An inverse routine to predict residual stress in sheet material

A method is presented to determine residual stress distribution in sheet material from data collected in a free bending test. It may be used where the residual stress distribution is symmetrical about the mid-surface as it is usually the case for frequently-used sheet metal post-processing techniques such as skin-pass or temper rolling, tension- and roller leveling. An existing inverse technique is used to obtain a residual stress profile and material constants that provide the best fit in a finite element analysis of bending with the experimentally derived moment-curvature relation. The method is verified for bending of a low-carbon stainless steel using measurement of residual stress by X-ray diffraction. The residual stresses were induced in the sheet by cold rolling. The technique described here can be used industrially as a rapid method of investigating residual stresses in incoming sheet. In processes where the deformation is principally one of bending, such as cold roll forming, it is known that residual stresses have an influence on shape defects and springback and the method presented here can be used to determine whether incoming sheet is suitable for further processing and also as a means of obtaining improved material data input for numerical simulation.