Plastic Surface Strain Mapping of Bent Sheets by Image Correlation

A technique using a single CCD camera, a precision rotation/translation stage, a telecentric zoom lens, and digital image correlation software is described for measuring surface profiles and surface plastic strain distributions of a bent thin sheet. The measurement principles, based on both parallel and pinhole perspective projections, are outlined and the relevant mathematical equations for computing the profiles and displacement fields on a curved surface are presented. The typical optical setup as well as the experimental measurement and digital image correlation analysis procedure are described. The maximum errors in the in-plane and out-of-plane coordinates or displacements are about ±5 and ±25 μm, respectively, and the maximum errors in surface strain mapping are about 0.1% or less based on a series of evaluation tests on flat and curved sample surfaces over a physical field of view of 15.2 × 11.4 mm2. As an application example, the shape and surface plastic strain distributions around a bent apex of a flat 2 mm thick automotive aluminum AA5182-O sheet, which underwent a 90◦ bend with three bend ratios of 2t, 1t, and 0.6t, are determined using the proposed technique. KEY WORDS—3D surface profiling measurement, 3D surface deformation field measurement, sheet metal forming, optical strain mapping method Introduction In many sheet metal forming processes, an initially flat sheet metal blank is often stamped into the complex shape of a desired product. The success of such a manufacturing process depends on avoiding severe strain concentrations that may lead to necking and ductile damage of the sheet metals while achieving excellent dimension accuracy of the formed part.1 Some sheet metal forming operations are primarily in-plane stretching and drawing, but there are many other processes such as bending, flanging, and hemming that result in large out-of-plane displacements over a relatively small lateral dimension, and thus large curvatures and strain concentrations. For example, sharp bending of copper alloy sheets and hemming of steel sheets are widely used in making various electrical connectors and automotive components, respectively.2,3 Hemming of 5XXX and 6XXX series automotive aluminum alloys is often more problematic (because of surface cracking and shear banding) as these aluminum alloy sheets have lower W. Tong (SEM member; [email protected]) is an Associate Professor, Department of Mechanical Engineering, Becton Engineering Center, Yale University, New Haven, CT 06520-8282 USA. Original manuscript submitted: November 19, 2003. Final manuscript received: May 11, 2004. DOI: 10.1177/0014485104047384 ductility than low-carbon automotive steel sheets. There is a need to measure the maximum plastic surface strain and strain gradients at the sharp bend apex of formed parts for selecting more suitable aluminum alloys and optimizing the hemming process parameters.4 Digital image correlation (DIC) has been increasingly used in recent years for whole-field surface strain mapping applications in many materials and mechanics research laboratories, in part due to the availability of many in-house and commercial software tools.5–16 Because of the optimization of many factors including the quality of images acquired and the algorithms and parameters adapted in image correlation processing, good reliability and accuracy of the strain mapping results can now be achieved routinely.16 For strain mapping of the planar deformation and motion of a flat object, the errors in global average strain and local pointwise strain variations can usually be limited to 10 and 100 μstrain or less, respectively.13,16 Using proper image magnifications and decorated surface contrast patterns, large plastic strains and high strain gradients over small gage dimensions (only a fraction of the original sheet thickness) of the necking region in thin sheets can be easily mapped out in detail.17 However, when it is necessary to measure the three-dimensional (3D) surface profile and its strain distributions by DIC, an elaborate procedure for camera calibration and lens corrections is usually required.18–22 In general, a dual-camera imaging system is used and the calibration of each camera is carried out by a nonlinear optimization of about 10 or more intrinsic and extrinsic parameters using precision square grids or cross-line gratings and multiple out-of-plane translations.19,20 When a single camera system is adopted, the additional calibration of the projector18 or multiple in-plane translations21 may be used. Again, multiple image correlation processing steps and a nonlinear optimization procedure are required to estimate the 10 or more camera parameters. When the 3D surface profile is known to be cylindrical and the deformation is symmetric about the cylindrical axis, a single camera imaging system with minimum calibration requirements has also been used for surface strain mapping.22 Here we present a simpler technique for measuring both the surface profile and its surface plastic strain distributions of a 3D object using a single camera imaging system with a telecentric zoom lens and a rotation/translation stage. In the following, the measurement principles, based on both parallel and pinhole perspective projections, are first described. The feasibility of the proposed technique is then assessed through a set of evaluation tests. The experimental procedure and results are given in detail for both surface profiling and surface strain mapping measurements. The measurement errors are 502 • Vol. 44, No. 5, October 2004 © 2004 Society for Experimental Mechanics