Constitutive modeling of void shearing effect in ductile fracture of porous materials

Many solids, including geomaterials and commercially available metallic alloys, can be considered as a porous media. The Gurson-like model has been proposed to describe plastic deformation for such type of materials. It has attracted a great deal of attention and various modifications to this model have been proposed. The constitutive equations of Gurson-like model are governed by the first and second stress invariants and the current void volume fraction of the material. Tvergaard and Needleman included void nucleation, growth and coalescence to Gurson model in a phenomenological way [Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 1984;32(1):157–69] – thus suggesting the so called GTN model. Meanwhile, little attention was given to the dependence of the damage evolution on the third stress invariant. McClintock et al. [McClintock FA, Kaplan SM, Berg CA. Ductile fracture by hole growth in shear bands. Int J Fract Mechan 1966;2(4):614–27] proposed damage model based on the void evolution in localized shear banding. In the present paper, a separate internal damage variable which differs from the conventional void volume fraction is introduced. The GTN model is further extended to incorporate the void shearing mechanism of damage, which depends on the third stress invariant. Numerical aspects are addressed concerning the integration of the proposed constitutive relations. A unit cell is studied to illustrate the intrinsic mechanical behavior of the modified model. Computations of the deformation in axisymmetric and transverse plane strain tension are also performed. Realistic crack modes in these simulations are achieved for the modified GTN model.