Digital Image Shape Measurement for the Monitoring and Control of Non-Homogeneous, Axisymmetric Plastic Deformation

The deformation of a cylinder is non-homogeneous in many plastic deformation processes. Examples include bulging in upset forging or compression testing and necking in tensile testing. The deformed shape provides valuable information that can be used to monitor or control the process. Shape can be used to estimate the von Mises equivalent stress and strain, to estimate foldover and the frictional interface conditions in compression, and to predict and possibly avoid fracture. Shape measurements can also be used in a closed loop control system to maintain a constant strain rate during non-homogeneous deformation. In this paper, a method is described to use coarse digital camera data to calculate the shape parameters. An assumed form of the deformed shape is used to provide sub-pixel resolution. Since the method uses moments of the data, which are integrals, the method is insensitive to noise in the data. Because of its simplicity, the moment method is practical for real time computation and control.