CRACK-TIP FIELDS IN A MATERIAL WITH 3 INDEPENDENT SLIP SYSTEMS - NIAL SINGLE-CRYSTAL

The crack tip stress and deformation field is analyzed for an ideally plastic ordered NiAl single crystal of B2 (BCC type) structure which has only three independent slip systems at room temperature, the {110}[100] systems. For the crack on the (010) plane growing in the [101] direction, only one of these systems is capable of sustaining considerable plane plastic flow. It involves slip planes lying parallel to the crack tip, making an angle of 90-degrees with the crack plane, and has the yield condition sigma12 = +/-tau0 (1 is the cracking direction, 2 the crack plane normal, and tau0 the critical resolved shear stress). An elastic-ideally plastic asymptotic solution is derived in which the stress field has a ln r type singularity, with a shearing discontinuity at 90-degrees. These features are verified and more fully quantified by a finite element solution. At regions very near the tip, the field is divided into 5 angular sectors of which 2 are plastic regions (sigma12 = +/-70), one inclined ahead of the crack front and one behind. Further away from the tip, at distances greater than about 0.01 of the overall plastic zone size, the plastic region ahead of the crack front, in which sigma12 = tau0, disappears resulting in 3 angular sectors of which one is plastic, which persists for the rest of the plastic region. While the plastic zone covers a broad angular range, the deformation field within it is dominated by the shear discontinuity of displacement. The stress on other possible systems such as {110}[111], which in NiAl becomes activated at higher temperatures, and on {112}[111] systems, which are the usual twinning systems for BCC crystals, is also investigated. The results show that zones over which the resolved shear stresses on these two set of systems become of the order of critical resolved shear stress on the soft {110}[100] system are either much smaller than, or of the same order as, the plastic zone for the {110}[100] system, although very close to the crack tip the stresses on some of these systems become significant due to the stress singularity. Thus, even though the shear strength is much larger for these two systems than for the {110}[100] system, over regions extremely near the tip they may become activated and alleviate the stress singularity. It is also possible that cleavage will occur first at lower temperatures or higher strain rates, and such is consistent with the brittleness of NiAl.