Thermodynamically consistent and scale-dependent phase field approach for crack propagation allowing for surface stresses

Date
2018-01-01
Authors
Levitas, Valery
Jafarzadeh, Hossein
Farrahi, Gholam
Javanbakht, Mahdi
Levitas, Valery
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Aerospace Engineering
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Ames Laboratory
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Mechanical Engineering
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Aerospace EngineeringAmes LaboratoryMechanical EngineeringMaterials Science and Engineering
Abstract

A thermodynamically-consistent phase field approach for crack propagation which includes the following novel features is presented. (1) Scale dependency was included by relating the length scale to the number of cohesive interatomic planes at the crack tip. Because of this, the developed theory is applicable from the atomistic to the macroscopic scales. (2) The surface stresses (tension) are introduced by employing some geometrical nonlinearities even in small strain theory. They produce multiple contributions to the Ginzburg-Landau equation for crack propagation. (3) Crack propagation in the region with compressive closing stresses is eliminated by employing a stress-state-dependent kinetic coefficient in the Ginzburg-Landau equation. (4) The importance of analysis of the thermodynamic potential in terms of stress-strain curves is shown. The developed theory includes a broad spectrum of the shapes of stress-strain relationships. The finite element method is utilized to solve the complete system of crack phase field and mechanics equations. The effect of the above novel features is analyzed numerically for various model problems.

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This is a manuscript of an article published as Levitas, Valery I., Hossein Jafarzadeh, Gholam Hossein Farrahi, and Mahdi Javanbakht. "Thermodynamically consistent and scale-dependent phase field approach for crack propagation allowing for surface stresses." International Journal of Plasticity (2018). doi: 10.1016/ j.ijplas.2018.07.005. Posted with permission.

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