3D analysis of failure modes in the Charpy impact test

Abstract

A three-dimensional analysis of the Charpy V-notch specimen subject to impact loading is carried out, using a data parallel implementation in a transient three-dimensional finite element programme. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Cleavage is modelled in terms of attaining a critical value of the maximum principal normal stress over a specified material volume. A convected coordinate Lagrangian formulation is employed and the discretization is based on twenty-node brick elements with 2*2*2 Gauss points. The equations of motion are integrated numerically by an explicit integration procedure using a lumped mass matrix. The predictions of the full three-dimensional calculations are compared with those of corresponding plane-strain analyses.

Numerical Modeling of the Ductile-Brittle Transition

“…The initial trends in Mathur et al [13] agreed rather well with those in Mathur et al [12], but as the crack extends from the notch tip, the differences between the three dimensional predictions and the two dimensional plane strain approximation increased. A significant amount of crack tunneling developed in the range of material behavior where cleavage plays an important role.…”

“…The plastic part of the rate of deformation, dp, is obtained as The contribution from the growth of existing voids is determined from the con21tion that plastic deformation of the matrix is volume preserving so that f = (1 -f)dP : I (13) The contribution from the nucleation of new voids is taken to be either strain controlled or stress controlled. In either case, void nucleation is taken to follow a normal distribution as suggested by Chu and Needleman [6].…”

“…In Mathur et al [13] ductile failure by the nucleation and growth of micro voids to coalescence and for crack growth by a cleavage mechanism were both accounted for, allow for a direct evaluation of the usefulness of failure mode predictions obtained by planar analyses. The presumption in the calculations in Mathur et al [13] is that the high stresses and strains induced by the Charpy Vnotch occur over a region that is large compared to relevant microstructural length scales such as the cleavage grain size or the spacing of void nucleating inclusions.…”

“…The presumption in the calculations in Mathur et al [13] is that the high stresses and strains induced by the Charpy Vnotch occur over a region that is large compared to relevant microstructural length scales such as the cleavage grain size or the spacing of void nucleating inclusions. Hence, such microstructural length scales are not explicitly accounted for in the modeling.…”

“…For ductile failure the difference is more like that expected based on the results with no damage, but there is still more crack growth in the central part of the specimen than near the free edge. Figure 1, from results in Mathur et al [13], shows contours of maximum principal stress (in MPa) exhibiting the mode of crack growth in a Charpy impact test for (a) ductile failure at 200 ,US and (b) brittle failure at 100 ps. Crack growth is occurring along the x = 0 plane, which is the notch root plane.…”