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Efficient prediction of local failures for metallic sandwich plates with pyramidal truss cores during the bending processes

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Abstract

An efficient method that employs the virtual equivalent projected model (VEPM) is introduced and formulated in this study to simulate local failures in face sheets and cores of sandwich plates with pyramidal truss cores. This approach is based on two-dimensional FE-analysis that uses the projected shapes of 3D pyramidal truss cores and utilizes virtual properties from the homogenized equivalent elastic-plastic properties of the original material and geometries. To establish the validity of this approach, virtual equivalent projected models are applied to three-point bending, clamped bending and U-bending analyses. The results of simulations have shown that the load-displacement curves and deformed shapes with local failures of the VEPM are analogous to 3D pyramidal cores in three types of bending processes irrespective of the materials and core geometries. In addition, the computational time was greatly reduced. The practicality of this approach has been shown through comparison with the experimental results.

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Abbreviations

b t1 :

half length of a unit structure of a sandwich plate with a 3D pyramidal truss core

b t2 :

half width of a unit structure of a sandwich plate with a 3D pyramidal truss core

b v :

half length of a unit structure of a sandwich plate with the VEPM

h :

total thickness of a sandwich plate

h c t :

core height of a 3D pyramidal truss

h c v :

core height of the VEPM

t c t :

core element thickness of a 3D pyramidal truss core

t f t :

thickness of a face sheet of a sandwich plate with a 3D pyramidal truss core

t f v :

thickness of a face sheet of a sandwich plate with the VEPM

t c v :

core element thickness of the VEPM

α t :

out of plane core angle of a 3D pyramidal truss

α v :

out of plane core angle of the VEPM

β t :

in-plane core angle of a 3D pyramidal truss

\(\bar \rho _c^t\) :

relative core density of a 3D pyramidal truss core

\(\bar \rho _c^v\) :

relative core density of the VEPM

E t :

elastic constants of a 3D pyramidal truss core

E v :

elastic constants of the VEPM

\(\bar E_{ij}^t\) (i, j =1,2,3 no sum.):

equivalent elastic constants of a 3D pyramidal truss core

\(\bar E_{xx}^v , \bar E_{yy}^v , \bar E_{xy}^v\) :

equivalent elastic constants of the VEPM

σ y t :

yield strength of a 3D pyramidal truss core

σ y v :

yield strength of the VEPM

\(\bar \sigma _{ij}^t\) (i, j =1,2,3 no sum.):

equivalent yield strength of a 3D pyramidal truss core

\(\bar \sigma _{xx}^v , \bar \sigma _{yy}^v , \bar \sigma _{xy}^v\) :

equivalent yield strength of the VEPM

\(\bar \sigma _b^t\) :

local face buckling strength of a 3D pyramidal truss core

\(\bar \sigma _b^v\) :

local face buckling strength of the VEPM

H t :

linear hardening function of a 3D pyramidal truss core

H v :

linear hardening function of the VEPM

\(\bar H_{ij}^t\) (i, j =1,2,3 no sum.):

equivalent linear hardening function of a 3D pyramidal truss core

\(\bar H_{xx}^v , \bar H_{yy}^v , \bar H_{xy}^v\) :

equivalent linear hardening function of the VEPM

P :

punch load per unit width

P yield :

analytic yield load per unit width

δ :

punch stroke

L :

half span length

R:

punch radius

c:

clearance

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Authors and Affiliations

  1. Dept. of Mechanical Eng., KAIST, Science Town, Daejeon, South Korea, 305-701

    Dae-Yong Seong, Chang-Gyun Jung & Dong-Yol Yang

  2. Dept. of Product Design and Manufacturing, Seoul National University of Technology, Seoul, South Korea, 139-743

    Wan-Jin Chung

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  1. Dae-Yong Seong
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  2. Chang-Gyun Jung
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Correspondence to Dong-Yol Yang.

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Seong, DY., Jung, CG., Yang, DY. et al. Efficient prediction of local failures for metallic sandwich plates with pyramidal truss cores during the bending processes. Int. J. Precis. Eng. Manuf. 12, 491–503 (2011). https://doi.org/10.1007/s12541-011-0063-2

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  • DOI: https://doi.org/10.1007/s12541-011-0063-2

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