Campus Units
Aerospace Engineering, Mechanical Engineering, Ames Laboratory
Document Type
Article
Publication Version
Submitted Manuscript
Publication Date
2020
Journal or Book Title
arXiv
Abstract
Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas in the deformed and undeformed configurations and with the gradient energy in terms of the gradient of the order parameter in the reference configuration. This results in an expression for the surface stresses which is consistent with the sharp surface approach. Namely, the structural part of the Cauchy surface stress represents an isotropic biaxial tension, with the magnitude of a force per unit length equal to the surface energy. The surface stresses are a result of the geometric nonlinearities, even when strains are infinitesimal. They make multiple contributions to the Ginzburg-Landau equation for damage evolution, both in the deformed and undeformed configurations. Important connections between material parameters are obtained using an analytical solution for two separating surfaces, as well as an analysis of the stress-strain curves for homogeneous tension for different degradation and interpolation functions. A complete system of equations is presented in the undeformed and deformed configurations. All the phase field parameters are obtained utilizing the existing first principle simulations for the uniaxial tension of Si crystal in the [100] and [111] directions
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright Owner
The Author(s)
Copyright Date
2020
Language
en
File Format
application/pdf
Recommended Citation
Jafarzadeh, Hossein; Farrahi, Gholam Hossein; Levitas, Valery I.; and Javanbakht, Mahdi, "Phase field theory for fracture at large strains including surface stresses" (2020). Aerospace Engineering Publications. 174.
https://lib.dr.iastate.edu/aere_pubs/174
Included in
Engineering Physics Commons, Mechanics of Materials Commons, Structures and Materials Commons
Comments
This is a pre-print of the article Jafarzadeh, Hossein, Gholam Hossein Farrahi, Valery I. Levitas, and Mahdi Javanbakht. "Phase field theory for fracture at large strains including surface stresses." arXiv preprint arXiv:2011.13324 (2020). Posted with permission.