9]. Li et al. developed an energy-based wrinkling prediction model for thin walled tube bending by applying the energy principle, combined with analytical and FE based numerical methods [10]. Orban et al. developed a finite element model to simulate rotary draw tube bending and applied the local variation of normal-to-surface velocity for wrinkling detection, and then provided a basis for developing an adaptive loading scheme to optimize end boost- ing without inducing wrinkles in the bent tube [11]. They ap- plied the velocity integral parameter which is the time integra- tion of the second-order normal velocity difference and is mathematically related to the curvature change along the tube wall. This parameter was developed in order to detect onset of wrinkling in the simulations. It was verified that a rapid in- * Corresponding author. Tel.: +98 3117934021, Fax.: +98 3117932746 E-mail address: hasanpour@eng.ui.ac.ir † Recommended by Associate Editor Kyeongsik Woo © KSME & Springer 2013