Abstract
Axial compression of aluminium spherical shells of R/t values ranging from 25 to 43 was performed under central loading. Quasi-static tests were conducted on an INSTRON machine (model 1197) of 50 T capacity. Spherical shells were tested to identify their modes of collapse and to study the associated energy absorption capacity. In experiments all the spherical shells were found to collapse due to formation of an axisymmetric inward dimple associated with a rolling plastic hinge. A Finite Element computational model of development of the axisymmetric mode of collapse is also presented. Experimental and computed results of the deformed shapes and their corresponding load–compression and energy–compression curves were presented and compared to validate the computational model. The computed variations of the different strains and stresses were also studied. On the basis of the computational results mechanics of the development of the axisymmetric inward dimple mode of collapse has been presented, analysed and discussed.
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Abbreviations
- R :
-
mean radius of the spherical shell
- L :
-
span of the spherical shell
- Z :
-
depth of the spherical shell
- t :
-
average thickness of the spherical shell
- r p :
-
radius of the rolling or travelling plastic hinge
- h :
-
total axial compression of the spherical shell at any stage of compression
- P :
-
load on the spherical shell at any stage of compression
- M p :
-
plastic moment per unit length
- \(\tilde{S}_{{ij}}\) :
-
deviatoric stress tensor
- K :
-
material consistency
- \(\dot{\bar\varepsilon}\) :
-
effective strain rate
- m :
-
strain rate sensitivity index
- K 0 :
-
constant term
- a :
-
strain hardening term
- \(\bar{\varepsilon}\) :
-
effective strain
- \(\bar{\sigma}\) :
-
effective stress
- β:
-
temperature sensitivity term
- T :
-
temperature in absolute value
- τ:
-
shearing stress
- α:
-
friction coefficient, α1 and α2 at top and bottom
- p :
-
sensitivity to sliding velocity
- ΔV :
-
relative sliding velocity between tube and platen
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Gupta, P.K., Gupta, N.K. Computational and experimental studies of crushing of metallic hemispherical shells. Arch Appl Mech 76, 511–524 (2006). https://doi.org/10.1007/s00419-006-0053-5
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DOI: https://doi.org/10.1007/s00419-006-0053-5