Mechanics of Bending, Flanging, and Deep Drawing on a Computer-Aided Modeling System for Predictions of Strain, Fracture, Wrinkling, and Springback in Sheet Metal Forming

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.