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GTN-Model

GTN-Model: Gurson Tvergaard Needleman damage model
Definition:Gurson Tvergaard Needleman micromechanical continuum damage model.
Explanation:During a large plastic deformation, voids and cavities form as a result of high strain and their coalescence causes the ductile fracture. Mechanisms of such coalescence consist of three stages which occur in parallel: (i) void growth, (ii) ligament shearing, and (iii) secondary void nucleation. These stages occur in parallel. Ductile failure after void growth and coalescence followed by crack initiation Explanation of void progression caused by a increasing stress. Consideration of the influence of voids on the flow behaviour through modification of the von Mises flow potential. The yield function of Gurson model is defined as in the equation below, where σeq is the equivalent von Mises stress, σM is the yield stress of matrix. For the matrix, associative von Mises plasticity is assumed for the undamaged surface as shown in figure below. σm is the mean stress.
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Diagram:


Stages of ductile failure: void nucleation, growth and coalescence (left), and yield surface according to GTN of a damaged continuum (right).
SFB-Link:The microstructure of engineering alloys is usually very complex and contains inclusions and second phase particles. From micromechanical point of view, ductile fracture is defined as material separation which is the result of void nucleation, evolution of existing micro voids and cracks, followed by progressive void coalescence. Voids are first initiated at material defects such as inclusions. It should be also noted that in many engineering alloys, voids usually pre-exist. Void coalescence is mainly the result of the failure of ligament between the voids (a) perpendicular to loading direction or (b) in the localized shear direction.
References:A. Needleman. A continuum model for void nucleation by inclusion debonding. J.Appl. Mech., 54(3):525–531, 1987
A.L. Gurson. Continuum theory of ductile rupture by void nucleation and growth,1. Yield criteria and flow rules for porous ductile media. J. Eng. Mater-T. Asme,99(1):2–15, 1977.
V. Tvergaard. Influence of voids on shear band instabilities under plane strain conditions.Int. J. Fract., 17:389–407, 1981.
V. Tvergaard. On localization in ductile materials containing spherical voids. Int. J.Fract., 18(4):237–252, 1982.