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Date of download: 1/23/2018 Copyright © ASME. All rights reserved.

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1 Date of download: 1/23/2018 Copyright © ASME. All rights reserved. From: Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal J. Manuf. Sci. Eng. 2014;136(5): doi: / Figure Legend: The illustration of a uniform thin sheet metal with applied in-plane stress

2 Date of download: 1/23/2018 Copyright © ASME. All rights reserved. From: Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal J. Manuf. Sci. Eng. 2014;136(5): doi: / Figure Legend: The comparison between the three r-values introduced bifurcation analysis and Stören–Rice bifurcation analysis with Hill's zero extension direction on left hand side

3 Date of download: 1/23/2018 Copyright © ASME. All rights reserved. From: Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal J. Manuf. Sci. Eng. 2014;136(5): doi: / Figure Legend: The comparison between the three r-values introduced bifurcation analysis and Stören–Rice bifurcation analysis with the minimum energy principal searching algorithm on left hand side

4 Date of download: 1/23/2018 Copyright © ASME. All rights reserved. From: Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal J. Manuf. Sci. Eng. 2014;136(5): doi: / Figure Legend: The comparison between the experimental results of Al6111-T4 from Graf and Hosford and predicted results

5 Date of download: 1/23/2018 Copyright © ASME. All rights reserved. From: Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal J. Manuf. Sci. Eng. 2014;136(5): doi: / Figure Legend: The comparison of yield surfaces for material scenario 1 to 4

6 Date of download: 1/23/2018 Copyright © ASME. All rights reserved. From: Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal J. Manuf. Sci. Eng. 2014;136(5): doi: / Figure Legend: The predicted forming limit results with different r-value combinations

7 Date of download: 1/23/2018 Copyright © ASME. All rights reserved. From: Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal J. Manuf. Sci. Eng. 2014;136(5): doi: / Figure Legend: The necking angle distributions with different r-value combinations

8 Date of download: 1/23/2018 Copyright © ASME. All rights reserved. From: Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal J. Manuf. Sci. Eng. 2014;136(5): doi: / Figure Legend: The necking band angle evolution under equibiaxial (β = 1) stretching mode with three different r-values

9 Date of download: 1/23/2018 Copyright © ASME. All rights reserved. From: Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal J. Manuf. Sci. Eng. 2014;136(5): doi: / Figure Legend: The necking band angle evolution under equibiaxial (β = 1) stretching mode with an average r-value

10 Date of download: 1/23/2018 Copyright © ASME. All rights reserved. From: Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal J. Manuf. Sci. Eng. 2014;136(5): doi: / Figure Legend: The comparison between the yield surface with or without r0 effect

11 Date of download: 1/23/2018 Copyright © ASME. All rights reserved. From: Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal J. Manuf. Sci. Eng. 2014;136(5): doi: / Figure Legend: Illustration of the flow direction determined by the changed curvature of the yield surface


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