7.2 Impact Test on 10CrNi3MoV21A Armor Steel/SiC Ceramic/UHPCC …
201
mass efficiency factors of S5/C6 configuration are almost twice higher than those of
the S5 configuration, which confirms the contribution of ceramic plate to the light
weight optimal design of the composite target.
7.2.2 Numerical Simulations
7.2.2.1 Numerical Model and Method
Generally, Lagrange, Euler and ALE (Arbitrary Lagrange Euler) are the three
widely applied numerical algorithms to deal with the problem of continuum in
solid mechanics. Based on the material coordinates, the Lagrange algorithm is often
adopted to analyze the response of solid structures in which the change of the structures is completely consistent with the change of the finite elements. Besides, the
spatial-coordinate-based Euler algorithm is usually suitable for the numerical analysis of fluid and fluid–solid coupling interaction. Therefore, the Lagrange algorithm
with finite elements has difficulty in handling large distortions subjected to extreme
loadings, such as impact or explosion. While for the Euler algorithm, in addition to
the relatively low computation efficiency, it is also difficult to capture the material
boundary during the simulation process. In order to overcome the aforementioned
drawbacks, ALE algorithm which has the advantages of both the Lagrange and Euler
algorithms is proposed (Benson 1989). The ALE algorithm introduces the characteristics of Lagrange algorithm in dealing with the movement of the material boundary,
and more importantly, the finite element in ALE algorithm is independent with the
material entity, and thus the elements can be adjusted properly during the numerical
process and will not appear serious distortions.
At present, the suitable numerical algorithm for reproducing the eroded projectile
with mushrooming deformation in test C11 was examined firstly. The commonly
employed 3D numerical simulation was conducted by adopting the commercial
finite element program LS-DYNA (2001) with Lagrange algorithm. The double
symmetries of the problem were exploited and only a quarter of the geometry was
discretized into eight-node hexahedral finite elements with the size of 1 mm. Besides,
the smoothed particle hydrodynamics (SPH), a special Lagrange and meshless algorithm, was further adopted to simulate the response of fracture and splash of the
brittle ceramic material. A total of 61,875 particles were distributed at the volume
center of the original finite elements of ceramic material, so that the corresponding
particle spacing was also 1 mm. The above two 3D numerical models as well as
the finite elements and SPH particles domain of the ceramic plate are depicted in
Fig. 7.13. The eroding-contact based algorithm was defined between the projectile and the target in which surface-to-surface algorithm was adopted for the finite
elements and nodes-to-surface algorithm was implemented for the SPH particles and
finite elements. The 3D numerical simulation results are shown in Fig. 7.14 where the
acceptable penetration depth and residual length of the projectile are predicted. The
fracture and splash response of the ceramic material are reasonably reproduced by
201
mass efficiency factors of S5/C6 configuration are almost twice higher than those of
the S5 configuration, which confirms the contribution of ceramic plate to the light
weight optimal design of the composite target.
7.2.2 Numerical Simulations
7.2.2.1 Numerical Model and Method
Generally, Lagrange, Euler and ALE (Arbitrary Lagrange Euler) are the three
widely applied numerical algorithms to deal with the problem of continuum in
solid mechanics. Based on the material coordinates, the Lagrange algorithm is often
adopted to analyze the response of solid structures in which the change of the structures is completely consistent with the change of the finite elements. Besides, the
spatial-coordinate-based Euler algorithm is usually suitable for the numerical analysis of fluid and fluid–solid coupling interaction. Therefore, the Lagrange algorithm
with finite elements has difficulty in handling large distortions subjected to extreme
loadings, such as impact or explosion. While for the Euler algorithm, in addition to
the relatively low computation efficiency, it is also difficult to capture the material
boundary during the simulation process. In order to overcome the aforementioned
drawbacks, ALE algorithm which has the advantages of both the Lagrange and Euler
algorithms is proposed (Benson 1989). The ALE algorithm introduces the characteristics of Lagrange algorithm in dealing with the movement of the material boundary,
and more importantly, the finite element in ALE algorithm is independent with the
material entity, and thus the elements can be adjusted properly during the numerical
process and will not appear serious distortions.
At present, the suitable numerical algorithm for reproducing the eroded projectile
with mushrooming deformation in test C11 was examined firstly. The commonly
employed 3D numerical simulation was conducted by adopting the commercial
finite element program LS-DYNA (2001) with Lagrange algorithm. The double
symmetries of the problem were exploited and only a quarter of the geometry was
discretized into eight-node hexahedral finite elements with the size of 1 mm. Besides,
the smoothed particle hydrodynamics (SPH), a special Lagrange and meshless algorithm, was further adopted to simulate the response of fracture and splash of the
brittle ceramic material. A total of 61,875 particles were distributed at the volume
center of the original finite elements of ceramic material, so that the corresponding
particle spacing was also 1 mm. The above two 3D numerical models as well as
the finite elements and SPH particles domain of the ceramic plate are depicted in
Fig. 7.13. The eroding-contact based algorithm was defined between the projectile and the target in which surface-to-surface algorithm was adopted for the finite
elements and nodes-to-surface algorithm was implemented for the SPH particles and
finite elements. The 3D numerical simulation results are shown in Fig. 7.14 where the
acceptable penetration depth and residual length of the projectile are predicted. The
fracture and splash response of the ceramic material are reasonably reproduced by