Experimental investigation and finite element modeling of hemispherically stretched steel sheet
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I.
INTRODUCTION
MODERN sheet metal
forming practices still include a great deal of trial and error. Research has concentrated on finding ways to model and predict press performance accurately through experiments and computer models. Simple hemispherical punches are used for laboratory formability experiments such as limiting dome height tests. These experiments have been used successfully to identify production problems but oversimplify a general forming operation. Computer modeling represents a more flexible approach. However, modeling of sheet metal formability is still in the relatively early stages, and many of the variables affecting formability are not well understood. Therefore, modeling efforts must be accompanied by attempts to isolate the factors which affect formability and verify the models by comparison with experiments. A computer model has been written for the analysis of sheet metal forming operations. In this study, verification has been made with hemispherical stretching experiments.
II.
BACKGROUND
The first successful attempts to model sheet forming conditions in the press shop have been with various forrnability tests. Early tests were designed primarily to comparatively test the material, but later tests have been designed to study various strain states and friction conditions as well. One of the milestones in sheet metal forming research was the notion of a critical level of strain for each strain state/1,21 The curve representing these limit strains is commonly referred to as either a forming limit diagram (FLD) or a Keeler-Goodwin diagram. The limiting dome height (LDH) test was introduced to rank material stretchability t31 and incorporates
the effect of strain distribution as well as the limiting strains. Attention is often centered on the minimum limiting dome height, LDH0, I4-71 which occurs at or near the plane-strain condition, where it has been estimated that about 85 pct of production part failures occur, tSl The correlation of FLD and LDH results with press shop behavior has been good. This early success of the formability tests accounts, at least partially, for their widespread use. Difficulty in modeling formability is largely the result of the many variables which must be considered. A high strain hardening exponent, n, produces a more uniform strain distribution and, consequently, a lower peak strain for dome heights up to the point of diffuse necking, thereby increasing the FLD. [3,9-111 However, the strain rate sensitivity, m, has the greatest effect on the strain distribution in its later stages, with a high m broadening the peak and delaying failureJ 9,1~ The n and m effects strongly enhance each other, t12j with the interaction increasing in importance for large n and m values. II3J A high normal anisotropy ratio, F, indicates resistance to thinning and improved drawability. While f is shown to have less effect on the FLD than r/, D4] neither n nor F has a significant effect on the FLD when varied within the range of values normally measured in mild steels, tll,14] O
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