This research establishes the failure criteria of localized necking, fracturing, and wrinkling in sheet metal forming and the fundamentals of deformation mechanics in plane-strain bending (bending around a straight line), contour flanging (bending around a curve), and stretch/draw forming operations, which are primarily used in forming the box-shaped and structural sheet components. The mechanics and the associated computer programs are able to predict the deformation (strains, stresses, and loads), the failures (necking, tearing, and wrinkling), and the springback in the forming operations.
Based on the advancements in continuum mechanics, plasticity, and the modern concepts in the understanding of sheet metal formability, the mechanics of plane-strain bending and contour flanging was established. A number of commonly as well as the newly developed bending and flanging processes were analyzed. A computer code BEND was developed to simulate air bending, rotary bending, and die bending (curved-die, tractrix-die, wiping-die, U-die, and V-die). A computer program FLANGE was developed to simulate the shrink and stretch flanging operations.
The bending effects were introduced to the membrane finite element program SECTIONFORM for analyzing stretch/draw forming processes. In order to maintain the computational efficiency and numerical stability, a decoupled method was proposed for step-by-step bending corrections for membrane solutions. This method is able to consider both the local and the global bending effects, as well as unbending and sliding. Extra strain hardening and thinning due to bending are also included in the formulation. The algorithm and subroutines were developed and implemented into SECTIONFORM program. The modified version of SECTIONFORM was tested by a number of examples. The simulations showed that the step-wise bending correction causes neither the numerical instability nor appreciable increase of computation time (CPU). The simulations of the plane-strain stretch forming and deep drawing using a flat bottom punch were compared with measurements. Good agreements were achieved for three punch radii (3.18, 7.14, 9.53 mm).
A number of failure criteria were developed for bending, flanging, and stretch/draw forming operations. New bendability criteria were proposed to determine the minimum bend ratio based on both localized necking and fracture modes and anisotropic material properties. A localized necking criterion was established for the stretch flangability analysis based on the modification of Hill's instability criterion and incorporating the strain hardening and the plastic anisotropy of sheet materials subjected to prestrain. With a bifurcation analysis of a double curved and anisotropic shell subjected to the forming stresses, the wrinkling criteria, incorporating sheet anisotropy, strain hardening, and deformation geometry, were developed to predict the local wrinkling phenomena in the unsupported region of sheet in deep drawing operations and to determine wrinkling at the flange edge in shrink flanging operation.
Experiments were conducted to verify the proposed process models for bending and flanging operations and the wrinkling criteria. Simulation results were compared with measurements. The springback and the relation between bending angle vs. punch stroke in various bending operations were successfully predicted with good accuracy. The strains and wrinkles in shrink flanging tests were also well predicted.
The practical aspect of this research is to provide a scientific approach to analyze the formability of complex sheet parts formed in multiple operations (bending, flanging, stretching and deep drawing). The mechanics models and the associated computer-aided analysis system are able to provide information necessary for engineers to design sheet parts, processes, and dies by a more efficient and optimum strategy which reduces and finally eliminates costly try-outs. This computer-aided analysis system can also be adopted to other CAD systems for formability analysis.