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

**CFRAC 2015 - the Fourth International Conference on Computational Modeling of Fracture and Failure of Materials and Structures**(2015)

[Konferensbidrag, övrigt]

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.

**Nyckelord: **Johnson-Cook, Mesh size dependence, ductile failure modeling, Phase-field

*References
[1] G. Ljustina, R. Larsson and M. Fagerstrom. Microstructure level Machining Simulation of Compacted Graphite Iron. Finite elements in analysis and design, 80:1–10(2014).
[2] GA. Francfort, JJ. Marigo, Revisiting brittle fracture as an energy minimization problem.
Journal of the Mechanics and Physics of Solids, 46:1319–1342 (1998).
[3] C. Miehe, M. Hofacker, L. Schanzel, F. Aldakheel, Phase field modeling of fracture
in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack
propagation in thermo-elastic-plastic solids, Comput. Methods Appl. Mech. Engrg.(2014).
[4] A. Huespe, A. Needleman, J. Oliver, Sanchez, A finite strain, finite band method for
modeling ductile fracture, International Journal of Plasticity 28:53–69 (2012).*

Denna post skapades 2016-03-17.

CPL Pubid: 233384