Brian Nyvang Legarth

Effects of plastic anisotropy on crack-tip behaviour

For a crack in a homogeneous material the effect of plastic anisotropy on crack-tip blunting and on the near-tip stress and strain fields is analyzed numerically. The full finite strain analyses are carried out for plane strain under small scale yielding conditions, with purely symmetric mode I loading remote from the crack-tip. In cases where the principal axes of the anisotropy are inclined to the plane of the crack it is found that the plastic zones as well as the stress and strain fields just around the blunted tip of the crack become non-symmetric. In these cases the peak strain on the blunted tip occurs off the center line of the crack, thus indicating that the crack may want to grow in a different direction. When the anisotropic axes are parallel to the crack symmetry is retained, but the plastic zones and the near-tip fields still differ from those predicted by standard isotropic plasticity.

Strain-gradient effects in anisotropic materials

The isotropic single-parameter strain-gradient plasticity model of Fleck and Hutchinson (2001 J. Mech. Phys. Solids 49 2245–71) is generalized in order to account for plastic anisotropy in a finite strain elastic–viscoplastic formulation. Plastic anisotropy is introduced through a phenomenological yield surface, which is described by a homogeneous function of degree 1. The anisotropy affects the plastic work done by the conventional effective plastic strain while the plastic work done by the strain-gradients remains unchanged. A modified measure of the effective stress arises naturally in the formulation. Local plasticity (isotropic and anisotropic) as well as nonlocal isotropic plasticity are special cases of this anisotropic nonlocal plasticity model. Results for an anisotropic nonlocal aluminium containing voids are obtained by a finite element implementation of the model.

Effect of plastic anisotropy on crack growth resistance under mode 1 loading

Crack growth in a solid with plastic anisotropy is modeled by representing the fracture process in terms of a traction-separation law specified on the crack plane, and crack growth resistance curves are calculated numerically. A phenomenological elastic-viscoplastic material model is applied, using one of two different anisotropic yield criteria to account for the plastic anisotropy. The analyses are carried out for conditions of small scale yielding, with mode I loading conditions far from the crack-tip. Different initial orientations of the principal axes relative to the crack plane are considered and it is found that the steady-state fracture toughness is quite sensitive to the type of anisotropy and to the angle of inclination of the principal axes relative to the crack plane.

Micromechanical Analyses of Debonding and Matrix Cracking in Dual-Phase Materials

Failure in elastic dual-phase materials under transverse tension is studied numerically. Cohesive zones represent failure along the interface and the augmented finite element method (A-FEM) is used for matrix cracking. Matrix cracks are formed at an angle of 55 deg−60 deg relative to the loading direction, which is in good agreement with experiments. Matrix cracks initiate at the tip of the debond, and for equi-biaxial loading cracks are formed at both tips. For elliptical reinforcement the matrix cracks initiate at the narrow end of the ellipse. The load carrying capacity is highest for ligaments in the loading direction greater than that of the transverse direction.

Effects of Plastic Anisotropy and Void Shape on Full Three-Dimensional Void Growth

Orbit (10/11/2019) Effects of Plastic Anisotropy and Void Shape on Full Three-Dimensional Void Growth Void growth in an anisotropic ductile solid is studied by numerical analyses for three dimensional unit cells initially containing a void. The effect of plastic anisotropy on void growth is the main focus, but the studies include effects of different void shapes, including oblate, prolate or general ellipsoidal voids. Also other 3D effects such as those of different spacings of voids in different material directions, and effects of different macroscopic principal stresses in three directions are accounted for. It is found that the presence of plastic anisotropy amplifies the differences between predictions obtained for different initial void shapes. Also, differences between principal transverse stresses show a strong interaction with the plastic anisotropy, such that the responseis very different for different anisotropies. The studies are carried out for one particular choice of void volume fraction and stress triaxiality.