A general and unified theory of the kinematic relationships in bulge tests

•Scaling laws between apex strain, radius of curvature and dome height are developed.•The power-law relationships hold for both circular and elliptical bulge tests.•The power-law relationships can be applied to any materials.•The general kinematic theory is validated numerically and experimentally....

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Bibliographic Details
Published in:Journal of the mechanics and physics of solids 2020-10, Vol.143 (C), p.104086, Article 104086
Main Author: Chen, Kelin
Format: Article
Language:English
Subjects:
Anisotropy
Circular bulge test
Domes
Elliptical bulge test
Exact solutions
Isotropic material
Kinematics
Material hardening
Material properties
Mathematical models
Mechanical properties
Power law
Scaling laws
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Summary:•Scaling laws between apex strain, radius of curvature and dome height are developed.•The power-law relationships hold for both circular and elliptical bulge tests.•The power-law relationships can be applied to any materials.•The general kinematic theory is validated numerically and experimentally. The hydraulic circular and elliptical bulge tests have been widely used in extracting mechanical properties of sheet materials. Theoretical analysis of bulge tests usually requires the kinematic relationships between the apex strains, radii of curvatures and dome heights to be established. Most of the available analytical solutions are derived on a case-by-case basis and are often limited to circular bulge tests of isotropic materials, and thus cannot be applied to materials with more complicated constitutive behaviors or non-circular bulge tests. Based on the variable-separable assumption and proportional kinematic conditions at the apex, this study develops a set of power-law relationships between the apex strains, radii of curvatures and dome heights that hold for both circular and elliptical bulge tests, irrespective of material properties. Numerical simulations of a set of circular and elliptical bulge tests with different material models are performed and the scaling laws between the apex strains, radii of curvatures and dome heights are verified. An extensive set of experimental results of circular and elliptical bulge tests from the literature are compared with the theoretical predictions and the power-law kinematic relationships are again validated. This general and unified theory contributes to the fundamental understanding of the intrinsic kinematic constraints in circular and elliptical bulge tests and is expected to facilitate the application of bulge tests to a broader class of sheet materials.
ISSN:0022-5096
1873-4782
DOI:10.1016/j.jmps.2020.104086