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Research Papers

Experimental and Numerical Investigation of Forming Limit Differences in Biaxial and Dome Test

[+] Author and Article Information
Chetan P. Nikhare

Department of Mechanical Engineering,
Penn State Erie—The Behrend College,
Erie, PA 16563
e-mail: cpn10@psu.edu

Manuscript received July 28, 2017; final manuscript received February 24, 2018; published online May 28, 2018. Assoc. Editor: Gracious Ngaile.

J. Manuf. Sci. Eng 140(8), 081005 (May 28, 2018) (12 pages) Paper No: MANU-17-1481; doi: 10.1115/1.4039587 History: Received July 28, 2017; Revised February 24, 2018

For centuries, metals and materials have been characterized using a traditional method called a uniaxial tension test. The data acquired from this test found to be adequate for operations of simple forming where one axis stretching is dominant. Currently, due to the demand of lightweight component production, multiple individual parts eliminated by stamping a single complex shape, which also further reduces many secondary operations. This change is driving by the new fuel-efficiency requirement by corporate average fuel economy of 55.8 miles per gallon by 2025.1 Due to complex part geometry, this forming method induces multiaxial stress states, which are difficult to predict using conventional tools. Thus, to analyze these multiaxial stress states limiting dome height tests and bulge tests were recommended in many research publications. However, these tests limit the possibilities of applying multiaxial loading and rather a sample geometry changes are required to imply multiaxial stresses. Even this capability is not an option in bulge test due to leakage issue. Thus, a test machine called a biaxial test was devised that would provide the capability to test the specimen in multiaxial stress states by varying the independent load or displacement on two independent axis. In this paper, two processes, limiting dome tests and biaxial tests were experimented, modeled, and compared. For the biaxial tests, a cruciform test specimen was utilized, and conventional forming limit specimens were used for the dome tests. Variation of sample geometry in limiting dome test and variation of loading in biaxial test were utilized to imply multiaxial stress states in order to capture the limit strain from uniaxial to equibiaxial strain mode. In addition, the strain path, forming, and formability investigated and the differences between the tests provided. From the results, it was noted that higher limit strains were acquired in dome tests than in biaxial tests due to contact pressure from the rigid punch. The literature shows that the contact pressure (which occurs when the rigid tool contacts the deformed body), increases the deformation and thus increases the limit strains to failure. This contact pressure parameter is unavailable in biaxial test, and thus, a pure material behavior can be obtained. However, limit strains from biaxial test cannot be considered for a process where rigid tool is processing the metal, and thus, calibration is necessary.

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Figures

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Fig. 1

True stress–true strain curve along with fitted power law (Permission to reprint from ASME @ 2017 [37])

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Fig. 2

Cruciform specimen with diamond center

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Fig. 3

Biaxial experiment setup with DIC

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Fig. 4

Seven specimen geometries to provide strain from uniaxial to equibiaxial strain in hemispherical dome test (diameter = 101.6 mm, radius = 38.1 mm, x = 12.7, 25.4, 38.1, 50.8, 63.5, and 76.2 from specimen 1 to 6) [41]

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Fig. 5

Electrochemically etched circles on samples

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Fig. 6

Nakajima hemispherical dome test setup

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Fig. 7

Cruciform specimen with center diamond (a) with boundary condition and (b) mesh specimen

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Fig. 8

Nakajima hemispherical dome test (a) numerical model, (b) specimen general dimension, and (c) mesh specimen

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Fig. 9

Schematic illustration of a sheet with pre-existing groove (Reproduced from [49])

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Fig. 10

Deformed samples using biaxial test machine: (a) uniaxial strain, (b) plane–strain, (c) between plane–strain and equibiaxial strain, (d) equibiaxial strain deformation mode, and (e) deformed diamond shape comparison for (a)–(d) deformation modes

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Fig. 11

All formed specimens using biaxial method captured at neck/fail frame: (a) uniaxial strain, (b) between uniaxial strain and plane–strain, (c) plane–strain, (d) between plane–strain and equibiaxial strain, and (e) equibiaxial strain deformation mode (legend shows engineering major strain, i.e., NE22 in abaqus)

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Fig. 12

Forming limit diagram from specimen simulated in biaxial model

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Fig. 13

Seven deformed specimens using dome test: (a) uniaxial strain, (b) and (c) between uniaxial strain and plane–strain, (d) plane–strain, (e) and (f) between plane–strain and equibiaxial strain, and (g) equibiaxial strain deformation mode

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Fig. 14

All formed specimens using dome test method captured at neck/fail frame: (a) uniaxial strain, (b) between uniaxial strain and plane–strain, (c) plane–strain, (d) between plane–strain and equibiaxial strain, and (e) equibiaxial strain deformation mode (legend shows engineering major strain, i.e., NE22 in abaqus)

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Fig. 15

Forming limit diagram from specimen simulated in dome test model

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Fig. 16

Forming limit diagram for limit comparison between biaxial test and dome test

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