Fig. The load-displacement curve
for asymmetrically notched specimen
5.4 Double notched specimen
A benchmark simulation has been performed in order to assess the
robustness of the computations for different critical equivalent plastic
strain. Motivated by the blanking process, a problem geometry with two
asymmetrically placed rounded notches is used for this
purpose.54 The geometry and boundary conditions are
given in Table 3-V. Vertical displacements are imposed on the top and
left boundaries, while horizontal displacements have been prevented. The
bottom and right boundaries are remained fixed. The material parameters
are those of Material III in Table 1. The adopted discretization
contains 13240 quadrilateral elements with mesh refinement in the
expected crack propagation region.
In this illustrative example, the damage fields aren’t quite smooth. The
tensile loading causes the development of a plastic shear band between
the two notches and gives rise to damage initiation at the notches. In
the context of ductile fracture, the same problem has been addressed
using a non-local damage model for the initial continuum damage phase,
followed by a discontinuous crack propagation phase predicted through a
remeshing strategy.54 Results showed the development
of a plastic shear band diagonally across the specimen, which in turn
results in a curved crack trajectory which initiates at both the notches
and propagates towards the center of the specimen where the two crack
branches merge, Fig.10. It is worth noting that, with the increasing
critical plastic strain, secondary cracks initiate at the surface of the
top and bottom boundaries and start to propagate to the other side.