Effects of crystallographic orientation and grain morphology on crack tip stress state and plasticity

Abstract

The Sih, Paris and Irwin analytical solution for cracks in anisotropic elastic media has been developed for an hcp Ti single crystal and shown to lead to crack tip normal stresses which are independent of crystal orientation but other stress components which are dependent.Detailed finite element studies confirm that the stress intensity remains independent of crystal orientation but ceases to do so in an edge-cracked bi-crystal.The incorporation of crystallographic slip demonstrates that single-crystal crack tip stresses largely remain independent of crystal orientation but that the plastic zone size and shape depends greatly upon it. Significant differences result in both the magnitude and extent of the plasticity at the crack tip with crystallographic orientation which can be quite different to that predicted using Mises plasticity. For an edge crack terminating in a bi-crystal, the slip fields which result depend upon both crystal mis-orientation and morphology.Keywords: Stress intensity; crystal plasticity; anisotropy; titanium alloys; cold dwell fatigue; crystallographic slip.

Fatigue crack nucleation: Mechanistic modelling across the length scales

“…The analysis of an edge crack in an hcp single crystal in [12] employs a 2D discrete dislocation modelling approach in which basal and pyramidal slip systems are incorporated and arranged in order to satisfy the plane strain requirement. The fracture toughness is found to be largely independent of the plastic anisotropy, as in the CP analysis in [56]. The toughness in a material with flow stress controlled by the (intrinsic) Peierls stress and in one with flow stress controlled by (extrinsic) dislocation obstacles was found to be unified by stress gradient plasticity.…”

“…The crystallographic orientation of the single crystal is shown to have a significant influence on the activation, or otherwise, of the deformation mechanisms (slip, twinning and stacking faults) at the crack tip. A consequence of this at the continuum level would be the development of differing slip fields for different crystal orientations, and this is just what was seen in the slip-based analysis in [56] for the single crystal.…”

“…The variation of crystal orientation of the adjacent grain was found to cause the crack tip opening displacement in the neighbouring grain to change. In a recent independent crystal-level study [56] of an edge crack terminating in an hcp Ti single and bicrystal arrangement, it was found that the crack tip stress intensity was largely independent of the slip anisotropy and that Mises (J 2 ) plasticity gave close agreement in crack tip stress response. The slip fields developed ahead of the crack tip, however, were strongly affected by crystallographic orientation.…”

Integrated experiment and modelling of microstructurally-sensitive crack growth

“…The study in [48] incorporated crystallographic slip in their modelling, and crack tip stresses were found to remain largely independent of crystal orientation and the local slip established, but plastic zone size and shape did depend upon it. Hence, in the crack modelling studies reported here, the maximum principal stress and its direction are considered as the criteria adopted and assessed to determine the experimentally observed crack growth directions within the X-FEM crack propagation model.…”

Molecular Dynamics Simulation of Crack Propagation in Nanoscale Polycrystal Nickel Based on Different Strain Rates

“…Therefore, CPFEM becomes a powerful candidate for understanding the mechanisms of crack propagation when the crack propagates in a single crystal or in a polycrystal with crystallographic texture [8,9]. Kartal et al [10] studied the effect of crystallographic orientation on stress state and plasticity at the crack tip in a hexagonal close-packed (HCP) single crystal Ti through CPFEM and they found that the size and shape of the plastic zone at the crack tip is strongly dependent on crystallographic orientation, but the stress state at the crack tip shows little dependence on crystallographic orientation. Sabnis et al [11] studied the influence of secondary orientation on plastic deformation near the notch tip in a notched Ni-based single crystal by means of CPFEM, where the slip patterns and the size and shape of plastic zone are strongly dependent on the secondary orientation of the notch, which has an important effect on the initiation and propagation of crack.…”