Large plastic deformations by sequential limit analysis: A finite element approach with applications in metal forming.

Abstract

A new method, Sequential Limit Analysis, has been developed for solving large plastic deformation problems of metal both in plane strain and axisymmetric conditions. This method is a modern limit analysis that employs a duality theorem to equate the least upper bound to the greatest lower bound and uses mathematical programming techniques to search for optimal solutions. It involves no complex stress calculations. It can treat material property nonlinearly by updating local yield criteria step by step and has the advantage of global stability of computation even in the case of increasing deformation under decreasing load. It can also treat frictional contact phenomena easily because this method is explicit in nature. Moreover, it is mathematically concise and computationally easy to implement. To verify the capability of this new method, extensive numerical experiments have been done. These numerical experiments include strip tension, block compression and extrusion through a wedge die in the plane strain condition, and bar/tube tension, heading, and ball indentation in the axisymmetric condition. The computed results have been compared in good agreement with existing analytical and/or experimental solutions. Because of its success and efficiency in solving the above problems, Sequential Limit Analysis is ready for studying more complex industrial forming problems. Although Sequential Limit Analysis is a powerful method and has been successfully employed to solve metal forming problems, it also exhibits limitations at present. First, it cannot predict unloading behavior due to the neglect of elastic behavior. Second, it is unable to treat rate-dependent problems, and thus cannot explore both impact and thermomechanical coupling phenomena in dynamic indentation and hot forming processes. Third, it may encounter slow or even difficult convergence of solution for problems having an almost flat functional which admits nonunique solutions. To extend the capability of Sequential Limit Analysis, adequate methodologies to overcome these limitations have to be proposed and studied.