Mesh objective models for ductile fracture based on a damage phase field concept
Other conference contribution, 2015
The Johnson-Cook (JC) model for ductile failure is simple and phenomenological. Being
derived for ductile fracture in metals with the involvement of only few parameters, the
model has been shown to work well in many other applications. In spite of its simplicity,
it catches the material behavior for large deformation/high speed/temperature applications
at a reasonable cost. In addition to its widespread use in commercial software, low cost
is an obvious advantage, which makes the model often used in machining simulations of
metal cutting, cf. [1]. A major drawback is that the JC–material model exhibits mesh
size dependence which is known from orthogonal machining simulations. In this context
many researchers have proposed remedies of various type, we mention: [2], [3] using
the concepts of a damage phase field, [4] using special element enhancement of the FE–
kinematics.
In this context, combined with concepts of a damage phase field (without gradient
enhancement), we consider the mesh objective element removal and progressive damage
models. Relating to the ideas of ref. [3], a central point in the modeling concerns the
handling of the maximum energy dissipation rate principle for scalar damage evolution
involving the total dissipation. To control evolution of the damage, both inelastic continuous
deformation and localized deformation due to damage evolution are thus considered
to define a total damage driving energy AT in the damage criterion. In order to link the
continuum damage to the fracture modeling some concept of the phase field formulation
of e.g. [3] are exploited. Based on the assumption of a localized damage field, a mesh objective
formulation is obtained in terms of scaling factor from the element diameters of the
reference FE–element mesh. In turn, the JC–model parameters are considered calibrated
with respect to the reference mesh.
We propose in this paper two FE–mesh objective technologies, enhancing the JC–
model for ductile fracture using the concept of scalar damage. Regardless of the damage
model used, a fracture state is achieved at the Gauss point level when the accumulated
effective plastic strain approaches the fracture strain of the JC–failure model. For the element
removal model an instantaneous damage evolution is achieved when the total damage
driven energy, AT , equals the scaled release energy at the Gauss point level. When
this is obtained the damage criterion is then met and the element is removed, corresponding
to full stress relaxation. For the progressive damage model a similar evaluation of
the damage is conducted, although the damage evolution is progressive.From the phase
field concept, in this case the mesh objective scaling depends on the parameters of the
progressive damage evolution.
The proposed models have been implemented in a large deformation setting in Matlab.
To illustrate the advantages using the mesh objective enhanced models a shear test of
a plate is investigated at plane strain conditions. A comparison is made between mesh objective
enhanced damage models and damage models without any objective enhancement.
Johnson-Cook
ductile failure modeling
Mesh size dependence
Phase-field