Axisymmetric plastic expansion of a cylindrical hole in isotropic metallic foam

By combining a finite element simulation with an analytical treatment, this paper provides quantitative information on the stress, strain and deformation states induced during the axisymmetric expansion of a cylindrical hole of an initial radius, located at the center of a block of closed-cell metallic foam of infinite size. Uniformly distributed radial loading is applied on the surface of the hole. A macroscopic phenomenological constitutive model of metal foam is first introduced, considering the initial and subsequent yielding surfaces in the space of the effective stress and hydrostatic stress. Isotropic hardening model is incorporated into the material property of the crushable foam. Two deformation stages are revealed from the numerical simulation, i.e. the initial yielding and then subsequent expansion of the hole accompanied with hardening. Preliminary analytical formulation is performed with respect to the pressure at the initial yielding and the size of the subsequent plastic deformation zone. It is found that after the onset of initial yielding, the maximum pressure is identical to that from the finite element analysis. The evolution of plastic zone during the expansion is discussed in terms of the results from the analytical and finite element studies. Furthermore, foam densification is observed from finite element analysis and a map is obtained showing the evolution of the three deforming zones, i.e. elastic, plastic and densification of the foam, when the applied pressure increases.

► Axisymmetric plastic expansion of a cylindrical hole in an infinite foam is studied.
► Quantitative information on stress state is provided by FE and analytical treatment.
► Analytic formulation is achieved on initial yield pressure and size of plastic zone.
► The evolution of plastic zone is discussed in terms of analytical and FE studies.
► Foam densification is observed from FEA and a deformation map is obtained.