Evaluation of springback prediction capability using uniform pure bending

Thumbnail Image
Issue Date
Patel, Kunal Indravadan
Madhavan, Viswanathan

The aim of this study is to develop uniform pure bending as an objective test for determining the accuracy of springback prediction by employing different FEA techniques. A complete theoretical solution for the bending moment and change in sheet thickness is available only for uniform pure bending of perfectly plastic sheets. However, plastic hinging develops naturally in simulations of bending perfectly plastic sheets. We have developed a method to prevent plastic hinging and achieve uniform pure bending of sheets by applying constraint equations to nodes along the center fiber. The error in the bending moment for forming (E1), the error due to incomplete unloading during springback (E2), and error in the change of curvature corresponding to the change in bending moment during unloading (E3) are considered independently to get insights into the reasons for discrepancies between finite element analysis and theoretical results for springback. Uniform pure bending is also used to study the bending moment and springback experienced with work-hardening materials. Comparisons have been made with analytical solutions containing minor approximations in terms of the behavior of the material near the center fiber, which is subject to reverse loading. The fact that two different theoretical models for the material undergoing reverse deformation yield results that differ by less than 1% leads to a high degree of confidence in the theoretical models. We have used uniform pure bending to study the inherent springback prediction capability of different types of element analysis, convergence parameters, and discretization level in two different finite element analysis packages, namely MARC and ABAQUS. For simulations in ABAQUS using two dimensional elements and a perfectly plastic material model, the bending moment given by FEA is less than that predicted by the theoretical model by about -3%, indicating lesser springback than that predicted by theory. However for three dimensional elements, the bending moment is higher by about 10% for a relative curvature (%) of 0.2. For a coarse discretization (about 4 elements around a 90° bend), this error increases to about 37%. For a work-hardening material model, two dimensional elements predict 12% less bending moment than the theory, indicating an under-prediction in springback. Shell elements with reduced integration give an under-prediction of springback and show a negative error value between 2% and 10% for the simulations with different integration points, while shell with full integration show a positive total error of abut 3%, indicating a higher springback than predicted by theory. Changing the convergence tolerance value by 100 from the default value shows a 2% change in calculated results. For MARC, the two dimensional elements under-predicts springback by 10%, while the three dimensional elements have shown over-prediction up to 30% in moment calculations. Based on the findings, uniform pure bending is recommended as a benchmark test for identifying the intrinsic accuracy with which springback can be predicted by FEA simulations using different simulation parameters. Uniform pure bending can be used to develop effective guidelines for reliable finite element simulations of springback.

Table of Content
Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Industrial and Manufacturing Engineering
"May 2006."
Includes bibliographic references (leaves 52-54)