Mesh objective models for ductile fracture based on a damage phase field concept

The Johnson-Cook (JC) model for ductile failure is simple and phenomenological. Beingderived for ductile fracture in metals with the involvement of only few parameters, themodel 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 applicationsat a reasonable cost. In addition to its widespread use in commercial software, low costis an obvious advantage, which makes the model often used in machining simulations ofmetal cutting, cf. [1]. A major drawback is that the JC–material model exhibits meshsize dependence which is known from orthogonal machining simulations. In this contextmany researchers have proposed remedies of various type, we mention: [2], [3] usingthe 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 gradientenhancement), we consider the mesh objective element removal and progressive damagemodels. Relating to the ideas of ref. [3], a central point in the modeling concerns thehandling of the maximum energy dissipation rate principle for scalar damage evolutioninvolving the total dissipation. To control evolution of the damage, both inelastic continuousdeformation and localized deformation due to damage evolution are thus consideredto define a total damage driving energy AT in the damage criterion. In order to link thecontinuum damage to the fracture modeling some concept of the phase field formulationof e.g. [3] are exploited. Based on the assumption of a localized damage field, a mesh objectiveformulation is obtained in terms of scaling factor from the element diameters of thereference FE–element mesh. In turn, the JC–model parameters are considered calibratedwith 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 damagemodel used, a fracture state is achieved at the Gauss point level when the accumulatedeffective plastic strain approaches the fracture strain of the JC–failure model. For the elementremoval model an instantaneous damage evolution is achieved when the total damagedriven energy, AT , equals the scaled release energy at the Gauss point level. Whenthis is obtained the damage criterion is then met and the element is removed, correspondingto full stress relaxation. For the progressive damage model a similar evaluation ofthe damage is conducted, although the damage evolution is progressive.From the phasefield concept, in this case the mesh objective scaling depends on the parameters of theprogressive 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 ofa plate is investigated at plane strain conditions. A comparison is made between mesh objectiveenhanced damage models and damage models without any objective enhancement