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Research Papers

Modeling and Experimental Assessment of Bending Characteristics of Laminated Bilayer Sheet Materials

[+] Author and Article Information
Ganesh Govindasamy

Forming Technologies Incorporated,
3370, South Service Road,
Burlington, ON L7N 3M6,
Canada e-mail: govindgn@mcmaster.ca

Mukesh K. Jain

Department of Mechanical Engineering,
McMaster University,
JHE 326G,
1280 Main Street West,
Hamilton, ON L8S 4L7, Canada
e-mail: jainmk@mcmaster.ca

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received August 29, 2015; final manuscript received March 3, 2016; published online May 13, 2016. Assoc. Editor: Huiling Duan.

J. Eng. Mater. Technol 138(3), 031014 (May 13, 2016) (18 pages) Paper No: MATS-15-1203; doi: 10.1115/1.4033283 History: Received August 29, 2015; Revised March 03, 2016

Many mathematical models based on the advanced theory of bending to predict bending characteristics for monolithic sheet materials are available in the literature. In this work, a similar approach is utilized to develop bending models for a bilayer laminated sheet material. The principal stresses and strains through the thickness and change in relative thickness, at specified bend curvatures, are obtained as a function of increasing curvature during bending. Additionally, three-dimensional (3D) finite element (FE) based models for bilayer laminate bending are developed to overcome simplifications of the analytical models. In order to experimentally validate the two models, a new experimental bend test-jig is developed and experiments are performed on bilayer steel–aluminum laminate for different clad to matrix thickness ratios. These experiments have enabled continuous measurements of strain along the width at the bend line and through the laminate thickness at one of the specimen edges using an online strain mapping system based on digital image correlation (DIC) method. Analytical model results indicate how the through-thickness strain distribution and relative thickness of the specimen in bending are influenced by the location and thickness of the soft clad material. The FE model and experimental results exhibit similar trends in the relative thickness change for different geometric arrangements of steel–aluminum layers. The tangential and radial stresses decrease in magnitude with increasing aluminum clad thickness ratios. The 3D FE model of laminate bending provided strain predictions across the specimen width at the bend line on the tension and compression sides that increased with increasing clad thickness ratios. Also, relative thickness data from the 3D FE model showed uniaxial and plane strain stress states at the edge and midwidth sections of the test specimen. The results from analytical and FE models and from DIC and microscopic thickness measurements indicate that thickness at the bend line increases with increasing clad thickness for the case of clad layer on the compressive side of the laminate (i.e., C-C case) and vice versa for clad layer on the tensile side (C-T).

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References

Figures

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Fig. 1

Classification of plastic zones in pure bending of bilayer laminate and corresponding boundary conditions for (a) and (c) clad under tension (C-T); (b) and (d) clad under compression (C-C), respectively

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Fig. 2

(a) M–K model for bending [6]; (b) schematic of FE M–K model design; (c) and (d) FE M–K model specimen showing development of anticlastic curvature in small radius bending

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Fig. 3

(a) As received sample view of SS400-AA1050 steel–aluminum bilayer laminate bonded by explosive welding; (b) uniaxial tensile stress–strain curves for AA1050 and SS400 at initial strain rate of 1/min

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Fig. 4

Experimental bend test jig: (a) schematic of bend test rig, (b) camera arrangement for strain measurement, and (c) experimental test setup

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Fig. 5

DIC based strain measurements from a bend specimen, (a) speckle pattern applied over specimen thickness, (b) DIC strain map for C-T specimen, and (c) DIC strain map for C-C specimen (ql = 0.25 for both specimens)

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Fig. 6

Through-thickness stress distributions in bilayer C-T specimen and monolithic SS400 steel layer at an inner radius of 25 mm: (a) tangential stress and (b) radial stress. Stress data is obtained from midsection in the FE model.

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Fig. 7

Through-thickness stress distributions in bilayer C-C specimen and monolithic SS400 steel layer at an inner radius of 25 mm: (a) tangential stress and (b) radial stress. Stress data is obtained from midsection in the FE model.

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Fig. 8

Through-thickness tangential strain distributions in bilayer: (a) C-T and (b) C-C specimens with monolithic SS400 steel layer at an inner radius of 25 mm. Strain data is obtained from midsection in the FE model.

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Fig. 9

Experimental through-thickness tangential strain distributions for C-T and C-C specimens for two different clad to core thickness ratios and monolithic SS400 steel layer at an inner radius (ri) of 25 mm

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Fig. 10

(a) FE Model versus experimental width strain distributions for C-T and C-C specimens for two different clad to core thickness ratios and monolithic SS400 steel layer for a specimen bent to an inner radius of 25 mm and (b) schematic of elongation and contraction along width section in bending

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Fig. 11

Models versus experimental relative thickness as a function of radius of curvature for bilayer specimens of two different thickness ratios and monolithic SS400 sheet: (a) C-T and (b) C-C specimens. Note that analytical and experimental results have been compared with midwidth section data from FE M–K method in the above graphs.

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Fig. 12

Models versus experimental relative thickness as a function of radius of curvature for bilayer specimens of two different thickness ratios and monolithic SS400 sheet: (a) C-T and (b) C-C. Note that analytical and experimental results have been compared with edge section data from FE M–K method in the above graphs.

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Fig. 13

Optical microscope images of SS400/AA1050 specimen: (a) specimen cross section before deformation at (100×); (b) undeformed magnified at 1000×; and (c) bent specimen at 1000 × showing no delamination in bend specimen

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Fig. 14

Thickness measurements across the specimen width at the bend line for (a) C-T and (b) C-C specimens for inner radius (ri) of 25 mm

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Fig. 15

Experimental relative thickness traces across specimen width at the bend line for inner radius (ri) of 25 mm

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Fig. 16

Reverse load zone and NFS characteristics for monolithic and various bilayer laminates from the analytical model: (a) reverse loaded zone versus curvature, (b) neutral fiber location and its movement for C-T configuration, (c) neutral fiber location and its movement for C-T configuration, (c) neutral fiber location and its movement for C-C configuration, and (d) NFS versus curvature

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Fig. 17

Width strain versus curvature characteristics from FE M–K model for (a) C-T and C-C bilayer laminates at a thickness ratio 0.25, (b). C-T bilayer laminate for two different thickness ratios of 0.1 and 0.25.

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Fig. 18

Relative thickness versus curvature curves from FE M–K model for C-T and C-C laminates at a thickness ratio of 0.25

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Fig. 19

Thickness changes to clad layers versus curvature for C-T and C-C cases for two laminate thickness ratios

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Fig. 20

Relative thickness versus curvature curves from FE M–K model for C-T laminate for two different thickness ratios of 0.1 and 0.25

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